Mathematical Induction: Deductive Logic Perspective
ERIC Educational Resources Information Center
Dogan, Hamide
2016-01-01
Many studies mentioned the deductive nature of Mathematical Induction (MI) proofs but almost all fell short in explaining its potential role in the formation of the misconceptions reported in the literature. This paper is the first of its kind looking at the misconceptions from the perspective of the abstract of the deductive logic from one's…
NASA Astrophysics Data System (ADS)
Klein, Moshe; Maimon, Oded
2016-11-01
We strive to understand, by using mathematical tools, the phenomena where the observer can interpret simultaneously opposite situations, such as the distinct interpretations of the Necker cube. In this study we present a new coordinate system that draws a distinction between -0 and +0. The central theorem presented here postulates that when divisions and multiplications of 0 are combined with real numbers, the Mobius strip provides a model for non-standard analysis. We also suggest that the axis 0 is the fifth dimension extension of the quaternions. We also propose to add the soft logic capability to humanoid type robots, as a way to overcome the Turing test.
Logic in Everyday Language and in Mathematics.
ERIC Educational Resources Information Center
Zepp, Raymond A.
1987-01-01
Discusses logical errors, such as converse reasoning, that are made by students in mathematics and science courses. States that many students apply incorrect forms of reasoning to concrete mathematical problems. Concludes that material should be taught as concretely as possible, and that mathematics students should be made aware of reasoning…
Calculator Logic Systems and Mathematical Understandings.
ERIC Educational Resources Information Center
Burrows, Enid R.
This monograph is aimed at helping the reader understand the built-in logic of various calculator operating systems. It is an outgrowth of workshop contacts with in-service and pre-service teachers of mathematics and is in response to their request for a book on the subject of calculator logic systems and calculator algorithms. The mathematical…
Can Mathematics be Justified by Natural Logic?
NASA Astrophysics Data System (ADS)
Schreiber, Lothar; Sommer, Hanns
2010-11-01
Charles Darwin claimed that the forms and the behaviour of living beings can be explained from their will to survive. But what are the consequences of this idea for humans knowledge, their theories of nature and their mathematics?. We discuss the view that even Plato's objective world of mathematical objects does not exist absolutely, without the intentions of mathematicians. Using Husserl's Phenomenological Method, cognition can be understood as a process by which meaning is deduced from empirical data relative to intentions. Thereby the essential structure of any cognition process can be detected and this structure is mirrored in logic. A natural logic becomes the direct result of cognition. Only in a second step, mathematics is obtained by abstraction from natural logic. In this way mathematics gains a well-defined foundation and is no longer part of a dubious 'a-priori knowledge' (Kant). This access to mathematics offers a new look on many old problems, e.g. the Petersburg problem and the problem 'P = NP?'. We demonstrate that this new justification of mathematics has also important applications in Artificial Intelligence. Our method provides a procedure to construct an adequate logic to solve most efficiently the problems of a given problem class. Thus, heuristics can be tailor-made for the necessities of applications.
Rebuilding mathematics on a quantum logical foundation
NASA Astrophysics Data System (ADS)
DeJonghe, Richard J., III
We construct a rich first-order quantum logic which generalizes the standard classical predicate logic used in the development of virtually all of modern mathematics, and we use this quantum logic to build the foundations of a new quantum mathematics. First, we prove both soundness and completeness for the quantum logic we develop, and also prove a powerful new completeness result which heretofore had been known to hold for classical, but not quantum, first-order logic. We then use our quantum logic to develop multiple areas of mathematics, including abstract algebra, axiomatic set theory, and arithmetic. In some preliminary investigations into quantum mathematics, Dunn found that the Peano axioms for arithmetic yield the same theorems using either classical or quantum logic. We prove a similar result for certain classes of abstract algebras, and then show that Dunn's result is not generic by presenting examples of quantum monoids, groups, lattices, vector spaces, and operator algebras, all which differ from their classical counterparts. Moreover, we find natural classes of quantum lattices, vector spaces, and operator algebras which all have a beautiful inter-relationship, and make some preliminary investigations into using these structures as a basis for a new mathematical formulation of quantum mechanics. We also develop a quantum set theory (equivalent to ZFC under classical logic) which is far more tractable than quantum set theory previously developed. We then use this set theory to construct a quantum version of the natural numbers, and develop an arithmetic of these numbers based upon an alternative to Peano's axioms (which avoids Dunn's theorem). Surprisingly, we find that these "quantum natural numbers" satisfy our arithmetical axioms if and only if the underlying truth values form a modular lattice, giving a new arithmetical characterization of this important lattice-theoretic property. Finally, we show that these numbers have a natural interpretation as
Mathematical logic in the human brain: semantics.
Friedrich, Roland M; Friederici, Angela D
2013-01-01
As a higher cognitive function in humans, mathematics is supported by parietal and prefrontal brain regions. Here, we give an integrative account of the role of the different brain systems in processing the semantics of mathematical logic from the perspective of macroscopic polysynaptic networks. By comparing algebraic and arithmetic expressions of identical underlying structure, we show how the different subparts of a fronto-parietal network are modulated by the semantic domain, over which the mathematical formulae are interpreted. Within this network, the prefrontal cortex represents a system that hosts three major components, namely, control, arithmetic-logic, and short-term memory. This prefrontal system operates on data fed to it by two other systems: a premotor-parietal top-down system that updates and transforms (external) data into an internal format, and a hippocampal bottom-up system that either detects novel information or serves as an access device to memory for previously acquired knowledge.
Mathematical Logic in the Human Brain: Semantics
Friedrich, Roland M.; Friederici, Angela D.
2013-01-01
As a higher cognitive function in humans, mathematics is supported by parietal and prefrontal brain regions. Here, we give an integrative account of the role of the different brain systems in processing the semantics of mathematical logic from the perspective of macroscopic polysynaptic networks. By comparing algebraic and arithmetic expressions of identical underlying structure, we show how the different subparts of a fronto-parietal network are modulated by the semantic domain, over which the mathematical formulae are interpreted. Within this network, the prefrontal cortex represents a system that hosts three major components, namely, control, arithmetic-logic, and short-term memory. This prefrontal system operates on data fed to it by two other systems: a premotor-parietal top-down system that updates and transforms (external) data into an internal format, and a hippocampal bottom-up system that either detects novel information or serves as an access device to memory for previously acquired knowledge. PMID:23301101
Mathematical classification of regulatory logics for compound environmental changes.
Tanaka, Reiko J; Kimura, Hidenori
2008-03-21
This paper is concerned with biological regulatory mechanisms in response to the simultaneous occurrence of a huge number of environmental changes. The restricted resources of cells strictly limit the number of their regulatory methods; hence, cells must adopt, as compensation, special mechanisms to deal with the simultaneous occurrence of environmental changes. We hypothesize that cells use various control logics to integrate information about independent environmental changes related to a cell task and represent the resulting effects of the different ways of integration by logical functions. Using the notion of equivalence classes in set theory, we describe the mathematical classification of the effects into biologically unequivalent ones realized by different control logics. Our purely mathematical and systematic classification of logical functions reveals three elementary control logics with different biological relevance. To better understand their biological significance, we consider examples of biological systems that use these elementary control logics.
Formal logic rewrite system bachelor in teaching mathematical informatics
NASA Astrophysics Data System (ADS)
Habiballa, Hashim; Jendryscik, Radek
2017-07-01
The article presents capabilities of the formal rewrite logic system - Bachelor - for teaching theoretical computer science (mathematical informatics). The system Bachelor enables constructivist approach to teaching and therefore it may enhance the learning process in hard informatics essential disciplines. It brings not only detailed description of formal rewrite process but also it can demonstrate algorithmical principles for logic formulae manipulations.
The Assessment of Mathematical Logic: Abstract Patterns and Familiar Contexts
ERIC Educational Resources Information Center
Teppo, Anne R.; Esty, Warren W.; Kirkpatrick, Kay
2003-01-01
Undergraduate students' written exams were analyzed from a freshman-level mathematics course that emphasized, among other topics, the study of mathematical logic. Findings indicate that on questions related to the negation of a conditional sentence, students performed much better when given natural-language contexts than they did on questions…
NASA Astrophysics Data System (ADS)
Jetli, Priyedarshi
Modern logic begins with Boole's The Mathematical Analysis of Logic when the algebra of logic was developed so that classical logic syllogisms were proven as algebraic equations and the turn from the logic of classes to propositional logic was suggested. The emergence was incomplete as Boole algebraised classical logic. Frege in Begriffsschrift replaced Aristotelian subject-predicate propositions by function and argument and displaced syllogisms with an axiomatic propositional calculus using conditionals, modus ponens and the law of substitution. Further Frege provided the breakthrough to lay down the groundwork for the development of quantified logic as well as the logic of relations. He achieved all of this through his innovative formal notations which have remained underrated. Frege hence completed the emergence of modern logic. Both Boole and Frege mathematised logic, but Frege's goal was to logicise mathematics. However the emergence of modern logic in Frege should be detached from his logicism.
Mathematical Logic in the Human Brain: Syntax
Friedrich, Roland; Friederici, Angela D.
2009-01-01
Theory predicts a close structural relation of formal languages with natural languages. Both share the aspect of an underlying grammar which either generates (hierarchically) structured expressions or allows us to decide whether a sentence is syntactically correct or not. The advantage of rule-based communication is commonly believed to be its efficiency and effectiveness. A particularly important class of formal languages are those underlying the mathematical syntax. Here we provide brain-imaging evidence that the syntactic processing of abstract mathematical formulae, written in a first order language, is, indeed efficient and effective as a rule-based generation and decision process. However, it is remarkable, that the neural network involved, consisting of intraparietal and prefrontal regions, only involves Broca's area in a surprisingly selective way. This seems to imply that despite structural analogies of common and current formal languages, at the neural level, mathematics and natural language are processed differently, in principal. PMID:19478999
EXPERIMENTAL TEACHING OF MATHEMATICAL LOGIC IN THE ELEMENTARY SCHOOL.
ERIC Educational Resources Information Center
BINFORD, FREDERICK; SUPPES, PATRICK
STUDY OBJECTIVES WERE DEVELOPED AROUND THE IDEA THAT DELIBERATE AND PLANNED TEACHING OF FORMAL SYMBOLIC LOGIC WILL BENEFIT THE STUDENT AT ANY AGE BY ENLARGING HIS SCOPE AND PROVIDING FOR A DEEPER AND MORE PENETRATING STUDY OF MATHEMATICS AND OTHER DEDUCTIVELY FORMULATED DISCIPLINES. IT WAS HYPOTHESIZED THAT THE ABLE STUDENT IN ELEMENTARY SCHOOL IS…
Children's Logical and Mathematical Cognition: Progress in Cognitive Development Research.
ERIC Educational Resources Information Center
Brainerd, Charles J., Ed.
The goal of books in this series is to present work that is on the growing tip of research in cognitive development. The theme of this volume is children's logical and mathematical cognition, a field in which Piaget's influence has been extensive. In the first of the six chapters, Acredolo presents a new theory of the cognitive bases for…
Reasoning with Computer Code: a new Mathematical Logic
NASA Astrophysics Data System (ADS)
Pissanetzky, Sergio
2013-01-01
A logic is a mathematical model of knowledge used to study how we reason, how we describe the world, and how we infer the conclusions that determine our behavior. The logic presented here is natural. It has been experimentally observed, not designed. It represents knowledge as a causal set, includes a new type of inference based on the minimization of an action functional, and generates its own semantics, making it unnecessary to prescribe one. This logic is suitable for high-level reasoning with computer code, including tasks such as self-programming, objectoriented analysis, refactoring, systems integration, code reuse, and automated programming from sensor-acquired data. A strong theoretical foundation exists for the new logic. The inference derives laws of conservation from the permutation symmetry of the causal set, and calculates the corresponding conserved quantities. The association between symmetries and conservation laws is a fundamental and well-known law of nature and a general principle in modern theoretical Physics. The conserved quantities take the form of a nested hierarchy of invariant partitions of the given set. The logic associates elements of the set and binds them together to form the levels of the hierarchy. It is conjectured that the hierarchy corresponds to the invariant representations that the brain is known to generate. The hierarchies also represent fully object-oriented, self-generated code, that can be directly compiled and executed (when a compiler becomes available), or translated to a suitable programming language. The approach is constructivist because all entities are constructed bottom-up, with the fundamental principles of nature being at the bottom, and their existence is proved by construction. The new logic is mathematically introduced and later discussed in the context of transformations of algorithms and computer programs. We discuss what a full self-programming capability would really mean. We argue that self
ERIC Educational Resources Information Center
Seltman, Muriel; Seltman, P. E. J.
1978-01-01
The authors stress the importance of bringing together the causal logic of history and the formal logic of mathematics in order to humanize mathematics and make it more accessible. An example of such treatment is given in a discussion of the centrality of Euclid and the Euclidean system to mathematics development. (MN)
ERIC Educational Resources Information Center
Seltman, Muriel; Seltman, P. E. J.
1978-01-01
The authors stress the importance of bringing together the causal logic of history and the formal logic of mathematics in order to humanize mathematics and make it more accessible. An example of such treatment is given in a discussion of the centrality of Euclid and the Euclidean system to mathematics development. (MN)
[Influence of music on a decision of mathematical logic tasks].
Pavlygina, R A; Karamysheva, N N; Sakharov, D S; Davydov, V I
2012-01-01
Accompaniment of a decision of mathematical logical tasks by music (different style and power) influenced on the time of the decision. Classical music 35 and 65 dB and roc-music 65 and 85 dB decreased the time of the decision. More powerful classical music (85 dB) did not effect like that. The decision without the musical accompaniment led to increasing of coherent values especially in beta1, beta2, gamma frequency ranges in EEG of occipital cortex. The intrahemispheric and the interhemispheric coherences of frontal EEG increased and EEG asymmetry (in a number of Coh-connections in left and right hemispheres) arose during the tasks decision accompanied by music. Application of classical music 35 and 65 dB caused left-side asymmetry in EEG. Using of more powerful classical or rock music led to prevalence of quantity of Coh-connections in a right hemisphere.
Teaching Proofs and Algorithms in Discrete Mathematics with Online Visual Logic Puzzles
ERIC Educational Resources Information Center
Cigas, John; Hsin, Wen-Jung
2005-01-01
Visual logic puzzles provide a fertile environment for teaching multiple topics in discrete mathematics. Many puzzles can be solved by the repeated application of a small, finite set of strategies. Explicitly reasoning from a strategy to a new puzzle state illustrates theorems, proofs, and logic principles. These provide valuable, concrete…
ERIC Educational Resources Information Center
Crestani, Fabio; Dominich, Sandor; Lalmas, Mounia; van Rijsbergen, Cornelis Joost
2003-01-01
Discusses the importance of research on the use of mathematical, logical, and formal methods in information retrieval to help enhance retrieval effectiveness and clarify underlying concepts of information retrieval. Highlights include logic; probability; spaces; and future research needs. (Author/LRW)
ERIC Educational Resources Information Center
Garrison, Laura A.
2005-01-01
This paper describes two classroom activities and a project that supplement a Liberal Arts Mathematics course's coverage of logic and reasoning. The first classroom activity introduces the writing of inductive and deductive arguments, and the second activity involves analyzing a guest speaker's arguments. The project consists of using logic and…
ERIC Educational Resources Information Center
Crestani, Fabio; Dominich, Sandor; Lalmas, Mounia; van Rijsbergen, Cornelis Joost
2003-01-01
Discusses the importance of research on the use of mathematical, logical, and formal methods in information retrieval to help enhance retrieval effectiveness and clarify underlying concepts of information retrieval. Highlights include logic; probability; spaces; and future research needs. (Author/LRW)
The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory
NASA Astrophysics Data System (ADS)
Frey, Kimberly
The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum
NASA Astrophysics Data System (ADS)
de Andrade, Thales Haddad Novaes; Vilela, Denise Silva
2013-09-01
In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of interlocutions and pose a dialogue between the field of mathematics education in Brazil and the sociology of science proposed by David Bloor. The main point of Bloor's theory is that logical-mathematical knowledge is far from being true and universal and is socially conditioned. In particular we will be discussing the first principle of the strong program, which deals with conditions that generate beliefs promoted by education policies in Brazil, such as the MEC/USAID treaties. In this case the "naturalization of logic" was stimulated by a widespread diffusion of both Piaget studies and the Modern Mathematics Movement.
Logic. Geometry Module for Use in a Mathematics Laboratory Setting.
ERIC Educational Resources Information Center
Brotherton, Sheila; And Others
Within this single module there are two approaches to this brief survey of logic. Since most geometry textbooks fail to give an adequate discussion of logic, a "textbook" treatment of the subject has been included. This is found as explanations interspersed in the exercises and these can be used as a textbook approach. However, also included is an…
ERIC Educational Resources Information Center
Novaes de Andrade, Thales Haddad; Vilela, Denise Silva
2013-01-01
In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of…
ERIC Educational Resources Information Center
Novaes de Andrade, Thales Haddad; Vilela, Denise Silva
2013-01-01
In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of…
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate
NASA Astrophysics Data System (ADS)
Dridi, G.; Julien, R.; Hliwa, M.; Joachim, C.
2015-08-01
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
Dridi, G; Julien, R; Hliwa, M; Joachim, C
2015-08-28
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
ERIC Educational Resources Information Center
Dawkins, Paul Christian; Cook, John Paul
2017-01-01
Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how…
ERIC Educational Resources Information Center
Dawkins, Paul Christian; Cook, John Paul
2017-01-01
Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how…
A Generalized Instructional System for Elementary Mathematical Logic.
ERIC Educational Resources Information Center
Goldberg, Adele
A computer-based instructional system for teaching the notion of mathematical proof is described. The system is capable of handling formalizations of the full predicate calculus with identity and, with minor work, definite description. Designed as an instructional device, the program is also the basis for a number of research projects involving…
The Importance of Mathematical and Logical Skills to Clothing Construction.
ERIC Educational Resources Information Center
Franz, Wanda; And Others
1985-01-01
Twenty-three female students, enrolled in the Apparel Construction and Fitting course at West Virginia University, were evaluated to determine whether the ability of the students to perform basic mathematical skills is related to performance in a clothing construction course. Educational implications of the results are discussed. (CT)
ERIC Educational Resources Information Center
Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri
2013-01-01
This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…
Science-Technology Coupling: The Case of Mathematical Logic and Computer Science.
ERIC Educational Resources Information Center
Wagner-Dobler, Roland
1997-01-01
In the history of science, there have often been periods of sudden rapprochements between pure science and technology-oriented branches of science. Mathematical logic as pure science and computer science as technology-oriented science have experienced such a rapprochement, which is studied in this article in a bibliometric manner. (Author)
The Role of Logic in the Validation of Mathematical Proofs. Technical Report. No. 1999-1
ERIC Educational Resources Information Center
Selden, Annie; Selden, John
1999-01-01
Mathematics departments rarely require students to study very much logic before working with proofs. Normally, the most they will offer is contained in a small portion of a "bridge" course designed to help students move from more procedurally-based lower-division courses (e.g., abstract algebra and real analysis). What accounts for this seeming…
ERIC Educational Resources Information Center
Yilmaz, Ismail
2014-01-01
This paper is a qualitative case study designed to identify prospective science teachers' mathematical-logical structures on the basis of their knowledge and achievement levels in magnetism. The study also made an attempt to reveal the effects of knowledge-level variables and procedural variables, which were considered to be potential…
ERIC Educational Resources Information Center
Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri
2013-01-01
This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…
ERIC Educational Resources Information Center
Yilmaz, Ismail
2014-01-01
This paper is a qualitative case study designed to identify prospective science teachers' mathematical-logical structures on the basis of their knowledge and achievement levels in magnetism. The study also made an attempt to reveal the effects of knowledge-level variables and procedural variables, which were considered to be potential…
Science-Technology Coupling: The Case of Mathematical Logic and Computer Science.
ERIC Educational Resources Information Center
Wagner-Dobler, Roland
1997-01-01
In the history of science, there have often been periods of sudden rapprochements between pure science and technology-oriented branches of science. Mathematical logic as pure science and computer science as technology-oriented science have experienced such a rapprochement, which is studied in this article in a bibliometric manner. (Author)
On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics
NASA Astrophysics Data System (ADS)
Kalanov, Temur Z.
2016-03-01
Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.
A Safety Conundrum Illustrated: Logic, Mathematics, and Science Are Not Enough
NASA Technical Reports Server (NTRS)
Holloway, C. M.; Johnson, C. W.; Collins, Kristine R.
2010-01-01
In an ideal world, conversations about whether a particular system is safe, or whether a particular method or tool enhances safety, would be emotion-free discussions concentrating on the level of safety required, available evidence, and coherent logical, mathematical, or scientific arguments based on that evidence. In the real world, discussions about safety are often not emotion-free. Political and economic arguments may play a bigger role than logical, mathematical, and scientific arguments, and psychological factors may be as important, or even more important, than purely technical factors. This paper illustrates the conundrum that can result from this clash of the ideal and the real by means of an imagined conversation among a collection of fictional characters representing various types of people who may be participating in a safety discussion.
Some Implications of a Behavioral Analysis of Verbal Behavior for Logic and Mathematics.
Palmer, David C
2013-01-01
The evident power and utility of the formal models of logic and mathematics pose a puzzle: Although such models are instances of verbal behavior, they are also essentialistic. But behavioral terms, and indeed all products of selection contingencies, are intrinsically variable and in this respect appear to be incommensurate with essentialism. A distinctive feature of verbal contingencies resolves this puzzle: The control of behavior by the nonverbal environment is often mediated by the verbal behavior of others, and behavior under control of verbal stimuli is blind to the intrinsic variability of the stimulating environment. Thus, words and sentences serve as filters of variability and thereby facilitate essentialistic model building and the formal structures of logic, mathematics, and science. Autoclitic frames, verbal chains interrupted by interchangeable variable terms, are ubiquitous in verbal behavior. Variable terms can be substituted in such frames almost without limit, a feature fundamental to formal models. Consequently, our fluency with autoclitic frames fosters generalization to formal models, which in turn permit deduction and other kinds of logical and mathematical inference.
Some Implications of a Behavioral Analysis of Verbal Behavior for Logic and Mathematics
2013-01-01
The evident power and utility of the formal models of logic and mathematics pose a puzzle: Although such models are instances of verbal behavior, they are also essentialistic. But behavioral terms, and indeed all products of selection contingencies, are intrinsically variable and in this respect appear to be incommensurate with essentialism. A distinctive feature of verbal contingencies resolves this puzzle: The control of behavior by the nonverbal environment is often mediated by the verbal behavior of others, and behavior under control of verbal stimuli is blind to the intrinsic variability of the stimulating environment. Thus, words and sentences serve as filters of variability and thereby facilitate essentialistic model building and the formal structures of logic, mathematics, and science. Autoclitic frames, verbal chains interrupted by interchangeable variable terms, are ubiquitous in verbal behavior. Variable terms can be substituted in such frames almost without limit, a feature fundamental to formal models. Consequently, our fluency with autoclitic frames fosters generalization to formal models, which in turn permit deduction and other kinds of logical and mathematical inference. PMID:28018038
Morsanyi, Kinga; Devine, Amy; Nobes, Alison; Szűcs, Dénes
2013-07-01
This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain-general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief-laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief-neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real-life referents) develops later than the ability to reason about belief-inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8. © 2013 Blackwell Publishing Ltd.
ERIC Educational Resources Information Center
Lubis, Asrin; Nasution, Andrea Arifsyah
2017-01-01
Mathematical reasoning in logical context has now received much attention in the mathematics curriculum documents of many countries, including Indonesia. In Indonesia, students start formally learning about logic when they pursue to senior-high school. Before, they previously have many experiences to deal with logic, but the earlier assignments do…
Non Locality Proofs in Quantum Mechanics Analyzed by Ordinary Mathematical Logic
NASA Astrophysics Data System (ADS)
Nisticò, Giuseppe
2014-10-01
The so-called non-locality theorems aim to show that Quantum Mechanics is not consistent with the Locality Principle. Their proofs require, besides the standard postulates of Quantum Theory, further conditions, as for instance the Criterion of Reality, which cannot be formulated in the language of Standard Quantum Theory; this difficulty makes the proofs not verifiable according to usual logico-mathematical methods, and therefore it is a source of the controversial debate about the real implications of these theorems. The present work addresses this difficulty for Bell-type and Stapp's arguments of non-locality. We supplement the formalism of Quantum Mechanics with formal statements inferred from the further conditions in the two different cases. Then an analysis of the two arguments is performed according to ordinary mathematical logic.
Davidson, P M
1987-12-01
Cognition of functions (i.e., y = f(x)) has been identified as an achievement of early childhood. To investigate the development of function concepts and their relation to mathematical and logical abilities typically acquired during the age period of 5-7 years, 72 children in this age range were tested on nonnumerical function tasks (functions as exchange of properties, functions as displacement of positions, and functions as preservation of structure), numerical tasks (number conservation and arithmetic problems), and aspects of logical reasoning (class inclusion, class vicariance, and seriation). Orderly developmental trends were found in function task performance, with younger children manifesting limited success through trial-and-error strategies and older children achieving substantial success with anticipatory strategies. Moreover, certain function abilities were associated with the numerical domain, whereas others were associated with the logical domain. The findings are consistent with the developmental model of Piaget et al. according to which cognition of functions lays the groundwork for reversible operations, but also suggest that this development occurs through parallel processes within separate conceptual domains.
NASA Astrophysics Data System (ADS)
Lanzalaco, Felix; Pissanetzky, Sergio
2013-12-01
A recent theory of physical information based on the fundamental principles of causality and thermodynamics has proposed that a large number of observable life and intelligence signals can be described in terms of the Causal Mathematical Logic (CML), which is proposed to encode the natural principles of intelligence across any physical domain and substrate. We attempt to expound the current definition of CML, the "Action functional" as a theory in terms of its ability to possess a superior explanatory power for the current neuroscientific data we use to measure the mammalian brains "intelligence" processes at its most general biophysical level. Brain simulation projects define their success partly in terms of the emergence of "non-explicitly programmed" complex biophysical signals such as self-oscillation and spreading cortical waves. Here we propose to extend the causal theory to predict and guide the understanding of these more complex emergent "intelligence Signals". To achieve this we review whether causal logic is consistent with, can explain and predict the function of complete perceptual processes associated with intelligence. Primarily those are defined as the range of Event Related Potentials (ERP) which include their primary subcomponents; Event Related Desynchronization (ERD) and Event Related Synchronization (ERS). This approach is aiming for a universal and predictive logic for neurosimulation and AGi. The result of this investigation has produced a general "Information Engine" model from translation of the ERD and ERS. The CML algorithm run in terms of action cost predicts ERP signal contents and is consistent with the fundamental laws of thermodynamics. A working substrate independent natural information logic would be a major asset. An information theory consistent with fundamental physics can be an AGi. It can also operate within genetic information space and provides a roadmap to understand the live biophysical operation of the phenotype
[Decision of mathematical logical tasks in sensory enriched environment (classical music)].
Pavlygina, R A; Karamysheva, N N; Tutushkina, M V; Sakharov, D S; Davydov, V I
2012-01-01
The time of a decision of mathematical logical tasks (MLT) was decreased during classical musical accompaniment (power 35 and 65 dB). Music 85 dB did not influence on the process of decision of MLT. Decision without the musical accompaniment led to increasing of coherent function values in beta1, beta2, gamma frequency ranges in EEG of occipital areas with prevalence in a left hemisphere. A coherence of potentials was decreased in EEG of frontal cortex. Music decreasing of making-decision time enhanced left-sided EEG asymmetry The intrahemispheric and the interhemispheric coherences of frontal cortex were increased during the decision of MLT accompanied by music. Using of musical accompaniment 85 dB produced a right-side asymmetry in EEG and formed a focus of coherent connections in EEG of temporal area of a right hemisphere.
NASA Astrophysics Data System (ADS)
Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi
2017-06-01
This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.
NASA Astrophysics Data System (ADS)
Schäfer, Andreas; Holz, Jan; Leonhardt, Thiemo; Schroeder, Ulrik; Brauner, Philipp; Ziefle, Martina
2013-06-01
In this study, we address the problem of low retention and high dropout rates of computer science university students in early semesters of the studies. Complex and high abstract mathematical learning materials have been identified as one reason for the dropout rate. In order to support the understanding and practicing of core mathematical concepts, we developed a game-based multitouch learning environment in which the need for a suitable learning environment for mathematical logic was combined with the ability to train cooperation and collaboration in a learning scenario. As application domain, the field of mathematical logic had been chosen. The development process was accomplished along three steps: First, ethnographic interviews were run with 12 students of computer science revealing typical problems with mathematical logic. Second, a multitouch learning environment was developed. The game consists of multiple learning and playing modes in which teams of students can collaborate or compete against each other. Finally, a twofold evaluation of the environment was carried out (user study and cognitive walk-through). Overall, the evaluation showed that the game environment was easy to use and rated as helpful: The chosen approach of a multiplayer game supporting competition, collaboration, and cooperation is perceived as motivating and "fun."
THRESHOLD LOGIC IN ARTIFICIAL INTELLIGENCE
COMPUTER LOGIC, ARTIFICIAL INTELLIGENCE , BIONICS, GEOMETRY, INPUT OUTPUT DEVICES, LINEAR PROGRAMMING, MATHEMATICAL LOGIC, MATHEMATICAL PREDICTION, NETWORKS, PATTERN RECOGNITION, PROBABILITY, SWITCHING CIRCUITS, SYNTHESIS
NASA Astrophysics Data System (ADS)
Včelař, František; Pátíková, Zuzana
2017-07-01
For the case of classical Tarski's theorem on fixed points of isotone maps we show that embedding of this statement into fuzzy logical environment leads to surprising results, which cannot be easily seen and awaited in classical logical environment.
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
One chapter in the fourteenth unit of this SMSG series deals with logic; simple and compound statements, truth tables, logical equivalence, rules of a logical argument, proof, quantifiers, and negations are the topics covered. The second chapter of the unit discusses applications of probability and statistics, including random sampling,…
NASA Astrophysics Data System (ADS)
Li, Jing; Ma, Sujuan; Ma, Linqing
Firstly, in this article, we expound the theory of the educational games and multiple intelligence and analyze the relationship between them. Then, further, we elaborate educational games' effect on the development of students' multiple intelligence, taking logic-mathematics intelligence for example. Also, we discuss the strategies of using educational games to improve students' intelligence. In a word, we can use the computer games to develop the students' multi-intelligence.
Black-box Brain Experiments, Causal Mathematical Logic, and the Thermodynamics of Intelligence
NASA Astrophysics Data System (ADS)
Pissanetzky, Sergio; Lanzalaco, Felix
2013-12-01
Awareness of the possible existence of a yet-unknown principle of Physics that explains cognition and intelligence does exist in several projects of emulation, simulation, and replication of the human brain currently under way. Brain simulation projects define their success partly in terms of the emergence of non-explicitly programmed biophysical signals such as self-oscillation and spreading cortical waves. We propose that a recently discovered theory of Physics known as Causal Mathematical Logic (CML) that links intelligence with causality and entropy and explains intelligent behavior from first principles, is the missing link. We further propose the theory as a roadway to understanding more complex biophysical signals, and to explain the set of intelligence principles. The new theory applies to information considered as an entity by itself. The theory proposes that any device that processes information and exhibits intelligence must satisfy certain theoretical conditions irrespective of the substrate where it is being processed. The substrate can be the human brain, a part of it, a worm's brain, a motor protein that self-locomotes in response to its environment, a computer. Here, we propose to extend the causal theory to systems in Neuroscience, because of its ability to model complex systems without heuristic approximations, and to predict emerging signals of intelligence directly from the models. The theory predicts the existence of a large number of observables (or "signals"), all of which emerge and can be directly and mathematically calculated from non-explicitly programmed detailed causal models. This approach is aiming for a universal and predictive language for Neuroscience and AGI based on causality and entropy, detailed enough to describe the finest structures and signals of the brain, yet general enough to accommodate the versatility and wholeness of intelligence. Experiments are focused on a black-box as one of the devices described above of which
NASA Technical Reports Server (NTRS)
Le Balleur, J. C.
1988-01-01
The applicability of conventional mathematical analysis (based on the combination of two-valued logic and probability theory) to problems in which human judgment, perception, or emotions play significant roles is considered theoretically. It is shown that dispositional logic, a branch of fuzzy logic, has particular relevance to the common-sense reasoning typical of human decision-making. The concepts of dispositionality and usuality are defined analytically, and a dispositional conjunctive rule and dispositional modus ponens are derived.
ERIC Educational Resources Information Center
Gazit, Avikam
2012-01-01
The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical-mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th…
ERIC Educational Resources Information Center
Gazit, Avikam
2012-01-01
The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical-mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th…
Exploring Logical Reasoning and Mathematical Proof in Grade 6 Elementary School Students
ERIC Educational Resources Information Center
Flegas, Konstantinos; Charalampos, Lemonidis
2013-01-01
Research and classroom experience reveal that the construction of mathematical proofs is difficult for all students. While many contemporary mathematics curricula recognize the importance of teaching reasoning and proof, in Greece these concepts are introduced at the secondary education level. In this study, we will attempt to investigate a group…
ERIC Educational Resources Information Center
Özdemir, Emine; Övez, Filiz Tuba Dikkartin
2017-01-01
The cognitive development of prospective teacher needs to be taken into estimate so that proofs are presented in forms that are potentially meaningful for them. This requires educators and mathematicians to rethink consider the use of types of proof related to the logical thinking improvement of the singular. The purpose of the study is to…
ERIC Educational Resources Information Center
Hogan, David; Chan, Melvin; Rahim, Ridzuan; Kwek, Dennis; Aye, Khin Maung; Loo, Siok Chen; Sheng, Yee Zher; Luo, Wenshu
2013-01-01
By any measure, Singapore's educational system has generated an extraordinary record of achievement over the past two or three decades. In this article, we report on one key component of a broader three year investigation into why Singapore has done so well, and explore the logic, strength, resilience and limits of the underlying pedagogical model…
ERIC Educational Resources Information Center
Hogan, David; Chan, Melvin; Rahim, Ridzuan; Kwek, Dennis; Aye, Khin Maung; Loo, Siok Chen; Sheng, Yee Zher; Luo, Wenshu
2013-01-01
By any measure, Singapore's educational system has generated an extraordinary record of achievement over the past two or three decades. In this article, we report on one key component of a broader three year investigation into why Singapore has done so well, and explore the logic, strength, resilience and limits of the underlying pedagogical model…
ERIC Educational Resources Information Center
Morsanyi, Kinga; Devine, Amy; Nobes, Alison; Szucs, Denes
2013-01-01
This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized…
ERIC Educational Resources Information Center
Morsanyi, Kinga; Devine, Amy; Nobes, Alison; Szucs, Denes
2013-01-01
This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized…
The Fallacy of Composition: Prospective Mathematics Teachers' Use of Logical Fallacies
ERIC Educational Resources Information Center
Chernoff, Egan J.; Russell, Gale L.
2012-01-01
The purpose of this article is to address the lack of research on teachers' knowledge of probability. As has been the case in prior research, we asked prospective mathematics teachers to determine which of the presented sequences of coin flips was least likely to occur. However, instead of using the traditional perspectives of heuristic and…
ERIC Educational Resources Information Center
Horn, Ilana Seidel; Kane, Britnie Delinger; Wilson, Jonee
2015-01-01
In the accountability era, educators are pressed to use evidence-based practice. In this comparative case study, we examine the learning opportunities afforded by teachers' data use conversations. Using situated discourse analysis, we compare two middle school mathematics teacher workgroups interpreting data from the same district assessment.…
ERIC Educational Resources Information Center
Horn, Ilana Seidel; Kane, Britnie Delinger; Wilson, Jonee
2015-01-01
In the accountability era, educators are pressed to use evidence-based practice. In this comparative case study, we examine the learning opportunities afforded by teachers' data use conversations. Using situated discourse analysis, we compare two middle school mathematics teacher workgroups interpreting data from the same district assessment.…
The Fallacy of Composition: Prospective Mathematics Teachers' Use of Logical Fallacies
ERIC Educational Resources Information Center
Chernoff, Egan J.; Russell, Gale L.
2012-01-01
The purpose of this article is to address the lack of research on teachers' knowledge of probability. As has been the case in prior research, we asked prospective mathematics teachers to determine which of the presented sequences of coin flips was least likely to occur. However, instead of using the traditional perspectives of heuristic and…
Cooper, D.K.; Cooper, J.A.; Ferson, S.
1999-01-21
Calculating safety and reliability probabilities with functions of uncertain variables can yield incorrect or misleading results if some precautions are not taken. One important consideration is the application of constrained mathematics for calculating probabilities for functions that contain repeated variables. This paper includes a description of the problem and develops a methodology for obtaining an accurate solution.
ERIC Educational Resources Information Center
Korkmaz, Özgen
2016-01-01
The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and…
NASA Astrophysics Data System (ADS)
Gazit, Avikam
2012-12-01
The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical-mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th graders was higher than that of the pre-service teachers. Unlike the 10th graders, some of whom used various strategies for representing the problem, most of the pre-service teachers' answers were based on a technical algorithm, without using control processes. The obvious conclusion drawn from the findings supports and recommends expanding and enhancing the development of logical-mathematical thinking, both in specific lessons and as an integral part of other lessons in pre-service frameworks.
ERIC Educational Resources Information Center
Laupa, Marta; Becker, Joe
2004-01-01
Arithmetic algorithms include two types of rules: conventional rules that may be changed by authority, and may legitimately vary from one classroom or country to another (e.g. putting the sum below, rather than above, the numbers added) and logical rules that involve the logic of the algorithm. Changes in the logical rules produce incorrect…
Logic via Computer Programming.
ERIC Educational Resources Information Center
Wieschenberg, Agnes A.
This paper proposed the question "How do we teach logical thinking and sophisticated mathematics to unsophisticated college students?" One answer among many is through the writing of computer programs. The writing of computer algorithms is mathematical problem solving and logic in disguise and it may attract students who would otherwise stop…
ERIC Educational Resources Information Center
Tularam, Gurudeo Anand; Hulsman, Kees
2015-01-01
This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The importance now placed on applied mathematics, however, means that students need to gain more conceptual and quantitative knowledge of mathematics in not…
ERIC Educational Resources Information Center
Tularam, Gurudeo Anand; Hulsman, Kees
2015-01-01
This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The importance now placed on applied mathematics, however, means that students need to gain more conceptual and quantitative knowledge of mathematics in not…
ERIC Educational Resources Information Center
Yopp, David
2010-01-01
Understanding logical necessity is an important component of proof and reasoning for teachers of grades K-8. The ability to determine exactly where young students' arguments are faulty offers teachers the chance to give youngsters feedback as they progress toward writing mathematically valid deductive proofs. As defined, logical necessity is the…
ERIC Educational Resources Information Center
Falsetti, Marcela; Alvarez, Marisa
2015-01-01
We present an analysis of students' formal constructions in mathematics regarding to syntactic, semantic and pragmatic aspects. The analyzed tasks correspond to students of the Course of Mathematics for the admission to the university. Our study was qualitative, consisted in the identification, analysis and interpretation, focused in logic…
Logic and the National Curriculum.
ERIC Educational Resources Information Center
Nelson, David
2000-01-01
Reviews the historic relationship between logic and the mathematics curriculum. Proposes a list of logical elements for modern school mathematics. Checks the current national curriculum against this list and finds it to be deficient, especially in relation to the development of ideas of proof. Presents arguments for reform. (Contains 29…
2014-10-03
introduce distributed logics. Distributed logics lift the distribution structure of a distributed system directly into the logic, thereby parameterizing...the logic by the distribution structure itself. Each domain supports a “local modal logic.” The connections between domains are realized as...There are also multi- agent logic systems [12]. What distinguishes distributed logics from these are that the morphisms, i.e., the nbd maps, have
Dilemma in Teaching Mathematics
ERIC Educational Resources Information Center
Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain
2012-01-01
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…
ERIC Educational Resources Information Center
Mac Lane, Saunders
1980-01-01
This is a review of the current research in mathematics involving breadth of ideas. Research includes topics in number theory, classification of all finite simple groups, the representation of group aids in their application to the study of symmetry. (Author/SA)
ERIC Educational Resources Information Center
Costellano, Janet; Scaffa, Matthew
The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…
NASA Astrophysics Data System (ADS)
Rohrlich, Fritz
2011-12-01
Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.
Lusk, E.L.; Overbeek, R.A.
1989-01-01
This book contains the proceedings of the 1989 North American Conference on Logic Programming. Included are the following papers: Expanding query power in constrain logic programming languages, Investigating the linguistics of DNA with definite clause grammars, An intermediate language to support prolog's unification.
Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic
ERIC Educational Resources Information Center
Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.
2016-01-01
Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…
Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic
ERIC Educational Resources Information Center
Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.
2016-01-01
Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…
NASA Astrophysics Data System (ADS)
Pascal, Robert; Pross, Addy
2016-11-01
In this paper we propose a logical connection between the physical and biological worlds, one resting on a broader understanding of the stability concept. We propose that stability manifests two facets - time and energy, and that stability's time facet, expressed as persistence, is more general than its energy facet. That insight leads to the logical formulation of the Persistence Principle, which describes the general direction of material change in the universe, and which can be stated most simply as: nature seeks persistent forms. Significantly, the principle is found to express itself in two mathematically distinct ways: in the replicative world through Malthusian exponential growth, and in the `regular' physical/chemical world through Boltzmann's probabilistic considerations. By encompassing both `regular' and replicative worlds, the principle appears to be able to help reconcile two of the major scientific theories of the 19th century - the Second Law of Thermodynamics and Darwin's theory of evolution - within a single conceptual framework.
Pascal, Robert; Pross, Addy
2016-11-01
In this paper we propose a logical connection between the physical and biological worlds, one resting on a broader understanding of the stability concept. We propose that stability manifests two facets - time and energy, and that stability's time facet, expressed as persistence, is more general than its energy facet. That insight leads to the logical formulation of the Persistence Principle, which describes the general direction of material change in the universe, and which can be stated most simply as: nature seeks persistent forms. Significantly, the principle is found to express itself in two mathematically distinct ways: in the replicative world through Malthusian exponential growth, and in the 'regular' physical/chemical world through Boltzmann's probabilistic considerations. By encompassing both 'regular' and replicative worlds, the principle appears to be able to help reconcile two of the major scientific theories of the 19th century - the Second Law of Thermodynamics and Darwin's theory of evolution - within a single conceptual framework.
NASA Technical Reports Server (NTRS)
Zadeh, Lofti A.
1988-01-01
The author presents a condensed exposition of some basic ideas underlying fuzzy logic and describes some representative applications. The discussion covers basic principles; meaning representation and inference; basic rules of inference; and the linguistic variable and its application to fuzzy control.
NASA Technical Reports Server (NTRS)
Zadeh, Lofti A.
1988-01-01
The author presents a condensed exposition of some basic ideas underlying fuzzy logic and describes some representative applications. The discussion covers basic principles; meaning representation and inference; basic rules of inference; and the linguistic variable and its application to fuzzy control.
A Mathematics Software Database Update.
ERIC Educational Resources Information Center
Cunningham, R. S.; Smith, David A.
1987-01-01
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
Indeterminacy, linguistic semantics and fuzzy logic
Novak, V.
1996-12-31
In this paper, we discuss the indeterminacy phenomenon which has two distinguished faces, namely uncertainty modeled especially by the probability theory and vagueness, modeled by fuzzy logic. Other important mathematical model of vagueness is provided by the Alternative Set Theory. We focus on some of the basic concepts of these theories in connection with mathematical modeling of the linguistic semantics.
Ambiguity and Paradox in Mathematics
ERIC Educational Resources Information Center
Byers, William
2007-01-01
Many people believe that mathematics provides a model of what thinking is, or should be. They imagine that mathematical thinking always proceeds in a logically rigorous, step-by-step fashion from one truth to another, like a formal proof or a computer program. In fact, insights in mathematics -- whether they are the scholar's breakthroughs or the…
Exploring Metacognition in Preservice Teachers: Problem Solving Processes in Elementary Mathematics
ERIC Educational Resources Information Center
Sparkman, Dana; Harris, Kymberly
2009-01-01
In Principles and Standards for School Mathematics (2000), the (U.S.) National Council of Teachers of Mathematics recommended that students communicate their mathematical thinking in a logical manner, and use the language of mathematics to express their thinking accurately and logically. Students should not only learn mathematics content, but…
Mix-valued logic-based formation control
NASA Astrophysics Data System (ADS)
Zhang, Lequn; Feng, Jun-e.
2013-06-01
The formation control (FC) problem is investigated via a mix-valued logic-based approach. First, a trajectory-tracking algorithm of mix-valued logic control networks is proposed. Then, a new formulation of FC problems is established and a feedback control is designed to solve FC problems. The mathematical description of partial-formation control (PFC) problems is then designed as a structure of logical networks. An interesting practical example of PFC is also presented and discussed in detail.
Cognitive Correlates of Performance in Advanced Mathematics
ERIC Educational Resources Information Center
Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin
2012-01-01
Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…
Cognitive Correlates of Performance in Advanced Mathematics
ERIC Educational Resources Information Center
Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin
2012-01-01
Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…
Automated deduction for first-order logic with equality
2001-06-01
Otter 3.2 is the current version of ANL's automated deduction system designed to search for proofs and countermodels of conjectures stated in first-order logic with equality. It is used mostly for research in mathematics and logic and also for various applications requiring deductive data processing.
Automated deduction for first-order logic with equality
2003-09-01
Otter 3.3 is the current version of ANL's automated deduction system designed to search for proofs and countermodels of conjectures stated in first-order logic with equality. It is used mostly for research in mathematics and logic and also for various applications requiring deductive data processing.
Pre-Service Primary School Teachers' Logical Reasoning Skills
ERIC Educational Resources Information Center
Marchis, Iuliana
2013-01-01
Logical reasoning skills are important for a successful mathematical learning and in students' future career. These skills are essential for a primary school teacher, because they need to explain solving methods and solutions to their pupils. In this research we studied pre-service primary school teachers' logical reasoning skills. The results…
Robust Fuzzy Logic Stabilization with Disturbance Elimination
Danapalasingam, Kumeresan A.
2014-01-01
A robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. Since it is challenging to derive a highly accurate mathematical model, the proposed controller requires only nominal functions of a control system. In this paper, a mathematical derivation is carried out to prove that the controller is able to achieve asymptotic stability by processing state measurements. Robustness here refers to the ability of the controller to asymptotically steer the state vector towards the origin in the presence of model uncertainties and a disturbance input. Simulation results of the robust fuzzy logic controller application in a magnetic levitation system demonstrate the feasibility of the control design. PMID:25177713
Robust fuzzy logic stabilization with disturbance elimination.
Danapalasingam, Kumeresan A
2014-01-01
A robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. Since it is challenging to derive a highly accurate mathematical model, the proposed controller requires only nominal functions of a control system. In this paper, a mathematical derivation is carried out to prove that the controller is able to achieve asymptotic stability by processing state measurements. Robustness here refers to the ability of the controller to asymptotically steer the state vector towards the origin in the presence of model uncertainties and a disturbance input. Simulation results of the robust fuzzy logic controller application in a magnetic levitation system demonstrate the feasibility of the control design.
Logic integer programming models for signaling networks.
Haus, Utz-Uwe; Niermann, Kathrin; Truemper, Klaus; Weismantel, Robert
2009-05-01
We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this, we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in molecular biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.
NASA Astrophysics Data System (ADS)
Itoh, Hideo; Mukai, Seiji; Watanabe, Masanobu; Mori, Masahiko; Yajima, Hiroyoshi
1990-07-01
A beam-scanning laser diode (BSLD) is presently applied to a novel optoelectronic logic operation, designated 'beam-scanning binary logic' (BSBL), that covers the implementation of both the basic logic gates and a spatial code encoder for photodetection, while allowing a greater reduction of the number of active devices than ordinary binary logic operations. BSBL executes multifunctional logic operations simultaneously. The data connections between logic gates in BSLD are flexible, due to the ability to electrically control both output power and laser-beam direction.
Philosophy and mathematics: interactions.
Rashed, Roshdi
From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems with which the philosophers have to contend: (1) Is there still a place for the philosophy of mathematics? and (2) To what extent is a philosophy of mathematics still possible? This article offers some reflections on these questions, which have preoccupied a good many philosophers and continue to do so.
Mythical systems: mathematic and logical theory
NASA Astrophysics Data System (ADS)
Nescolarde-Selva, J.; Usó-Doménech, J. L.; Lloret-Climent, M.
2015-01-01
The process of elaboration of the symbolic universe leads to exciting insights regarding the search for human emotional security. The symbols end up as explanatory axes of universal reality and on them are constructed myths that form a superstructure for belief systems. Human society is a multi-level system with a material structure (society), an ideological superstructure (belief systems, values, etc.) and a super superstructure with two parts: mythical (origin and justification) and utopic (final goal). All mythical belief systems have a numinous-religious nature.
Fuzzy logic controller optimization
Sepe, Jr., Raymond B; Miller, John Michael
2004-03-23
A method is provided for optimizing a rotating induction machine system fuzzy logic controller. The fuzzy logic controller has at least one input and at least one output. Each input accepts a machine system operating parameter. Each output produces at least one machine system control parameter. The fuzzy logic controller generates each output based on at least one input and on fuzzy logic decision parameters. Optimization begins by obtaining a set of data relating each control parameter to at least one operating parameter for each machine operating region. A model is constructed for each machine operating region based on the machine operating region data obtained. The fuzzy logic controller is simulated with at least one created model in a feedback loop from a fuzzy logic output to a fuzzy logic input. Fuzzy logic decision parameters are optimized based on the simulation.
From Searle's Chinese Room to the Mathematics Classroom: Technical and Cognitive Mathematics
ERIC Educational Resources Information Center
Gavalas, Dimitris
2007-01-01
Employing Searle's views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call "Cognitive Mathematics" and "Technical Mathematics" respectively. The former type relates to concepts and meanings, logic and sense, whilst the…
From Searle's Chinese Room to the Mathematics Classroom: Technical and Cognitive Mathematics
ERIC Educational Resources Information Center
Gavalas, Dimitris
2007-01-01
Employing Searle's views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call "Cognitive Mathematics" and "Technical Mathematics" respectively. The former type relates to concepts and meanings, logic and sense, whilst the…
Reversible logic for supercomputing.
DeBenedictis, Erik P.
2005-05-01
This paper is about making reversible logic a reality for supercomputing. Reversible logic offers a way to exceed certain basic limits on the performance of computers, yet a powerful case will have to be made to justify its substantial development expense. This paper explores the limits of current, irreversible logic for supercomputers, thus forming a threshold above which reversible logic is the only solution. Problems above this threshold are discussed, with the science and mitigation of global warming being discussed in detail. To further develop the idea of using reversible logic in supercomputing, a design for a 1 Zettaflops supercomputer as required for addressing global climate warming is presented. However, to create such a design requires deviations from the mainstream of both the software for climate simulation and research directions of reversible logic. These deviations provide direction on how to make reversible logic practical.
Fuzzy Logic for Incidence Geometry
2016-01-01
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133
Fuzzy Logic for Incidence Geometry.
Tserkovny, Alex
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects "as if they were points." Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation "extended lines sameness" is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy "degree of indiscernibility" and "discernibility measure" of extended points.
Mathematical Modeling and Computational Thinking
ERIC Educational Resources Information Center
Sanford, John F.; Naidu, Jaideep T.
2017-01-01
The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…
Designing a Software Tool for Fuzzy Logic Programming
NASA Astrophysics Data System (ADS)
Abietar, José M.; Morcillo, Pedro J.; Moreno, Ginés
2007-12-01
Fuzzy Logic Programming is an interesting and still growing research area that agglutinates the efforts for introducing fuzzy logic into logic programming (LP), in order to incorporate more expressive resources on such languages for dealing with uncertainty and approximated reasoning. The multi-adjoint logic programming approach is a recent and extremely flexible fuzzy logic paradigm for which, unfortunately, we have not found practical tools implemented so far. In this work, we describe a prototype system which is able to directly translate fuzzy logic programs into Prolog code in order to safely execute these residual programs inside any standard Prolog interpreter in a completely transparent way for the final user. We think that the development of such fuzzy languages and programing tools might play an important role in the design of advanced software applications for computational physics, chemistry, mathematics, medicine, industrial control and so on.
Separation Logic and Concurrency
NASA Astrophysics Data System (ADS)
Bornat, Richard
Concurrent separation logic is a development of Hoare logic adapted to deal with pointers and concurrency. Since its inception, it has been enhanced with a treatment of permissions to enable sharing of data between threads, and a treatment of variables as resource alongside heap cells as resource. An introduction to the logic is given with several examples of proofs, culminating in a treatment of Simpson's 4-slot algorithm, an instance of racy non-blocking concurrency.
NASA Technical Reports Server (NTRS)
Du Fresne, E. R.; Dowler, W. L.
1985-01-01
Logic gates for light signals constructed from combinations of prisms, polarizing plates, and quarterwave plates. Optical logic gate performs elementary logic operation on light signals received along two optical fibers. Whether gate performs OR function or exclusive-OR function depends on orientation of analyzer. Nonbinary truth tables also obtained by rotating polarizer or analyzer to other positions or inserting other quarter-wave plates.
NASA Technical Reports Server (NTRS)
Preston, K., Jr.
1972-01-01
The characteristics of the holographic logic computer are discussed. The holographic operation is reviewed from the Fourier transform viewpoint, and the formation of holograms for use in performing digital logic are described. The operation of the computer with an experiment in which the binary identity function is calculated is discussed along with devices for achieving real-time performance. An application in pattern recognition using neighborhood logic is presented.
Logical and layout structures of documents
NASA Astrophysics Data System (ADS)
Eickel, Jürgen
1990-11-01
Document preparation systems are commonly layout oriented in that way that the user interactively creates and modifies frames for text, mathematical formulas, raster or geometric graphics, etc. For batch-oriented systems the user manipulates the process of formatting by inserting control commands into the plain text. These modify the position or graphic aspect of the following text portion. Many systems provide a macro mechanism to combine lengthy and repeatedly used control commands to macros, with the result that the text is interpersed with macrocalls. Macro calls. Macro calls are often logical delimiters. They subdivide the plain text into a linear of document objects, which forms the linear description of the logical document structure similar to a tree. It must be mentioned that in most systems there is no direct support or representation of the logical document structure. The logical structure exists only in the author's mind and the author himself compiles the logical document objects and their hierarchical relationship to physical layout representation. More flexiblw and interactively formatting editors for structured document preparation presuppose a strong distinction of logical and layout structure and incorporate a formal description of the mapping, how the layout is derived from the logical structure. The logical structure is an enriched tree-oriented representation, in which between pbjects are constrained by grammatical specification. The layout structures define the layout relationships on the physical pages of the document and they are also constrained by grammatical spedifications. Another goal is to define the mapping well known as formatting by high-level specification for classes of documents, in order to be able to generate automatically formatting editors by high-level specifications.
Mathematical Texts as Narrative: Rethinking Curriculum
ERIC Educational Resources Information Center
Dietiker, Leslie
2013-01-01
This paper proposes a framework for reading mathematics texts as narratives. Building from a narrative framework of Meike Bal, a reader's experience with the mathematical content as it unfolds in the text (the "mathematical story") is distinguished from his or her logical reconstruction of the content beyond the text (the…
Unified Modern Mathematics, Course 2, Part 1.
ERIC Educational Resources Information Center
Secondary School Mathematics Curriculum Improvement Study, New York, NY.
This is Part 1 of the second course in a series which focuses on building fundamental mathematical structures. Topics considered in this book include: an introduction to mathematical logic and mathematical proof, a continuation of the study of groups, an introduction to axiomatic affine geometry, fields, the real number system, and coordinate…
NASA Technical Reports Server (NTRS)
Howard, Ayanna
2005-01-01
The Fuzzy Logic Engine is a software package that enables users to embed fuzzy-logic modules into their application programs. Fuzzy logic is useful as a means of formulating human expert knowledge and translating it into software to solve problems. Fuzzy logic provides flexibility for modeling relationships between input and output information and is distinguished by its robustness with respect to noise and variations in system parameters. In addition, linguistic fuzzy sets and conditional statements allow systems to make decisions based on imprecise and incomplete information. The user of the Fuzzy Logic Engine need not be an expert in fuzzy logic: it suffices to have a basic understanding of how linguistic rules can be applied to the user's problem. The Fuzzy Logic Engine is divided into two modules: (1) a graphical-interface software tool for creating linguistic fuzzy sets and conditional statements and (2) a fuzzy-logic software library for embedding fuzzy processing capability into current application programs. The graphical- interface tool was developed using the Tcl/Tk programming language. The fuzzy-logic software library was written in the C programming language.
Electrically reconfigurable logic array
NASA Technical Reports Server (NTRS)
Agarwal, R. K.
1982-01-01
To compose the complicated systems using algorithmically specialized logic circuits or processors, one solution is to perform relational computations such as union, division and intersection directly on hardware. These relations can be pipelined efficiently on a network of processors having an array configuration. These processors can be designed and implemented with a few simple cells. In order to determine the state-of-the-art in Electrically Reconfigurable Logic Array (ERLA), a survey of the available programmable logic array (PLA) and the logic circuit elements used in such arrays was conducted. Based on this survey some recommendations are made for ERLA devices.
Ferrite logic reliability study
NASA Technical Reports Server (NTRS)
Baer, J. A.; Clark, C. B.
1973-01-01
Development and use of digital circuits called all-magnetic logic are reported. In these circuits the magnetic elements and their windings comprise the active circuit devices in the logic portion of a system. The ferrite logic device belongs to the all-magnetic class of logic circuits. The FLO device is novel in that it makes use of a dual or bimaterial ferrite composition in one physical ceramic body. This bimaterial feature, coupled with its potential for relatively high speed operation, makes it attractive for high reliability applications. (Maximum speed of operation approximately 50 kHz.)
A Logical Characterization of Systolic Languages
NASA Astrophysics Data System (ADS)
Monti, Angelo; Peron, Adriano
In this paper we study, in the framework of mathematical logic, ℒ(SBTA) i.e. the class of languages accepted by Systolic Binary Tree Automata. We set a correspondence (in the style of Büchi Theorem for regular languages) between ℒ(SBTA) and MSO[Sig], i.e. a decidable Monadic Second Order logic over a suitable infinite signature Sig. We also introduce a natural subclass of ℒ(SBTA) which still properly contains the class of regular languages and which is proved to be characterized by Monadic Second Order logic over a finite signature Sig' ⊂ Sig. Finally, in the style of McNaughton Theorem for star free regular languages, we introduce an expression language which precisely denotes the class of languages defined by the first order fragment of MSO[Sig'].
Simulators' validation study: Problem solution logic
NASA Technical Reports Server (NTRS)
Schoultz, M. B.
1974-01-01
A study was conducted to validate the ground based simulators used for aircraft environment in ride-quality research. The logic to the approach for solving this problem is developed. The overall problem solution flow chart is presented. The factors which could influence the human response to the environment on board the aircraft are analyzed. The mathematical models used in the study are explained. The steps which were followed in conducting the validation tests are outlined.
Fundamentals of Digital Logic.
ERIC Educational Resources Information Center
Noell, Monica L.
This course is designed to prepare electronics personnel for further training in digital techniques, presenting need to know information that is basic to any maintenance course on digital equipment. It consists of seven study units: (1) binary arithmetic; (2) boolean algebra; (3) logic gates; (4) logic flip-flops; (5) nonlogic circuits; (6)…
Programmable Logic Controllers.
ERIC Educational Resources Information Center
Insolia, Gerard; Anderson, Kathleen
This document contains a 40-hour course in programmable logic controllers (PLC), developed for a business-industry technology resource center for firms in eastern Pennsylvania by Northampton Community College. The 10 units of the course cover the following: (1) introduction to programmable logic controllers; (2) DOS primer; (3) prerequisite…
AROUSAL AND LOGICAL INFERENCE.
ERIC Educational Resources Information Center
KOEN, FRANK
THE PURPOSE OF THE EXPERIMENT WAS TO DETERMINE THE DEGREE TO WHICH PHYSIOLOGICAL AROUSAL, AS INDEXED BY THE GRASON STADLER TYPE OPERANT CONDITIONING APPARATUS (GSR), IS RELATED TO THE ACCURACY OF LOGICAL REASONING. THE STIMULI WERE 12 SYLLOGISMS, THREE OF EACH OF FOUR DIFFERENT LOGICAL FORMS. THE 14 SUBJECTS (SS) INDICATED THEIR AGREEMENT OR…
Fundamentals of Digital Logic.
ERIC Educational Resources Information Center
Noell, Monica L.
This course is designed to prepare electronics personnel for further training in digital techniques, presenting need to know information that is basic to any maintenance course on digital equipment. It consists of seven study units: (1) binary arithmetic; (2) boolean algebra; (3) logic gates; (4) logic flip-flops; (5) nonlogic circuits; (6)…
ERIC Educational Resources Information Center
Lopez, Antonio M., Jr.
1989-01-01
Provides background material on logic programing and presents PROLOG as a high-level artificial intelligence programing language that borrows its basic constructs from logic. Suggests the language is one which will help the educator to achieve various goals, particularly the promotion of problem solving ability. (MVL)
Microelectromechanical reprogrammable logic device
Hafiz, M. A. A.; Kosuru, L.; Younis, M. I.
2016-01-01
In modern computing, the Boolean logic operations are set by interconnect schemes between the transistors. As the miniaturization in the component level to enhance the computational power is rapidly approaching physical limits, alternative computing methods are vigorously pursued. One of the desired aspects in the future computing approaches is the provision for hardware reconfigurability at run time to allow enhanced functionality. Here we demonstrate a reprogrammable logic device based on the electrothermal frequency modulation scheme of a single microelectromechanical resonator, capable of performing all the fundamental 2-bit logic functions as well as n-bit logic operations. Logic functions are performed by actively tuning the linear resonance frequency of the resonator operated at room temperature and under modest vacuum conditions, reprogrammable by the a.c.-driving frequency. The device is fabricated using complementary metal oxide semiconductor compatible mass fabrication process, suitable for on-chip integration, and promises an alternative electromechanical computing scheme. PMID:27021295
Amplifying genetic logic gates.
Bonnet, Jerome; Yin, Peter; Ortiz, Monica E; Subsoontorn, Pakpoom; Endy, Drew
2013-05-03
Organisms must process information encoded via developmental and environmental signals to survive and reproduce. Researchers have also engineered synthetic genetic logic to realize simpler, independent control of biological processes. We developed a three-terminal device architecture, termed the transcriptor, that uses bacteriophage serine integrases to control the flow of RNA polymerase along DNA. Integrase-mediated inversion or deletion of DNA encoding transcription terminators or a promoter modulates transcription rates. We realized permanent amplifying AND, NAND, OR, XOR, NOR, and XNOR gates actuated across common control signal ranges and sequential logic supporting autonomous cell-cell communication of DNA encoding distinct logic-gate states. The single-layer digital logic architecture developed here enables engineering of amplifying logic gates to control transcription rates within and across diverse organisms.
Microelectromechanical reprogrammable logic device
NASA Astrophysics Data System (ADS)
Hafiz, M. A. A.; Kosuru, L.; Younis, M. I.
2016-03-01
In modern computing, the Boolean logic operations are set by interconnect schemes between the transistors. As the miniaturization in the component level to enhance the computational power is rapidly approaching physical limits, alternative computing methods are vigorously pursued. One of the desired aspects in the future computing approaches is the provision for hardware reconfigurability at run time to allow enhanced functionality. Here we demonstrate a reprogrammable logic device based on the electrothermal frequency modulation scheme of a single microelectromechanical resonator, capable of performing all the fundamental 2-bit logic functions as well as n-bit logic operations. Logic functions are performed by actively tuning the linear resonance frequency of the resonator operated at room temperature and under modest vacuum conditions, reprogrammable by the a.c.-driving frequency. The device is fabricated using complementary metal oxide semiconductor compatible mass fabrication process, suitable for on-chip integration, and promises an alternative electromechanical computing scheme.
Regulatory Conformance Checking: Logic and Logical Form
ERIC Educational Resources Information Center
Dinesh, Nikhil
2010-01-01
We consider the problem of checking whether an organization conforms to a body of regulation. Conformance is studied in a runtime verification setting. The regulation is translated to a logic, from which we synthesize monitors. The monitors are evaluated as the state of an organization evolves over time, raising an alarm if a violation is…
Regulatory Conformance Checking: Logic and Logical Form
ERIC Educational Resources Information Center
Dinesh, Nikhil
2010-01-01
We consider the problem of checking whether an organization conforms to a body of regulation. Conformance is studied in a runtime verification setting. The regulation is translated to a logic, from which we synthesize monitors. The monitors are evaluated as the state of an organization evolves over time, raising an alarm if a violation is…
Uncertainty, energy, and multiple-valued logics
Hayes, J.P.
1986-02-01
The multiple-valued logics obtained by introducing uncertainty and energy considerations into classical switching theory are studied in this paper. First, the nature of uncertain or unknown signals is examined, and two general uncertainty types called U-values and P-values are identified. It is shown that multiple-valued logics composed of U/P-values can be systematically derived from 2-valued Boolean algebra. These are useful for timing and hazard analysis, and provide a rigorous framework for designing gate-level logic simulation programs. Next, signals of the form (..nu..,S) are considered where ..nu.. and S denote logic level and strength, respectively, and the product vs corresponds to energy flow or power. It is shown that these signals from a type of lattice called a Pseudo-Boolean algebra. Such algebras characterize the behavior of digital circuits at a level (the switch level) intermediate between the conventional analog and logical levels. They provide the mathematical basis for an efficient new class of switch-level simulation programs used in MOS VLSI design.
Fuzzy logic based robotic controller
NASA Technical Reports Server (NTRS)
Attia, F.; Upadhyaya, M.
1994-01-01
Existing Proportional-Integral-Derivative (PID) robotic controllers rely on an inverse kinematic model to convert user-specified cartesian trajectory coordinates to joint variables. These joints experience friction, stiction, and gear backlash effects. Due to lack of proper linearization of these effects, modern control theory based on state space methods cannot provide adequate control for robotic systems. In the presence of loads, the dynamic behavior of robotic systems is complex and nonlinear, especially where mathematical modeling is evaluated for real-time operators. Fuzzy Logic Control is a fast emerging alternative to conventional control systems in situations where it may not be feasible to formulate an analytical model of the complex system. Fuzzy logic techniques track a user-defined trajectory without having the host computer to explicitly solve the nonlinear inverse kinematic equations. The goal is to provide a rule-based approach, which is closer to human reasoning. The approach used expresses end-point error, location of manipulator joints, and proximity to obstacles as fuzzy variables. The resulting decisions are based upon linguistic and non-numerical information. This paper presents a solution to the conventional robot controller which is independent of computationally intensive kinematic equations. Computer simulation results of this approach as obtained from software implementation are also discussed.
Meaning and Process in Mathematics and Programming.
ERIC Educational Resources Information Center
Grogono, Peter
1989-01-01
Trends in computer programing language design are described and children's difficulties in learning to write programs for mathematics problems are considered. Languages are compared under the headings of imperative programing, functional programing, logic programing, and pictures. (DC)
Zargham, M.R.
1995-06-01
Recently, fuzzy logic has been applied to many areas, such as process control, image understanding, robots, expert systems, and decision support systems. This paper will explain the basic concepts of fuzzy logic and its application in different fields. The steps to design a control system will be explained in detail. Fuzzy control is the first successful industrial application of fuzzy logic. A fuzzy controller is able to control systems which previously could only be controlled by skilled operators. In recent years Japan has achieved significant progress in this area and has applied it to variety of products such as cruise control for cars, video cameras, rice cookers, washing machines, etc.
Modeling the switching processes in the Josephson AND and OR logic gates
NASA Astrophysics Data System (ADS)
Tyhanskyi, M. V.; Krysko, R. R.
2013-02-01
We propose a design principle of digital logic gates based on Josephson cryotrons. The operation mode of digital logic gates AND and OR based on tunnel junctions "superconductor-insulator-superconductor" was described. Mathematical models of the switching processes in the logic elements were developed, the transient characteristics during the logic state change were calculated, and the basic parameters of these models were determined. It was shown that digital logic gates "AND" and "OR" can be realized based on individual Josephson cryotrons and their logic state can be controlled by using current pulses as control inputs. Such logic gates satisfy all the requirements for digital logic elements and have switching time of about 2-3 ps.
1981-01-01
79/7, Imperial College, University of London. [Colmerauer 1973] Colmerauer, A., Un Systeme de Communication Homme - machine Kanoui, H., en Francais...any of the LOGIC interface functions (,-, THE, ALL, ANY, etc.) can be obtained by invoking the command (DOC fn), where "fn" is the name of the function...well as for output) illustrates one more way in which the LOGLISP programmer can fruitfully exploit the interface between LOGIC and LISP. GIVE is just a
2008-07-14
as a basis for Phase II research. 2 Background 2.1 Event logic 2.1.1 Event structures Intuitively, an event structure is an abstract algebraic ...Theoretical Computer Science, 149:257–298, 1995. [2] Uri Abraham. Models for Concurrency, volume 11 of Algebra , Logic and Applications Series. Gordon...the ordering of events in a distributed system. Comms. ACM, 21(7):558–65, 1978. [28] Leslie Lamport. Hybrid systems in TLA+. In Grossman , Nerode, Ravn
The Rocky Road to Logical Thinking.
ERIC Educational Resources Information Center
Burch, Fern; Aaronson, Tim
1985-01-01
Presents offline logic activities to extend concepts in "Rocky's Boots." Activities focus on: (1) building logic circuits; (2) recognizing logic in language; (3) playing logic games; and (4) testing logic circuits. Detailed procedures accompanied by illustrative examples are included. (JN)
From Indexed Lax Logic to Intuitionistic Logic
2008-01-07
Categorical and Kripke semantics for constructive S4 modal logic. In CSL ’01: Proceedings of the 15th International Workshop on Computer Science Logic, pages...af(K,a) ⇒ af(K,a) by ⊥L 2. Σ, a; pΓ,⊥q, pCq ⊃ af(K,a) ⇒ af(K,a) by definition of p·q Case: D = D1 Σ;Γ, A ⊃ B ⇒ A D2 Σ;Γ, A ⊃ B,B ⇒ C Σ;Γ, A ⊃ B ⇒ C...L 1. Σ; pΓ, A ⊃ Bq ⇒ pAq by i.h. on D1 2. Σ; pΓq, pAq ⊃ pBq ⇒ pAq by definition of p·q 3. Σ; pΓ, A ⊃ B,Bq ⇒ pCq by i.h. on D2 4. Σ; pΓq, pAq ⊃ pBq
Prakash, Manu; Gershenfeld, Neil
2007-02-09
We demonstrate universal computation in an all-fluidic two-phase microfluidic system. Nonlinearity is introduced into an otherwise linear, reversible, low-Reynolds number flow via bubble-to-bubble hydrodynamic interactions. A bubble traveling in a channel represents a bit, providing us with the capability to simultaneously transport materials and perform logical control operations. We demonstrate bubble logic AND/OR/NOT gates, a toggle flip-flop, a ripple counter, timing restoration, a ring oscillator, and an electro-bubble modulator. These show the nonlinearity, gain, bistability, synchronization, cascadability, feedback, and programmability required for scalable universal computation. With increasing complexity in large-scale microfluidic processors, bubble logic provides an on-chip process control mechanism integrating chemistry and computation.
Diagnosable structured logic array
NASA Technical Reports Server (NTRS)
Whitaker, Sterling (Inventor); Miles, Lowell (Inventor); Gambles, Jody (Inventor); Maki, Gary K. (Inventor)
2009-01-01
A diagnosable structured logic array and associated process is provided. A base cell structure is provided comprising a logic unit comprising a plurality of input nodes, a plurality of selection nodes, and an output node, a plurality of switches coupled to the selection nodes, where the switches comprises a plurality of input lines, a selection line and an output line, a memory cell coupled to the output node, and a test address bus and a program control bus coupled to the plurality of input lines and the selection line of the plurality of switches. A state on each of the plurality of input nodes is verifiably loaded and read from the memory cell. A trusted memory block is provided. The associated process is provided for testing and verifying a plurality of truth table inputs of the logic unit.
Context-Based Exercises in Logic: To Park or Not to Park, 'Tis the Question
ERIC Educational Resources Information Center
Munakata, Mika
2011-01-01
In this article, ambiguous street and park signs are analysed and deciphered using symbolic logic. These examples showcase the ways in which instructors of undergraduate mathematics courses can blend their students' everyday exposure to logical reasoning with classroom experiences. (Contains 4 tables and 6 figures.)
Context-Based Exercises in Logic: To Park or Not to Park, 'Tis the Question
ERIC Educational Resources Information Center
Munakata, Mika
2011-01-01
In this article, ambiguous street and park signs are analysed and deciphered using symbolic logic. These examples showcase the ways in which instructors of undergraduate mathematics courses can blend their students' everyday exposure to logical reasoning with classroom experiences. (Contains 4 tables and 6 figures.)
Twenty-Five Years of the Fuzzy Factor: Fuzzy Logic, the Courts, and Student Press Law.
ERIC Educational Resources Information Center
Plopper, Bruce L.; McCool, Lauralee
A study applied the structure of fuzzy logic, a fairly modern development in mathematical set theory, to judicial opinions concerning non-university, public school student publications, from 1975 to 1999. The study examined case outcomes (19 cases generated 27 opinions) as a function of fuzzy logic, and it evaluated interactions between fuzzy…
Group Solutions, Too! More Cooperative Logic Activities for Grades K-4. Teacher's Guide. LHS GEMS.
ERIC Educational Resources Information Center
Goodman, Jan M.; Kopp, Jaine
There is evidence that structured cooperative logic is an effective way to introduce or reinforce mathematics concepts, explore thinking processes basic to both math and science, and develop the important social skills of cooperative problem-solving. This book contains a number of cooperative logic activities for grades K-4 in order to improve…
Teaching of Mathematics in Higher Education.
ERIC Educational Resources Information Center
Soares, Eliana Maria do Sacramento; Botome, Silvio Paulo
Logic and deductive thinking as well as formal and precise language characterize mathematics as a powerful tool in scientific and technological development as it offers conceptual elements that represent reality phenomena. Thus, teaching mathematics in higher education aims at developing forms of behavior or cognitive competency related to the…
Applications of Algebraic Logic and Universal Algebra to Computer Science
1989-06-21
conference, with roughly equal representation from Mathematics and Computer Science . The conference consisted of eight invited lectures (60 minutes...each) and 26 contributed talks (20-40 minutes each). There was also a round-table discussion on the role of algebra and logic in computer science . Keywords
Research on teacher education programs: logic model approach.
Newton, Xiaoxia A; Poon, Rebecca C; Nunes, Nicole L; Stone, Elisa M
2013-02-01
Teacher education programs in the United States face increasing pressure to demonstrate their effectiveness through pupils' learning gains in classrooms where program graduates teach. The link between teacher candidates' learning in teacher education programs and pupils' learning in K-12 classrooms implicit in the policy discourse suggests a one-to-one correspondence. However, the logical steps leading from what teacher candidates have learned in their programs to what they are doing in classrooms that may contribute to their pupils' learning are anything but straightforward. In this paper, we argue that the logic model approach from scholarship on evaluation can enhance research on teacher education by making explicit the logical links between program processes and intended outcomes. We demonstrate the usefulness of the logic model approach through our own work on designing a longitudinal study that focuses on examining the process and impact of an undergraduate mathematics and science teacher education program.
Radiation tolerant combinational logic cell
NASA Technical Reports Server (NTRS)
Maki, Gary R. (Inventor); Gambles, Jody W. (Inventor); Whitaker, Sterling (Inventor)
2009-01-01
A system has a reduced sensitivity to Single Event Upset and/or Single Event Transient(s) compared to traditional logic devices. In a particular embodiment, the system includes an input, a logic block, a bias stage, a state machine, and an output. The logic block is coupled to the input. The logic block is for implementing a logic function, receiving a data set via the input, and generating a result f by applying the data set to the logic function. The bias stage is coupled to the logic block. The bias stage is for receiving the result from the logic block and presenting it to the state machine. The state machine is coupled to the bias stage. The state machine is for receiving, via the bias stage, the result generated by the logic block. The state machine is configured to retain a state value for the system. The state value is typically based on the result generated by the logic block. The output is coupled to the state machine. The output is for providing the value stored by the state machine. Some embodiments of the invention produce dual rail outputs Q and Q'. The logic block typically contains combinational logic and is similar, in size and transistor configuration, to a conventional CMOS combinational logic design. However, only a very small portion of the circuits of these embodiments, is sensitive to Single Event Upset and/or Single Event Transients.
Programmable Logic Application Notes
NASA Technical Reports Server (NTRS)
Katz, Richard
2000-01-01
This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter will start a series of notes concentrating on analysis techniques with this issues section discussing worst-case analysis requirements.
ERIC Educational Resources Information Center
Welty, Gordon A.
The logic of the evaluation of educational and other action programs is discussed from a methodological viewpoint. However, no attempt is made to develop methods of evaluating programs. In Part I, the structure of an educational program is viewed as a system with three components--inputs, transformation of inputs into outputs, and outputs. Part II…
Quantum probabilistic logic programming
NASA Astrophysics Data System (ADS)
Balu, Radhakrishnan
2015-05-01
We describe a quantum mechanics based logic programming language that supports Horn clauses, random variables, and covariance matrices to express and solve problems in probabilistic logic. The Horn clauses of the language wrap random variables, including infinite valued, to express probability distributions and statistical correlations, a powerful feature to capture relationship between distributions that are not independent. The expressive power of the language is based on a mechanism to implement statistical ensembles and to solve the underlying SAT instances using quantum mechanical machinery. We exploit the fact that classical random variables have quantum decompositions to build the Horn clauses. We establish the semantics of the language in a rigorous fashion by considering an existing probabilistic logic language called PRISM with classical probability measures defined on the Herbrand base and extending it to the quantum context. In the classical case H-interpretations form the sample space and probability measures defined on them lead to consistent definition of probabilities for well formed formulae. In the quantum counterpart, we define probability amplitudes on Hinterpretations facilitating the model generations and verifications via quantum mechanical superpositions and entanglements. We cast the well formed formulae of the language as quantum mechanical observables thus providing an elegant interpretation for their probabilities. We discuss several examples to combine statistical ensembles and predicates of first order logic to reason with situations involving uncertainty.
Temporal logics meet telerobotics
NASA Technical Reports Server (NTRS)
Rutten, Eric; Marce, Lionel
1989-01-01
The specificity of telerobotics being the presence of a human operator, decision assistance tools are necessary for the operator, especially in hostile environments. In order to reduce execution hazards due to a degraded ability for quick and efficient recovery of unexpected dangerous situations, it is of importance to have the opportunity, amongst others, to simulate the possible consequences of a plan before its actual execution, in order to detect these problematic situations. Hence the idea of providing the operator with a simulator enabling him to verify the temporal and logical coherence of his plans. Therefore, the power of logical formalisms is used for representation and deduction purposes. Starting from the class of situations that are represented, a STRIPS (the STanford Research Institute Problem Solver)-like formalism and its underlying logic are adapted to the simulation of plans of actions in time. The choice of a temporal logic enables to build a world representation, on which the effects of plans, grouping actions into control structures, will be transcribed by the simulation, resulting in a verdict and information about the plan's coherence.
Programmable Logic Application Notes
NASA Technical Reports Server (NTRS)
Katz, Richard; Day, John H. (Technical Monitor)
2001-01-01
This report will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter will continue a series of notes concentrating on analysis techniques with this issue's section discussing the use of Root-Sum-Square calculations for digital delays.
Substructural Logical Specifications
2012-11-14
pronounced “A mobile” or, whimsically, “gnab A” in reference to the pronunciation of !A as “bang A.” The primary sequent of ordered logic is Γ; ∆; Ω =⇒ A...distinguished atomic proposition by inserting a rule into the signature that teaches the atomic proposition how to act like the nested rule. (Or, looking at it
Metacomputation and logic programming
Abramov, S.M.
1992-03-01
This paper presents an approach to logic programming based on implementing reverse semantics of programming languages. The interpreter that implements reverse semantics is called a Universal Resolving Algorithm (URA). Implementation and methods for application of a URA are based on methods of metacomputation. 12 refs., 2 figs.
Mapping Individual Logical Processes
ERIC Educational Resources Information Center
Smetana, Frederick O.
1975-01-01
A technique to measure and describe concisely a certain class of individual mental reasoning processes has been developed. The measurement is achieved by recording the complete dialog between a large, varied computerized information system with a broad range of logical operations and options and a human information seeker. (Author/RC)
ERIC Educational Resources Information Center
Straumanis, Joan
A major problem in teaching symbolic logic is that of providing individualized and early feedback to students who are learning to do proofs. To overcome this difficulty, a computer program was developed which functions as a line-by-line proof checker in Sentential Calculus. The program, DEMON, first evaluates any statement supplied by the student…
Active structural control by fuzzy logic rules: An introduction
Tang, Yu; Wu, Kung C.
1996-12-31
A zeroth level introduction to fuzzy logic control applied to the active structural control to reduce the dynamic response of structures subjected to earthquake excitations is presented. It is hoped that this presentation will increase the attractiveness of the methodology to structural engineers in research as well as in practice. The basic concept of the fuzzy logic control are explained by examples and by diagrams with a minimum of mathematics. The effectiveness and simplicity of the fuzzy logic control is demonstrated by a numerical example in which the response of a single- degree-of-freedom system subjected to earthquake excitations is controlled by making use of the fuzzy logic controller. In the example, the fuzzy rules are first learned from the results obtained from linear control theory; then they are fine tuned to improve their performance. It is shown that the performance of fuzzy logic control surpasses that of the linear control theory. The paper shows that linear control theory provides experience for fuzzy logic control, and fuzzy logic control can provide better performance; therefore, two controllers complement each other.
Active structural control by fuzzy logic rules: An introduction
Tang, Y.
1995-07-01
An introduction to fuzzy logic control applied to the active structural control to reduce the dynamic response of structures subjected to earthquake excitations is presented. It is hoped that this presentation will increase the attractiveness of the methodology to structural engineers in research as well as in practice. The basic concept of the fuzzy logic control are explained by examples and by diagrams with a minimum of mathematics. The effectiveness and simplicity of the fuzzy logic control is demonstrated by a numerical example in which the response of a single-degree-of-freedom system subjected to earthquake excitations is controlled by making use of the fuzzy logic controller. In the example, the fuzzy rules are first learned from the results obtained from linear control theory; then they are fine tuned to improve their performance. It is shown that the performance of fuzzy logic control surpasses that of the linear control theory. The paper shows that linear control theory provides experience for fuzzy logic control, and fuzzy logic control can provide better performance; therefore, two controllers complement each other.
Sandia ATM SONET Interface Logic
Kitta, Joseph P.
1994-07-21
SASIL is used to program the EPLD's (Erasable Programmable Logic Devices) and PAL's (Programmable Array Logic) that make up a large percentage of the Sandia ATM SONET Interface (OC3 version) for the INTEL Paragon.
Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition
ERIC Educational Resources Information Center
Su, Hui Fang Huang; Ricci, Frederick A.; Mnatsakanian, Mamikon
2016-01-01
A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…
Conditional Logic and Primary Children.
ERIC Educational Resources Information Center
Ennis, Robert H.
Conditional logic, as interpreted in this paper, means deductive logic characterized by "if-then" statements. This study sought to investigate the knowledge of conditional logic possessed by primary children and to test their readiness to learn such concepts. Ninety students were designated the experimental group and participated in a…
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
2015-01-01
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
2015-01-01
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806
ERIC Educational Resources Information Center
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
ERIC Educational Resources Information Center
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Programmable Logic Application Notes
NASA Technical Reports Server (NTRS)
Katz, Richard
1998-01-01
This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter's column will include some announcements and some recent radiation test results and evaluations of interest. Specifically, the following topics will be covered: the Military and Aerospace Applications of Programmable Devices and Technologies Conference to be held at GSFC in September, 1998, proton test results, heavy ion test results, and some total dose results.
Programmable Logic Application Notes
NASA Technical Reports Server (NTRS)
Katz, Richard
1998-01-01
This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter's column will include some announcements and some recent radiation test results and evaluations of interest. Specifically, the following topics will be covered: the Military and Aerospace Applications of Programmable Devices and Technologies Conference to be held at GSFC in September, 1998, proton test results, and some total dose results.
1986-12-01
determining the consequences of assumptions about the behavior of a system . If the space of behaviors is represented by an envisionment , many such...consequences can be represented by pruning states from the envisionment . This paper provides a formal logic of occurrence which justifies the...algorithms involved and provides a language for relating specific histories to envisionments . The concepts and axioms are general enough to be applicable to
Kompa, K. L.; Levine, R. D.
2001-01-01
We propose a scheme for molecule-based information processing by combining well-studied spectroscopic techniques and recent results from chemical dynamics. Specifically it is discussed how optical transitions in single molecules can be used to rapidly perform classical (Boolean) logical operations. In the proposed way, a restricted number of states in a single molecule can act as a logical gate equivalent to at least two switches. It is argued that the four-level scheme can also be used to produce gain, because it allows an inversion, and not only a switching ability. The proposed scheme is quantum mechanical in that it takes advantage of the discrete nature of the energy levels but, we here discuss the temporal evolution, with the use of the populations only. On a longer time range we suggest that the same scheme could be extended to perform quantum logic, and a tentative suggestion, based on an available experiment, is discussed. We believe that the pumping can provide a partial proof of principle, although this and similar experiments were not interpreted thus far in our terms. PMID:11209046
ERIC Educational Resources Information Center
Waisman, Ilana; Leikin, Mark; Leikin, Roza
2016-01-01
Mathematical processing associated with solving short geometry problems requiring logical inference was examined among students who differ in their levels of general giftedness (G) and excellence in mathematics (EM) using ERP research methodology. Sixty-seven male adolescents formed four major research groups designed according to various…
ERIC Educational Resources Information Center
Waisman, Ilana; Leikin, Mark; Leikin, Roza
2016-01-01
Mathematical processing associated with solving short geometry problems requiring logical inference was examined among students who differ in their levels of general giftedness (G) and excellence in mathematics (EM) using ERP research methodology. Sixty-seven male adolescents formed four major research groups designed according to various…
ERIC Educational Resources Information Center
Bayekolaei, Mehraneh Delaviz; Nor, Norjoharuddeen Bin Mohd; Sohaei, Reza; Berneti, Abdul Karim Maleki; Zerafat, Romina; Saravi, Hanieh Rasouli
2015-01-01
This research aimed to examine the application of two-valued and fuzzy logics teaching in better understanding the precise approximate concepts of chapter 4 of Sixth grade mathematics. Participants of this study were 30 Sixth grade mathematics students from an elementary school in Sari (a city in the north of Iran) in the academic year of…
Concrete Quantum Logics and Δ -Logics, States and Δ -States
NASA Astrophysics Data System (ADS)
Hroch, Michal; Pták, Pavel
2017-04-01
By a concrete quantum logic (in short, by a logic) we mean the orthomodular poset that is set-representable. If L=({Ω },L) is a logic and L is closed under the formation of symmetric difference, Δ , we call L a Δ -logic. In the first part we situate the known results on logics and states to the context of Δ -logics and Δ -states (the Δ -states are the states that are subadditive with respect to the symmetric difference). Moreover, we observe that the rather prominent logic E^{even}_{Ω } of all even-coeven subsets of the countable set Ω possesses only Δ -states. Then we show when a state on the logics given by the divisibility relation allows for an extension as a state. In the next paragraph we consider the so called density logic and its Δ -closure. We find that the Δ -closure coincides with the power set. Then we investigate other properties of the density logic and its factor.
NASA Astrophysics Data System (ADS)
Stefaneas, Petros; Vandoulakis, Ioannis M.
2015-12-01
This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.
NASA Astrophysics Data System (ADS)
Stefaneas, Petros; Vandoulakis, Ioannis M.
2015-12-01
This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.
The mysterious connection between mathematics and physics.
Kauffman, Louis H; Ul-Haq, Rukhsan
2015-12-01
The essay is in the form of a dialogue between the two authors. We take John Wheeler's idea of "It from Bit" as an essential clue and we rework the structure of the bit not to the qubit, but to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We emphasize that mathematics is a combination of calculation and concept. At the conceptual level, mathematics is structured to be independent of time and multiplicity. Mathematics in this way occurs before number and counting. From this timeless domain, mathematics and mathematicians can explore worlds of multiplicity and infinity beyond the apparent limitations of the physical world and see that among these possible worlds there are coincidences with what is observed.
Connectable DNA logic gates: OR and XOR logics.
Gerasimova, Yulia V; Kolpashchikov, Dmitry M
2012-03-05
Modern computer processors are based on semiconductor logic gates connected to each other in complex circuits. This study contributes to the development of a new class of connectable logic gates made of DNA in which the transfer of oligonucleotide fragments as input/output signals occurs upon hybridization of DNA sequences. The DNA strands responsible for a logic function form associates containing immobile DNA four-way junction structures when the signal is high and dissociate into separate strands when the signal is low. A basic set of logic gates (NOT, AND, and OR) was designed. Two NOT gates, two AND gates, and an OR gate were connected in a network that corresponds to an XOR logic function. The design of the logic gates presented here may contribute to the development of the first biocompatible molecular computer. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Develop reusable and combinable designs for transcriptional logic gates.
Zhan, Jian; Ding, Bo; Ma, Rui; Ma, Xiaoyu; Su, Xiaofeng; Zhao, Yun; Liu, Ziqing; Wu, Jiarui; Liu, Haiyan
2010-07-13
One limit on developing complex synthetic gene circuits is the lack of basic components such as transcriptional logic gates that can process combinatorial inputs. Here, we propose a strategy to construct such components based on reusable designs and convergent reengineering of well-studied natural systems. We demonstrated the strategy using variants of the transcription factor (TF) LacI and operator Olac that form specifically interacting pairs. Guided by a mathematical model derived from existing quantitative knowledge, rational designs of transcriptional NAND, NOR and NOT gates have been realized. The NAND gates have been designed based on direct protein-protein interactions in coupling with DNA looping. We demonstrated that the designs are reusable: a multiplex of logic devices can be readily created using the same designs but different combinations of sequence variants. The designed logic gates are combinable to form compound circuits: a demonstration logic circuit containing all three types of designed logic gates has been synthesized, and the circuit truthfully reproduces the pre-designed input-output logic relations.
Multi/infinite dimensional neural networks, multi/infinite dimensional logic theory.
Murthy, Garimella Rama
2005-06-01
A mathematical model of an arbitrary multi-dimensional neural network is developed and a convergence theorem for an arbitrary multi-dimensional neural network represented by a fully symmetric tensor is stated and proved. The input and output signal states of a multi-dimensional neural network/logic gate are related through an energy function, defined over the fully symmetric tensor (representing the connection structure of a multi-dimensional neural network). The inputs and outputs are related such that the minimum/maximum energy states correspond to the output states of the logic gate/neural network realizing a logic function. Similarly, a logic circuit consisting of the interconnection of logic gates, represented by a block symmetric tensor, is associated with a quadratic/higher degree energy function. Infinite dimensional logic theory is discussed through the utilization of infinite dimension/order tensors.
Programmable Logic Application Notes
NASA Technical Reports Server (NTRS)
Katz, Richard
1999-01-01
This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter the focus is on some experimental data on low voltage drop out regulators to support mixed 5 and 3.3 volt systems. A discussion of the Small Explorer WIRE spacecraft will also be given. Lastly, we show take a first look at robust state machines in Hardware Description Languages (VHDL) and their use in critical systems. If you have information that you would like to submit or an area you would like discussed or researched, please give me a call or e-mail.
Bright, Liam Kofi
2017-07-10
The logical empiricists expressed a consistent attitude to racial categorisation in both the ethical and scientific spheres. Their attitude may be captured in the following slogan: human racial taxonomy is an empirically meaningful mode of classifying persons that we should refrain from deploying. I offer an interpretation of their position that would render coherent their remarks on race with positions they adopted on the scientific status of taxonomy in general, together with their potential moral or political motivations for adopting that position. Copyright © 2017. Published by Elsevier Ltd.
Flexible programmable logic module
Robertson, Perry J.; Hutchinson, Robert L.; Pierson, Lyndon G.
2001-01-01
The circuit module of this invention is a VME board containing a plurality of programmable logic devices (PLDs), a controlled impedance clock tree, and interconnecting buses. The PLDs are arranged to permit systolic processing of a problem by offering wide data buses and a plurality of processing nodes. The board contains a clock reference and clock distribution tree that can drive each of the PLDs with two critically timed clock references. External clock references can be used to drive additional circuit modules all operating from the same synchronous clock reference.
Adaptive parallel logic networks
NASA Technical Reports Server (NTRS)
Martinez, Tony R.; Vidal, Jacques J.
1988-01-01
Adaptive, self-organizing concurrent systems (ASOCS) that combine self-organization with massive parallelism for such applications as adaptive logic devices, robotics, process control, and system malfunction management, are presently discussed. In ASOCS, an adaptive network composed of many simple computing elements operating in combinational and asynchronous fashion is used and problems are specified by presenting if-then rules to the system in the form of Boolean conjunctions. During data processing, which is a different operational phase from adaptation, the network acts as a parallel hardware circuit.
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
Barriers in Concurrent Separation Logic
NASA Astrophysics Data System (ADS)
Hobor, Aquinas; Gherghina, Cristian
We develop and prove sound a concurrent separation logic for Pthreads-style barriers. Although Pthreads barriers are widely used in systems, and separation logic is widely used for verification, there has not been any effort to combine the two. Unlike locks and critical sections, Pthreads barriers enable simultaneous resource redistribution between multiple threads and are inherently stateful, leading to significant complications in the design of the logic and its soundness proof. We show how our logic can be applied to a specific example program in a modular way. Our proofs are machine-checked in Coq.
NASA Technical Reports Server (NTRS)
Canaris, J.
1991-01-01
A new logic family, which is immune to single event upsets, is described. Members of the logic family are capable of recovery, regardless of the shape of the upsetting event. Glitch propagation from an upset node is also blocked. Logic diagrams for an Inverter, Nor, Nand, and Complex Gates are provided. The logic family can be implemented in a standard, commercial CMOS process with no additional masks. DC, transient, static power, upset recovery and layout characteristics of the new family, based on a commercial 1 micron CMOS N-Well process, are described.
Fuzzy logic and coarse coding using programmable logic devices
NASA Astrophysics Data System (ADS)
Brooks, Geoffrey
2009-05-01
Naturally-occurring sensory signal processing algorithms, such as those that inspired fuzzy-logic control, can be integrated into non-naturally-occurring high-performance technology, such as programmable logic devices, to realize novel bio-inspired designs. Research is underway concerning an investigation into using field programmable logic devices (FPLD's) to implement fuzzy logic sensory processing. A discussion is provided concerning the commonality between bio-inspired fuzzy logic algorithms and coarse coding that is prevalent in naturally-occurring sensory systems. Undergraduate design projects using fuzzy logic for an obstacle-avoidance robot has been accomplished at our institution and other places; numerous other successful fuzzy logic applications can be found as well. The long-term goal is to leverage such biomimetic algorithms for future applications. This paper outlines a design approach for implementing fuzzy-logic algorithms into reconfigurable computing devices. This paper is presented in an effort to connect with others who may be interested in collaboration as well as to establish a starting point for future research.
Parsing with logical variables (logic-based programming systems)
Finin, T.W.; Stone Palmer, M.
1983-01-01
Logic based programming systems have enjoyed an increasing popularity in applied AI work in the last few years. One of the contributions to computational linguistics made by the logic programming paradigm has been the definite clause grammar. In comparing DCGS with previous parsing mechanisms such as ATNS, certain clear advantages are seen. The authors feel that the most important of these advantages are due to the use of logical variables with unification as the fundamental operation on them. To illustrate the power of the logical variable, they have implemented an experimental atn system which treats atn registers as logical variables and provides a unification operation over them. They aim to simultaneously encourage the use of the powerful mechanisms available in DCGS and demonstrate that some of these techniques can be captured without reference to a resolution theorem prover. 14 references.
NASA Technical Reports Server (NTRS)
2005-01-01
A new all-electronic Particle Image Velocimetry technique that can efficiently map high speed gas flows has been developed in-house at the NASA Lewis Research Center. Particle Image Velocimetry is an optical technique for measuring the instantaneous two component velocity field across a planar region of a seeded flow field. A pulsed laser light sheet is used to illuminate the seed particles entrained in the flow field at two instances in time. One or more charged coupled device (CCD) cameras can be used to record the instantaneous positions of particles. Using the time between light sheet pulses and determining either the individual particle displacements or the average displacement of particles over a small subregion of the recorded image enables the calculation of the fluid velocity. Fuzzy logic minimizes the required operator intervention in identifying particles and computing velocity. Using two cameras that have the same view of the illumination plane yields two single exposure image frames. Two competing techniques that yield unambiguous velocity vector direction information have been widely used for reducing the single-exposure, multiple image frame data: (1) cross-correlation and (2) particle tracking. Correlation techniques yield averaged velocity estimates over subregions of the flow, whereas particle tracking techniques give individual particle velocity estimates. For the correlation technique, the correlation peak corresponding to the average displacement of particles across the subregion must be identified. Noise on the images and particle dropout result in misidentification of the true correlation peak. The subsequent velocity vector maps contain spurious vectors where the displacement peaks have been improperly identified. Typically these spurious vectors are replaced by a weighted average of the neighboring vectors, thereby decreasing the independence of the measurements. In this work, fuzzy logic techniques are used to determine the true
Simulation and Verification of Synchronous Set Relations in Rewriting Logic
NASA Technical Reports Server (NTRS)
Rocha, Camilo; Munoz, Cesar A.
2011-01-01
This paper presents a mathematical foundation and a rewriting logic infrastructure for the execution and property veri cation of synchronous set relations. The mathematical foundation is given in the language of abstract set relations. The infrastructure consists of an ordersorted rewrite theory in Maude, a rewriting logic system, that enables the synchronous execution of a set relation provided by the user. By using the infrastructure, existing algorithm veri cation techniques already available in Maude for traditional asynchronous rewriting, such as reachability analysis and model checking, are automatically available to synchronous set rewriting. The use of the infrastructure is illustrated with an executable operational semantics of a simple synchronous language and the veri cation of temporal properties of a synchronous system.
Reversible logic gates on Physarum Polycephalum
Schumann, Andrew
2015-03-10
In this paper, we consider possibilities how to implement asynchronous sequential logic gates and quantum-style reversible logic gates on Physarum polycephalum motions. We show that in asynchronous sequential logic gates we can erase information because of uncertainty in the direction of plasmodium propagation. Therefore quantum-style reversible logic gates are more preferable for designing logic circuits on Physarum polycephalum.
Use of fuzzy logic in signal processing and validation
Heger, A.S.; Alang-Rashid, N.K. ); Holbert, K.E. )
1993-01-01
The advent of fuzzy logic technology has afforded another opportunity to reexamine the signal processing and validation process (SPV). The features offered by fuzzy logic can lend themselves to a more reliable and perhaps fault-tolerant approach to SPV. This is particularly attractive to complex system operations, where optimal control for safe operation depends on reliable input data. The reason for the use of fuzzy logic as the tool for SPV is its ability to transform information from the linguistic domain to a mathematical domain for processing and then transformation of its result back into the linguistic domain for presentation. To ensure the safe and optimal operation of a nuclear plant, for example, reliable and valid data must be available to the human and computer operators. Based on these input data, the operators determine the current state of the power plant and project corrective actions for future states. This determination is based on available data and the conceptual and mathematical models for the plant. A fault-tolerant SPV based on fuzzy logic can help the operators meet the objective of effective, efficient, and safe operation of the nuclear power plant. The ultimate product of this project will be a code that will assist plant operators in making informed decisions under uncertain conditions when conflicting signals may be present.
Borresen, Jon; Lynch, Stephen
2012-01-01
In the 1940s, the first generation of modern computers used vacuum tube oscillators as their principle components, however, with the development of the transistor, such oscillator based computers quickly became obsolete. As the demand for faster and lower power computers continues, transistors are themselves approaching their theoretical limit and emerging technologies must eventually supersede them. With the development of optical oscillators and Josephson junction technology, we are again presented with the possibility of using oscillators as the basic components of computers, and it is possible that the next generation of computers will be composed almost entirely of oscillatory devices. Here, we demonstrate how coupled threshold oscillators may be used to perform binary logic in a manner entirely consistent with modern computer architectures. We describe a variety of computational circuitry and demonstrate working oscillator models of both computation and memory.
Quantificational logic of context
Buvac, Sasa
1996-12-31
In this paper we extend the Propositional Logic of Context, to the quantificational (predicate calculus) case. This extension is important in the declarative representation of knowledge for two reasons. Firstly, since contexts are objects in the semantics which can be denoted by terms in the language and which can be quantified over, the extension enables us to express arbitrary first-order properties of contexts. Secondly, since the extended language is no longer only propositional, we can express that an arbitrary predicate calculus formula is true in a context. The paper describes the syntax and the semantics of a quantificational language of context, gives a Hilbert style formal system, and outlines a proof of the system`s completeness.
Borresen, Jon; Lynch, Stephen
2012-01-01
In the 1940s, the first generation of modern computers used vacuum tube oscillators as their principle components, however, with the development of the transistor, such oscillator based computers quickly became obsolete. As the demand for faster and lower power computers continues, transistors are themselves approaching their theoretical limit and emerging technologies must eventually supersede them. With the development of optical oscillators and Josephson junction technology, we are again presented with the possibility of using oscillators as the basic components of computers, and it is possible that the next generation of computers will be composed almost entirely of oscillatory devices. Here, we demonstrate how coupled threshold oscillators may be used to perform binary logic in a manner entirely consistent with modern computer architectures. We describe a variety of computational circuitry and demonstrate working oscillator models of both computation and memory. PMID:23173034
NASA Technical Reports Server (NTRS)
Cleaveland, Rance; Luettgen, Gerald; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
This paper presents the Logical Process Calculus (LPC), a formalism that supports heterogeneous system specifications containing both operational and declarative subspecifications. Syntactically, LPC extends Milner's Calculus of Communicating Systems with operators from the alternation-free linear-time mu-calculus (LT(mu)). Semantically, LPC is equipped with a behavioral preorder that generalizes Hennessy's and DeNicola's must-testing preorder as well as LT(mu's) satisfaction relation, while being compositional for all LPC operators. From a technical point of view, the new calculus is distinguished by the inclusion of: (1) both minimal and maximal fixed-point operators and (2) an unimple-mentability predicate on process terms, which tags inconsistent specifications. The utility of LPC is demonstrated by means of an example highlighting the benefits of heterogeneous system specification.
Nanoparticle Based Logic Gates
NASA Astrophysics Data System (ADS)
Berven, Christopher; Wybourne, Martin; Longstreth, Lydia
2003-05-01
Ligand stabilized gold nanoparticles have novel properties that can be exploited for their use as possible building blocks for room-temperature single electron devices. With a core of 70 gold atoms or less (diameter <= 1.4 nm), the self-capacitance of these particles is a fraction of an atto-Farad. This small capacitance translates into an electrostatic charging energy well in excess of the thermal energy at room temperature. Single electron behavior has been demonstrated in one- and two-dimensional arrays of nanoparticles. In traditional single electron devices, the self-capacitance is negligible, whereas the self-capacitance in nanoparticle based devices can be the dominant capacitance. This means that the effect of charging a nanoparticle chain is highly localized which is in contrast to traditional single electron devices where the induced potential due to an excess electron on an island is felt by many neighboring islands. As a result, the current-voltage characteristics and plots of stable electron occupancy in the arrays have different behavior to that found in traditional devices. We show that this new regime of tunneling behavior can be exploited to create a novel family of single-electron logic gate devices. Using numerical simulation we have found that when a one-dimensional array of nanoparticles is gated in an electron-pump arrangement and properly biased, the behavior is that of an AND gate. The addition of an inverter circuit results in NAND gate behavior, the inverter providing the power necessary for the cascading of multiple NAND gates and the generation of arbitrary logic circuits.
Simulated Laboratory in Digital Logic.
ERIC Educational Resources Information Center
Cleaver, Thomas G.
Design of computer circuits used to be a pencil and paper task followed by laboratory tests, but logic circuit design can now be done in half the time as the engineer accesses a program which simulates the behavior of real digital circuits, and does all the wiring and testing on his computer screen. A simulated laboratory in digital logic has been…
Simulated Laboratory in Digital Logic.
ERIC Educational Resources Information Center
Cleaver, Thomas G.
Design of computer circuits used to be a pencil and paper task followed by laboratory tests, but logic circuit design can now be done in half the time as the engineer accesses a program which simulates the behavior of real digital circuits, and does all the wiring and testing on his computer screen. A simulated laboratory in digital logic has been…
Programmable Logic Controllers. Teacher Edition.
ERIC Educational Resources Information Center
Rauh, Bob; Kaltwasser, Stan
These materials were developed for a seven-unit secondary or postsecondary education course on programmable logic controllers (PLCs) that treats most of the skills needed to work effectively with PLCs as programming skills. The seven units of the course cover the following topics: fundamentals of programmable logic controllers; contracts, timers,…
Japanese Logic Puzzles and Proof
ERIC Educational Resources Information Center
Wanko, Jeffrey J.
2009-01-01
An understanding of proof does not start in a high school geometry course. Rather, attention to logical reasoning throughout a student's school experience can help the development of proof readiness. In the spirit of problem solving, the author has begun to use some Japanese logic puzzles other than sudoku to help students develop additional…
Logic, Probability, and Human Reasoning
2015-01-01
multiplication, it needs a working memory to hold intermediate results. Syllogism: a form of inference that Aristotle formulated based on two premises and a...where knowledge itself takes the form of fully Box 1. The application of p-logic to syllogistic reasoning Aristotle formulated the logic of syllogisms
Logic, reasoning, and verbal behavior
Terrell, Dudley J.; Johnston, J. M.
1989-01-01
This paper analyzes the traditional concepts of logic and reasoning from the perspective of radical behaviorism and in the terms of Skinner's treatment of verbal behavior. The topics covered in this analysis include the proposition, premises and conclusions, logicality and rules, and deductive and inductive reasoning. PMID:22478015
Zapatrin, R.R.
1992-02-01
Given a finite ortholattice L, the *-semigroup is explicitly built whose annihilator ortholattice is isomorphic to L. Thus, it is shown that any finite quantum logic is the additive part of a binary logic. Some areas of possible applications are outlined. 7 refs.
Formal verification of mathematical software
NASA Technical Reports Server (NTRS)
Sutherland, D.
1984-01-01
Methods are investigated for formally specifying and verifying the correctness of mathematical software (software which uses floating point numbers and arithmetic). Previous work in the field was reviewed. A new model of floating point arithmetic called the asymptotic paradigm was developed and formalized. Two different conceptual approaches to program verification, the classical Verification Condition approach and the more recently developed Programming Logic approach, were adapted to use the asymptotic paradigm. These approaches were then used to verify several programs; the programs chosen were simplified versions of actual mathematical software.
Power optimization in logic isomers
NASA Technical Reports Server (NTRS)
Panwar, Ramesh; Rennels, David; Alkalaj, Leon
1993-01-01
Logic isomers are labeled, 2-isomorphic graphs that implement the same logic function. Logic isomers may have significantly different power requirements even though they have the same number of transistors in the implementation. The power requirements of the isomers depend on the transition activity of the input signals. The power requirements of isomorphic graph isomers of n-input NAND and NOR gates are shown. Choosing the less power-consuming isomer instead of the others can yield significant power savings. Experimental results on a ripple-carry adder are presented to show that the implementation using the least power-consuming isomers requires approximately 10 percent less power than the implementation using the most power-consuming isomers. Simulations of other random logic designs also confirm that designs using less power-consuming isomers can reduce the logic power demand by approximately 10 percent as compared to designs using more power-consuming isomers.
Weighted Automata and Weighted Logics
NASA Astrophysics Data System (ADS)
Droste, Manfred; Gastin, Paul
In automata theory, a fundamental result of Büchi and Elgot states that the recognizable languages are precisely the ones definable by sentences of monadic second order logic. We will present a generalization of this result to the context of weighted automata. We develop syntax and semantics of a quantitative logic; like the behaviors of weighted automata, the semantics of sentences of our logic are formal power series describing ‘how often’ the sentence is true for a given word. Our main result shows that if the weights are taken in an arbitrary semiring, then the behaviors of weighted automata are precisely the series definable by sentences of our quantitative logic. We achieve a similar characterization for weighted Büchi automata acting on infinite words, if the underlying semiring satisfies suitable completeness assumptions. Moreover, if the semiring is additively locally finite or locally finite, then natural extensions of our weighted logic still have the same expressive power as weighted automata.
Nucleic acid based logical systems.
Han, Da; Kang, Huaizhi; Zhang, Tao; Wu, Cuichen; Zhou, Cuisong; You, Mingxu; Chen, Zhuo; Zhang, Xiaobing; Tan, Weihong
2014-05-12
Researchers increasingly visualize a significant role for artificial biochemical logical systems in biological engineering, much like digital logic circuits in electrical engineering. Those logical systems could be utilized as a type of servomechanism to control nanodevices in vitro, monitor chemical reactions in situ, or regulate gene expression in vivo. Nucleic acids (NA), as carriers of genetic information with well-regulated and predictable structures, are promising materials for the design and engineering of biochemical circuits. A number of logical devices based on nucleic acids (NA) have been designed to handle various processes for technological or biotechnological purposes. This article focuses on the most recent and important developments in NA-based logical devices and their evolution from in vitro, through cellular, even towards in vivo biological applications.
Computerized logic design of digital circuits
NASA Technical Reports Server (NTRS)
Gussow, S.; Oglesby, R.
1974-01-01
Procedure performs all work required for logic design of digital counters or sequential circuits and simplification of Boolean expressions. Program provides simple, accurate, and comprehensive logic design capability to users both experienced and totally inexperienced in logic design
A hierarchical cellular logic for pyramid computers
Tanimoto, S.L.
1984-11-01
Hierarchical structure occurs in biological vision systems and there is good reason to incorporate it into a model of computation for processing binary images. A mathematical formalism is presented which can describe a wide variety of operations useful in image processing and graphics. The formalism allows for two kinds of simple transformations on the values (called pyramids) of a set of cells called a hierarchical domain: the first are binary operations on boolean values, and the second are neighborhood-matching operations. The implied model of computation is more structured than previously discussed pyramidal models, and is more readily realized in parallel hardware, while it remains sufficiently rich to provide efficient solutions to a wide variety of problems. The model has a simplicity which is due to the restricted nature of the operations and the implied synchronization across the hierarchical domain. A corresponding algebraic simplicity in the logic makes possible the concise representation of many cellular-data operations.
ERIC Educational Resources Information Center
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
ERIC Educational Resources Information Center
Carman, Robert A.
1971-01-01
A mathematical misteak" is an incorrect operation that leads to a correct result. An introduction to the use of the misteak" to emphasize the mathematical operations being taught. Examples and brief explanations of several types of misteaks" are given. (FL)
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
ERIC Educational Resources Information Center
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
ERIC Educational Resources Information Center
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Contradicting logics in everyday practice.
Kristiansen, Margrethe; Obstfelder, Aud; Lotherington, Ann Therese
2016-01-01
Performance management is criticised as a direct challenge to the dominant logic of professionalism in health care organisations. The purpose of this paper is to report an ethnographic study that investigates how performance management and professionalism as contradicting logics are interpreted and implemented by managers and nurses in everyday practice within Norwegian nursing homes. The paper presents an analysis of 18 semistructured interviews and 100 hours of observation of managers and nurses from three nursing homes. The study draws on the institutional logic perspective as a theoretical framework. In the analysis, the authors searched for patterns of activities and interactions that reflected managers and nurses' coping strategies for handling contradicting logics. Qualitative content analysis was used to systematically code the data, supported by NVIVO software. The authors identified three forms of coping strategies: the adjustment of professionalism to standards, the reinforcement of professional flexibility and problem solving, and the strategic adoption of documentation. These patterns of activities and interactions reflect new organisational structures that allowed contradicting logics to co-exist. The study demonstrates that a new complex dimension of governing processes within nursing homes is the way in which managers and nurses handle the tension between contradicting logics in their daily work and clinicians' everyday practice. The study provides new insight into how managers and nurses reshape internal organisational structures to cope with contradicting logics in nursing homes.
Using LogicWorks to Teach Logic Design.
ERIC Educational Resources Information Center
Spoerri, Peter
1988-01-01
Discusses a computer simulation to teach logic design using a Macintosh computer which allows circuits to be built piece by piece. Describes features of the simulation and presents several schematics drawn by the software. (MVL)
Fuzzy logic in control systems: Fuzzy logic controller. I, II
NASA Technical Reports Server (NTRS)
Lee, Chuen Chien
1990-01-01
Recent advances in the theory and applications of fuzzy-logic controllers (FLCs) are examined in an analytical review. The fundamental principles of fuzzy sets and fuzzy logic are recalled; the basic FLC components (fuzzification and defuzzification interfaces, knowledge base, and decision-making logic) are described; and the advantages of FLCs for incorporating expert knowledge into a control system are indicated. Particular attention is given to fuzzy implication functions, the interpretation of sentence connectives (and, also), compositional operators, and inference mechanisms. Applications discussed include the FLC-guided automobile developed by Sugeno and Nishida (1985), FLC hardware systems, FLCs for subway trains and ship-loading cranes, fuzzy-logic chips, and fuzzy computers.
Using LogicWorks to Teach Logic Design.
ERIC Educational Resources Information Center
Spoerri, Peter
1988-01-01
Discusses a computer simulation to teach logic design using a Macintosh computer which allows circuits to be built piece by piece. Describes features of the simulation and presents several schematics drawn by the software. (MVL)
Formalized Epistemology, Logic, and Grammar
NASA Astrophysics Data System (ADS)
Bitbol, Michel
The task of a formal epistemology is defined. It appears that a formal epistemology must be a generalization of "logic" in the sense of Wittgenstein's Tractatus. The generalization is required because, whereas logic presupposes a strict relation between activity and language, this relation may be broken in some domains of experimental enquiry (e.g., in microscopic physics). However, a formal epistemology should also retain a major feature of Wittgenstein's "logic": It must not be a discourse about scientific knowledge, but rather a way of making manifest the structures usually implicit in knowledge-gaining activity. This strategy is applied to the formalism of quantum mechanics.
Sequentialization of logic programs
Treitel, R.J.
1987-01-01
Logical inference can be done in two directions, either forwards from facts already known to other facts that may be of interest, or backwards from goals whose answers are needed to subgoals whose answers may be available. Some programs and languages use on direction exclusively because it is clearly better (in the sense of computational efficiency) for their purposes. There are, however, problems that are better solved by using some rules for forwards inference and other backwards. In theorem-providing and artificial-intelligence work over the past two decades, numerous systems have been developed that allow inference to be drawn either forwards or backwards, and a number of heuristics have evolved for deciding which direction to use a rule in. This dissertation attempts to put these decisions on a quantitative footing by developing algorithms for estimating the computational cost of a set of directions for rules and applying standard optimization techniques to derive the best set of choices. In ascending order of difficulty, it is assumed first that no forward rule uses any facts deduced by a backward rule; then that directions can be chosen freely; and finally that each rule can be split up and used partly forwards, partly backwards. All of these problems, except for a highly constrained version of the first one, are shown to be NP-complete.
NASA Technical Reports Server (NTRS)
Smith, David E.; Jonsson, Ari K.; Clancy, Daniel (Technical Monitor)
2001-01-01
In recent years, Graphplan style reachability analysis and mutual exclusion reasoning have been used in many high performance planning systems. While numerous refinements and extensions have been developed, the basic plan graph structure and reasoning mechanisms used in these systems are tied to the very simple STRIPS model of action. In 1999, Smith and Weld generalized the Graphplan methods for reachability and mutex reasoning to allow actions to have differing durations. However, the representation of actions still has some severe limitations that prevent the use of these techniques for many real-world planning systems. In this paper, we 1) separate the logic of reachability from the particular representation and inference methods used in Graphplan, and 2) extend the notions of reachability and mutual exclusion to more general notions of time and action. As it turns out, the general rules for mutual exclusion reasoning take on a remarkably clean and simple form. However, practical instantiations of them turn out to be messy, and require that we make representation and reasoning choices.
NASA Astrophysics Data System (ADS)
Dougherty, Edward R.; Chen, Yidong
1998-06-01
Binary granulometric filters are formed from unions of parameterized openings, a point passing the filter if and only if a translate of at least one structuring element fits in the image and contains the point. A granulometry induces a reconstructive granulometry by passing any image component not eliminated by the granulometry. As historically studied in the context of Matheron's granulometric theory, reconstructive granulometries appear as unions of reconstructive parameterized openings. The theory is extended to a much wider class of filters: a logical structural filter (LSF) is formed as a union of intersections of both reconstructive and complementary reconstructive openings. A reconstructive opening passes a component if and only if at least one translate of the structuring element fits inside; a complementary reconstructive opening passes a component if and only if no translate of the structuring element fits inside. The original reconstructive granulometries form the special class of disjunctive LSFs. Complement-free LSFs form granulometries in a slightly more general sense; LSFs containing complements are not increasing and therefore not openings. Along with the relevant algebraic representations for LSFs, the theories of optimal and adaptive granulometric filters are extended to LSFs, a systematic formulation of adaptive transitions is given, transition probabilities for adaptation are found, and two applications to biological imaging are presented.
Kral, M J
1994-01-01
Although suicide is not viewed as a mental disorder per se, it is viewed by many if not most clinicians, researchers, and lay people as a real or natural symptom of depression. It is at least most typically seen as the unfortunate, severe, yet logical end result of a chain of negative self-appraisals, negative events, and hopelessness. Extending an approach articulated by the early French sociologist Gabriel Tarde, in this paper I argue that suicide is merely an idea, albeit a very bad one, having more in common with societal beliefs and norms regarding such things as divorce, abortion, sex, politics, consumer behavior, and fashion. I make a sharp contrast between perturbation and lethality, concepts central to Edwin S. Shneidman's theory of suicide. Evidence supportive of suicide as an idea is discussed based on what we are learning from the study of history and culture, and about contagion/cluster phenomena, media/communication, and choice of method. It is suggested that certain individuals are more vulnerable to incorporate the idea and act of suicide into their concepts of self, based on the same principles by which ideas are spread throughout society. Just as suicide impacts on society, so does society impact on suicide.
The materiality of mathematics: presenting mathematics at the blackboard.
Greiffenhagen, Christian
2014-09-01
Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics.
Proof in Mathematics ("If,""Then," and "Perhaps").
ERIC Educational Resources Information Center
Baxandall, P. R.; And Others
This collection of material is designed to illustrate the nature and variety of the idea of proof in mathematics. It is intended to be a "background book" for the use of teachers, particularly those in initial training courses. Individual chapter titles are: (1) The Role of Proof in Mathematics; (2) Logical Reasoning: The Idea of Implication; (3)…
Investigating Student Use of Electronic Support Tools and Mathematical Reasoning
ERIC Educational Resources Information Center
Higgins, Kristina N.; Crawford, Lindy; Huscroft-D'Angelo, Jacqueline; Horney, Mark
2016-01-01
Mathematical reasoning involves comprehending mathematical information and concepts in a logical way and forming conclusions and generalizations based on this comprehension. Computer-based learning has been incorporated into classrooms across the country, and specific aspects of technology need to be studied to determine how programs are…
A Mathematics Educator's Introduction to Rural Policy Issues
ERIC Educational Resources Information Center
Waters, Michael S., Ed.
2005-01-01
Most of the scholarship and commentary on mathematics education deals with issues of curriculum and instruction; this is understandable in a field logically belonging to the domain of curriculum and instruction. Moreover, issues of teaching and learning are compelling to people who love to learn and teach mathematics. Policy receives shorter…
Mathematiques 14-24 (Mathematics 14-24).
ERIC Educational Resources Information Center
Alberta Learning, Edmonton.
To set goals and make informed choices, students need an array of thinking and problem-solving skills. Fundamental to this is an understanding of mathematical techniques and processes that will enable them to apply the basic skills necessary to address everyday mathematical situations, as well as acquire higher order skills in logical analysis and…
Secondary School Mathematics Curriculum Improvement Study Information Bulletin 7.
ERIC Educational Resources Information Center
Secondary School Mathematics Curriculum Improvement Study, New York, NY.
The background, objectives, and design of Secondary School Mathematics Curriculum Improvement Study (SSMCIS) are summarized. Details are given of the content of the text series, "Unified Modern Mathematics," in the areas of algebra, geometry, linear algebra, probability and statistics, analysis (calculus), logic, and computer…
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
ERIC Educational Resources Information Center
Schauble, Leona; Peel, Tina
Problem solving is a main topic in mathematics education, and considerable headway has been made in identifying the processes involved in solving well-formed problems like algebra word problems, mathematical algorithms, and logical puzzles like the Tower of Hanoi. The "Mathnet" format of the SQUARE ONE TV program, however, requires…
Explorations in Mathematics, Student Discussion Guide.
ERIC Educational Resources Information Center
Davis, Robert B.
This student discussion guide is intended to accompany "Explorations in Mathematics," a text for teachers. The materials in this booklet relate mainly to variables, graphs, signed numbers, logic, identities, functions and matrices. The materials were designed to be used as supplementary materials with students in grades 5 through 9. (RP)
COMPUTER ORIENTED MATHEMATICS, AN INTRODUCTION FOR TEACHERS.
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, Inc., Reston, VA.
THIS MANUAL IS INTENDED TO BE OF USE TO TEACHERS, AND TO STUDENTS IN GRADES SEVEN THROUGH TWELVE, AS ENRICHMENT OR BACKGROUND MATERIAL FOR MATHEMATICS COURSES. IT ATTEMPTS TO ESTABLISH AN UNDERSTANDING OF THE PROCESS OF LOGICAL STEP-BY-STEP ANALYSIS OF PROBLEMS FOR COMPUTERS, OF THE WAYS IN WHICH COMPUTER CAPABILITIES CAN SUGGEST DIFFERENT…
Ancient Paradoxes Can Extend Mathematical Thinking
ERIC Educational Resources Information Center
Czocher, Jennifer A.; Moss, Diana L.
This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…
A Teacher's Notebook: Mathematics, K-9.
ERIC Educational Resources Information Center
National Association of Independent Schools, Boston, MA.
This guide is divided into seven sections according to specific topics rather than by grade levels and/or grade level expectations. The topics encompass a K-9 program and include: numeration; measurement; operations and computational skills; algebra; informal geometry; sets, logic, and proof; and mathematical patterns. Each section lists concepts…
Knowledge representation in fuzzy logic
NASA Technical Reports Server (NTRS)
Zadeh, Lotfi A.
1989-01-01
The author presents a summary of the basic concepts and techniques underlying the application of fuzzy logic to knowledge representation. He then describes a number of examples relating to its use as a computational system for dealing with uncertainty and imprecision in the context of knowledge, meaning, and inference. It is noted that one of the basic aims of fuzzy logic is to provide a computational framework for knowledge representation and inference in an environment of uncertainty and imprecision. In such environments, fuzzy logic is effective when the solutions need not be precise and/or it is acceptable for a conclusion to have a dispositional rather than categorical validity. The importance of fuzzy logic derives from the fact that there are many real-world applications which fit these conditions, especially in the realm of knowledge-based systems for decision-making and control.
Knowledge representation in fuzzy logic
NASA Technical Reports Server (NTRS)
Zadeh, Lotfi A.
1989-01-01
The author presents a summary of the basic concepts and techniques underlying the application of fuzzy logic to knowledge representation. He then describes a number of examples relating to its use as a computational system for dealing with uncertainty and imprecision in the context of knowledge, meaning, and inference. It is noted that one of the basic aims of fuzzy logic is to provide a computational framework for knowledge representation and inference in an environment of uncertainty and imprecision. In such environments, fuzzy logic is effective when the solutions need not be precise and/or it is acceptable for a conclusion to have a dispositional rather than categorical validity. The importance of fuzzy logic derives from the fact that there are many real-world applications which fit these conditions, especially in the realm of knowledge-based systems for decision-making and control.
Adamatzky, Andrew; Sirakoulis, Georgios Ch; Martínez, Genaro J; Baluška, Frantisek; Mancuso, Stefano
Theoretical constructs of logical gates implemented with plant roots are morphological computing asynchronous devices. Values of Boolean variables are represented by plant roots. A presence of a plant root at a given site symbolises the logical True, an absence the logical False. Logical functions are calculated via interaction between roots. Two types of two-inputs-two-outputs gates are proposed: a gate 〈x, y〉→〈xy, x+y〉 where root apexes are guided by gravity and a gate 〈x,y〉→〈x¯y,x〉 where root apexes are guided by humidity. We propose a design of binary half-adder based on the gates. Copyright © 2017 Elsevier B.V. All rights reserved.
Emerging Standards for Medical Logic
Clayton, Paul D.; Hripcsak, George; Pryor, T. Allan
1990-01-01
Sharing medical logic has traditionally occurred in the form of lectures, conversations, books and journals. As knowledge based computer systems have demonstrated their utility in the health care arena, individuals have pondered the best way to transfer knowledge in a computer based representation (1). A simple representation which allows the knowledge to be shared can be constructed when the knowledge base is modular. Within this representation, units have been named Medical Logic Modules (MLM's) and a syntax has emerged which would allow multiple users to create, criticize, and share those types of medical logic which can be represented in this format. In this paper we talk about why standards exist and why they emerge in some areas and not in others. The appropriateness of using the proposed standards for medical logic modules is then examined against this broader context.
Digital logic testing and testability
NASA Astrophysics Data System (ADS)
Debany, Warren H., Jr.
1991-02-01
Electronic hardware is subject to defects that are introduced at the time of manufacture and failures that occur in the field. Because of the complexity of digital logic circuits, they are difficult to test. This report provides an overview of digital logic testing. It provides access to the literature and unifies terminology and concepts that have evolved in this field. It discusses the types and causes of failures in digital logic. This report presents the topics of logic and fault simulation, fault grading, test generation algorithms, and fault isolation. The discussion of testability measurement is useful for understanding testability requirements and analysis techniques. Design-for-testability and built in test techniques are presented.
Heat exchanger expert system logic
NASA Technical Reports Server (NTRS)
Cormier, R.
1988-01-01
The reduction is described of the operation and fault diagnostics of a Deep Space Network heat exchanger to a rule base by the application of propositional calculus to a set of logic statements. The value of this approach lies in the ease of converting the logic and subsequently implementing it on a computer as an expert system. The rule base was written in Process Intelligent Control software.
Temporal Reasoning and Default Logics.
1985-10-01
cases. But the examples that break these logics always seem to have an artificial, or even perverse , nature to them. Davis’s demonstration that...since we are so controlled in our use of the default rules, we can expect better behavior from the three logics. The point of the rest of the paper...pred- icates) pcause, event, persist, point, contradict, clipped, , < .To the extent we could then precisely characterize the programs 1i/ behavior we
Fuzzy logic and neural networks
Loos, J.R.
1994-11-01
Combine fuzzy logic`s fuzzy sets, fuzzy operators, fuzzy inference, and fuzzy rules - like defuzzification - with neural networks and you can arrive at very unfuzzy real-time control. Fuzzy logic, cursed with a very whimsical title, simply means multivalued logic, which includes not only the conventional two-valued (true/false) crisp logic, but also the logic of three or more values. This means one can assign logic values of true, false, and somewhere in between. This is where fuzziness comes in. Multi-valued logic avoids the black-and-white, all-or-nothing assignment of true or false to an assertion. Instead, it permits the assignment of shades of gray. When assigning a value of true or false to an assertion, the numbers typically used are {open_quotes}1{close_quotes} or {open_quotes}0{close_quotes}. This is the case for programmed systems. If {open_quotes}0{close_quotes} means {open_quotes}false{close_quotes} and {open_quotes}1{close_quotes} means {open_quotes}true,{close_quotes} then {open_quotes}shades of gray{close_quotes} are any numbers between 0 and 1. Therefore, {open_quotes}nearly true{close_quotes} may be represented by 0.8 or 0.9, {open_quotes}nearly false{close_quotes} may be represented by 0.1 or 0.2, and {close_quotes}your guess is as good as mine{close_quotes} may be represented by 0.5. The flexibility available to one is limitless. One can associate any meaning, such as {open_quotes}nearly true{close_quotes}, to any value of any granularity, such as 0.9999. 2 figs.
Developing Learning Materials Using an Ontology of Mathematical Logic
ERIC Educational Resources Information Center
Boyatt, Russell; Joy, Mike
2012-01-01
Ontologies describe a body of knowledge and give formal structure to a domain by describing concepts and their relationships. The construction of an ontology provides an opportunity to develop a shared understanding and a consistent vocabulary to be used for a given activity. This paper describes the construction of an ontology for an area of…
Use of mathematical logical concepts in quantum mechanics: an example
NASA Astrophysics Data System (ADS)
Benioff, Paul
2002-07-01
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has meaning. A simple example of such a system, based on an example described by Smullyan, is studied here. Based on a path interpretation for some word states, definitions of truth, validity, consistency and completeness are given and their properties studied. It is also shown that the relation between the potential meaning, if any, of word states and the quantum algorithmic complexity of the process generating the word states must be quite complex or nonexistent.
Motivating Computer Engineering Freshmen through Mathematical and Logical Puzzles
ERIC Educational Resources Information Center
Parhami, B.
2009-01-01
As in many other fields of science and technology, college students in computer engineering do not come into full contact with the key ideas and challenges of their chosen discipline until the third year of their studies. This situation poses a problem in terms of keeping the students motivated as they labor through their foundational, basic…
Cognitive Rationality and Its Logic-Mathematical Language
ERIC Educational Resources Information Center
Masalova, Svetlana
2012-01-01
The article deals with the cognitive (flexible) rationality, combining rational and irrational moments of the scientific search of the cognizing subject. Linguo-cognitive model of the concept as the flexible regulative rationality reveals the activity of the cognitive processes and the mentality of the epistemological-ontic subject, its leading…
Motivating Computer Engineering Freshmen through Mathematical and Logical Puzzles
ERIC Educational Resources Information Center
Parhami, B.
2009-01-01
As in many other fields of science and technology, college students in computer engineering do not come into full contact with the key ideas and challenges of their chosen discipline until the third year of their studies. This situation poses a problem in terms of keeping the students motivated as they labor through their foundational, basic…
Optically controllable molecular logic circuits
Nishimura, Takahiro Fujii, Ryo; Ogura, Yusuke; Tanida, Jun
2015-07-06
Molecular logic circuits represent a promising technology for observation and manipulation of biological systems at the molecular level. However, the implementation of molecular logic circuits for temporal and programmable operation remains challenging. In this paper, we demonstrate an optically controllable logic circuit that uses fluorescence resonance energy transfer (FRET) for signaling. The FRET-based signaling process is modulated by both molecular and optical inputs. Based on the distance dependence of FRET, the FRET pathways required to execute molecular logic operations are formed on a DNA nanostructure as a circuit based on its molecular inputs. In addition, the FRET pathways on the DNA nanostructure are controlled optically, using photoswitching fluorescent molecules to instruct the execution of the desired operation and the related timings. The behavior of the circuit can thus be controlled using external optical signals. As an example, a molecular logic circuit capable of executing two different logic operations was studied. The circuit contains functional DNAs and a DNA scaffold to construct two FRET routes for executing Input 1 AND Input 2 and Input 1 AND NOT Input 3 operations on molecular inputs. The circuit produced the correct outputs with all possible combinations of the inputs by following the light signals. Moreover, the operation execution timings were controlled based on light irradiation and the circuit responded to time-dependent inputs. The experimental results demonstrate that the circuit changes the output for the required operations following the input of temporal light signals.
Theorem Proving In Higher Order Logics
NASA Technical Reports Server (NTRS)
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
NASA Astrophysics Data System (ADS)
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Mathematics for understanding disease.
Bies, R R; Gastonguay, M R; Schwartz, S L
2008-06-01
The application of mathematical models to reflect the organization and activity of biological systems can be viewed as a continuum of purpose. The far left of the continuum is solely the prediction of biological parameter values, wherein an understanding of the underlying biological processes is irrelevant to the purpose. At the far right of the continuum are mathematical models, the purposes of which are a precise understanding of those biological processes. No models in present use fall at either end of the continuum. Without question, however, the emphasis in regards to purpose has been on prediction, e.g., clinical trial simulation and empirical disease progression modeling. Clearly the model that ultimately incorporates a universal understanding of biological organization will also precisely predict biological events, giving the continuum the logical form of a tautology. Currently that goal lies at an immeasurable distance. Nonetheless, the motive here is to urge movement in the direction of that goal. The distance traveled toward understanding naturally depends upon the nature of the scientific question posed with respect to comprehending and/or predicting a particular disease process. A move toward mathematical models implies a move away from static empirical modeling and toward models that focus on systems biology, wherein modeling entails the systematic study of the complex pattern of organization inherent in biological systems.
Adding structure to the transition process to advanced mathematical activity
NASA Astrophysics Data System (ADS)
Engelbrecht, Johann
2010-03-01
The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical deductive reasoning, required in advanced mathematics. It is necessary to assist students in this transition process, in moving from general to mathematical thinking. In this article some structure is suggested for this transition period. This essay is an argumentative exposition supported by personal experience and international literature. This makes this study theoretical rather than empirical.
Fuzzy logic control of the building structure with CLEMR dampers
NASA Astrophysics Data System (ADS)
Zhang, Xiang-Cheng; Xu, Zhao-Dong; Huang, Xing-Huai; Zhu, Jun-Tao
2013-04-01
The semi-active control technology has been paid more attention in the field of structural vibration control due to its high controllability, excellent control effect and low power requirement. When semi-active control device are used for vibration control, some challenges must be taken into account, such as the reliability and the control strategy of the device. This study presents a new large tonnage compound lead extrusion magnetorheological (CLEMR) damper, whose mathematical model is introduced to describe the variation of damping force with current and velocity. Then a current controller based on the fuzzy logic control strategy is designed to determine control currents of the CLEMR dampers rapidly. A ten-floor frame structure with CLEMR dampers using the fuzzy logic control strategy is built and calculated by using MATLAB. Calculation results show that CLEMR dampers can reduce the seismic responses of structures effectively. Calculation results of the fuzzy logic control strategy are compared with those of the semi-active limit Hrovat control structure, the passive-off control structure, and the uncontrolled structure. Comparison results show that the fuzzy logic control strategy can determine control currents of CLEMR dampers quickly and can reduce seismic responses of the structures more effectively than the passive-off control strategy and the uncontrolled structure.
Experimental Mathematics and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
ERIC Educational Resources Information Center
McClellan, Kathryn T.
Why mathematics should be learned is discussed. Its role as an important active force in the development of our civilization, and as the most useful subject taught in our schools, next to English, is noted. The primary objective of all mathematics work is to help man study nature, and some practical achievements of this connection are noted.…
ERIC Educational Resources Information Center
Davis, Robert B.
Suggestions are offered for more effective implementation and creativity in developing new mathematics programs. The new mathematics materials and projects have not significantly altered the educational experiences of students because of (1) difficulty in identifying distinctive features of the various projects, (2) widespread assumptions that the…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Martin, Hope
2007-01-01
"Mathematical literacy" implies that a person is able to reason, analyze, formulate, and solve problems in a real-world setting. Mathematically literate individuals are informed citizens and intelligent consumers. They have the ability to interpret and analyze the vast amount of information they are inundated with daily in newspapers, on…
Fuzzy logic particle tracking velocimetry
NASA Technical Reports Server (NTRS)
Wernet, Mark P.
1993-01-01
Fuzzy logic has proven to be a simple and robust method for process control. Instead of requiring a complex model of the system, a user defined rule base is used to control the process. In this paper the principles of fuzzy logic control are applied to Particle Tracking Velocimetry (PTV). Two frames of digitally recorded, single exposure particle imagery are used as input. The fuzzy processor uses the local particle displacement information to determine the correct particle tracks. Fuzzy PTV is an improvement over traditional PTV techniques which typically require a sequence (greater than 2) of image frames for accurately tracking particles. The fuzzy processor executes in software on a PC without the use of specialized array or fuzzy logic processors. A pair of sample input images with roughly 300 particle images each, results in more than 200 velocity vectors in under 8 seconds of processing time.
Intersecting Adjectives in Syllogistic Logic
NASA Astrophysics Data System (ADS)
Moss, Lawrence S.
The goal of natural logic is to present and study logical systems for reasoning with sentences of (or which are reasonably close to) ordinary language. This paper explores simple systems of natural logic which make use of intersecting adjectives; these are adjectives whose interpretation does not vary with the noun they modify. Our project in this paper is to take one of the simplest syllogistic fragments, that of all and some, and to add intersecting adjectives. There are two ways to do this, depending on whether one allows iteration or prefers a "flat" structure of at most one adjective. We present rules of inference for both types of syntax, and these differ. The main results are four completeness theorems: for each of the two types of syntax we have completeness for the all fragment and for the full language of this paper.
Logic, probability, and human reasoning.
Johnson-Laird, P N; Khemlani, Sangeet S; Goodwin, Geoffrey P
2015-04-01
This review addresses the long-standing puzzle of how logic and probability fit together in human reasoning. Many cognitive scientists argue that conventional logic cannot underlie deductions, because it never requires valid conclusions to be withdrawn - not even if they are false; it treats conditional assertions implausibly; and it yields many vapid, although valid, conclusions. A new paradigm of probability logic allows conclusions to be withdrawn and treats conditionals more plausibly, although it does not address the problem of vapidity. The theory of mental models solves all of these problems. It explains how people reason about probabilities and postulates that the machinery for reasoning is itself probabilistic. Recent investigations accordingly suggest a way to integrate probability and deduction.
Reversible logic gate using adiabatic superconducting devices
Takeuchi, N.; Yamanashi, Y.; Yoshikawa, N.
2014-01-01
Reversible computing has been studied since Rolf Landauer advanced the argument that has come to be known as Landauer's principle. This principle states that there is no minimum energy dissipation for logic operations in reversible computing, because it is not accompanied by reductions in information entropy. However, until now, no practical reversible logic gates have been demonstrated. One of the problems is that reversible logic gates must be built by using extremely energy-efficient logic devices. Another difficulty is that reversible logic gates must be both logically and physically reversible. Here we propose the first practical reversible logic gate using adiabatic superconducting devices and experimentally demonstrate the logical and physical reversibility of the gate. Additionally, we estimate the energy dissipation of the gate, and discuss the minimum energy dissipation required for reversible logic operations. It is expected that the results of this study will enable reversible computing to move from the theoretical stage into practical usage. PMID:25220698
Reversible logic gate using adiabatic superconducting devices
NASA Astrophysics Data System (ADS)
Takeuchi, N.; Yamanashi, Y.; Yoshikawa, N.
2014-09-01
Reversible computing has been studied since Rolf Landauer advanced the argument that has come to be known as Landauer's principle. This principle states that there is no minimum energy dissipation for logic operations in reversible computing, because it is not accompanied by reductions in information entropy. However, until now, no practical reversible logic gates have been demonstrated. One of the problems is that reversible logic gates must be built by using extremely energy-efficient logic devices. Another difficulty is that reversible logic gates must be both logically and physically reversible. Here we propose the first practical reversible logic gate using adiabatic superconducting devices and experimentally demonstrate the logical and physical reversibility of the gate. Additionally, we estimate the energy dissipation of the gate, and discuss the minimum energy dissipation required for reversible logic operations. It is expected that the results of this study will enable reversible computing to move from the theoretical stage into practical usage.
Reversible logic gate using adiabatic superconducting devices.
Takeuchi, N; Yamanashi, Y; Yoshikawa, N
2014-09-15
Reversible computing has been studied since Rolf Landauer advanced the argument that has come to be known as Landauer's principle. This principle states that there is no minimum energy dissipation for logic operations in reversible computing, because it is not accompanied by reductions in information entropy. However, until now, no practical reversible logic gates have been demonstrated. One of the problems is that reversible logic gates must be built by using extremely energy-efficient logic devices. Another difficulty is that reversible logic gates must be both logically and physically reversible. Here we propose the first practical reversible logic gate using adiabatic superconducting devices and experimentally demonstrate the logical and physical reversibility of the gate. Additionally, we estimate the energy dissipation of the gate, and discuss the minimum energy dissipation required for reversible logic operations. It is expected that the results of this study will enable reversible computing to move from the theoretical stage into practical usage.
Abstract quantum computing machines and quantum computational logics
NASA Astrophysics Data System (ADS)
Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto
2016-06-01
Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.
An exercise in "anhomomorphic logic"
NASA Astrophysics Data System (ADS)
Sorkin, Rafael D.
2007-05-01
A classical logic exhibits a threefold inner structure comprising an algebra of propositions fraktur U, a space of "truth values" V, and a distinguished family of mappings phi from propositions to truth values. Classically fraktur U is a Boolean algebra, V = Bbb Z2, and the admissible maps phi: fraktur U Bbb Z2 are homomorphisms. If one admits a larger set of maps, one obtains an anhomomorphic logic that seems better suited to quantal reality (and the needs of quantum gravity). I explain these ideas and illustrate them with three simple examples.
A Logical Approach to Entanglement
NASA Astrophysics Data System (ADS)
Das, Abhishek
2016-10-01
In this paper we innovate a logical approach to develop an intuition regarding the phenomenon of quantum entanglement. In the vein of the logic introduced we substantiate that particles that were entangled in the past will be entangled in perpetuity and thereby abide a rule that restricts them to act otherwise. We also introduce a game and by virtue of the concept of Nash equilibrium we have been able to show that entangled particles will mutually correspond to an experiment that is performed on any one of the particle.
Superconducting gates with fluxon logics
NASA Astrophysics Data System (ADS)
Nacak, H.; Kusmartsev, F. V.
2010-10-01
We have developed several logic gates (OR, XOR, AND and NAND) made of superconducting Josephson junctions. The gates based of the flux cloning phenomenon and high speed of fluxons moving in Josephson junctions of different shapes. In a contrast with previous design the gates operates extremely fast since fluxons are moving with the speed close to the speed of light. We have demonstrated their operations and indicated several ways to made a more complicated logic elements which have at the same time a compact form.
Critique of Putnam's quantum logic
NASA Astrophysics Data System (ADS)
Bacciagaluppi, Guido
1993-10-01
Putnam gives a strongly realist account of quantum logic. This has been criticised as suggesting a hidden variable interpretation for quantum mechanics. Friedman and Glymour have done this in the framework of noncontextual hidden variable theories, which, however, does not fully represent Putnam's ideas. Here Putnam's approach to quantum logic is understood in terms of contextual truth-value assignments. The concept of a measurement is discussed. It follows that in order to reproduce quantum mechanical predictions a kind of disturbance is necessary, which is then analyzed. Finally, it is shown that the Putnam approach does not escape proofs of nonlocality, and thus shares, indeed, the unwelcome features of a hidden variable theory.
Defining Datalog in Rewriting Logic
NASA Astrophysics Data System (ADS)
Alpuente, M.; Feliú, M. A.; Joubert, C.; Villanueva, A.
In recent work, the effectiveness of using declarative languages has been demonstrated for many problems in program analysis. Using a simple relational query language, like Datalog, complex interprocedural analyses involving dynamically created objects can be expressed in just a few lines. By exploiting the power of the Rewriting Logic language Maude, we aim at transforming Datalog programs into efficient rewrite systems that compute the same answers. A prototype has been implemented and applied to some real-world Datalog-based analyses. Experimental results show that the performance of solving Datalog queries in rewriting logic is comparable to state-of-the-art Datalog solvers.
NASA Technical Reports Server (NTRS)
Ruspini, Enrique H.
1991-01-01
Summarized here are the results of recent research on the conceptual foundations of fuzzy logic. The focus is primarily on the principle characteristics of a model that quantifies resemblance between possible worlds by means of a similarity function that assigns a number between 0 and 1 to every pair of possible worlds. Introduction of such a function permits one to interpret the major constructs and methods of fuzzy logic: conditional and unconditional possibility and necessity distributions and the generalized modus ponens of Zadeh on the basis of related metric relationships between subsets of possible worlds.
Dynamic Logic Assigned to Automata
NASA Astrophysics Data System (ADS)
Chajda, Ivan; Paseka, Jan
2017-02-01
A dynamic logic B can be assigned to every automaton [InlineMediaObject not available: see fulltext.] without regard if [InlineMediaObject not available: see fulltext.] is deterministic or nondeterministic. This logic enables us to formulate observations on [InlineMediaObject not available: see fulltext.] in the form of composed propositions and, due to a transition functor T, it captures the dynamic behaviour of [InlineMediaObject not available: see fulltext.]. There are formulated conditions under which the automaton [InlineMediaObject not available: see fulltext.] can be recovered by means of B and T.
Logic programming and metadata specifications
NASA Technical Reports Server (NTRS)
Lopez, Antonio M., Jr.; Saacks, Marguerite E.
1992-01-01
Artificial intelligence (AI) ideas and techniques are critical to the development of intelligent information systems that will be used to collect, manipulate, and retrieve the vast amounts of space data produced by 'Missions to Planet Earth.' Natural language processing, inference, and expert systems are at the core of this space application of AI. This paper presents logic programming as an AI tool that can support inference (the ability to draw conclusions from a set of complicated and interrelated facts). It reports on the use of logic programming in the study of metadata specifications for a small problem domain of airborne sensors, and the dataset characteristics and pointers that are needed for data access.
Computer-Assisted Instruction in Elementary Logic at the University Level. Technical Report No. 239.
ERIC Educational Resources Information Center
Goldberg, Adele; Suppes, Patrick
Earlier research by the authors in the design and use of computer-assisted instructional systems and curricula for teaching mathematical logic to gifted elementary school students has been extended to the teaching of university-level courses. This report is a description of the curriculum and problem types of a computer-based course offered at…
Proof and Proving: Logic, Impasses, and the Relationship to Problem Solving
ERIC Educational Resources Information Center
Savic, Milos
2012-01-01
Becoming a skillful prover is critical for success in advanced undergraduate and graduate mathematics courses. In this dissertation, I report my investigations of proof and the proving process in three separate studies. In the first study, I examined the amount of logic used in student-constructed proofs to help in the design of…
ERIC Educational Resources Information Center
Satake, Eiki; Amato, Philip P.
2008-01-01
This paper presents an alternative version of formulas of conditional probabilities and Bayes' rule that demonstrate how the truth table of elementary mathematical logic applies to the derivations of the conditional probabilities of various complex, compound statements. This new approach is used to calculate the prior and posterior probabilities…
Log(F): An Optimal Combination of Logic Programming, Rewriting, and Lazy Evaluation
1988-04-01
References conference on automated deduction. Frege , G. [ 1879]. Begriffsschrift. A formula language, modelled upon that of arithmetic, for pure thought...In From Frege to Goedel: A source book in mathematical logic, 1879- 1931. Harvard University Press, Cambridge, MA. Fribourg, L. [1984]. Oriented
Interaction Between Structure of Intellect Factors and Two Methods of Presenting Concepts of Logic.
ERIC Educational Resources Information Center
Eastman, Phillip; Behr, Merlyn
This paper reports a study which attempted to generalize earlier results obtained by Eastman to another mathematical content area. Two hundred eight ninth-grade algebra students were randomly assigned to one of the two treatments. The figural-inductive treatment presented concepts of logic through the use of Euler diagrams in an inductive mode;…
ERIC Educational Resources Information Center
Satake, Eiki; Amato, Philip P.
2008-01-01
This paper presents an alternative version of formulas of conditional probabilities and Bayes' rule that demonstrate how the truth table of elementary mathematical logic applies to the derivations of the conditional probabilities of various complex, compound statements. This new approach is used to calculate the prior and posterior probabilities…
IT0: Discrete Math and Programming Logic Topics as a Hybrid Alternative to CS0
ERIC Educational Resources Information Center
Martin, Nancy L.
2015-01-01
This paper describes the development of a hybrid introductory course for students in their first or second year of an information systems technologies degree program at a large Midwestern university. The course combines topics from discrete mathematics and programming logic and design, a unique twist on most introductory courses. The objective of…
Fuzzy logic controller for the electric motor driving the astronomical telescope
NASA Astrophysics Data System (ADS)
Soliman, Hussein F.; Attia, Abdel-Fattah A.; Badr, Mohammed A.; Osman, Anas M.; Gamaleldin, Abdul A.
1998-05-01
The paper presents an application of fuzzy logic controller to regulate the DC motor driver system of astronomical telescope. The mathematical model of such a telescope is highly nonlinear coupled equations. However, the accuracy requirement in telescope system exceed those of other industrial plants. Fuzzy logic controller provides means to deal with nonlinear functions. A fuzzy logic controller (FLC) was designed to enhance the performance of a two-link model of astronomical telescope. The proposed FLC utilizes the position deviation for the desired value, and its rate of change to regulate the armature voltage of the DC motor drive of each link. The final action of FLC is equivalent to PD controller with a variable gain by using an expert look- up table. This work presents the derivation of the mathematical model of 14 inch Celestron telescope and computer simulation of its motion. The FLC contains two groups of fuzzy sets.
The reasonable effectiveness of mathematics in the natural sciences
NASA Astrophysics Data System (ADS)
Harvey, Alex
2011-12-01
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.
Characteristics of mathematics teaching in Shanghai, China: Through the lens of a Malaysian
NASA Astrophysics Data System (ADS)
Lim, Chap Sam
2007-06-01
The mathematical performance of Chinese students, from mainland China, Hong Kong and Taiwan, is widely acclaimed in international comparisons of mathematics achievement. However, in the eyes of the Western educators, the environments established in Chinese schools are deemed relatively unfavourable for mathematics learning. This paper reports on a study that investigates the characteristics of effective mathematics teaching in five Shanghai schools. Findings reveal that those characteristics include (a) teaching with variation; (b) emphasis of precise and elegant mathematical language; (c) emphasis of logical reasoning, mathematical thinking and proofing during teaching; (d) order and serious classroom discipline; (e) strong and coherence teacher-student rapport, and (f) strong collaborative culture amongst mathematics teachers.
Boggle Logic Puzzles: Minimal Solutions
ERIC Educational Resources Information Center
Needleman, Jonathan
2013-01-01
Boggle logic puzzles are based on the popular word game Boggle played backwards. Given a list of words, the problem is to recreate the board. We explore these puzzles on a 3 x 3 board and find the minimum number of three-letter words needed to create a puzzle with a unique solution. We conclude with a series of open questions.
Program Theory Evaluation: Logic Analysis
ERIC Educational Resources Information Center
Brousselle, Astrid; Champagne, Francois
2011-01-01
Program theory evaluation, which has grown in use over the past 10 years, assesses whether a program is designed in such a way that it can achieve its intended outcomes. This article describes a particular type of program theory evaluation--logic analysis--that allows us to test the plausibility of a program's theory using scientific knowledge.…
Logic Programming and Knowledge Maintenance.
1987-08-13
the literature , and became convinced that many of the advantages of frames and semantic nets can be captured in logic programming systems by a...consists of: needs(john,money). married_to(john,mary). loves(john,mary). (mary is the dead victim in this thriller .) The victim’s sister sara consists of
Gateways to Writing Logical Arguments
ERIC Educational Resources Information Center
McCann, Thomas M.
2010-01-01
Middle school and high school students have a conception of what the basic demands of logic are, and they draw on this understanding in anticipating certain demands of parents and teachers when the adolescents have to defend positions. At the same time, many adolescents struggle to "write" highly elaborated arguments. Teaching students lessons in…
Program Theory Evaluation: Logic Analysis
ERIC Educational Resources Information Center
Brousselle, Astrid; Champagne, Francois
2011-01-01
Program theory evaluation, which has grown in use over the past 10 years, assesses whether a program is designed in such a way that it can achieve its intended outcomes. This article describes a particular type of program theory evaluation--logic analysis--that allows us to test the plausibility of a program's theory using scientific knowledge.…
Guide on Logical Database Design.
ERIC Educational Resources Information Center
Fong, Elizabeth N.; And Others
This report discusses an iterative methodology for logical database design (LDD). The methodology includes four phases: local information-flow modeling, global information-flow modeling, conceptual schema design, and external schema modeling. These phases are intended to make maximum use of available information and user expertise, including the…
Logical Empiricism, Politics, and Professionalism
ERIC Educational Resources Information Center
Edgar, Scott
2009-01-01
This paper considers George A. Reisch's account of the role of Cold War political forces in shaping the apolitical stance that came to dominate philosophy of science in the late 1940s and 1950s. It argues that at least as early as the 1930s, Logical Empiricists such as Rudolf Carnap already held that philosophy of science could not properly have…
Logical Empiricism, Politics, and Professionalism
ERIC Educational Resources Information Center
Edgar, Scott
2009-01-01
This paper considers George A. Reisch's account of the role of Cold War political forces in shaping the apolitical stance that came to dominate philosophy of science in the late 1940s and 1950s. It argues that at least as early as the 1930s, Logical Empiricists such as Rudolf Carnap already held that philosophy of science could not properly have…
Logical Reasoning and Retrieval Performance.
ERIC Educational Resources Information Center
Allen, Bryce
1993-01-01
A study of logical reasoning ability of endusers searching a CD-ROM index and its correlation to searching performance was conducted at the University of Illinois at Urbana-Champaign. Findings showed a correlation between cognitive skills and citation selection and indicated that computer system design can be improved using a cognitive engineering…
Olbright, G.R.; Bryan, R.P.; Brennan, T.M.; Lear, K.; Poirier, G.E.; Fu, W.S. ); Jewell, J.L.; Lee, Y.H. )
1990-10-31
We describe a new class of optical logic devices which consist of integrated phototransistors and surface-emitting lasers. The devices function as optical neurons having high gain and, as arrays, are ideal for neural networks, parallel optical signal processing and optical computing applications. 3 refs., 3 figs.
Generic physical protection logic trees
Paulus, W.K.
1981-10-01
Generic physical protection logic trees, designed for application to nuclear facilities and materials, are presented together with a method of qualitative evaluation of the trees for design and analysis of physical protection systems. One or more defense zones are defined where adversaries interact with the physical protection system. Logic trees that are needed to describe the possible scenarios within a defense zone are selected. Elements of a postulated or existing physical protection system are tagged to the primary events of the logic tree. The likelihood of adversary success in overcoming these elements is evaluated on a binary, yes/no basis. The effect of these evaluations is propagated through the logic of each tree to determine whether the adversary is likely to accomplish the end event of the tree. The physical protection system must be highly likely to overcome the adversary before he accomplishes his objective. The evaluation must be conducted for all significant states of the site. Deficiencies uncovered become inputs to redesign and further analysis, closing the loop on the design/analysis cycle.
Logic synthesis from DDL description
NASA Technical Reports Server (NTRS)
Shiva, S. G.
1980-01-01
The implementation of DDLTRN and DDLSIM programs on SEL-2 computer system is reported. These programs were tested with DDL descriptions of various complexity. An algorithm to synthesize the combinational logic using the cells available in the standard IC cell library was formulated. The algorithm is implemented as a FORTRAN program and a description of the program is given.
Learning fuzzy logic control system
NASA Technical Reports Server (NTRS)
Lung, Leung Kam
1994-01-01
The performance of the Learning Fuzzy Logic Control System (LFLCS), developed in this thesis, has been evaluated. The Learning Fuzzy Logic Controller (LFLC) learns to control the motor by learning the set of teaching values that are generated by a classical PI controller. It is assumed that the classical PI controller is tuned to minimize the error of a position control system of the D.C. motor. The Learning Fuzzy Logic Controller developed in this thesis is a multi-input single-output network. Training of the Learning Fuzzy Logic Controller is implemented off-line. Upon completion of the training process (using Supervised Learning, and Unsupervised Learning), the LFLC replaces the classical PI controller. In this thesis, a closed loop position control system of a D.C. motor using the LFLC is implemented. The primary focus is on the learning capabilities of the Learning Fuzzy Logic Controller. The learning includes symbolic representation of the Input Linguistic Nodes set and Output Linguistic Notes set. In addition, we investigate the knowledge-based representation for the network. As part of the design process, we implement a digital computer simulation of the LFLCS. The computer simulation program is written in 'C' computer language, and it is implemented in DOS platform. The LFLCS, designed in this thesis, has been developed on a IBM compatible 486-DX2 66 computer. First, the performance of the Learning Fuzzy Logic Controller is evaluated by comparing the angular shaft position of the D.C. motor controlled by a conventional PI controller and that controlled by the LFLC. Second, the symbolic representation of the LFLC and the knowledge-based representation for the network are investigated by observing the parameters of the Fuzzy Logic membership functions and the links at each layer of the LFLC. While there are some limitations of application with this approach, the result of the simulation shows that the LFLC is able to control the angular shaft position of the
Mathematical algorithms for approximate reasoning
NASA Technical Reports Server (NTRS)
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
Logic Dynamics for Deductive Inference -- Its Stability and Neural Basis
NASA Astrophysics Data System (ADS)
Tsuda, Ichiro
2014-12-01
We propose a dynamical model that represents a process of deductive inference. We discuss the stability of logic dynamics and a neural basis for the dynamics. We propose a new concept of descriptive stability, thereby enabling a structure of stable descriptions of mathematical models concerning dynamic phenomena to be clarified. The present theory is based on the wider and deeper thoughts of John S. Nicolis. In particular, it is based on our joint paper on the chaos theory of human short-term memories with a magic number of seven plus or minus two.
Quantitative and logic modelling of gene and molecular networks
Le Novère, Nicolas
2015-01-01
Behaviours of complex biomolecular systems are often irreducible to the elementary properties of their individual components. Explanatory and predictive mathematical models are therefore useful for fully understanding and precisely engineering cellular functions. The development and analyses of these models require their adaptation to the problems that need to be solved and the type and amount of available genetic or molecular data. Quantitative and logic modelling are among the main methods currently used to model molecular and gene networks. Each approach comes with inherent advantages and weaknesses. Recent developments show that hybrid approaches will become essential for further progress in synthetic biology and in the development of virtual organisms. PMID:25645874
Burton, Anthony; Kowalski, Robert; Gacic-Dobo, Marta; Karimov, Rouslan; Brown, David
2012-01-01
Production of official statistics frequently requires expert judgement to evaluate and reconcile data of unknown and varying quality from multiple and potentially conflicting sources. Moreover, exceptional events may be difficult to incorporate in modelled estimates. Computational logic provides a methodology and tools for incorporating analyst's judgement, integrating multiple data sources and modelling methods, ensuring transparency and replicability, and making documentation computationally accessible. Representations using computational logic can be implemented in a variety of computer-based languages for automated production. Computational logic complements standard mathematical and statistical techniques and extends the flexibility of mathematical and statistical modelling. A basic overview of computational logic is presented and its application to official statistics is illustrated with the WHO & UNICEF estimates of national immunization coverage. PMID:23133527
Apalit, Nathan
2010-01-01
The world of musculoskeletal disorders (MSDs) is complicated and fuzzy. Fuzzy logic provides a precise framework for complex problems characterized by uncertainty, vagueness and imprecision. Although fuzzy logic would appear to be an ideal modeling language to help address the complexity of MSDs, little research has been done in this regard. The Work Ratio is a novel mathematical model that uses fuzzy logic to provide a numerical and linguistic valuation of the likelihood of return to work and remaining at work. It can be used for a worker with any MSD at any point in time. Basic mathematical concepts from set theory and fuzzy logic are reviewed. A case study is then used to illustrate the use of the Work Ratio. Its potential strengths and limitations are discussed. Further research of its use with a variety of MSDs, settings and multidisciplinary teams is needed to confirm its universal value.
ERIC Educational Resources Information Center
McCammon, Richard B.
1979-01-01
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
ERIC Educational Resources Information Center
Johnson, Jerry
1997-01-01
Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)
Cognitive correlates of performance in advanced mathematics.
Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin
2012-03-01
Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.
Quantum Logics of Idempotents of Unital Rings
NASA Astrophysics Data System (ADS)
Bikchentaev, Airat; Navara, Mirko; Yakushev, Rinat
2015-06-01
We introduce some new examples of quantum logics of idempotents in a ring. We continue the study of symmetric logics, i.e., collections of subsets generalizing Boolean algebras and closed under the symmetric difference.
SASIL. Sandia ATM SONET Interface Logic
Kitta, J P
1994-07-01
SASIL is used to program the EPLD`s (Erasable Programmable Logic Devices) and PAL`s (Programmable Array Logic) that make up a large percentage of the Sandia ATM SONET Interface (OC3 version) for the INTEL Paragon.
ERIC Educational Resources Information Center
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
2016-01-01
Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…
ERIC Educational Resources Information Center
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
2016-01-01
Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…
Tribotronic Logic Circuits and Basic Operations.
Zhang, Chi; Zhang, Li Min; Tang, Wei; Han, Chang Bao; Wang, Zhong Lin
2015-06-17
A tribotronic logic device is fabricated to convert external mechanical stimuli into logic level signals, and tribotronic logic circuits such as NOT, AND, OR, NAND, NOR, XOR, and XNOR gates are demonstrated for performing mechanical-electrical coupled tribotronic logic operations, which realize the direct interaction between the external environment and the current silicon integrated circuits. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Computerized logic design of digital circuits
NASA Technical Reports Server (NTRS)
Sussow, S.; Oglesby, R.
1973-01-01
This manual presents a computer program that performs all the work required for the logic design of digital counters or sequential circuits and the simplification of Boolean logic expressions. The program provides both the experienced and inexperienced logic designer with a comprehensive logic design capability. The manual contains Boolean simplification and sequential design theory, detailed instructions for use of the program, a large number of illustrative design examples, and complete program documentation.
An Objectivist Critique of Relativism in Mathematics Education
NASA Astrophysics Data System (ADS)
Rowlands, Stuart; Graham, Ted; Berry, John
Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself, oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of logical necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of logical necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.
An Introduction to Calculator Logic Systems.
ERIC Educational Resources Information Center
Mitchell, Charles E.; Blume, Glendon W.
1980-01-01
Each of the hand-held calculator logic systems found on the market today is introduced, along with some of the advantages and disadvantages of each. The systems reviewed are: arithmetic logic, algebraic logic-no hierarchy, algebraic operating system, and reverse polish notation. (MP)
Logics of Business Education for Sustainability
ERIC Educational Resources Information Center
Andersson, Pernilla; Öhman, Johan
2016-01-01
This paper explores various kinds of logics of "business education for sustainability" and how these "logics" position the subject business person, based on eight teachers' reasoning of their own practices. The concept of logics developed within a discourse theoretical framework is employed to analyse the teachers' reasoning.…
Piaget's Logic of Meanings: Still Relevant Today
ERIC Educational Resources Information Center
Wavering, Michael James
2011-01-01
In his last book, "Toward a Logic of Meanings" (Piaget & Garcia, 1991), Jean Piaget describes how thought can be categorized into a form of propositional logic, a logic of meanings. The intent of this article is to offer this analysis by Piaget as a means to understand the language and teaching of science. Using binary propositions, conjunctions,…
Lakoff on Linguistics and Natural Logic.
ERIC Educational Resources Information Center
Wilks, Yorick
This paper examines and criticizes Lakoff's notions of a natural logic and of a generative semantics described in terms of logic. The author argues that the relationship of these notions to logic as normally understood is unclear but suggests a number of possible interpretations of the thesis of generative semantics. Further, on these…
Piaget's Logic of Meanings: Still Relevant Today
ERIC Educational Resources Information Center
Wavering, Michael James
2011-01-01
In his last book, "Toward a Logic of Meanings" (Piaget & Garcia, 1991), Jean Piaget describes how thought can be categorized into a form of propositional logic, a logic of meanings. The intent of this article is to offer this analysis by Piaget as a means to understand the language and teaching of science. Using binary propositions, conjunctions,…
Logics of Business Education for Sustainability
ERIC Educational Resources Information Center
Andersson, Pernilla; Öhman, Johan
2016-01-01
This paper explores various kinds of logics of "business education for sustainability" and how these "logics" position the subject business person, based on eight teachers' reasoning of their own practices. The concept of logics developed within a discourse theoretical framework is employed to analyse the teachers' reasoning.…
Applications of Logic Coverage Criteria and Logic Mutation to Software Testing
ERIC Educational Resources Information Center
Kaminski, Garrett K.
2011-01-01
Logic is an important component of software. Thus, software logic testing has enjoyed significant research over a period of decades, with renewed interest in the last several years. One approach to detecting logic faults is to create and execute tests that satisfy logic coverage criteria. Another approach to detecting faults is to perform mutation…
Applications of Logic Coverage Criteria and Logic Mutation to Software Testing
ERIC Educational Resources Information Center
Kaminski, Garrett K.
2011-01-01
Logic is an important component of software. Thus, software logic testing has enjoyed significant research over a period of decades, with renewed interest in the last several years. One approach to detecting logic faults is to create and execute tests that satisfy logic coverage criteria. Another approach to detecting faults is to perform mutation…
Noisy signaling through promoter logic gates
NASA Astrophysics Data System (ADS)
Gerstung, Moritz; Timmer, Jens; Fleck, Christian
2009-01-01
We study the influence of noisy transcription factor signals on cis-regulatory promoter elements. These elements process the probability of binary binding events analogous to computer logic gates. At equilibrium, this probability is given by the so-called input function. We show that transcription factor noise causes deviations from the equilibrium value due to the nonlinearity of the input function. For a single binding site, the correction is always negative resulting in an occupancy below the mean-field level. Yet for more complex promoters it depends on the correlation of the transcription factor signals and the geometry of the input function. We present explicit solutions for the basic types of AND and OR gates. The correction size varies among these different types of gates and signal types, mainly being larger in AND gates and for correlated fluctuations. In all cases we find excellent agreement between the analytical results and numerical simulations. We also study the E. coli Lac operon as an example of an AND NOR gate. We present a consistent mathematical method that allows one to separate different sources of noise and quantifies their effect on promoter occupation. A surprising result of our analysis is that Poissonian molecular fluctuations, in contrast to external fluctuations, do no contribute to the correction.
Mathematical wit and mathematical cognition.
Aberdein, Andrew
2013-04-01
The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed.
Glimm, J.
2009-10-14
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
Malkevitch, J. ); McCarthy, D. )
1990-01-01
The papers in this volume represent talks given at the monthly meetings of the Mathematics Section of the New York Academy of Sciences. They reflect the operating philosophy of the Section in its efforts to make a meaningful contribution to the mathematical life of a community that is exceedingly rich in cultural resources and intellectual opportunities. Each week during the academic year a dazzling abundance of mathematical seminars and colloquia is available in the New York metropolitan area. Most of these offer highly technical treatments intended for specialists. At the New York Academy we try to provide a forum of a different sort, where interesting ideas are presented in a congenial atmosphere to a broad mathematical audience. Many of the Section talks contain substantial specialized material, but we ask our speakers to include a strong expository component aimed at working mathematicians presumed to have no expert knowledge of the topic at hand. We urge speakers to try to provide the motivating interest they themselves would like to find in an introduction to a field other than their own. The same advice has been given to the authors of the present papers, with the goal of producing a collection that will be both accessible and stimulating to mathematical minds at large. We have tried to provide variety in the mathematical vistas offered; both pure and applied mathematics are well represented. Since the papers are presented alphabetically by author, some guidance seems appropriate as to what sorts of topics are treated, and where. There are three papers in analysis: those by Engber, Narici and Beckenstein, and Todd. Engber's deals with complex analysis on compact Riemann surfaces; Narici and Beckenstein provide an introduction to analysis on non-Archimendean fields; Todd surveys an area of contemporary functional analysis.
Fuzzy Versions of Epistemic and Deontic Logic
NASA Technical Reports Server (NTRS)
Gounder, Ramasamy S.; Esterline, Albert C.
1998-01-01
Epistemic and deontic logics are modal logics, respectively, of knowledge and of the normative concepts of obligation, permission, and prohibition. Epistemic logic is useful in formalizing systems of communicating processes and knowledge and belief in AI (Artificial Intelligence). Deontic logic is useful in computer science wherever we must distinguish between actual and ideal behavior, as in fault tolerance and database integrity constraints. We here discuss fuzzy versions of these logics. In the crisp versions, various axioms correspond to various properties of the structures used in defining the semantics of the logics. Thus, any axiomatic theory will be characterized not only by its axioms but also by the set of properties holding of the corresponding semantic structures. Fuzzy logic does not proceed with axiomatic systems, but fuzzy versions of the semantic properties exist and can be shown to correspond to some of the axioms for the crisp systems in special ways that support dependency networks among assertions in a modal domain. This in turn allows one to implement truth maintenance systems. For the technical development of epistemic logic, and for that of deontic logic. To our knowledge, we are the first to address fuzzy epistemic and fuzzy deontic logic explicitly and to consider the different systems and semantic properties available. We give the syntax and semantics of epistemic logic and discuss the correspondence between axioms of epistemic logic and properties of semantic structures. The same topics are covered for deontic logic. Fuzzy epistemic and fuzzy deontic logic discusses the relationship between axioms and semantic properties for these logics. Our results can be exploited in truth maintenance systems.
An Embedded Reconfigurable Logic Module
NASA Technical Reports Server (NTRS)
Tucker, Jerry H.; Klenke, Robert H.; Shams, Qamar A. (Technical Monitor)
2002-01-01
A Miniature Embedded Reconfigurable Computer and Logic (MERCAL) module has been developed and verified. MERCAL was designed to be a general-purpose, universal module that that can provide significant hardware and software resources to meet the requirements of many of today's complex embedded applications. This is accomplished in the MERCAL module by combining a sub credit card size PC in a DIMM form factor with a XILINX Spartan I1 FPGA. The PC has the ability to download program files to the FPGA to configure it for different hardware functions and to transfer data to and from the FPGA via the PC's ISA bus during run time. The MERCAL module combines, in a compact package, the computational power of a 133 MHz PC with up to 150,000 gate equivalents of digital logic that can be reconfigured by software. The general architecture and functionality of the MERCAL hardware and system software are described.
Nanowire NMOS Logic Inverter Characterization.
Hashim, Yasir
2016-06-01
This study is the first to demonstrate characteristics optimization of nanowire N-Channel Metal Oxide Semiconductor (NW-MOS) logic inverter. Noise margins and inflection voltage of transfer characteristics are used as limiting factors in this optimization. A computer-based model used to produce static characteristics of NW-NMOS logic inverter. In this research two circuit configuration of NW-NMOS inverter was studied, in first NW-NMOS circuit, the noise margin for (low input-high output) condition was very low. For second NMOS circuit gives excellent noise margins, and results indicate that optimization depends on applied voltage to the inverter. Increasing gate to source voltage with (2/1) nanowires ratio results better noise margins. Increasing of applied DC load transistor voltage tends to increasing in decreasing noise margins; decreasing this voltage will improve noise margins significantly.
The logic of medical diagnosis.
Stanley, Donald E; Campos, Daniel G
2013-01-01
Establishing diagnoses is a crucial aspect of medical practice. However, this process has received comparatively little logical and pedagogical attention when compared to statistical methods for evaluating evidence. This article investigates the logic of medical diagnosis in order to fill this void. It is organized in three parts: the first attempts to explain why more attention ought to be paid to diagnosis, at least as much as to evidence; the second calls attention to the method of diagnosis by abductive reasoning developed in the 19th century by Charles Sanders Peirce (1839-1914); and the third demonstrates the use and pervasiveness of abduction by any other name in clinical diagnosis. We examine six diagnostic strategies in common use that contain most, if not all, of Peirce's structure of inquiry in science.
The Logic Behind Feynman's Paths
NASA Astrophysics Data System (ADS)
García Álvarez, Edgardo T.
The classical notions of continuity and mechanical causality are left in order to reformulate the Quantum Theory starting from two principles: (I) the intrinsic randomness of quantum process at microphysical level, (II) the projective representations of symmetries of the system. The second principle determines the geometry and then a new logic for describing the history of events (Feynman's paths) that modifies the rules of classical probabilistic calculus. The notion of classical trajectory is replaced by a history of spontaneous, random and discontinuous events. So the theory is reduced to determining the probability distribution for such histories accordingly with the symmetries of the system. The representation of the logic in terms of amplitudes leads to Feynman rules and, alternatively, its representation in terms of projectors results in the Schwinger trace formula.
Parallel optical logic operations on reversible networks
NASA Astrophysics Data System (ADS)
Shamir, Joseph
2013-03-01
A generic optical network architecture is proposed for the implementation of programmable logic operations. Based on reversible optical gate elements the processor is highly energy efficient and intrinsically fast. In this architecture the whole logic operation is executed by light propagating through the system with no energy dissipation. Energy must be spent only at the input interface and at discrete locations where the logic operation results are to be detected. As a consequence, the theoretical lower limit for energy dissipation in logic operations must be reconsidered. The strength of this approach is demonstrated by examples showing the implementation of various lossless logic operations, including Half Adder and Full Adder.
All-optical symmetric ternary logic gate
NASA Astrophysics Data System (ADS)
Chattopadhyay, Tanay
2010-09-01
Symmetric ternary number (radix=3) has three logical states (1¯, 0, 1). It is very much useful in carry free arithmetical operation. Beside this, the logical operation using this type of number system is also effective in high speed computation and communication in multi-valued logic. In this literature all-optical circuits for three basic symmetrical ternary logical operations (inversion, MIN and MAX) are proposed and described. Numerical simulation verifies the theoretical model. In this present scheme the different ternary logical states are represented by different polarized state of light. Terahertz optical asymmetric demultiplexer (TOAD) based interferometric switch has been used categorically in this manuscript.
Anaesthesia monitoring using fuzzy logic.
Baig, Mirza Mansoor; Gholamhosseini, Hamid; Kouzani, Abbas; Harrison, Michael J
2011-10-01
Humans have a limited ability to accurately and continuously analyse large amount of data. In recent times, there has been a rapid growth in patient monitoring and medical data analysis using smart monitoring systems. Fuzzy logic-based expert systems, which can mimic human thought processes in complex circumstances, have indicated potential to improve clinicians' performance and accurately execute repetitive tasks to which humans are ill-suited. The main goal of this study is to develop a clinically useful diagnostic alarm system based on fuzzy logic for detecting critical events during anaesthesia administration. The proposed diagnostic alarm system called fuzzy logic monitoring system (FLMS) is presented. New diagnostic rules and membership functions (MFs) are developed. In addition, fuzzy inference system (FIS), adaptive neuro fuzzy inference system (ANFIS), and clustering techniques are explored for developing the FLMS' diagnostic modules. The performance of FLMS which is based on fuzzy logic expert diagnostic systems is validated through a series of off-line tests. The training and testing data set are selected randomly from 30 sets of patients' data. The accuracy of diagnoses generated by the FLMS was validated by comparing the diagnostic information with the one provided by an anaesthetist for each patient. Kappa-analysis was used for measuring the level of agreement between the anaesthetist's and FLMS's diagnoses. When detecting hypovolaemia, a substantial level of agreement was observed between FLMS and the human expert (the anaesthetist) during surgical procedures. The diagnostic alarm system FLMS demonstrated that evidence-based expert diagnostic systems can diagnose hypovolaemia, with a substantial degree of accuracy, in anaesthetized patients and could be useful in delivering decision support to anaesthetists.
Cosmic logic: a computational model
Vanchurin, Vitaly
2016-02-01
We initiate a formal study of logical inferences in context of the measure problem in cosmology or what we call cosmic logic. We describe a simple computational model of cosmic logic suitable for analysis of, for example, discretized cosmological systems. The construction is based on a particular model of computation, developed by Alan Turing, with cosmic observers (CO), cosmic measures (CM) and cosmic symmetries (CS) described by Turing machines. CO machines always start with a blank tape and CM machines take CO's Turing number (also known as description number or Gödel number) as input and output the corresponding probability. Similarly, CS machines take CO's Turing number as input, but output either one if the CO machines are in the same equivalence class or zero otherwise. We argue that CS machines are more fundamental than CM machines and, thus, should be used as building blocks in constructing CM machines. We prove the non-computability of a CS machine which discriminates between two classes of CO machines: mortal that halts in finite time and immortal that runs forever. In context of eternal inflation this result implies that it is impossible to construct CM machines to compute probabilities on the set of all CO machines using cut-off prescriptions. The cut-off measures can still be used if the set is reduced to include only machines which halt after a finite and predetermined number of steps.
Skelton, R M
1995-04-01
This paper introduces the reader to modern logic, more particularly the branch of logic called 'Model Theory', which is extensively used by Bion. Logic today is no longer described as the study of 'valid inference', but rather by the notion of consistency of beliefs. This central concern of the logician with consistency is also seen to be that of the psychoanalyst when he aims for eventual resolution of conflict between a patient's contradictory beliefs. Models are explained as the use of the already familiar to explain the unfamiliar, as when, for example, we invoke our familiar planetary system to understand the complex structure of the atom. In psychoanalysis we seek to find the old childhood models underpinning a patient's contemporary model of himself and others. Thus both Model Theory and psychoanalysis are interested in how we 'see the new in terms of the old'. Finally, the creation of models is assimilated to the integrative tendency of depressive activity and the dissolving or collapsing of models linked to paranoid-schizoid activity. As these two processes in the individual are linked by Bion we can see human beings as continually oscillating between creating and destroying models of their inner and outer worlds.
Qualitative information modeling: The role of fuzzy logic in project economic evaluations
Warnken, P.G.
1995-12-31
Conventional models rely on a precise mathematical formalism to express the quantitative essentials of the system being modeled. In contrast, decisionmakers in the real world employ cognitive skills to process information and arrive at decisions based on judgement and experience. Bridging the gap between the two analytic approaches -- that is, formulating intelligent models -- has met with very limited success using traditional computational methods. The difficulty stems from two problems. First, imprecision, which is the distinguishing feature of qualitative factors, is an information attribute that is not easily computable using the rules of traditional set theory and Boolean (bivalent) logic. Second, cognitive information processing is cumbersome using the numerical rule-based approaches common in today`s expert systems. Fuzzy models overcome these problems by employing new mathematical rules for expressing and processing knowledge. These rules are based on fuzzy logic. Fuzzy logic is the formal symbolic language used to represent linguistic terms and verbal rules for computational and modeling purposes. This language provides model builders with the means to incorporate subjective judgements, imprecise information, and human reasoning capabilities as part of a model`s framework. This paper outlines the concepts needed to understand fuzzy modeling systems. The key concepts discussed include fuzzy sets, fuzzy logical operators, linguistic variables, and verbal rules. A simple fuzzy economic rating model for project investments is presented to demonstrate the fuzzy modeling technique. Finally, the paper discusses the role of fuzzy logic in the economic modeling process.
All-photonic multifunctional molecular logic device.
Andréasson, Joakim; Pischel, Uwe; Straight, Stephen D; Moore, Thomas A; Moore, Ana L; Gust, Devens
2011-08-03
Photochromes are photoswitchable, bistable chromophores which, like transistors, can implement binary logic operations. When several photochromes are combined in one molecule, interactions between them such as energy and electron transfer allow design of simple Boolean logic gates and more complex logic devices with all-photonic inputs and outputs. Selective isomerization of individual photochromes can be achieved using light of different wavelengths, and logic outputs can employ absorption and emission properties at different wavelengths, thus allowing a single molecular species to perform several different functions, even simultaneously. Here, we report a molecule consisting of three linked photochromes that can be configured as AND, XOR, INH, half-adder, half-subtractor, multiplexer, demultiplexer, encoder, decoder, keypad lock, and logically reversible transfer gate logic devices, all with a common initial state. The system demonstrates the advantages of light-responsive molecules as multifunctional, reconfigurable nanoscale logic devices that represent an approach to true molecular information processing units.
All-Photonic Multifunctional Molecular Logic Device
2011-01-01
Photochromes are photoswitchable, bistable chromophores which, like transistors, can implement binary logic operations. When several photochromes are combined in one molecule, interactions between them such as energy and electron transfer allow design of simple Boolean logic gates and more complex logic devices with all-photonic inputs and outputs. Selective isomerization of individual photochromes can be achieved using light of different wavelengths, and logic outputs can employ absorption and emission properties at different wavelengths, thus allowing a single molecular species to perform several different functions, even simultaneously. Here, we report a molecule consisting of three linked photochromes that can be configured as AND, XOR, INH, half-adder, half-subtractor, multiplexer, demultiplexer, encoder, decoder, keypad lock, and logically reversible transfer gate logic devices, all with a common initial state. The system demonstrates the advantages of light-responsive molecules as multifunctional, reconfigurable nanoscale logic devices that represent an approach to true molecular information processing units. PMID:21563823
Quotable Quotes in Mathematics
ERIC Educational Resources Information Center
Lo, Bruce W. N.
1983-01-01
As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)
The principle of least action as the logical empiricist's Shibboleth
NASA Astrophysics Data System (ADS)
Stöltzner, Michael
The present paper investigates why logical empiricists remained silent about one of the most philosophy-laden matters of theoretical physics of their day, the principle of least action (PLA). In the two decades around 1900, the PLA enjoyed a remarkable renaissance as a formal unification of mechanics, electrodynamics, thermodynamics, and relativity theory. Taking Ernst Mach's historico-critical stance, it could be liberated from much of its physico-theological dross. Variational calculus, the mathematical discipline on which the PLA was based, obtained a new rigorous basis. These three developments prompted Max Planck to consider the PLA as formal embodiment of his convergent realist methodology. Typically rejecting ontological reductionism, David Hilbert took the PLA as the key concept in his axiomatizations of physical theories. It served one of the main goals of the axiomatic method: "deepening the foundations." Although Moritz Schlick was a student of Planck's, and Hans Hahn and Philipp Frank enjoyed close ties to Göttingen, the PLA became a veritable Shibboleth to them. Rather than being worried by its historical connections with teleology and determinism, they erroneously identified Hilbert's axiomatic method tout court with Planck's metaphysical realism. Logical empiricists' strict containment policy against metaphysics required so strict a separation between physics and mathematics to exclude even those features of the PLA and the axiomatic method not tainted with metaphysics.
The logic of relations and the logic of management.
Buntinx, W
2008-07-01
Increasing emphasis on financial and administrative control processes is affecting service culture in support organisations for persons with intellectual disability. This phenomenon is currently obvious in Dutch service organisations that find themselves in transition towards more community care and at the same time under pressure from new administrative and funding managerial bureaucracy. As a result, the logic of management is becoming more dominant in direct support settings and risk to overshadow the logic of relationships between staff and clients. The article presents a reflection on this phenomenon, starting from a description of service team characteristics as found in the literature. Next, findings about direct support staff (DSS) continuity are summarised from four Dutch studies. Following up these findings, the concept of 'microsystems' is explored as a possible answer to the organisational challenges demonstrated in the studies. Team characteristics, especially team size and membership continuity for DSS, appear relevant factors for assuring supportive relationships and service quality in direct support teams. The structure of the primary support team shows to be of special interest. The organisational concept of 'microsystems' is explored with respect to transcending the present conflict between bureaucratic managerial pressure and the need for supportive relationships. Service organisations need to create structural conditions for the efficacy of direct support teams in terms of client relationships and relevant client outcomes. At the same time, the need for administrative and control processes can not be denied. The concept of 'microsystems', application of a Quality of Life framework and the use of new instruments, such as the Supports Intensity Scale, can contribute to an organisational solution for the present conflicting logic of relations and management.
Logical gaps in the approximate solutions of the social learning game and an exact solution.
Dai, Wenjie; Wang, Xin; Di, Zengru; Wu, Jinshan
2014-01-01
After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and offer an exact solution of our own. We also introduce a minor extension to the original game so that not only logical differences but also differences in action outcomes among those solutions become visible.
The universal magnetic tunnel junction logic gates representing 16 binary Boolean logic operations
NASA Astrophysics Data System (ADS)
Lee, Junwoo; Suh, Dong Ik; Park, Wanjun
2015-05-01
The novel devices are expected to shift the paradigm of a logic operation by their own nature, replacing the conventional devices. In this study, the nature of our fabricated magnetic tunnel junction (MTJ) that responds to the two external inputs, magnetic field and voltage bias, demonstrated seven basic logic operations. The seven operations were obtained by the electric-field-assisted switching characteristics, where the surface magnetoelectric effect occurs due to a sufficiently thin free layer. The MTJ was transformed as a universal logic gate combined with three supplementary circuits: A multiplexer (MUX), a Wheatstone bridge, and a comparator. With these circuits, the universal logic gates demonstrated 16 binary Boolean logic operations in one logic stage. A possible further approach is parallel computations through a complimentary of MUX and comparator, capable of driving multiple logic gates. A reconfigurable property can also be realized when different logic operations are produced from different level of voltages applying to the same configuration of the logic gate.
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
ERIC Educational Resources Information Center
Kennard, Jackie
2007-01-01
One of the most interesting developments in teaching has been the growing importance of the outdoor environment. Whether it be playground, garden or field, the outdoors offers a range of challenging experiences, especially in the delivery of early mathematics. Oral feedback to parents, together with photographic displays, can show them that…
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
ERIC Educational Resources Information Center
Kennard, Jackie
2007-01-01
One of the most interesting developments in teaching has been the growing importance of the outdoor environment. Whether it be playground, garden or field, the outdoors offers a range of challenging experiences, especially in the delivery of early mathematics. Oral feedback to parents, together with photographic displays, can show them that…
ERIC Educational Resources Information Center
Rogness, Jonathan
2011-01-01
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
A Formalized Design Process for Bacterial Consortia That Perform Logic Computing
Sun, Rui; Xi, Jingyi; Wen, Dingqiao; Feng, Jingchen; Chen, Yiwei; Qin, Xiao; Ma, Yanrong; Luo, Wenhan; Deng, Linna; Lin, Hanchi; Yu, Ruofan; Ouyang, Qi
2013-01-01
The concept of microbial consortia is of great attractiveness in synthetic biology. Despite of all its benefits, however, there are still problems remaining for large-scaled multicellular gene circuits, for example, how to reliably design and distribute the circuits in microbial consortia with limited number of well-behaved genetic modules and wiring quorum-sensing molecules. To manage such problem, here we propose a formalized design process: (i) determine the basic logic units (AND, OR and NOT gates) based on mathematical and biological considerations; (ii) establish rules to search and distribute simplest logic design; (iii) assemble assigned basic logic units in each logic operating cell; and (iv) fine-tune the circuiting interface between logic operators. We in silico analyzed gene circuits with inputs ranging from two to four, comparing our method with the pre-existing ones. Results showed that this formalized design process is more feasible concerning numbers of cells required. Furthermore, as a proof of principle, an Escherichia coli consortium that performs XOR function, a typical complex computing operation, was designed. The construction and characterization of logic operators is independent of “wiring” and provides predictive information for fine-tuning. This formalized design process provides guidance for the design of microbial consortia that perform distributed biological computation. PMID:23468999
A formalized design process for bacterial consortia that perform logic computing.
Ji, Weiyue; Shi, Handuo; Zhang, Haoqian; Sun, Rui; Xi, Jingyi; Wen, Dingqiao; Feng, Jingchen; Chen, Yiwei; Qin, Xiao; Ma, Yanrong; Luo, Wenhan; Deng, Linna; Lin, Hanchi; Yu, Ruofan; Ouyang, Qi
2013-01-01
The concept of microbial consortia is of great attractiveness in synthetic biology. Despite of all its benefits, however, there are still problems remaining for large-scaled multicellular gene circuits, for example, how to reliably design and distribute the circuits in microbial consortia with limited number of well-behaved genetic modules and wiring quorum-sensing molecules. To manage such problem, here we propose a formalized design process: (i) determine the basic logic units (AND, OR and NOT gates) based on mathematical and biological considerations; (ii) establish rules to search and distribute simplest logic design; (iii) assemble assigned basic logic units in each logic operating cell; and (iv) fine-tune the circuiting interface between logic operators. We in silico analyzed gene circuits with inputs ranging from two to four, comparing our method with the pre-existing ones. Results showed that this formalized design process is more feasible concerning numbers of cells required. Furthermore, as a proof of principle, an Escherichia coli consortium that performs XOR function, a typical complex computing operation, was designed. The construction and characterization of logic operators is independent of "wiring" and provides predictive information for fine-tuning. This formalized design process provides guidance for the design of microbial consortia that perform distributed biological computation.
Pan, Deng; Wei, Hong; Xu, Hongxing
2013-04-22
Optical interferometric logic gates in metal slot waveguide network are designed and investigated by electromagnetic simulations. The designed logic gates can realize all fundamental logic operations. A single Y-shaped junction can work as logic gate for four logic functions: AND, NOT, OR and XOR. By cascading two Y-shaped junctions, NAND, NOR and XNOR can be realized. The working principle is analyzed in detail. In the simulations, these gates show large intensity contrast for the Boolean logic states of the output. These results can be useful for future integrated optical computing.
NASA Technical Reports Server (NTRS)
Pryor, Richard Lee (Inventor)
1977-01-01
A line driver including a pair of complementary transistors having their conduction paths serially connected between an operating and a reference potential and their bases connected through a first switch to a signal input terminal. A second switch is connected between the common base connection and the common connection of the conduction paths. With the second switch open and the first closed, an output voltage, responsive to the input signal, corresponding to first or second binary values is obtained. When the second switch is closed and the first opened, the transistor pair is turned off, disconnecting the line driver from its load, thereby providing tri-state logic operation.
Freedman, Michael H.
1998-01-01
We introduce “ultrafilter limits” into the classical Turing model of computation and develop a paradigm for interpreting the problem of distinguishing the class P from NP as a logical problem of decidability. We use P(NP) to denote decision problems which can be solved on a (nondeterministic) Turing machine in polynomial time. The concept is that in an appropriate limit it may be possible to prove that problems in P are still decidable, so a problem whose limit is undecidable would be established as lying outside of P. PMID:9419334
NASA Astrophysics Data System (ADS)
Kalanov, Temur Z.
2015-04-01
Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.
Mathematics Curriculum Guide. Mathematics IV.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
Synthesizing Biomolecule-based Boolean Logic Gates
Miyamoto, Takafumi; Razavi, Shiva; DeRose, Robert; Inoue, Takanari
2012-01-01
One fascinating recent avenue of study in the field of synthetic biology is the creation of biomolecule-based computers. The main components of a computing device consist of an arithmetic logic unit, the control unit, memory, and the input and output devices. Boolean logic gates are at the core of the operational machinery of these parts, hence to make biocomputers a reality, biomolecular logic gates become a necessity. Indeed, with the advent of more sophisticated biological tools, both nucleic acid- and protein-based logic systems have been generated. These devices function in the context of either test tubes or living cells and yield highly specific outputs given a set of inputs. In this review, we discuss various types of biomolecular logic gates that have been synthesized, with particular emphasis on recent developments that promise increased complexity of logic gate circuitry, improved computational speed, and potential clinical applications. PMID:23526588
Molecular processors: from qubits to fuzzy logic.
Gentili, Pier Luigi
2011-03-14
Single molecules or their assemblies are information processing devices. Herein it is demonstrated how it is possible to process different types of logic through molecules. As long as decoherent effects are maintained far away from a pure quantum mechanical system, quantum logic can be processed. If the collapse of superimposed or entangled wavefunctions is unavoidable, molecules can still be used to process either crisp (binary or multi-valued) or fuzzy logic. The way for implementing fuzzy inference engines is declared and it is supported by the examples of molecular fuzzy logic systems devised so far. Fuzzy logic is drawing attention in the field of artificial intelligence, because it models human reasoning quite well. This ability may be due to some structural analogies between a fuzzy logic system and the human nervous system. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Electronic logic for enhanced switch reliability
Cooper, J.A.
1984-01-20
A logic circuit is used to enhance redundant switch reliability. Two or more switches are monitored for logical high or low output. The output for the logic circuit produces a redundant and fail-safe representation of the switch outputs. When both switch outputs are high, the output is high. Similarly, when both switch outputs are low, the logic circuit's output is low. When the output states of the two switches do not agree, the circuit resolves the conflict by memorizing the last output state which both switches were simultaneously in and produces the logical complement of this output state. Thus, the logic circuit of the present invention allows the redundant switches to be treated as if they were in parallel when the switches are open and as if they were in series when the switches are closed. A failsafe system having maximum reliability is thereby produced.
Synthesizing biomolecule-based Boolean logic gates.
Miyamoto, Takafumi; Razavi, Shiva; DeRose, Robert; Inoue, Takanari
2013-02-15
One fascinating recent avenue of study in the field of synthetic biology is the creation of biomolecule-based computers. The main components of a computing device consist of an arithmetic logic unit, the control unit, memory, and the input and output devices. Boolean logic gates are at the core of the operational machinery of these parts, and hence to make biocomputers a reality, biomolecular logic gates become a necessity. Indeed, with the advent of more sophisticated biological tools, both nucleic acid- and protein-based logic systems have been generated. These devices function in the context of either test tubes or living cells and yield highly specific outputs given a set of inputs. In this review, we discuss various types of biomolecular logic gates that have been synthesized, with particular emphasis on recent developments that promise increased complexity of logic gate circuitry, improved computational speed, and potential clinical applications.
[Continuity and transformation of body logic].
Bolens, Guillemette
2003-01-01
This article is concerned with two distinct corporeal logics. In the first, corporeality is founded on joints, tendons, and mobility; in the second, the envelope and its apertures are considered primordial. The first logic is extant in very few works. Although these texts (e.g. The Iliad, Beowulf) clearly share the same, very specific, conception of the body, they belong to different histories. The corporeal logic of the 'jointed body' (corps articulaire) cannot, therefore, be appraised in terms of longue durée. The texts represent, instead, a moment of transition between the psychodynamics of orality and literacy. A problem correlated to this fact is that readers (ancient and modern) no longer think using the same logic as that pertaining to the jointed body. They tend to translate information regarding the logic of the jointed body into data meaningful in their own logic.
Minuteman Weapon System Test Set logic replacement
NASA Astrophysics Data System (ADS)
Royse, S. D.
In the late 1960s, the Minuteman Weapon System Test Set was constructed as a part of the Minuteman development program. The missile Reentry Vehicle is that portion of the Minuteman missile system which reenters the atmosphere with the nuclear warhead. The test set has the objective to test the electrical/electro-mechanical systems and components of the reentry vehicle at both the repair depot and missile maintenance squadron levels. With the recent advances in semiconductor technologies, the Diode Transistor Logic (DTL) technology used to implement the test set logic became obsolete. The present paper is concerned with efforts to develop a prototype replacement for the test set logic. Attention is given to the functions of the test set, the documentation of existing logic, and the prototype design approach, which involves the subdivision of the logic into three basic functional groups. The logic replacement is based on the utilization of a multiple microprocessor system.
People Like Logical Truth: Testing the Intuitive Detection of Logical Value in Basic Propositions
2016-01-01
Recent studies on logical reasoning have suggested that people are intuitively aware of the logical validity of syllogisms or that they intuitively detect conflict between heuristic responses and logical norms via slight changes in their feelings. According to logical intuition studies, logically valid or heuristic logic no-conflict reasoning is fluently processed and induces positive feelings without conscious awareness. One criticism states that such effects of logicality disappear when confounding factors such as the content of syllogisms are controlled. The present study used abstract propositions and tested whether people intuitively detect logical value. Experiment 1 presented four logical propositions (conjunctive, biconditional, conditional, and material implications) regarding a target case and asked the participants to rate the extent to which they liked the statement. Experiment 2 tested the effects of matching bias, as well as intuitive logic, on the reasoners’ feelings by manipulating whether the antecedent or consequent (or both) of the conditional was affirmed or negated. The results showed that both logicality and matching bias affected the reasoners’ feelings, and people preferred logically true targets over logically false ones for all forms of propositions. These results suggest that people intuitively detect what is true from what is false during abstract reasoning. Additionally, a Bayesian mixed model meta-analysis of conditionals indicated that people’s intuitive interpretation of the conditional “if p then q” fits better with the conditional probability, q given p. PMID:28036402
Mixed Methods Study Using Constructive Learning Team Model for Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Ritter, Kristy L.
2010-01-01
The constructive learning team model for secondary mathematics teachers (CLTM) was created to provide students with learning opportunities and experiences that address deficiencies in oral and written communication, logical processes and analysis, mathematical operations, independent learning, teamwork, and technology utilization. This study…
Using the Tower of Hanoi Puzzle to Infuse Your Mathematics Classroom with Computer Science Concepts
ERIC Educational Resources Information Center
Marzocchi, Alison S.
2016-01-01
This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…
The Beauty of "and" and "or": Connections within Mathematics for Students with Learning Differences.
ERIC Educational Resources Information Center
Bosse, Michael J.
2003-01-01
Investigates a way to assist students with learning differences. Considers mathematical connections appropriate in middle grades through college mathematics centered around the words "and" and "or" within the fields of logic, set theory, algebra, number theory, and probability. Teachers and students should be encouraged to investigate mathematical…
Explaining Definitions in Secondary School Mathematics: A[superscript 0], A[superscript n], 0!
ERIC Educational Resources Information Center
Guan, Tay Eng; Hoong, Leong Yew
2012-01-01
Educators look for "teaching opportunities" within the curriculum to "bring the practice of knowing mathematics in school closer to what it means to know within the discipline". The need to emphasise disciplinarity--and the concomitant canons of logic, consistency, and connections--in the teaching of mathematics is in line with…
Sequential Mathematics Course III. Volume One. Staff Development Program 1986-1987.
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.
The Sequential Mathematics Sequence provides students with an integrated course of study, including lessons which interweave algebra, geometry, logic, probability, and mathematical systems. This handbook is designed to meet the needs of teachers who will be teaching Course III in the sequence. The handbook, for use with staff development programs,…
Calculus and More: Computers, Finite Mathematics, and an Innovative Service Course.
ERIC Educational Resources Information Center
Hoffman, Kenneth R.
1989-01-01
A course for life science and social science students at Hampshire College is a combination of mathematics and computer science. Through actively involving students in manipulations and simulations, their appreciation for the logical and aesthetic properties of mathematical tools and their capacity for the independent work is enhanced. (MLW)
ERIC Educational Resources Information Center
Knight, Bruce Allen; Casey, Maria; Dekkers, John
2017-01-01
Textbooks have been used to enhance teaching in mathematics at all levels of schooling for many years. The use of textbooks enables the mathematics content to be presented in a sequenced, coherent and logical way. There are very few studies, however, that explore student thoughts about the use of electronic textbooks (e-texts) in secondary…
1994-06-01
THEORY OF CONDITIONAL INFORMATION FOR PROBABILISTIC PR: CD32 INFERENCE IN INTELLIGENT SYSTEMS : Il, MATHEMATICAL PE: 0305108K APPENDIX WU: DN488828 6...AvailabiiitCo, A THEORY OF CONDITIONAL INFORMATION FOR PROBABILISTIC INFERENCE IN INTELLIGENT SYSTEMS : III, MATHEMATICAL APPENDIX ABSTRACT This...statements, implications, intelligent systems , logic of conditionals, probabilistic inference, quantification of if-then rules -1- OVERVIEW This
Using the Tower of Hanoi Puzzle to Infuse Your Mathematics Classroom with Computer Science Concepts
ERIC Educational Resources Information Center
Marzocchi, Alison S.
2016-01-01
This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…
Explaining Definitions in Secondary School Mathematics: A[superscript 0], A[superscript n], 0!
ERIC Educational Resources Information Center
Guan, Tay Eng; Hoong, Leong Yew
2012-01-01
Educators look for "teaching opportunities" within the curriculum to "bring the practice of knowing mathematics in school closer to what it means to know within the discipline". The need to emphasise disciplinarity--and the concomitant canons of logic, consistency, and connections--in the teaching of mathematics is in line with…
Characterizing Kripke Structures in Temporal Logic.
1987-12-01
Emerson, A.P. Sistla . Automatic Verification of Finite-State Concurrent Systems using Temporal Logic Specifications: A Practical Approach. Tenth ACM...Machinery, Austin, Texas, January, 1982. to appear in JACM. 5. E. A. Emerson and P. Sistla . Deciding Full Branching-time Logic. The Sixteenth Annual... Sistla , E.M. Clarke. "Complexity of Propositional Linear Temporal Logics". Journal of the Association for Computing Machinery 32, 3 (July 1985), 733-749
Logic circuits from zero forcing.
Burgarth, Daniel; Giovannetti, Vittorio; Hogben, Leslie; Severini, Simone; Young, Michael
We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices to encode each logical bit, we obtain universal computation. We also highlight a phenomenon of "back forcing" as a property of each function. Such a phenomenon occurs in a circuit when the input of gates which have been already used at a given time step is further modified by a computation actually performed at a later stage. Finally, we show that zero forcing can be also used to implement reversible computation. The model introduced here provides a potentially new tool in the analysis of Boolean functions, with particular attention to monotonicity. Moreover, in the light of applications of zero forcing in quantum mechanics, the link with Boolean functions may suggest a new directions in quantum control theory and in the study of engineered quantum spin systems. It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits.
HDL to verification logic translator
NASA Astrophysics Data System (ADS)
Gambles, J. W.; Windley, P. J.
The increasingly higher number of transistors possible in VLSI circuits compounds the difficulty in insuring correct designs. As the number of possible test cases required to exhaustively simulate a circuit design explodes, a better method is required to confirm the absence of design faults. Formal verification methods provide a way to prove, using logic, that a circuit structure correctly implements its specification. Before verification is accepted by VLSI design engineers, the stand alone verification tools that are in use in the research community must be integrated with the CAD tools used by the designers. One problem facing the acceptance of formal verification into circuit design methodology is that the structural circuit descriptions used by the designers are not appropriate for verification work and those required for verification lack some of the features needed for design. We offer a solution to this dilemma: an automatic translation from the designers' HDL models into definitions for the higher-ordered logic (HOL) verification system. The translated definitions become the low level basis of circuit verification which in turn increases the designer's confidence in the correctness of higher level behavioral models.
HDL to verification logic translator
NASA Technical Reports Server (NTRS)
Gambles, J. W.; Windley, P. J.
1992-01-01
The increasingly higher number of transistors possible in VLSI circuits compounds the difficulty in insuring correct designs. As the number of possible test cases required to exhaustively simulate a circuit design explodes, a better method is required to confirm the absence of design faults. Formal verification methods provide a way to prove, using logic, that a circuit structure correctly implements its specification. Before verification is accepted by VLSI design engineers, the stand alone verification tools that are in use in the research community must be integrated with the CAD tools used by the designers. One problem facing the acceptance of formal verification into circuit design methodology is that the structural circuit descriptions used by the designers are not appropriate for verification work and those required for verification lack some of the features needed for design. We offer a solution to this dilemma: an automatic translation from the designers' HDL models into definitions for the higher-ordered logic (HOL) verification system. The translated definitions become the low level basis of circuit verification which in turn increases the designer's confidence in the correctness of higher level behavioral models.
River Protection Project (RPP) Level 0 Logic
SEEMAN, S.E.
2000-01-20
The following modifications were made to the River Protection Project Level-0 logic in going from Rev. I to Rev. 2. The first change was the change to the heading at the top of the drawing: ''TWRS Program Logic'' to ''River Protection Project Mission Logic''. Note that purely format changes (e.g., fonts, location of boxes, date format, addition of numbers to ''ghost'' boxes) are not discussed. However, the major format change was to show DOE-BNFL Inc. Interface Control Documents (ICDs) on the logic.
Special relativity from observer's mathematics point of view
NASA Astrophysics Data System (ADS)
Khots, Boris; Khots, Dmitriy
2015-09-01
When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.
Level of Student's Creative Thinking in Classroom Mathematics
ERIC Educational Resources Information Center
Siswono, Tatag Yuli Eko
2011-01-01
It is reasonable to assume that people are creative, but the degree of creativity is different. The Idea of the level of student's creative thinking has been expressed by experts, such as Gotoh (2004), and Krulik and Rudnick (1999). The perspective of the mathematics creative thinking refers to a combination of logical and divergent thinking which…
Leveling Students' Creative Thinking in Solving and Posing Mathematical Problem
ERIC Educational Resources Information Center
Siswono, Tatag Yuli Eko
2010-01-01
Many researchers assume that people are creative, but their degree of creativity is different. The notion of creative thinking level has been discussed .by experts. The perspective of mathematics creative thinking refers to a combination of logical and divergent thinking which is based on intuition but has a conscious aim. The divergent thinking…
Understanding Early Mathematical Competencies in American and Chinese Children
ERIC Educational Resources Information Center
Zhou, Zheng; Peverly, Stephen T.; Lin, Jiasui
2005-01-01
Most cross-cultural research on Chinese and American children's early mathematical competencies has focused on their understanding of number and number operations. The present study broadened the range of tasks assessed to include geometric shapes, problem solving and logical reasoning, as well as number and numerical operations, in an effort to…
Communication Theory Offers Insight into Mathematics Teachers' Talk
ERIC Educational Resources Information Center
Forrest, Denise B.
2008-01-01
This article discusses how communication theory is used to understand the thoughts mathematics teachers employ when creating messages intended for students. According to communication theory, individuals have different premises about the act of communicating, and these thoughts, called message design logics, guide the process of reasoning from…
Actualizacion Matematica, AM-2 (Modernizing Mathematics, AM-2).
ERIC Educational Resources Information Center
[Parot, Jean Jacques
This document presents a series of exercises designed to help elementary school children develop skills in mathematics and logic. By means of stories, games, questions, and illustrations, the first set of exercises presents the idea of number systems with bases other than 10. Similar means are used to explain the concept of exponents and to teach…
Mathematics Worth Teaching, Mathematics Worth Understanding.
ERIC Educational Resources Information Center
Romberg, Thomas A.; Kaput, James J.
This chapter examines the scope of the mathematical content educators expect students to understand after they have participated in mathematics courses. It is organized under four headings: (1) Traditional School Mathematics, to clarify what the shift is away from; (2) Mathematics as Human Activity, to portray the direction the shift is toward;…
Mathematical Literacy and Standardized Mathematical Assessments
ERIC Educational Resources Information Center
Matteson, Shirley M.
2006-01-01
Mathematical literacy is an important skill that is gaining the attention of mathematics educators. Students are increasingly challenged on standardized assessments to read, create, use, and comprehend numerous mathematical representations as a way of demonstrating mathematical literacy. Test items assessing algebra concepts from the Texas…
Teachers' Mathematics as Mathematics-at-Work
ERIC Educational Resources Information Center
Bednarz, Nadine; Proulx, Jérôme
2017-01-01
Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…
Teaching Mathematical Modeling in Mathematics Education
ERIC Educational Resources Information Center
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
Probabilistic and fuzzy logic in clinical diagnosis.
Licata, G
2007-06-01
In this study I have compared classic and fuzzy logic and their usefulness in clinical diagnosis. The theory of probability is often considered a device to protect the classical two-valued logic from the evidence of its inadequacy to understand and show the complexity of world [1]. This can be true, but it is not possible to discard the theory of probability. I will argue that the problems and the application fields of the theory of probability are very different from those of fuzzy logic. After the introduction on the theoretical bases of fuzzy approach to logic, I have reported some diagnostic argumentations employing fuzzy logic. The state of normality and the state of disease often fight their battle on scalar quantities of biological values and it is not hard to establish a correspondence between the biological values and the percent values of fuzzy logic. Accordingly, I have suggested some applications of fuzzy logic in clinical diagnosis and in particular I have utilised a fuzzy curve to recognise subjects with diabetes mellitus, renal failure and liver disease. The comparison between classic and fuzzy logic findings seems to indicate that fuzzy logic is more adequate to study the development of biological events. In fact, fuzzy logic is useful when we have a lot of pieces of information and when we dispose to scalar quantities. In conclusion, increasingly the development of technology offers new instruments to measure pathological parameters through scalar quantities, thus it is reasonable to think that in the future fuzzy logic will be employed more in clinical diagnosis.
Logical Empiricism, Politics, and Professionalism
NASA Astrophysics Data System (ADS)
Edgar, Scott
2009-02-01
This paper considers George A. Reisch’s account of the role of Cold War political forces in shaping the apolitical stance that came to dominate philosophy of science in the late 1940s and 1950s. It argues that at least as early as the 1930s, Logical Empiricists such as Rudolf Carnap already held that philosophy of science could not properly have political aims, and further suggests that political forces alone cannot explain this view’s rise to dominance during the Cold War, since political forces cannot explain why a philosophy of science with liberal democratic, anti-communist aims did not flourish. The paper then argues that if professionalization is understood in the right way, it might point toward an explanation of the apolitical stance of Cold War philosophy of science.
A Logic for Qualified Syllogisms
NASA Astrophysics Data System (ADS)
Schwartz, Daniel G.
In various works, L.A. Zadeh has introduced fuzzy quantifiers, fuzzy usuality modifiers, and fuzzy likelihood modifiers. This paper provides these notions with a unified semantics and uses this to define a formal logic capable of expressing and validating arguments such as 'Most birds can fly; Tweety is a bird; therefore, it is likely that Tweety can fly'. In effect, these are classical Aristotelean syllogisms that have been "qualified" through the use of fuzzy quantifiers. It is briefly outlined how these, together with some likelihood combination rules, can be used to address some well-known problems in the theory of nonmonotonic reasoning. The work is aimed at future applications in expert systems and robotics, including both hardware and software agents.
[Gaston Bachelard in front of mathematics].
Alunni, Charles
2015-01-01
The issue regarding the bond between Bachelard's thought and contemporaneous mathematics has for a long time been concealed, aiming at the restricted benefit of an entirely misrepresented interpretation. The interpretation that indeed prevails, and in particular following the colloquium of Cerisy in 1974, is that of a man nurtured in the domain of both, physics and chemistry, and that has never drawn significant attention to mathematics. That is precisely the standpoint of the logician Roger Martin who sustains that the matters concerning the foundational problems (set theory, axiomatization and logicism) are in fact buried in a guilty silence. Departing from a meticulous assessment of the philosopher's texts, the present study thus aims at restoring a more appropriate image of a Bachelard, for whom mathematics is no less than the "superego" of science.
Intuitionistic Quantum Logic of an n-level System
NASA Astrophysics Data System (ADS)
Caspers, Martijn; Heunen, Chris; Landsman, Nicolaas P.; Spitters, Bas
2009-07-01
A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in
1990-06-01
yielding information useful in mathematics and in computing. Resource-aware logics restrict the number of times an assumption may be used in a proof and...family of quasi-structures any cut-reduction reduces the total number of formula-occurrences in the proof-network. As indicated in section (1.1.2), the...problems in practice, say, in number theory or in combinatorics - at least not without additional extensive work on the practical conditions of their
Towards bioelectronic logic (Conference Presentation)
NASA Astrophysics Data System (ADS)
Meredith, Paul; Mostert, Bernard; Sheliakina, Margarita; Carrad, Damon J.; Micolich, Adam P.
2016-09-01
One of the critical tasks in realising a bioelectronic interface is the transduction of ion and electron signals at high fidelity, and with appropriate speed, bandwidth and signal-to-noise ratio [1]. This is a challenging task considering ions and electrons (or holes) have drastically different physics. For example, even the lightest ions (protons) have mobilities much smaller than electrons in the best semiconductors, effective masses are quite different, and at the most basic level, ions are `classical' entities and electrons `quantum mechanical'. These considerations dictate materials and device strategies for bioelectronic interfaces alongside practical aspects such as integration and biocompatibility [2]. In my talk I will detail these `differences in physics' that are pertinent to the ion-electron transduction challenge. From this analysis, I will summarise the basic categories of device architecture that are possibilities for transducing elements and give recent examples of their realisation. Ultimately, transducing elements need to be combined to create `bioelectronic logic' capable of signal processing at the interface level. In this regard, I will extend the discussion past the single element concept, and discuss our recent progress in delivering all-solids-state logic circuits based upon transducing interfaces. [1] "Ion bipolar junction transistors", K. Tybrandt, K.C. Larsson, A. Richter-Dahlfors and M. Berggren, Proc. Natl Acad. Sci., 107, 9929 (2010). [2] "Electronic and optoelectronic materials and devices inspired by nature", P Meredith, C.J. Bettinger, M. Irimia-Vladu, A.B. Mostert and P.E. Schwenn, Reports on Progress in Physics, 76, 034501 (2013).
Natural language understanding and logic programming
Dahl, V.; Saint-Dizier, P.
1985-01-01
Logic programming has been used in many natural language understanding applications, mainly in the areas of analysis, metagrammatical formalisms, logical treatment of linguistic problems, and meaning representations for naturla language. The particular methods and formal systems developed in this context usually exhibit attractive features of logic while remaining in the more pragmatic area of programming: conciseness, modularity, a declarative meaning that is independent from machine behaviour, and logical inference. All of these features, common to logic programming and to logic metagrammars, have been made possible through a chaining of various fundamental ideas. Outstanding among these are the resolution principle. Prolog itself; and interpretation of logic as a programming language. The machines of a relatively near future are likely to incorporate many related capabilities while increasing their speed manyfold. The Japanese Fifth Generation Computer project has triggered efforts towards future generations of computer systems based on these concepts. The potential in understanding natural language through logic programming is growing rapidly, and it might be wise to integrate the various theoretical and practical aspects involved, rather than yielding to the temptation of using all the extra power for programming ad-hoc systems. This conference is an effort toward such an integration.
Fuzzy Logic in Medicine and Bioinformatics
Torres, Angela; Nieto, Juan J.
2006-01-01
The purpose of this paper is to present a general view of the current applications of fuzzy logic in medicine and bioinformatics. We particularly review the medical literature using fuzzy logic. We then recall the geometrical interpretation of fuzzy sets as points in a fuzzy hypercube and present two concrete illustrations in medicine (drug addictions) and in bioinformatics (comparison of genomes). PMID:16883057
Rationality and the Logic of Good Reasons.
ERIC Educational Resources Information Center
Fisher, Walter R.
This paper contends that the rationality of the logic of good reasons is constituted in its use. To support this claim, the paper presents an analysis of the relationship between being reasonable and being rational. It then considers how following the logic of good reasons leads to rationality in the behavior of individuals and groups; the latter…
Logic in Educational Research and Policy Making.
ERIC Educational Resources Information Center
Garlikov, Rick
2000-01-01
Analyzes S. Bauer's article on the use of achievement tests to judge school quality to demonstrate the importance of logic, philosophy (especially conceptual analysis), and insights based on anecdotal evidence for educational research and policy making. Emphasizes the place for logical reasoning and anecdotal evidence in the empirical enterprise…
Logic Design Pathology and Space Flight Electronics
NASA Technical Reports Server (NTRS)
Katz, Richard B.; Barto, Rod L.; Erickson, Ken
1999-01-01
This paper presents a look at logic design from early in the US Space Program and examines faults in recent logic designs. Most examples are based on flight hardware failures and analysis of new tools and techniques. The paper is presented in viewgraph form.
Magnetic-field-controlled reconfigurable semiconductor logic.
Joo, Sungjung; Kim, Taeyueb; Shin, Sang Hoon; Lim, Ju Young; Hong, Jinki; Song, Jin Dong; Chang, Joonyeon; Lee, Hyun-Woo; Rhie, Kungwon; Han, Suk Hee; Shin, Kyung-Ho; Johnson, Mark
2013-02-07
Logic devices based on magnetism show promise for increasing computational efficiency while decreasing consumed power. They offer zero quiescent power and yet combine novel functions such as programmable logic operation and non-volatile built-in memory. However, practical efforts to adapt a magnetic device to logic suffer from a low signal-to-noise ratio and other performance attributes that are not adequate for logic gates. Rather than exploiting magnetoresistive effects that result from spin-dependent transport of carriers, we have approached the development of a magnetic logic device in a different way: we use the phenomenon of large magnetoresistance found in non-magnetic semiconductors in high electric fields. Here we report a device showing a strong diode characteristic that is highly sensitive to both the sign and the magnitude of an external magnetic field, offering a reversible change between two different characteristic states by the application of a magnetic field. This feature results from magnetic control of carrier generation and recombination in an InSb p-n bilayer channel. Simple circuits combining such elementary devices are fabricated and tested, and Boolean logic functions including AND, OR, NAND and NOR are performed. They are programmed dynamically by external electric or magnetic signals, demonstrating magnetic-field-controlled semiconductor reconfigurable logic at room temperature. This magnetic technology permits a new kind of spintronic device, characterized as a current switch rather than a voltage switch, and provides a simple and compact platform for non-volatile reconfigurable logic devices.
The Logic of Creative and Critical Thinking.
ERIC Educational Resources Information Center
Paul, Richard
This paper explores the intimate connection between creative and critical thinking, by arguing that both are inseparable in everyday reasoning. The details of the relationship between creative and critical thinking are worked out in relation to the processes of: (1) thinking through the logic of things; (2) taking command of reasoning and logic;…
A Device for Logic Information Processing.
ERIC Educational Resources Information Center
Levinskiy, L. S.; Vissonova, I. A.
Two essential components of the information-logic problem are: (1) choosing some known part of the total information block for parallel review of the entire block and (2) parallel logic processing of a sequence of codes. The described device fulfills these essential components thereby improving information processing and increasing the speed of…
Instruction for Using the PLATO Logic, GENERAL.
ERIC Educational Resources Information Center
Lyman, Elisabeth R.
This report contains instructions for the use of GENERAL, a tutorial type teaching logic developed for the PLATO system. The logic of GENERAL is first introduced and diagrammed for the user. Then lesson planning for program authors is discussed in terms of format rules, branching pages, challenge pages, and information retrieval pages. Control…
2014-09-13
specialists in mathematics , logic, and computer science with diverse backgrounds rang- ing from homotopical algebra and category theory to theoretical and...AFRL-OSR-VA-TR-2014-0227 New Mathematics of Information Homotopical Steven Awodey CARNEGIE MELLON UNIVERSITY Final Report 09/24/2014 DISTRIBUTION A...RESPONSIBLE PERSON 19b. TELEPHONE NUMBER (Include area code) 13-09-2014 FINAL 15 JUNE 2011 - 30 APR 2014 FINAL REPORT FOR AWARD: "NEW MATHEMATICS OF
Wu, Cuichen; Wan, Shuo; Hou, Weijia; Zhang, Liqin; Xu, Jiehua; Cui, Cheng; Wang, Yanyue; Hu, Jun
2015-01-01
Nucleic acid-based logic devices were first introduced in 1994. Since then, science has seen the emergence of new logic systems for mimicking mathematical functions, diagnosing disease and even imitating biological systems. The unique features of nucleic acids, such as facile and high-throughput synthesis, Watson-Crick complementary base pairing, and predictable structures, together with the aid of programming design, have led to the widespread applications of nucleic acids (NA) for logic gating and computing in biotechnology and biomedicine. In this feature article, the development of in vitro NA logic systems will be discussed, as well as the expansion of such systems using various input molecules for potential cellular, or even in vivo, applications. PMID:25597946
Wu, Cuichen; Wan, Shuo; Hou, Weijia; Zhang, Liqin; Xu, Jiehua; Cui, Cheng; Wang, Yanyue; Hu, Jun; Tan, Weihong
2015-03-04
Nucleic acid-based logic devices were first introduced in 1994. Since then, science has seen the emergence of new logic systems for mimicking mathematical functions, diagnosing disease and even imitating biological systems. The unique features of nucleic acids, such as facile and high-throughput synthesis, Watson-Crick complementary base pairing, and predictable structures, together with the aid of programming design, have led to the widespread applications of nucleic acids (NA) for logic gate and computing in biotechnology and biomedicine. In this feature article, the development of in vitro NA logic systems will be discussed, as well as the expansion of such systems using various input molecules for potential cellular, or even in vivo, applications.
ERIC Educational Resources Information Center
Dundar, Sefa
2015-01-01
The pattern, which is a key concept in understanding the mathematical information and concepts, is the basis in comprehending mathematical relations and in understanding mathematical order and logic. The fact that students discover the relationships contained within the patterns and generalize them helps them develop their skills to better…
ERIC Educational Resources Information Center
Dundar, Sefa
2015-01-01
The pattern, which is a key concept in understanding the mathematical information and concepts, is the basis in comprehending mathematical relations and in understanding mathematical order and logic. The fact that students discover the relationships contained within the patterns and generalize them helps them develop their skills to better…
ERIC Educational Resources Information Center
Levin-Rozalis, Miri
2010-01-01
Background: Two kinds of research logic prevail in scientific research: deductive research logic and inductive research logic. However, both fail in the field of evaluation, especially evaluation conducted in unfamiliar environments. Purpose: In this article I wish to suggest the application of a research logic--"abduction"--"the logic of…
ERIC Educational Resources Information Center
Levin-Rozalis, Miri
2010-01-01
Background: Two kinds of research logic prevail in scientific research: deductive research logic and inductive research logic. However, both fail in the field of evaluation, especially evaluation conducted in unfamiliar environments. Purpose: In this article I wish to suggest the application of a research logic--"abduction"--"the logic of…
Interpreting Quantum Logic as a Pragmatic Structure
NASA Astrophysics Data System (ADS)
Garola, Claudio
2017-02-01
Many scholars maintain that the language of quantum mechanics introduces a quantum notion of truth which is formalized by (standard, sharp) quantum logic and is incompatible with the classical (Tarskian) notion of truth. We show that quantum logic can be identified (up to an equivalence relation) with a fragment of a pragmatic language LGP of assertive formulas, that are justified or unjustified rather than trueor false. Quantum logic can then be interpreted as an algebraic structure that formalizes properties of the notion of empirical justification according to quantum mechanics rather than properties of a quantum notion of truth. This conclusion agrees with a general integrationist perspective that interprets nonstandard logics as theories of metalinguistic notions different from truth, thus avoiding incompatibility with classical notions and preserving the globality of logic.
Processing device with self-scrubbing logic
Wojahn, Christopher K.
2016-03-01
An apparatus includes a processing unit including a configuration memory and self-scrubber logic coupled to read the configuration memory to detect compromised data stored in the configuration memory. The apparatus also includes a watchdog unit external to the processing unit and coupled to the self-scrubber logic to detect a failure in the self-scrubber logic. The watchdog unit is coupled to the processing unit to selectively reset the processing unit in response to detecting the failure in the self-scrubber logic. The apparatus also includes an external memory external to the processing unit and coupled to send configuration data to the configuration memory in response to a data feed signal outputted by the self-scrubber logic.
Advanced Mathematical Study and the Development of Conditional Reasoning Skills
Attridge, Nina; Inglis, Matthew
2013-01-01
Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general ‘thinking skills’. Today, this argument, known as the ‘Theory of Formal Discipline’ is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought. PMID:23869241
Advanced mathematical study and the development of conditional reasoning skills.
Attridge, Nina; Inglis, Matthew
2013-01-01
Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general 'thinking skills'. Today, this argument, known as the 'Theory of Formal Discipline' is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought.
Bio-logic builder: a non-technical tool for building dynamical, qualitative models.
Helikar, Tomáš; Kowal, Bryan; Madrahimov, Alex; Shrestha, Manish; Pedersen, Jay; Limbu, Kahani; Thapa, Ishwor; Rowley, Thaine; Satalkar, Rahul; Kochi, Naomi; Konvalina, John; Rogers, Jim A
2012-01-01
Computational modeling of biological processes is a promising tool in biomedical research. While a large part of its potential lies in the ability to integrate it with laboratory research, modeling currently generally requires a high degree of training in mathematics and/or computer science. To help address this issue, we have developed a web-based tool, Bio-Logic Builder, that enables laboratory scientists to define mathematical representations (based on a discrete formalism) of biological regulatory mechanisms in a modular and non-technical fashion. As part of the user interface, generalized "bio-logic" modules have been defined to provide users with the building blocks for many biological processes. To build/modify computational models, experimentalists provide purely qualitative information about a particular regulatory mechanisms as is generally found in the laboratory. The Bio-Logic Builder subsequently converts the provided information into a mathematical representation described with Boolean expressions/rules. We used this tool to build a number of dynamical models, including a 130-protein large-scale model of signal transduction with over 800 interactions, influenza A replication cycle with 127 species and 200+ interactions, and mammalian and budding yeast cell cycles. We also show that any and all qualitative regulatory mechanisms can be built using this tool.
Project W-058 monitor and control system logic
ROBERTS, J.B.
1999-05-12
This supporting document contains the printout of the control logic for the Project W-058 Monitor and Control System, as developed by Programmable Control Services, Inc. The logic is arranged in five appendices, one for each programmable logic controller console.
Probabilistic logic modeling of network reliability for hybrid network architectures
Wyss, G.D.; Schriner, H.K.; Gaylor, T.R.
1996-10-01
Sandia National Laboratories has found that the reliability and failure modes of current-generation network technologies can be effectively modeled using fault tree-based probabilistic logic modeling (PLM) techniques. We have developed fault tree models that include various hierarchical networking technologies and classes of components interconnected in a wide variety of typical and atypical configurations. In this paper we discuss the types of results that can be obtained from PLMs and why these results are of great practical value to network designers and analysts. After providing some mathematical background, we describe the `plug-and-play` fault tree analysis methodology that we have developed for modeling connectivity and the provision of network services in several current- generation network architectures. Finally, we demonstrate the flexibility of the method by modeling the reliability of a hybrid example network that contains several interconnected ethernet, FDDI, and token ring segments. 11 refs., 3 figs., 1 tab.
DAIDALUS: Detect and Avoid Alerting Logic for Unmanned Systems
NASA Technical Reports Server (NTRS)
Munoz, Cesar; Narkawicz, Anthony; Hagen, George; Upchurch, Jason; Dutle, Aaron; Consiglio, Maria; Chamberlain, James
2015-01-01
This paper presents DAIDALUS (Detect and Avoid Alerting Logic for Unmanned Systems), a reference implementation of a detect and avoid concept intended to support the integration of Unmanned Aircraft Systems into civil airspace. DAIDALUS consists of self-separation and alerting algorithms that provide situational awareness to UAS remote pilots. These algorithms have been formally specified in a mathematical notation and verified for correctness in an interactive theorem prover. The software implementation has been verified against the formal models and validated against multiple stressing cases jointly developed by the US Air Force Research Laboratory, MIT Lincoln Laboratory, and NASA. The DAIDALUS reference implementation is currently under consideration for inclusion in the appendices to the Minimum Operational Performance Standards for Unmanned Aircraft Systems presently being developed by RTCA Special Committee 228.
Promoting Mathematical Argumentation
ERIC Educational Resources Information Center
Rumsey, Chepina; Langrall, Cynthia W.
2016-01-01
The Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) highlight the mathematical habits that educators should be fostering in mathematics classrooms throughout K-grade 12 education. That argumentation and discourse are important components of developing mathematically proficient…
Authenticity of Mathematical Modeling
ERIC Educational Resources Information Center
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Promoting Mathematical Argumentation
ERIC Educational Resources Information Center
Rumsey, Chepina; Langrall, Cynthia W.
2016-01-01
The Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) highlight the mathematical habits that educators should be fostering in mathematics classrooms throughout K-grade 12 education. That argumentation and discourse are important components of developing mathematically proficient…
Stock and option portfolio using fuzzy logic approach
NASA Astrophysics Data System (ADS)
Sumarti, Novriana; Wahyudi, Nanang
2014-03-01
Fuzzy Logic in decision-making process has been widely implemented in various problems in industries. It is the theory of imprecision and uncertainty that was not based on probability theory. Fuzzy Logic adds values of degree between absolute true and absolute false. It starts with and builds on a set of human language rules supplied by the user. The fuzzy systems convert these rules to their mathematical equivalents. This could simplify the job of the system designer and the computer, and results in much more accurate representations of the way systems behave in the real world. In this paper we examine the decision making process of stock and option trading by the usage of MACD (Moving Average Convergence Divergence) technical analysis and Option Pricing with Fuzzy Logic approach. MACD technical analysis is for the prediction of the trends of underlying stock prices, such as bearish (going downward), bullish (going upward), and sideways. By using Fuzzy C-Means technique and Mamdani Fuzzy Inference System, we define the decision output where the value of MACD is high then decision is "Strong Sell", and the value of MACD is Low then the decision is "Strong Buy". We also implement the fuzzification of the Black-Scholes option-pricing formula. The stock and options methods are implemented on a portfolio of one stock and its options. Even though the values of input data, such as interest rates, stock price and its volatility, cannot be obtain accurately, these fuzzy methods can give a belief degree of the calculated the Black-Scholes formula so we can make the decision on option trading. The results show the good capability of the methods in the prediction of stock price trends. The performance of the simulated portfolio for a particular period of time also shows good return.
Toward a fuzzy logic control of the infant incubator.
Reddy, Narender P; Mathur, Garima; Hariharan, S I
2009-10-01
Premature birth is a world wide problem. Thermo regulation is a major problem in premature infants. Premature infants are often kept in infant incubators providing convective heating. Currently either the incubator air temperature is sensed and used to control the heat flow, or infant's skin temperature is sensed and used in the close loop control. Skin control often leads to large fluctuations in the incubator air temperature. Air control also leads to skin temperature fluctuations. The question remains if both the infant's skin temperature and the incubator air temperature can be simultaneously used in the control. The purpose of the present study was to address this question by developing a fuzzy logic control which incorporates both incubator air temperature and infant's skin temperature to control the heating. The control was evaluated using a lumped parameter mathematical model of infant-incubator system (Simon, B. N., N. P. Reddy, and A. Kantak, J. Biomech. Eng. 116:263-266, 1994). Simulation results confirmed previous experimental results that the on-off skin control could lead to fluctuations in the incubator air temperature, and the air control could lead to too slow rise time in the core temperature. The fuzzy logic provides a smooth control with the desired rise time.
Use of LOGIC to support lidar operations
NASA Astrophysics Data System (ADS)
Davis-Lunde, Kimberley; Jugan, Laurie A.; Shoemaker, J. Todd
1999-10-01
The Naval Oceanographic Office (NAVOCEANO) and Planning Systems INcorporated are developing the Littoral Optics Geospatial Integrated Capability (LOGIC). LOGIC supports NAVOCEANO's directive to assess the impact of the environment on Fleet systems in areas of operational interest. LOGIC is based in the Geographic Information System (GIS) ARC/INFO and offers a method to view and manipulate optics and ancillary data to support emerging Fleet lidar systems. LOGIC serves as a processing (as required) and quality-checking mechanism for data entering NAVOCEANO's Data Warehouse and handles both remotely sensed and in-water data. LOGIC provides a link between these data and the GIS-based Graphical User Interface, allowing the user to select data manipulation routines and/or system support products. The results of individual modules are displayed via the GIS to provide such products as lidar system performance, laser penetration depth, and asset vulnerability from a lidar threat. LOGIC is being developed for integration into other NAVOCEANO programs, most notably for Comprehensive Environmental Assessment System, an established tool supporting sonar-based systems. The prototype for LOGIC was developed for the Yellow Sea, focusing on a diver visibility support product.
NASA Astrophysics Data System (ADS)
Kasturirangan, Rajesh
2014-07-01
Mathematics is a human pursuit. Whether the truths of mathematics lie outside the human mind or emerge out of it, the actual practice of mathematics is conducted by human beings. In other words, human mathematics is the only kind of mathematics that we can pursue and human mathematics has to be built on top of cognitive capacities that are possessed by all human beings. Another way of stating the same claim is that mathematics is experienced by human beings using their cognitive capacities. This paper argues that exploring the experience of mathematics is a useful way to make headway on the foundations of mathematics. Focusing on the experience of mathematics is an empirical approach to the study of mathematics that sidesteps some of the thorniest debates from an earlier era about Platonism and Formalism in the foundations of mathematics.
Coordination Logic for Repulsive Resolution Maneuvers
NASA Technical Reports Server (NTRS)
Narkawicz, Anthony J.; Munoz, Cesar A.; Dutle, Aaron M.
2016-01-01
This paper presents an algorithm for determining the direction an aircraft should maneuver in the event of a potential conflict with another aircraft. The algorithm is implicitly coordinated, meaning that with perfectly reliable computations and information, it will in- dependently provide directional information that is guaranteed to be coordinated without any additional information exchange or direct communication. The logic is inspired by the logic of TCAS II, the airborne system designed to reduce the risk of mid-air collisions between aircraft. TCAS II provides pilots with only vertical resolution advice, while the proposed algorithm, using a similar logic, provides implicitly coordinated vertical and horizontal directional advice.
Software Safety Assurance of Programmable Logic
NASA Technical Reports Server (NTRS)
Berens, Kalynnda
2002-01-01
Programmable Logic (PLC, FPGA, ASIC) devices are hybrids - hardware devices that are designed and programmed like software. As such, they fall in an assurance gray area. Programmable Logic is usually tested and verified as hardware, and the software aspects are ignored, potentially leading to safety or mission success concerns. The objective of this proposal is to first determine where and how Programmable Logic (PL) is used within NASA and document the current methods of assurance. Once that is known, raise awareness of the PL software aspects within the NASA engineering community and provide guidance for the use and assurance of PL form a software perspective.
Bilayer avalanche spin-diode logic
Friedman, Joseph S. Querlioz, Damien; Fadel, Eric R.; Wessels, Bruce W.; Sahakian, Alan V.
2015-11-15
A novel spintronic computing paradigm is proposed and analyzed in which InSb p-n bilayer avalanche spin-diodes are cascaded to efficiently perform complex logic operations. This spin-diode logic family uses control wires to generate magnetic fields that modulate the resistance of the spin-diodes, and currents through these devices control the resistance of cascaded devices. Electromagnetic simulations are performed to demonstrate the cascading mechanism, and guidelines are provided for the development of this innovative computing technology. This cascading scheme permits compact logic circuits with switching speeds determined by electromagnetic wave propagation rather than electron motion, enabling high-performance spintronic computing.
On the complexity of stratified logics
NASA Astrophysics Data System (ADS)
Vercelli, Luca
2010-02-01
Our primary motivation is the comparison of two different traditions used in ICC to characterize the class FPTIME of the polynomial time computable functions. On one side, FPTIME can be captured by Intuitionistic Light Affine Logic (ILAL), a logic derived from Linear Logic, characterized by the structural invariant Stratification. On the other side, FPTIME can be captured by Safe Recursion on Notation (SRN), an algebra of functions based on Predicative Recursion, a restriction of the standard recursion schema used to defiine primitive recursive functions. Stratifiication and Predicative Recursion seem to share common underlying principles, whose study is the main subject of this work.
Magnetic logic using nanowires with perpendicular anisotropy.
Jaworowicz, J; Vernier, N; Ferré, J; Maziewski, A; Stanescu, D; Ravelosona, D; Jacqueline, A S; Chappert, C; Rodmacq, B; Diény, B
2009-05-27
In addition to a storage function through the magnetization of nanowires, domain wall propagation can be used to trigger magnetic logic functions. Here, we present a new way to realize a pure magnetic logic operation by using magnetic nanowires with perpendicular anisotropy. Emphasis is given on the generation of the logic function 'NOT' that is based on the dipolar interaction between two neighbouring magnetic wires, which favours the creation of a domain wall. This concept has been validated on several prototypes and the results fit well with the expectations.
Logic model needs for diverse facility types
Wilson, J.R.
1995-10-01
This paper compares the characteristics of fault trees (where initiators are developed within the fault tree) vs. event trees (where the nodes are developed by fault trees). This comparison requires some additional discussion on the subtlety of initiators. Difficulties when analyzing various reactor-type and processing facilities are discussed to illustrate the particular characteristics of each type of logic. The intent is to allow probabilistic risk assessment (PRA) analysts to be {open_quotes}bi-logical,{close_quotes} or equally comfortable with event-tree or fault-tree logic, knowing when to apply each.
Binary logic based purely on Fresnel diffraction
NASA Astrophysics Data System (ADS)
Hamam, H.; de Bougrenet de La Tocnaye, J. L.
1995-09-01
Binary logic operations on two-dimensional data arrays are achieved by use of the self-imaging properties of Fresnel diffraction. The fields diffracted by periodic objects can be considered as the superimposition of weighted and shifted replicas of original objects. We show that a particular spatial organization of the input data can result in logical operations being performed on these data in the considered diffraction planes. Among various advantages, this approach is shown to allow the implementation of dual-track, nondissipative logical operators. Image algebra is presented as an experimental illustration of this principle.
A Logical Analysis of Quantum Voting Protocols
NASA Astrophysics Data System (ADS)
Rad, Soroush Rafiee; Shirinkalam, Elahe; Smets, Sonja
2017-07-01
In this paper we provide a logical analysis of the Quantum Voting Protocol for Anonymous Surveying as developed by Horoshko and Kilin in (Phys. Lett. A 375, 1172-1175 2011). In particular we make use of the probabilistic logic of quantum programs as developed in (Int. J. Theor. Phys. 53, 3628-3647 2014) to provide a formal specification of the protocol and to derive its correctness. Our analysis is part of a wider program on the application of quantum logics to the formal verification of protocols in quantum communication and quantum computation.
Software Safety Assurance of Programmable Logic
NASA Technical Reports Server (NTRS)
Berens, Kalynnda
2002-01-01
Programmable Logic (PLC, FPGA, ASIC) devices are hybrids - hardware devices that are designed and programmed like software. As such, they fall in an assurance gray area. Programmable Logic is usually tested and verified as hardware, and the software aspects are ignored, potentially leading to safety or mission success concerns. The objective of this proposal is to first determine where and how Programmable Logic (PL) is used within NASA and document the current methods of assurance. Once that is known, raise awareness of the PL software aspects within the NASA engineering community and provide guidance for the use and assurance of PL form a software perspective.
Inference System Integration Via Logic Morphisms
NASA Technical Reports Server (NTRS)
Bjorner, Nikolaj S.; Espinosa, David
2000-01-01
This is a final report on the accomplishments during the period of the NASA grant. The work on inference servers accomplished the integration of the SLANG logic (Specware's default specification logic) with a number of inference servers in order to make their complementary strengths available. These inverence servers are (1) SNARK. (2) Gandalf, Setheo, and Spass, (3) the Prototype Verification System (PVS) from SRI. (4) HOL98. We designed and implemented MetaSlang, an ML-like language, which we are using to specify and implement all our logic morphisms.
NASA Astrophysics Data System (ADS)
Kapit, Eliot
Superconducting qubits are among the most promising platforms for building a quantum computer. However, individual qubit coherence times are not far past the scalability threshold for quantum error correction, meaning that millions of physical devices would be required to construct a useful quantum computer. Consequently, further increases in coherence time are very desirable. In this letter, we blueprint a simple circuit consisting of two transmon qubits and two additional lossy qubits or resonators, which is passively protected against all single qubit quantum error channels through a combination of continuous driving and engineered dissipation. Photon losses are rapidly corrected through two-photon drive fields implemented with driven SQUID couplings, and dephasing from random potential fluctuations is heavily suppressed by the drive fields used to implement the multi-qubit Hamiltonian. Comparing our theoretical model to published noise estimates from recent experiments on flux and transmon qubits, we find that logical state coherence could be improved by a factor of forty or more compared to the individual qubit T1 and T2 using this technique.
Closed terminologies in description logics
Weida, R.A. |
1996-12-31
We introduce a predictive concept recognition methodology for description logics based on a new closed terminology assumption. During knowledge engineering, our system adopts the standard open terminology assumption as it automatically classifies concept descriptions into a taxonomy via subsumption inferences. However, for applications like configuration, the terminology becomes fixed during problem solving. Then, closed terminology reasoning is more appropriate. In our interactive configuration application, a user incrementally specifies an individual computer system in collaboration with a configuration engine. Choices can be made in any order and at any level of abstraction. We distinguish between abstract and concrete concepts to formally define when an individual`s description may be considered finished. We also take advantage of the closed terminology assumption, together with the terminology`s subsumption-based organization, to efficiently track the types of systems and components consistent with current choices, infer additional constraints on current choices, and appropriately guide future choices. Thus, we can help focus the efforts of both user and configuration engine.
Earthquake Archaeology: a logical approach?
NASA Astrophysics Data System (ADS)
Stewart, I. S.; Buck, V. A.
2001-12-01
Ancient earthquakes can leave their mark in the mythical and literary accounts of ancient peoples, the stratigraphy of their site histories, and the structural integrity of their constructions. Within this broad cross-disciplinary tramping ground, earthquake geologists have tended to focus on those aspects of the cultural record that are most familiar to them; the physical effects of seismic deformation on ancient constructions. One of the core difficulties with this 'earthquake archaeology' approach is that recent attempts to isolate structural criteria that are diagnostic or strongly suggestive of a seismic origin are undermined by the recognition that signs of ancient seismicity are generally indistinguishable from non-seismic mechanisms (poor construction, adverse geotechnical conditions). We illustrate the difficulties and inconsistencies in current proposed 'earthquake diagnostic' schemes by reference to two case studies of archaeoseismic damage in central Greece. The first concerns fallen columns at various Classical temple localities in mainland Greece (Nemea, Sounio, Olympia, Bassai) which, on the basis of observed structural criteria, are earthquake-induced but which are alternatively explained by archaeologists as the action of human disturbance. The second re-examines the almost type example of the Kyparissi site in the Atalanti region as a Classical stoa offset across a seismic surface fault, arguing instead for its deformation by ground instability. Finally, in highlighting the inherent ambiguity of archaeoseismic data, we consider the value of a logic-tree approach for quantifying and quantifying our uncertainities for seismic-hazard analysis.
Logical gates in actin monomer.
Adamatzky, Andrew
2017-09-18
We evaluate information processing capacity of a single actin molecule by calculating distributions of logical gates implemented by the molecule via propagating patterns of excitation. We represent a filamentous actin molecule as an excitable automaton network (F-actin automaton). where every atom updates its state depending on states of atoms its connected to with chemical bonds (hard neighbours) and atoms being in physical proximity to the atom (soft neighbours). A resting atom excites if a sum of its excited hard neighbours and a weighted sum of its soft neighbours belong to some specified interval. We demonstrate that F-actin automata implement OR, AND, XOR and AND-NOT gates via interacting patterns of excitation. Gate AND is the most common gate and gate XOR is the rarest. Using the architectures of gates discovered we implement one bit half-adder and controlled-not circuits in the F-actin automata. Speed and space values of the F-actin molecular computers are discussed.
The Logic of Reflection: Samuel Taylor Coleridge's "treatise on Logic"
NASA Astrophysics Data System (ADS)
Land, Janet Sanders
Though others discuss Coleridge's interest in science, light imagery, the phenomenon of reflection, and his references to Newton and Opticks,^1 this is the first study to examine Coleridge's art in terms of optics, its developing theories, and the nature-of-light debate. This study examines Coleridge's early predilection for visions, illusions, and the supernatural and demonstrates that he gradually shifts from the supernatural to the scientific aspects of "visions" and "illusions," concentrating on causes of illusions and the effects of their deceptive qualities rather than their mystical features. By the 1820's, his preoccupation with illusions had become an interest in optics, fueled, no doubt, by the increasing controversy of the nature-of-light debate and the number of advances in optics resulting from the efforts of its opponents to prove their theories. Tracing the development of the debate, its escalation in the early nineteenth century, and the formation of Coleridge's opinion concerning key issues of the debate, I outline the evolution of Coleridge's theory of reflection and examine the exposition of that theory in his treatise, Logic (1981). Finally, I analyze the relationship between the advances in optics and Coleridge's concepts of thought and knowledge and his notion of the mind as an instrument of knowledge. These ideas in turn, altered his opinions concerning the validity of knowledge resulting from philosophic debate, scientific experiment, and poetic exploration. ftn^1John Beer, "Coleridge and Wordsworth on Reflection," The Wordsworth Circle 20 (1989): 20-29; Coleridge the Visionary. London: Chatto and Windus, 1959; and Coleridge's Poetic Intelligence. London: Macmillan, 1977 and M. H. Abrams Natural Supernaturalism: Tradition and Revolution in Romantic Literature. New York: Norton, 1971; and "Coleridge's 'A Light in Sound': Science, Metascience, and Poetic Imagination." The Correspondent Breeze: Essays on English Romanticism. Eds. M. H. Abrams
Mathematics Education Computer Software and Mathematics Teachers.
ERIC Educational Resources Information Center
Ozgun-Koca, S. Asli
2000-01-01
Presents results from a study that uses questionnaires to ask mathematics teachers' (N=64) opinions about mathematics education computer software. Indicates that respondents overwhelmingly favored discovery and remediation as the purpose of using software in mathematics classrooms. Teachers believed that real world situations and multiple…
Mathematical Story: A Metaphor for Mathematics Curriculum
ERIC Educational Resources Information Center
Dietiker, Leslie
2015-01-01
This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…
Mathematical Modelling Approach in Mathematics Education
ERIC Educational Resources Information Center
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Discrete Mathematics and the Secondary Mathematics Curriculum.
ERIC Educational Resources Information Center
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Gate-Controlled BP-WSe2 Heterojunction Diode for Logic Rectifiers and Logic Optoelectronics.
Li, Dong; Wang, Biao; Chen, Mingyuan; Zhou, Jun; Zhang, Zengxing
2017-06-01
p-n junctions play an important role in modern semiconductor electronics and optoelectronics, and field-effect transistors are often used for logic circuits. Here, gate-controlled logic rectifiers and logic optoelectronic devices based on stacked black phosphorus (BP) and tungsten diselenide (WSe2 ) heterojunctions are reported. The gate-tunable ambipolar charge carriers in BP and WSe2 enable a flexible, dynamic, and wide modulation on the heterojunctions as isotype (p-p and n-n) and anisotype (p-n) diodes, which exhibit disparate rectifying and photovoltaic properties. Based on such characteristics, it is demonstrated that BP-WSe2 heterojunction diodes can be developed for high-performance logic rectifiers and logic optoelectronic devices. Logic optoelectronic devices can convert a light signal to an electric one by applied gate voltages. This work should be helpful to expand the applications of 2D crystals. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Wei, Hua; Hu, Bo; Tang, Suming; Zhao, Guojie; Guan, Yifu
2016-01-01
Small molecule metabolites and their allosterically regulated repressors play an important role in many gene expression and metabolic disorder processes. These natural sensors, though valuable as good logic switches, have rarely been employed without transcription machinery in cells. Here, two pairs of repressors, which function in opposite ways, were cloned, purified and used to control DNA replication in rolling circle amplification (RCA) in vitro. By using metabolites and repressors as inputs, RCA signals as outputs, four basic logic modules were constructed successfully. To achieve various logic computations based on these basic modules, we designed series and parallel strategies of circular templates, which can further assemble these repressor modules in an RCA platform to realize twelve two-input Boolean logic gates and a three-input logic gate. The RCA-output and RCA-assembled platform was proved to be easy and flexible for complex logic processes and might have application potential in molecular computing and synthetic biology. PMID:27869177
Detection of Floating Inputs in Logic Circuits
NASA Technical Reports Server (NTRS)
Cash, B.; Thornton, M. G.
1984-01-01
Simple modification of oscilloscope probe allows easy detection of floating inputs or tristate outputs in digital-IC's. Oscilloscope probe easily modified with 1/4 W resistor and switch for detecting floating inputs in CMOS logic circuits.
Understanding of Logical Connectives in History.
ERIC Educational Resources Information Center
Wishart, Elizabeth; Smith, J. Lea
1983-01-01
Uses data from high ability students in two comprehensive schools in Britain to show that the use of logical connectives in history texts can be a stumbling block to comprehension. Compares these findings to those generated in Australia. (FL)
Procedural and Logic Programming: A Comparison.
ERIC Educational Resources Information Center
Watkins, Will; And Others
1988-01-01
Examines the similarities and fundamental differences between procedural programing and logic programing by comparing LogoWriter and PROLOG. Suggests that PROLOG may be a good first programing language for students to learn. (MVL)
Queuing register uses fluid logic elements
NASA Technical Reports Server (NTRS)
1966-01-01
Queuing register /a multistage bit-shifting device/ uses a series of pure fluid elements to perform the required logic operations. The register has several stages of three-state pure fluid elements combined with two-input NOR gates.
Control loop noise rejection using fuzzy logic.
Hay, Glen; Svrcek, William; Ross, Timothy; Young, Brent
2005-10-01
This paper describes an application of fuzzy logic to noise rejection in a control loop. This new use of fuzzy logic solves the problem of sluggish control loop response when using a set-point range to stop constant valve chattering due to noise in the output signal being sent to a control valve. Multiple related variables and a general understanding of their inter-relationship must be available for this method to be successfully applied. An overview of the specific fuzzy logic method used for this application is presented along with guidelines for the practical application. In addition, this paper includes results from the successful implementation of fuzzy logic to a control loop on a pilot plant distillation column.
Implementing neural nets with programmable logic
NASA Technical Reports Server (NTRS)
Vidal, Jacques J.
1988-01-01
Networks of Boolean programmable logic modules are presented as one purely digital class of artificial neural nets. The approach contrasts with the continuous analog framework usually suggested. Programmable logic networks are capable of handling many neural-net applications. They avoid some of the limitations of threshold logic networks and present distinct opportunities. The network nodes are called dynamically programmable logic modules. They can be implemented with digitally controlled demultiplexers. Each node performs a Boolean function of its inputs which can be dynamically assigned. The overall network is therefore a combinational circuit and its outputs are Boolean global functions of the network's input variables. The approach offers definite advantages for VLSI implementation, namely, a regular architecture with limited connectivity, simplicity of the control machinery, natural modularity, and the support of a mature technology.
Nursing and fuzzy logic: an integrative review.
Jensen, Rodrigo; Lopes, Maria Helena Baena de Moraes
2011-01-01
This study conducted an integrative review investigating how fuzzy logic has been used in research with the participation of nurses. The article search was carried out in the CINAHL, EMBASE, SCOPUS, PubMed and Medline databases, with no limitation on time of publication. Articles written in Portuguese, English and Spanish with themes related to nursing and fuzzy logic with the authorship or participation of nurses were included. The final sample included 21 articles from eight countries. For the purpose of analysis, the articles were distributed into categories: theory, method and model. In nursing, fuzzy logic has significantly contributed to the understanding of subjects related to: imprecision or the need of an expert; as a research method; and in the development of models or decision support systems and hard technologies. The use of fuzzy logic in nursing has shown great potential and represents a vast field for research.
Using interval logic for order assembly
Cui, Z.
1994-12-31
Temporal logic, in particular, interval logic has been used to represent genome maps and to assist genome map constructions. However, interval logic itself appears to be limited in its expressive power because genome mapping requires various information such as partial order, distance and local orientation. In this paper, we first propose an integrated formalism based on a spatial-temporal logic where the concepts of metric information, local orientation and uncertainty are merged. Then, we present and discuss a deductive and object-oriented data model based on this formalism for a genetic deductive database, and the inference rules required. The formalism supports the maintenance of coarser knowledge of unordered, partially ordered and completely ordered genetic data in a relational hierarchy. We believe that this integrated formalism also provides a formal basis for designing a declarative query language.
Purification of Logic-Qubit Entanglement
Zhou, Lan; Sheng, Yu-Bo
2016-01-01
Recently, the logic-qubit entanglement shows its potential application in future quantum communication and quantum network. However, the entanglement will suffer from the noise and decoherence. In this paper, we will investigate the first entanglement purification protocol for logic-qubit entanglement. We show that both the bit-flip error and phase-flip error in logic-qubit entanglement can be well purified. Moreover, the bit-flip error in physical-qubit entanglement can be completely corrected. The phase-flip in physical-qubit entanglement error equals to the bit-flip error in logic-qubit entanglement, which can also be purified. This entanglement purification protocol may provide some potential applications in future quantum communication and quantum network. PMID:27377165
Detection of Floating Inputs in Logic Circuits
NASA Technical Reports Server (NTRS)
Cash, B.; Thornton, M. G.
1984-01-01
Simple modification of oscilloscope probe allows easy detection of floating inputs or tristate outputs in digital-IC's. Oscilloscope probe easily modified with 1/4 W resistor and switch for detecting floating inputs in CMOS logic circuits.
Implementing neural nets with programmable logic
NASA Technical Reports Server (NTRS)
Vidal, Jacques J.
1988-01-01
Networks of Boolean programmable logic modules are presented as one purely digital class of artificial neural nets. The approach contrasts with the continuous analog framework usually suggested. Programmable logic networks are capable of handling many neural-net applications. They avoid some of the limitations of threshold logic networks and present distinct opportunities. The network nodes are called dynamically programmable logic modules. They can be implemented with digitally controlled demultiplexers. Each node performs a Boolean function of its inputs which can be dynamically assigned. The overall network is therefore a combinational circuit and its outputs are Boolean global functions of the network's input variables. The approach offers definite advantages for VLSI implementation, namely, a regular architecture with limited connectivity, simplicity of the control machinery, natural modularity, and the support of a mature technology.
Novel Design for Reversible Arithmetic Logic Unit
NASA Astrophysics Data System (ADS)
Zhou, Rigui; Li, Yancheng; Zhang, Manqun; Hu, BenQiong
2015-02-01
Reversible logic circuits are of high interests to calculate with minimum energy consumption having applications in low-power CMOS design, optical computing and nanotechnology, especially in quantum computer. Quantum computer requires quantum arithmetic. A new design of a reversible arithmetic logic unit (reversible ALU) for quantum arithmetic has been proposed in this article. As we known, ALU is an important part of central processing unit (CPU) as the execution unit. So this article provides explicit construction of reversible ALU effecting basic arithmetic operations. By provided the corresponding control unit, the proposed reversible ALU can combine the classical arithmetic and logic operation in a reversible integrated system. This article provides a new more powerful ALU which contains more functions and it will make contribute to the realization of reversible Programmable Logic Device (RPLD) in future using reversible ALU.
Procedural and Logic Programming: A Comparison.
ERIC Educational Resources Information Center
Watkins, Will; And Others
1988-01-01
Examines the similarities and fundamental differences between procedural programing and logic programing by comparing LogoWriter and PROLOG. Suggests that PROLOG may be a good first programing language for students to learn. (MVL)
Hierarchical structure of the logical Internet graph
NASA Astrophysics Data System (ADS)
Ge, Zihui; Figueiredo, Daniel R.; Jaiswal, Sharad; Gao, Lixin
2001-07-01
The study of the Internet topology has recently received much attention from the research community. In particular, the observation that the network graph has interesting properties, such as power laws, that might be explored in a myriad of ways. Most of the work in characterizing the Internet graph is based on the physical network graph, i.e., the connectivity graph. In this paper we investigate how logical relationships between nodes of the AS graph can be used to gain insight to its structure. We characterize the logical graph using various metrics and identify the presence of power laws in the number of customers that a provider has. Using these logical relationships we define a structural model of the AS graph. The model highlights the hierarchical nature of logical relationships and the preferential connection to larger providers. We also investigate the consistency of this model over time and observe interesting properties of the hierarchical structure.
Acerbi, Alberto; Ghirlanda, Stefano; Enquist, Magnus
2012-01-01
Many cultural traits exhibit volatile dynamics, commonly dubbed fashions or fads. Here we show that realistic fashion-like dynamics emerge spontaneously if individuals can copy others' preferences for cultural traits as well as traits themselves. We demonstrate this dynamics in simple mathematical models of the diffusion, and subsequent abandonment, of a single cultural trait which individuals may or may not prefer. We then simulate the coevolution between many cultural traits and the associated preferences, reproducing power-law frequency distributions of cultural traits (most traits are adopted by few individuals for a short time, and very few by many for a long time), as well as correlations between the rate of increase and the rate of decrease of traits (traits that increase rapidly in popularity are also abandoned quickly and vice versa). We also establish that alternative theories, that fashions result from individuals signaling their social status, or from individuals randomly copying each other, do not satisfactorily reproduce these empirical observations.
The development of a digital logic concept inventory
NASA Astrophysics Data System (ADS)
Herman, Geoffrey Lindsay
Instructors in electrical and computer engineering and in computer science have developed innovative methods to teach digital logic circuits. These methods attempt to increase student learning, satisfaction, and retention. Although there are readily accessible and accepted means for measuring satisfaction and retention, there are no widely accepted means for assessing student learning. Rigorous assessment of learning is elusive because differences in topic coverage, curriculum and course goals, and exam content prevent direct comparison of two teaching methods when using tools such as final exam scores or course grades. Because of these difficulties, computing educators have issued a general call for the adoption of assessment tools to critically evaluate and compare the various teaching methods. Science, Technology, Engineering, and Mathematics (STEM) education researchers commonly measure students' conceptual learning to compare how much different pedagogies improve learning. Conceptual knowledge is often preferred because all engineering courses should teach a fundamental set of concepts even if they emphasize design or analysis to different degrees. Increasing conceptual learning is also important, because students who can organize facts and ideas within a consistent conceptual framework are able to learn new information quickly and can apply what they know in new situations. If instructors can accurately assess their students' conceptual knowledge, they can target instructional interventions to remedy common problems. To properly assess conceptual learning, several researchers have developed concept inventories (CIs) for core subjects in engineering sciences. CIs are multiple-choice assessment tools that evaluate how well a student's conceptual framework matches the accepted conceptual framework of a discipline or common faulty conceptual frameworks. We present how we created and evaluated the digital logic concept inventory (DLCI).We used a Delphi process to
Application of Fuzzy Logic to Matrix FMECA
NASA Astrophysics Data System (ADS)
Shankar, N. Ravi; Prabhu, B. S.
2001-04-01
A methodology combining the benefits of Fuzzy Logic and Matrix FMEA is presented in this paper. The presented methodology extends the risk prioritization beyond the conventional Risk Priority Number (RPN) method. Fuzzy logic is used to calculate the criticality rank. Also the matrix approach is improved further to develop a pictorial representation retaining all relevant qualitative and quantitative information of several FMEA elements relationships. The methodology presented is demonstrated by application to an illustrative example.
Reconfigurable Optical Directed-Logic Circuits
2015-11-20
routing-table lookup. 2. Integrated Photonics for Directed-Logic Circuits As a proof-of-concept demonstration we developed a 2×2-arrayed directed...improved electro-optic directed-logic circuit with increased operational speed by using integrated optical switches based on the carrier depletion effect... circuit . In this project, we will develop a new cellular DL architecture based on large-scale integrated silicon photonic circuits . The circuit is
Firmware Modification Analysis in Programmable Logic Controllers
2014-03-27
MODIFICATION ANALYSIS IN PROGRAMMABLE LOGIC CONTROLLERS Arturo M. Garcia Jr., B.S.S.E.C.A. Captain, USA Approved: //signed// Robert F. Mills , PhD...Matthew 5:37 v Acknowledgments My sincere gratitude to my committee for their guidance and teamwork which made this thesis possible. Dr. Mills ...2012. 2012. [5] Bolton, William. Programmable logic controllers. Newnes, 2009. [6] Boyer, Stuart . SCADA: Supervisory Control and Data Aquisition 4th
Can fuzzy logic make things more clear?
Hazelzet, Jan A
2009-01-01
Intensive care is a complex environment involving many signals, data and observations. Clinical decision support and artificial intelligence using fuzzy logic and closed loop techniques are methods that might help us to handle this complexity in a safe, effective and efficient way. Merouani and colleagues have performed a study using fuzzy logic and closed loop techniques to more effectively wean patients with sepsis from norepinephrine infusion.
Does logic moderate the fundamental attribution error?
Stalder, D R
2000-06-01
The fundamental attribution error was investigated from an individual difference perspective. Mathematicians were compared with nonmathematicians (Exp. 1; n: 84), and undergraduates who scored high on a test of logical reasoning ability were compared with those who scored low (Exp. 2; n: 62). The mathematicians and those participants scoring higher on logic appeared less prone to the fundamental attribution error, primarily using a measure of confidence in attributions.
Pattern recognition using linguistic fuzzy logic predictors
NASA Astrophysics Data System (ADS)
Habiballa, Hashim
2016-06-01
The problem of pattern recognition has been solved with numerous methods in the Artificial Intelligence field. We present an unconventional method based on Lingustic Fuzzy Logic Forecaster which is primarily used for the task of time series analysis and prediction through logical deduction wtih linguistic variables. This method should be used not only to the time series prediction itself, but also for recognition of patterns in a signal with seasonal component.
ERIC Educational Resources Information Center
Cupani, Marcos; de Minzi, Maria Cristina Richaud; Perez, Edgardo Raul; Pautassi, Ricardo Marcos
2010-01-01
This study tested a set of hypotheses derived from the model of academic achievement in mathematics of the Social Cognitive Career Theory in a sample of Argentinean middle school students. To this aim, 277 students (male and female; age: 13-15 years) were assessed using the following instruments: logical-mathematical self-efficacy scale,…
ERIC Educational Resources Information Center
Cupani, Marcos; de Minzi, Maria Cristina Richaud; Perez, Edgardo Raul; Pautassi, Ricardo Marcos
2010-01-01
This study tested a set of hypotheses derived from the model of academic achievement in mathematics of the Social Cognitive Career Theory in a sample of Argentinean middle school students. To this aim, 277 students (male and female; age: 13-15 years) were assessed using the following instruments: logical-mathematical self-efficacy scale,…
Convection automated logic oven control
Boyer, M.A.; Eke, K.I.
1998-03-01
For the past few years, there has been a greater push to bring more automation to the cooling process. There have been attempts at automated cooking using a wide range of sensors and procedures, but with limited success. The authors have the answer to the automated cooking process; this patented technology is called Convection AutoLogic (CAL). The beauty of the technology is that it requires no extra hardware for the existing oven system. They use the existing temperature probe, whether it is an RTD, thermocouple, or thermistor. This means that the manufacturer does not have to be burdened with extra costs associated with automated cooking in comparison to standard ovens. The only change to the oven is the program in the central processing unit (CPU) on the board. As for its operation, when the user places the food into the oven, he or she is required to select a category (e.g., beef, poultry, or casseroles) and then simply press the start button. The CAL program then begins its cooking program. It first looks at the ambient oven temperature to see if it is a cold, warm, or hot start. CAL stores this data and then begins to look at the food`s thermal footprint. After CAL has properly detected this thermal footprint, it can calculate the time and temperature at which the food needs to be cooked. CAL then sets up these factors for the cooking stage of the program and, when the food has finished cooking, the oven is turned off automatically. The total time for this entire process is the same as the standard cooking time the user would normally set. The CAL program can also compensate for varying line voltages and detect when the oven door is opened. With all of these varying factors being monitored, CAL can produce a perfectly cooked item with minimal user input.
Noise-based logic: Binary, multi-valued, or fuzzy, with optional superposition of logic states
NASA Astrophysics Data System (ADS)
Kish, Laszlo B.
2009-03-01
A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises. The orthogonality of these processes provides a natural way to construct binary or multi-valued logic circuitry with arbitrary number N of logic values by using analog circuitry. Moreover, the logic values on a single wire can be made a (weighted) superposition of the N distinct logic values. Fuzzy logic is also naturally represented by a two-component superposition within the binary case ( N=2). Error propagation and accumulation are suppressed. Other relevant advantages are reduced energy dissipation and leakage current problems, and robustness against circuit noise and background noises such as 1/f, Johnson, shot and crosstalk noise. Variability problems are also non-existent because the logic value is an AC signal. A similar logic system can be built with orthogonal sinusoidal signals (different frequency or orthogonal phase) however that has an extra 1/N type slowdown compared to the noise-based logic system with increasing number of N furthermore it is less robust against time delay effects than the noise-based counterpart.
Interpreting Abstract Interpretations in Membership Equational Logic
NASA Technical Reports Server (NTRS)
Fischer, Bernd; Rosu, Grigore
2001-01-01
We present a logical framework in which abstract interpretations can be naturally specified and then verified. Our approach is based on membership equational logic which extends equational logics by membership axioms, asserting that a term has a certain sort. We represent an abstract interpretation as a membership equational logic specification, usually as an overloaded order-sorted signature with membership axioms. It turns out that, for any term, its least sort over this specification corresponds to its most concrete abstract value. Maude implements membership equational logic and provides mechanisms to calculate the least sort of a term efficiently. We first show how Maude can be used to get prototyping of abstract interpretations "for free." Building on the meta-logic facilities of Maude, we further develop a tool that automatically checks and abstract interpretation against a set of user-defined properties. This can be used to select an appropriate abstract interpretation, to characterize the specified loss of information during abstraction, and to compare different abstractions with each other.
Synchronous universal droplet logic and control
NASA Astrophysics Data System (ADS)
Katsikis, Georgios; Cybulski, James S.; Prakash, Manu
2015-07-01
Droplets are versatile digital materials; they can be produced at high throughput, perform chemical reactions as miniature beakers and carry biological entities. Droplets have been manipulated with electric, optical, acoustic and magnetic forces, but all these methods use serial controls to address individual droplets. An alternative is algorithmic manipulation based on logic operations that automatically compute where droplets are stored or directed, thereby enabling parallel control. However, logic previously implemented in low-Reynolds-number droplet hydrodynamics is asynchronous and thus prone to errors that prevent scaling up the complexity of logic operations. Here we present a platform for error-free physical computation via synchronous universal logic. Our platform uses a rotating magnetic field that enables parallel manipulation of arbitrary numbers of ferrofluid droplets on permalloy tracks. Through the coupling of magnetic and hydrodynamic interaction forces between droplets, we developed AND, OR, XOR, NOT and NAND logic gates, fanouts, a full adder, a flip-flop and a finite-state machine. Our platform enables large-scale integration of droplet logic, analogous to the scaling seen in digital electronics, and opens new avenues in mesoscale material processing.
Nonmonotonic Logic for Use in Information Retrieval: An Exploratory Paper.
ERIC Educational Resources Information Center
Hurt, C. D.
1998-01-01
Monotonic logic requires reexamination of the entire logic string when there is a contradiction. Nonmonotonic logic allows the user to withdraw conclusions in the face of contradiction without harm to the logic string, which has considerable application to the field of information searching. Artificial intelligence models and neural networks based…
The Temporal Logic of the Tower Chief System
NASA Technical Reports Server (NTRS)
Hazelton, Lyman R., Jr.
1990-01-01
The purpose is to describe the logic used in the reasoning scheme employed in the Tower Chief system, a runway configuration management system. First, a review of classical logic is given. Defensible logics, truth maintenance, default logic, temporally dependent propositions, and resource allocation and planning are discussed.
On symbolic models for Single-Conclusion Logic of Proofs
Krupski, Vladimir N
2011-05-31
In this paper we define symbolic models for Single-Conclusion Logics of Proofs. We prove the soundness and completeness of these logics with respect to the corresponding classes of symbolic models. We apply the semantic methods developed in this paper to justify the use of terms of single-conclusion logic of proofs as notation for derivations in this logic. Bibliography: 17 titles.
Nonmonotonic Logic for Use in Information Retrieval: An Exploratory Paper.
ERIC Educational Resources Information Center
Hurt, C. D.
1998-01-01
Monotonic logic requires reexamination of the entire logic string when there is a contradiction. Nonmonotonic logic allows the user to withdraw conclusions in the face of contradiction without harm to the logic string, which has considerable application to the field of information searching. Artificial intelligence models and neural networks based…
Problems with Fallibilism as a Philosophy of Mathematics Education
NASA Astrophysics Data System (ADS)
Rowlands, Stuart; Graham, Ted; Berry, John
2011-07-01
Much reference has been made to Paul Ernest's `philosophy of mathematics education' to legitimise a strong fallibilist trend in mathematics education. This article presents the argument that: (1) This philosophy makes unwarranted assumptions that have been taken as `given'. For example, that `absolutist' or `Platonist' views of mathematics necessarily imply the transmission model of teaching mathematics. (2) The very basis of this philosophy contains a contradiction: that mathematics cannot be separated from its social origins, yet mathematics has a logical necessity that is independent of its origin. (3) This philosophy downplays mathematics as a formal, academic system of knowledge in the attempt to promote a child-centred pedagogy or the mathematics of social practices. (4) Ernest's attempt to semiotically reduce proof to calculation is flawed. This article explores what is meant by fallibilism in relation to the views of many educationalists who appear not to like mathematics as a formal, academic body of knowledge and draws out the educational implications of these views.
NASA Astrophysics Data System (ADS)
Tegmark, Max
2014-02-01
The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.
ERIC Educational Resources Information Center
Lo, Jane-Jane; And Others
Calls for increased student involvement in mathematics classroom learning situations are due primarily to the recognition that a traditional lecture/demonstration format within school mathematics instruction is not effective in fostering and promoting students' problem-solving abilities, mathematical reasoning power, and mathematical communication…
Students as Mathematics Consultants
ERIC Educational Resources Information Center
Jensen, Jennifer L.
2013-01-01
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
Mathematics Lessons without ...
ERIC Educational Resources Information Center
Cross, Kath; Hibbs, John
2006-01-01
In the Association of Teachers of Mathematics (ATM) Easter conference, 2006, the authors presented a list of important aspects of mathematics lessons, recommended for students to have a positive attitude to mathematics and for teachers to acquire effective teaching. The following are discussed in detail: (1) Mathematics lessons without good…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…