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…
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.
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)
[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…
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.
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…
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
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)
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…
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.
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)
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
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,…
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
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
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…
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
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…
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.
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
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
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…
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 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.
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.
1989-01-01
and Func- tional Programming. Pitman, London, 1986. [14] Valeria C.V. de Paiva. The Dialectica Categories. PhD thesis, Mathematics Department...Columbia University. [461 F.W. Lawvere. Adjointness in foundations. Dialectica , 23(3/4):281-296, 1969. [471 Saunders MacLane. Categories for 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…
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…
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.
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…
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.
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.
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.
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.
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
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…
Okamoto, Akimitsu; Tanaka, Kazuo; Saito, Isao
2004-08-04
A conceptually new logic gate based on DNA has been devised. Methoxybenzodeazaadenine ((MD)A), an artificial nucleobase which we recently developed for efficient hole transport through DNA, formed stable base pairs with T and C. However, a reasonable hole-transport efficiency was observed in the reaction for the duplex containing an (MD)A/T base pair, whereas the hole transport was strongly suppressed in the reaction using a duplex where the base opposite (MD)A was replaced by C. The influence of complementary pyrimidines on the efficiency of hole transport through (MD)A was quite contrary to the selectivity observed for hole transport through G. The orthogonality of the modulation of these hole-transport properties by complementary pyrimidine bases is promising for the design of a new molecular logic gate. The logic gate system was executed by hole transport through short DNA duplexes, which consisted of the "logic gate strand", containing hole-transporting nucleobases, and the "input strand", containing pyrimidines which modulate the hole-transport efficiency of logic bases. A logic gate strand containing multiple (MD)A bases in series provided the basis for a sharp AND logic action. On the other hand, for OR logic and combinational logic, conversion of Boolean expressions to standard sum-of-product (SOP) expressions was indispensable. Three logic gate strands were designed for OR logic according to each product term in the standard SOP expression of OR logic. The hole-transport efficiency observed for the mixed sample of logic gate strands exhibited an OR logic behavior. This approach is generally applicable to the design of other complicated combinational logic circuits such as the full-adder.
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.
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.
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
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.
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…
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.
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.
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'].
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…
ERIC Educational Resources Information Center
Osborne, Alan R.
1973-01-01
This article reports one search for factors or conditions shaping the child's growth in logical ability. The search indicated the existence of a relationship between the quantity of teacher talk that contains the language of logic and the change exhibited by students. Implications for classroom practice are discussed. (JA)
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)
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.
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.
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
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…
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.
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
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.
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.)
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…
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
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…
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.
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.
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.
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.
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.
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.
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.
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…
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.
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…
Conceptual Modeling via Logic Programming
1990-01-01
31 2.7 Approaches Other Than Logic Programming ............................. 33 2.7.1 L isp...Development Environment Needs ................................ 84 5.1.4 Alternative Logic Programming Implementation Approaches ......... 85 5.1.5 User... APPROACH and logic programming techniques. Section 2 The CMLP project consisted of three describes the task outputs. interrelated investi ations: 3
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…
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.
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.
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.
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…
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.
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…
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.
Substructural Logical Specifications
2012-11-14
a more natural correspondence with our physical intuitions about consumable resources. Linear conjunction A ⊗ B (“A tensor B”) represents the...sketch a radically different, vaguely Feynman - diagram-inspired, way of presenting traces in Figure 4.14. Resources are the edges in the DAG and steps or...70th Birthday, volume 17 of Studies in Logic. College Publications, 2008. 3.3.3, 4.1.2, 4.7.3 [Pfe12a] Frank Pfenning. Lecture notes on backtracking
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.
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.
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.
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.
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.
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.
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
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
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…
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.
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,…
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.
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)
... 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 ...
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.
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.
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.
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…
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.
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…
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.
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)
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.
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.
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.
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…
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)…
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…
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.
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…
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…
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.
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…
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.
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.
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.
Logic, Probability, and Human Reasoning
2015-01-01
logics developed in artificial intelligence, which allow conclusions to be withdrawn [38–42]. Second, conditional assertions (e.g., ‘If she insulted him...N. (2014) Probabilistic single function dual process theory and logic programming as approaches to non- monotonicity in human vs artificial reasoning...How can we solve this crisis? Leibniz dreamed of a calculus that settles any argument. Can cognitive scientists devise such a system? Feature
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.
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.
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.
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.
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.
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
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
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
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
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
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…
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.
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.
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.
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.
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.
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.
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.
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.
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.
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)
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…
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…
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…
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.
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
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…
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…
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…
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.…
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.
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
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…
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 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.
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.
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.
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.
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.
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.
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,…
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.
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.
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)
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.
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.
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.
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.
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…
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…
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.
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.
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…
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.
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.
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.
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.
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.
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
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.
[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.
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
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…
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…
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…
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,…
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…
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.
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 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.
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;…
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…
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…
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…
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…
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.
[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.
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.
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).
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…
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;…
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.
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
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
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
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…
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.
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.
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…
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…
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.
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
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.
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.
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.
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.
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…
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…
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…
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.
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.
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
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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)
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.
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.
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.
Fault Analysis-based Logic Encryption (Preprint)
2013-11-01
work on logic encryption. Section 8 concludes the paper . 2. METRIC FOR LOGIC ENCRYPTION The defender (designer) has to prevent his IP from being...publication of this paper . This material is based on work fund- ed by AFRL under contract No. FA8750-11-2-0274. Received and cleared for public release by...USENIX Se- curity, pp. 291-306, 2007. [4] Defense Science Board (DSB) study on High Performance Microchip Supply. [Online]. http://www.aoq.osd.mil
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
Simplified Quantum Logic with Trapped Ions
2016-06-23
PHYSICAL REVIEW A ATOMIC , MOLECULAR, AND OPTICAL PHYSICS THIRD SERIES, VOLUME 55, NUMBER 4 APRIL 1997Simplified quantum logic with trapped ions C...Received 17 December 1996! We describe a simplified scheme for quantum logic with a collection of laser-cooled trapped atomic ions. Building on the...in a system of laser-cooled trapped atomic ions. In the simplest form of the ion trap quantum computer, two internal electronic levels of each ion in
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
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
Mumcu, Hayal Yavuz
2016-01-01
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
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…
ERIC Educational Resources Information Center
Ricks, Thomas E.
2010-01-01
Mathematics is motivating; at least, it should be. I argue that mathematical activity is an inherently attractive enterprise for human beings because as intellectual organisms, we are naturally enticed by the intellectual stimulation of mathematizing, and, as social beings, we are drawn to the socializing aspects of mathematical activity. These…
Computer Mathematics: An Introduction.
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.
This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…
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…
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.
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…
Transforming Primary Mathematics
ERIC Educational Resources Information Center
Askew, Mike
2011-01-01
What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in "Transforming Primary Mathematics", a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings…
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.
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.
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.
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.
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…
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.
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. PMID:22412887
Advanced logic gates for ultrafast network interchanges
NASA Astrophysics Data System (ADS)
Islam, Mohammed N.
1995-08-01
By overcoming speed bottlenecks from electronic switching as well as optical/electronic conversions, all-optical logic gates can permit further exploitation of the nearly 40 THz of bandwidth available from optical fibers. We focus on the use of optical solitons and all-optical logic gates to implement ultrafast ``interchanges'' or switching nodes on packet networks with speeds of 100 Gbit/s or greater. For example, all-optical logic gates have been demonstrated with speeds up to 200 Gbit/s, and they may be used to decide whether to add or drop a data packet. The overall goal of our effort is to demonstrate the key enabling technologies and their combination for header processing in 100 Gbit/s, time-division-multiplexed, packed switched networks. Soliton-based fiber logic gates are studied with the goal of combining attractive features of soliton-dragging logic gates, nonlinear loop mirrors, and erbium-doped fiber amplifiers to design logic gates with optimum switching energy, contrast ratio, and timing sensitivity. First, the experimental and numerical work studies low-latency soliton logic gates based on frequency shifts associated with cross-phase modulation. In preliminary experiments, switching in 15 m long low-birefringent fibers has been demonstrated with a contrast ratio of 2.73:1. Using dispersion-shifted fiber in the gate should lower the switching energy and improve the contrast ratio. Next, the low-birefringent fiber can be cross-spliced and wrapped into a nonlinear optical loop mirror to take advantage of mechanisms from both soliton dragging and loop mirrors. The resulting device can have low switching energy and a timing window that results from a combination of soliton dragging and the loop mirror mechanisms.
The logical interpretation and the measurement problem
NASA Astrophysics Data System (ADS)
Vuletic, Mark I.
The measurement problem is one of the two key problems in the foundations of quantum mechanics, carrying with it the seeming implication that instead of the familiar definite states of affairs we think we experience, there typically should exist only phenomenologically ill-defined "superpositions" of such states of affairs. Dissatisfaction with this implication has led to the development of many wildly different interpretations of quantum mechanics, positing everything from pilot waves to splitting universes. A recent tradition of interpretation draws heavily upon decoherence and a "consistent histories" formalism to try to resolve the standard conceptual problems of quantum mechanics. Roland Omnes, one physicist in this tradition, argues that his own "logical interpretation" resolves every paradox and conceptual difficulty raised by quantum mechanics, except for what he calls the "objectification problem." Figuring out what relation the objectification problem has to the measurement problem, and, more generally, what the logical interpretation has to say about the measurement problem, turns out to be very difficult, even with the benefit of correspondence. In my dissertation, I have tried to narrow down the possibilities for what Omnes might have in mind with respect to the measurement problem, and considered whether any of these constitutes an advance over what came before. I conclude that there are two plausible possibilities: either (i) an overly aggressive pragmatic spirit has caused Omnes to fail to even realize that a critical part of the measurement problem exists, or (ii) the logical interpretation is best understood as offering a stochastic hidden factor interpretation, with complementarity operating at the level of the hidden factors, even though Omnes himself would resist describing the logical interpretation in this way. I also conclude that the logical interpretation, far from saving classical logic, actually undermines it. While this may not
Embodiment awareness, mathematics discourse, and the blind.
Quek, Francis; McNeill, David
2006-12-01
Blindness might be described as a biological condition, and thus remedies could be in the realm of biotechnology. However, the convergence of information technology and cognitive science offers great opportunities for understanding and helping blind children as they learn mathematics, the crosscutting discipline most important for all branches of science and engineering. This article outlines our logic and approach for providing blind students with awareness of the embodiment of their teachers to maintain situated communication. First, we shall show that math discourse is inherently spatiotemporal, and that this information is carried by gesticulation in conjunction with speech. Second, we shall explore the capacity of those who are blind for the imagism necessary for mathematics reasoning. Third, we shall advance a set of augmentative devices suggested by our analysis. Finally, we shall outline our ongoing experiments to validate our rationale.
Cognitive algorithms: dynamic logic, working of the mind, evolution of consciousness and cultures
NASA Astrophysics Data System (ADS)
Perlovsky, Leonid I.
2007-04-01
The paper discusses evolution of consciousness driven by the knowledge instinct, a fundamental mechanism of the mind which determines its higher cognitive functions. Dynamic logic mathematically describes the knowledge instinct. It overcomes past mathematical difficulties encountered in modeling intelligence and relates it to mechanisms of concepts, emotions, instincts, consciousness and unconscious. The two main aspects of the knowledge instinct are differentiation and synthesis. Differentiation is driven by dynamic logic and proceeds from vague and unconscious states to more crisp and conscious states, from less knowledge to more knowledge at each hierarchical level of the mind. Synthesis is driven by dynamic logic operating in a hierarchical organization of the mind; it strives to achieve unity and meaning of knowledge: every concept finds its deeper and more general meaning at a higher level. These mechanisms are in complex relationship of symbiosis and opposition, which leads to complex dynamics of evolution of consciousness and cultures. Modeling this dynamics in a population leads to predictions for the evolution of consciousness, and cultures. Cultural predictive models can be compared to experimental data and used for improvement of human conditions. We discuss existing evidence and future research directions.
NASA Technical Reports Server (NTRS)
Burgin, G. H.; Owens, A. J.
1975-01-01
A detailed description is presented of the computer programs in order to provide an understanding of the mathematical and geometrical relationships as implemented in the programs. The individual sbbroutines and their underlying mathematical relationships are described, and the required input data and the output provided by the program are explained. The relationship of the adaptive maneuvering logic program with the program to drive the differential maneuvering simulator is discussed.
NASA Technical Reports Server (NTRS)
Richardson, Albert O.
1997-01-01
This research has investigated the use of fuzzy logic, via the Matlab Fuzzy Logic Tool Box, to design optimized controller systems. The engineering system for which the controller was designed and simulate was the container crane. The fuzzy logic algorithm that was investigated was the 'predictive control' algorithm. The plant dynamics of the container crane is representative of many important systems including robotic arm movements. The container crane that was investigated had a trolley motor and hoist motor. Total distance to be traveled by the trolley was 15 meters. The obstruction height was 5 meters. Crane height was 17.8 meters. Trolley mass was 7500 kilograms. Load mass was 6450 kilograms. Maximum trolley and rope velocities were 1.25 meters per sec. and 0.3 meters per sec., respectively. The fuzzy logic approach allowed the inclusion, in the controller model, of performance indices that are more effectively defined in linguistic terms. These include 'safety' and 'cargo swaying'. Two fuzzy inference systems were implemented using the Matlab simulation package, namely the Mamdani system (which relates fuzzy input variables to fuzzy output variables), and the Sugeno system (which relates fuzzy input variables to crisp output variable). It is found that the Sugeno FIS is better suited to including aspects of those plant dynamics whose mathematical relationships can be determined.
PC based speed control of dc motor using fuzzy logic controller
Mandal, S.K.; Kanphade, R.D.; Lavekar, K.P.
1998-07-01
The dc motor is extensively used as constant speed drive in textile mills, paper mills, printing press, etc.. If the load and supply voltage are time varying, the speed will be changed. Since last few decades the conventional PID controllers are used to maintain the constant speed by controlling the duty ratio of Chopper. Generally, four quadrant chopper is used for regenerative braking and reverse motoring operation. Fuzzy Logic is newly introduced in control system. Fuzzy Control is based on Fuzzy Logic, a logical system which is too much closer in spirit to human thinking and natural language. The Fuzzy Logic Controller (FLC) provides a linguistic control strategy based on knowledge base of the system. Firstly, the machine is started very smoothly from zero to reference speed in the proposed scheme by increasing the duty ratio. Then change and rate of change of speed (dN, dN/dt), change and rate of change input voltage (dV, dV/dt) and load current are input to FLC. The new value of duty ratio is determined from the Fuzzy rule base and defuzzification method. The chopper will be 'ON' according to new duty ratio to maintain the constant speed. The dynamic and steady state performance of the proposed system is better than conventional control system. In this paper mathematical simulation and experimental implementation are carried out to investigate the drive performance.
A computational paradigm for dynamic logic-gates in neuronal activity
Goldental, Amir; Guberman, Shoshana; Vardi, Roni; Kanter, Ido
2014-01-01
In 1943 McCulloch and Pitts suggested that the brain is composed of reliable logic-gates similar to the logic at the core of today's computers. This framework had a limited impact on neuroscience, since neurons exhibit far richer dynamics. Here we propose a new experimentally corroborated paradigm in which the truth tables of the brain's logic-gates are time dependent, i.e., dynamic logic-gates (DLGs). The truth tables of the DLGs depend on the history of their activity and the stimulation frequencies of their input neurons. Our experimental results are based on a procedure where conditioned stimulations were enforced on circuits of neurons embedded within a large-scale network of cortical cells in-vitro. We demonstrate that the underlying biological mechanism is the unavoidable increase of neuronal response latencies to ongoing stimulations, which imposes a non-uniform gradual stretching of network delays. The limited experimental results are confirmed and extended by simulations and theoretical arguments based on identical neurons with a fixed increase of the neuronal response latency per evoked spike. We anticipate our results to lead to better understanding of the suitability of this computational paradigm to account for the brain's functionalities and will require the development of new systematic mathematical methods beyond the methods developed for traditional Boolean algebra. PMID:24808856
Zhou, Ming; Du, Yan; Chen, Chaogui; Li, Bingling; Wen, Dan; Dong, Shaojun; Wang, Erkang
2010-02-24
This communication demonstrates for the first time the controlled power release of biofuel cells (BFCs) by aptamer logic systems processed according to the Boolean logic operations "programmed" into the biocomputing systems. On the basis of the built-in Boolean NAND logic, the fabricated aptamer-based BFCs logically controlled by biochemical signals enabled us to construct self-powered and intelligent logic aptasensors that can determine whether the two specific targets are both present in a sample.
Neurocognitive mechanisms of mathematical giftedness: A literature review.
Zhang, Li; Gan, John Q; Wang, Haixian
2017-01-01
Mathematically gifted children/adolescents have demonstrated exceptional abilities and traits in logical reasoning, mental imagery, and creative thinking. In the field of cognitive neuroscience, the past studies on mathematically gifted brains have concentrated on investigating event-related brain activation regions, cerebral laterality of cognitive functions, functional specialization that is uniquely dedicated for specific cognitive purposes, and functional interactions among discrete brain regions. From structural and functional perspectives, these studies have witnessed both "general" and "unique" neural characteristics of mathematically gifted brains. In this article, the theoretical background, empirical studies, and neurocognitive mechanisms of mathematically gifted children/adolescents are reviewed. Based on the integration of the findings, some potential directions for the future research are identified and discussed.
Discover Mathematical Knowledge through Recreational Mathematics Problems
ERIC Educational Resources Information Center
Sodhi, Amar
2004-01-01
The way in which a mathematical problem was used as a vehicle to introduce the joy of mathematical research to a high school student is demonstrated. The student was interested in learning about other classical problems delighting an eager high school student.
Mathematics Coursework Regulates Growth in Mathematics Achievement
ERIC Educational Resources Information Center
Ma, Xin; Wilkins, Jesse L. M.
2007-01-01
Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…
Mathematics and Sports. Mathematical World. Volume 3.
ERIC Educational Resources Information Center
Sadovskii, L. E.; Sadovskii, A. L.
This volume contains some examples of mathematical applications in sports. Sports discussed include tennis, figure skating, gymnastics, track and field, soccer, skiing, hockey, and swimming. Problems and situations are posed and answers with thorough explanations are provided. Chapters include: (1) Mathematics and Sports; (2) What Is Applied…
Mathematics for Language, Language for Mathematics
ERIC Educational Resources Information Center
Prochazkova, Lenka Tejkalova
2013-01-01
The author discusses the balance and mutual influence of the language of instruction and mathematics in the context of CLIL, Content and Language Integrated Learning. Different aspects of the relationship of language and Mathematics teaching and learning are discussed: the benefits of using a foreign language of instruction, as well as the…
Logic models used to enhance critical thinking.
Ellermann, Caroline R; Kataoka-Yahiro, Merle R; Wong, Lorrie C
2006-06-01
Over time, various methods have been used to stimulate critical thinking in undergraduate nursing students, and although many have been successful in helping students integrate the essential knowledge, experiences, and clinical reasoning that support practice, it is also useful to explore new methods. Faculty at the University of Hawaii at Manoa, School of Nursing and Dental Hygiene have taken an innovative approach of using logic models to further enhance critical thinking. This article presents an application of varying experiences and methods of using logic models to support the development of critical thinking and reasoning skills in nursing students. The processes in which logic models are used in the curriculum are described. The models are used to connect concepts from concrete to abstract levels in diverse and often nonlinear diagrams, guided discourse, and written assignments. The specific instructional methods used include concept mapping, concept papers, conceptual linking, and substruction.
On Logic and Standards for Structuring Documents
NASA Astrophysics Data System (ADS)
Eyers, David M.; Jones, Andrew J. I.; Kimbrough, Steven O.
The advent of XML has been widely seized upon as an opportunity to develop document representation standards that lend themselves to automated processing. This is a welcome development and much good has come of it. That said, present standardization efforts may be criticized on a number of counts. We explore two issues associated with document XML standardization efforts. We label them (i) the dynamic point and (ii) the logical point. Our dynamic point is that in many cases experience has shown that the search for a final, or even reasonably permanent, document representation standard is futile. The case is especially strong for electronic data interchange (EDI). Our logical point is that formalization into symbolic logic is materially helpful for understanding and designing dynamic document standards.
a Logical Account of Quantum Superpositions
NASA Astrophysics Data System (ADS)
Krause, Décio Arenhart, Jonas R. Becker
In this paper we consider the phenomenon of superpositions in quantum mechanics and suggest a way to deal with the idea in a logical setting from a syntactical point of view, that is, as subsumed in the language of the formalism, and not semantically. We restrict the discussion to the propositional level only. Then, after presenting the motivations and a possible world semantics, the formalism is outlined and we also consider within this scheme the claim that superpositions may involve contradictions, as in the case of the Schrödinger's cat, which (it is usually said) is both alive and dead. We argue that this claim is a misreading of the quantum case. Finally, we sketch a new form of quantum logic that involves three kinds of negations and present the relationships among them. The paper is a first approach to the subject, introducing some main guidelines to be developed by a `syntactical' logical approach to quantum superpositions.
Fuzzy logic and neural network technologies
NASA Technical Reports Server (NTRS)
Villarreal, James A.; Lea, Robert N.; Savely, Robert T.
1992-01-01
Applications of fuzzy logic technologies in NASA projects are reviewed to examine their advantages in the development of neural networks for aerospace and commercial expert systems and control. Examples of fuzzy-logic applications include a 6-DOF spacecraft controller, collision-avoidance systems, and reinforcement-learning techniques. The commercial applications examined include a fuzzy autofocusing system, an air conditioning system, and an automobile transmission application. The practical use of fuzzy logic is set in the theoretical context of artificial neural systems (ANSs) to give the background for an overview of ANS research programs at NASA. The research and application programs include the Network Execution and Training Simulator and faster training algorithms such as the Difference Optimized Training Scheme. The networks are well suited for pattern-recognition applications such as predicting sunspots, controlling posture maintenance, and conducting adaptive diagnoses.
Fuzzy logic in autonomous orbital operations
NASA Technical Reports Server (NTRS)
Lea, Robert N.; Jani, Yashvant
1991-01-01
Fuzzy logic can be used advantageously in autonomous orbital operations that require the capability of handling imprecise measurements from sensors. Several applications are underway to investigate fuzzy logic approaches and develop guidance and control algorithms for autonomous orbital operations. Translational as well as rotational control of a spacecraft have been demonstrated using space shuttle simulations. An approach to a camera tracking system has been developed to support proximity operations and traffic management around the Space Station Freedom. Pattern recognition and object identification algorithms currently under development will become part of this camera system at an appropriate level in the future. A concept to control environment and life support systems for large Lunar based crew quarters is also under development. Investigations in the area of reinforcement learning, utilizing neural networks, combined with a fuzzy logic controller, are planned as a joint project with the Ames Research Center.
Nanomechanical logic elements based on coupled nanopillars
NASA Astrophysics Data System (ADS)
Kim, S. H.; Hong, S. J.; Rana, A. S.; Kim, H. S.
2014-10-01
We demonstrate the possibility of using coupled nanopillars as nanomechanical logic elements by regulating the flow of electric current between the nanopillars and the source and drain electrodes. The nanopillar, which is fabricated from a silicon-on-insulator (SOI) wafer and is located between two facing electrodes, oscillates with frequencies in the radiofrequency range of 10 - 1000 MHz. Electrons are transported between the nanopillar and the electrodes via an island-like gold layer thermally deposited on the top of the nanopillar in response to externally applied ac and dc biases. Nanomechanical logic gates are designed using the coupled nanopillars and a switched-capacitor model. With this configuration, several logic gates, such as an inverter and NAND, NOR, and XOR gates, can be effectively implemented.
Logic Design Pathology and Space Flight Electronics
NASA Technical Reports Server (NTRS)
Katz, Richard; Barto, Rod L.; Erickson, K.
1997-01-01
Logic design errors have been observed in space flight missions and the final stages of ground test. The technologies used by designers and their design/analysis methodologies will be analyzed. This will give insight to the root causes of the failures. These technologies include discrete integrated circuit based systems, systems based on field and mask programmable logic, and the use computer aided engineering (CAE) systems. State-of-the-art (SOTA) design tools and methodologies will be analyzed with respect to high-reliability spacecraft design and potential pitfalls are discussed. Case studies of faults from large expensive programs to "smaller, faster, cheaper" missions will be used to explore the fundamental reasons for logic design problems.
Molecular implementation of simple logic programs
NASA Astrophysics Data System (ADS)
Ran, Tom; Kaplan, Shai; Shapiro, Ehud
2009-11-01
Autonomous programmable computing devices made of biomolecules could interact with a biological environment and be used in future biological and medical applications. Biomolecular implementations of finite automata and logic gates have already been developed. Here, we report an autonomous programmable molecular system based on the manipulation of DNA strands that is capable of performing simple logical deductions. Using molecular representations of facts such as Man(Socrates) and rules such as Mortal(X) <-- Man(X) (Every Man is Mortal), the system can answer molecular queries such as Mortal(Socrates)? (Is Socrates Mortal?) and Mortal(X)? (Who is Mortal?). This biomolecular computing system compares favourably with previous approaches in terms of expressive power, performance and precision. A compiler translates facts, rules and queries into their molecular representations and subsequently operates a robotic system that assembles the logical deductions and delivers the result. This prototype is the first simple programming language with a molecular-scale implementation.
Anatomy Ontology Matching Using Markov Logic Networks
Li, Chunhua; Zhao, Pengpeng; Wu, Jian; Cui, Zhiming
2016-01-01
The anatomy of model species is described in ontologies, which are used to standardize the annotations of experimental data, such as gene expression patterns. To compare such data between species, we need to establish relationships between ontologies describing different species. Ontology matching is a kind of solutions to find semantic correspondences between entities of different ontologies. Markov logic networks which unify probabilistic graphical model and first-order logic provide an excellent framework for ontology matching. We combine several different matching strategies through first-order logic formulas according to the structure of anatomy ontologies. Experiments on the adult mouse anatomy and the human anatomy have demonstrated the effectiveness of proposed approach in terms of the quality of result alignment. PMID:27382498
Development of ferrite logic devices for an arithmetic processor
NASA Technical Reports Server (NTRS)
Heckler, C. H., Jr.
1972-01-01
A number of fundamentally ultra-reliable, all-magnetic logic circuits are developed using as a basis a single element ferrite structure wired as a logic delay element. By making minor additions or changes to the basic wiring pattern of the delay element other logic functions such as OR, AND, NEGATION, MAJORITY, EXCLUSIVE-OR, and FAN-OUT are developed. These logic functions are then used in the design of a full-adder, a set/reset flip-flop, and an edge detector. As a demonstration of the utility of all the developed devices, an 8-bit, all-magnetic, logic arithmetic unit capable of controlled addition, subtraction, and multiplication is designed. A new basic ferrite logic element and associated complementary logic scheme with the potential of improved performance is also described. Finally, an improved batch process for fabricating joint-free power drive and logic interconnect conductors for this basic class of all-magnetic logic is presented.
Why Mathematical Computer Simulations Are the New Laboratory for Scientists.
Buscema, Massimo
2015-01-01
In this paper, we introduce a new powerful scientific paradigm to understand natural and cultural processes. This new paradigm is based on two fundamental keywords: Data, as representative sample of the process we need to analyze, and Artificial Adaptive Systems, as a new mathematical technique able to make explicit the nonlinearity embedded in the process. We will try to make explicit these concepts analyzing how the distribution of events into the physical space may reveal the hidden logic connecting these events together.
Unlimited multistability and Boolean logic in microbial signalling
Kothamachu, Varun B.; Feliu, Elisenda; Cardelli, Luca; Soyer, Orkun S.
2015-01-01
The ability to map environmental signals onto distinct internal physiological states or programmes is critical for single-celled microbes. A crucial systems dynamics feature underpinning such ability is multistability. While unlimited multistability is known to arise from multi-site phosphorylation seen in the signalling networks of eukaryotic cells, a similarly universal mechanism has not been identified in microbial signalling systems. These systems are generally known as two-component systems comprising histidine kinase (HK) receptors and response regulator proteins engaging in phosphotransfer reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger fraction of these proteins compared with regular HKs. Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them. These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology. PMID:26040599
Refining fuzzy logic controllers with machine learning
NASA Technical Reports Server (NTRS)
Berenji, Hamid R.
1994-01-01
In this paper, we describe the GARIC (Generalized Approximate Reasoning-Based Intelligent Control) architecture, which learns from its past performance and modifies the labels in the fuzzy rules to improve performance. It uses fuzzy reinforcement learning which is a hybrid method of fuzzy logic and reinforcement learning. This technology can simplify and automate the application of fuzzy logic control to a variety of systems. GARIC has been applied in simulation studies of the Space Shuttle rendezvous and docking experiments. It has the potential of being applied in other aerospace systems as well as in consumer products such as appliances, cameras, and cars.
Universal programmable logic gate and routing method
NASA Technical Reports Server (NTRS)
Fijany, Amir (Inventor); Vatan, Farrokh (Inventor); Akarvardar, Kerem (Inventor); Blalock, Benjamin (Inventor); Chen, Suheng (Inventor); Cristoloveanu, Sorin (Inventor); Kolawa, Elzbieta (Inventor); Mojarradi, Mohammad M. (Inventor); Toomarian, Nikzad (Inventor)
2009-01-01
An universal and programmable logic gate based on G.sup.4-FET technology is disclosed, leading to the design of more efficient logic circuits. A new full adder design based on the G.sup.4-FET is also presented. The G.sup.4-FET can also function as a unique router device offering coplanar crossing of signal paths that are isolated and perpendicular to one another. This has the potential of overcoming major limitations in VLSI design where complex interconnection schemes have become increasingly problematic.
Runtime Analysis of Linear Temporal Logic Specifications
NASA Technical Reports Server (NTRS)
Giannakopoulou, Dimitra; Havelund, Klaus
2001-01-01
This report presents an approach to checking a running program against its Linear Temporal Logic (LTL) specifications. LTL is a widely used logic for expressing properties of programs viewed as sets of executions. Our approach consists of translating LTL formulae to finite-state automata, which are used as observers of the program behavior. The translation algorithm we propose modifies standard LTL to B chi automata conversion techniques to generate automata that check finite program traces. The algorithm has been implemented in a tool, which has been integrated with the generic JPaX framework for runtime analysis of Java programs.
Nonlinear dynamics based digital logic and circuits.
Kia, Behnam; Lindner, John F; Ditto, William L
2015-01-01
We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two.
Nonlinear dynamics based digital logic and circuits
Kia, Behnam; Lindner, John. F.; Ditto, William L.
2015-01-01
We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two. PMID:26029096
Valve system incorporating single failure protection logic
Ryan, Rodger; Timmerman, Walter J. H.
1980-01-01
A valve system incorporating single failure protective logic. The system consists of a valve combination or composite valve which allows actuation or de-actuation of a device such as a hydraulic cylinder or other mechanism, integral with or separate from the valve assembly, by means of three independent input signals combined in a function commonly known as two-out-of-three logic. Using the input signals as independent and redundant actuation/de-actuation signals, a single signal failure, or failure of the corresponding valve or valve set, will neither prevent the desired action, nor cause the undesired action of the mechanism.
Digital Poetry: A Narrow Relation between Poetics and the Codes of the Computational Logic
NASA Astrophysics Data System (ADS)
Laurentiz, Silvia
The project "Percorrendo Escrituras" (Walking Through Writings Project) has been developed at ECA-USP Fine Arts Department. Summarizing, it intends to study different structures of digital information that share the same universe and are generators of a new aesthetics condition. The aim is to search which are the expressive possibilities of the computer among the algorithm functions and other of its specific properties. It is a practical, theoretical and interdisciplinary project where the study of programming evolutionary language, logic and mathematics take us to poetic experimentations. The focus of this research is the digital poetry, and it comes from poetics of permutation combinations and culminates with dynamic and complex systems, autonomous, multi-user and interactive, through agents generation derivations, filtration and emergent standards. This lecture will present artworks that use some mechanisms introduced by cybernetics and the notion of system in digital poetry that demonstrate the narrow relationship between poetics and the codes of computational logic.
Mathematical and statistical analysis
NASA Technical Reports Server (NTRS)
Houston, A. Glen
1988-01-01
The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.
Developing My Mathematics Identity
ERIC Educational Resources Information Center
Gonzalez, Lidia
2016-01-01
Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.
Brain Computation Is Organized via Power-of-Two-Based Permutation Logic
Xie, Kun; Fox, Grace E.; Liu, Jun; Lyu, Cheng; Lee, Jason C.; Kuang, Hui; Jacobs, Stephanie; Li, Meng; Liu, Tianming; Song, Sen; Tsien, Joe Z.
2016-01-01
algorithm is indeed organized by the power-of-two-based permutation logic. This simple mathematical logic can account for brain computation across the entire evolutionary spectrum, ranging from the simplest neural networks to the most complex. PMID:27895562
ERIC Educational Resources Information Center
Gallian, Joseph A., Ed.
2010-01-01
"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…
Mathematics and Mobile Learning
ERIC Educational Resources Information Center
Sayed, Fayez
2015-01-01
The wide range of Mathematical Apps targeting different mathematical concepts and the various types of mobile devices available present a demanding and challenging problem to the teaching and learning in the field of mathematics. In an attempt to address this issue, a few Apps were selected, implemented and tested in this work. [For complete…
ERIC Educational Resources Information Center
Clary, Joseph R.; Nery, Karen P.
This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…
Defining Mathematical Giftedness
ERIC Educational Resources Information Center
Parish, Linda
2014-01-01
This theoretical paper outlines the process of defining "mathematical giftedness" for a present study on how primary school teaching shapes the mindsets of children who are mathematically gifted. Mathematical giftedness is not a badge of honour or some special value attributed to a child who has achieved something exceptional.…
Mathematics. [SITE 2001 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2001 conference: "Secondary Mathematics Methods Course with Technology Units: Encouraging Pre-Service Teachers To Use Technology" (Rajee Amarasinghe); "Competency Exams in College Mathematics"…
Mathematics, Programming, and STEM
ERIC Educational Resources Information Center
Yeh, Andy; Chandra, Vinesh
2015-01-01
Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10- week teaching experiment, mathematical meaning-making was enriched when primary…
ERIC Educational Resources Information Center
Nisbet, Steven
1991-01-01
The relationship between mathematics and music has been investigated for thousands of years. Presented are the mathematical features of music through a study of melody, harmony, and rhythm, and the musical features of mathematics through a study of pattern, ratio, modular arithmetic, Pythagorean triples, and number sequences. (MDH)
ERIC Educational Resources Information Center
Ortiz-Franco, Luis
An historical perspective reveals that sophisticated mathematical activity has been going on in the Latino culture for thousands of years. This paper provides a general definition of the area of mathematics education that deals with issues of culture and mathematics (ethnomathematics) and defines what is meant by the term Latino in this essay.…
Translations toward Connected Mathematics
ERIC Educational Resources Information Center
Applebaum, Mark; Leikin, Roza
2010-01-01
The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one…
ERIC Educational Resources Information Center
Darlington, Ellie
2014-01-01
This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…
Applied Vocational Mathematics.
ERIC Educational Resources Information Center
South Carolina State Dept. of Education, Columbia. Office of Vocational Education.
Developed for use in teaching a two-semester, one-unit course, this course guide is intended to aid the high school instructor in teaching mathematical problem-solving and computational skills to vocational education students. The state-adopted textbook for general mathematics III, "Applied General Mathematics" serves as the major…
Mathematical Discovery: Hadamard Resurected
ERIC Educational Resources Information Center
Liljedahl, Peter
2004-01-01
In 1943 Jacques Hadamard gave a series of lectures on mathematical invention at the Ecole Libre des Hautes Etudes in New York City. These talks were subsequently published as The Psychology of Mathematical Invention in the Mathematical Field (Hadamard, 1945). In this article I present a study that mirrors the work of Hadamard. Results both…
ERIC Educational Resources Information Center
Walshaw, Margaret
2014-01-01
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
A "Mathematics Background Check"
ERIC Educational Resources Information Center
Hubisz, John
2009-01-01
Early in my career someone else reported that the best indicator of success in calculus-based physics (CBP) at our school was whether students had taken mathematics in a certain region of New Brunswick. I sat down with a very longtime mathematics teacher and asked him what he thought students should know in mathematics after high school to succeed…
Mathenger Hunt: Mathematics Matters.
ERIC Educational Resources Information Center
Falba, Christy J.; Weiss, Maria J.
1991-01-01
Presented is an activity which shows how mathematics is used in real life and helps to establish a need for mathematics in students' futures. Adapted from a scavenger-hunt idea, this activity helps students to discover that almost every career makes use of mathematics. (KR)
Students' Mathematical Noticing
ERIC Educational Resources Information Center
Lobato, Joanne; Hohensee, Charles; Rhodehamel, Bohdan
2013-01-01
Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…
Mathematics and Global Survival.
ERIC Educational Resources Information Center
Schwartz, Richard H.
This resource was written to provide students with an awareness of critical issues facing the world today. In courses for college students, it can motivate their study of mathematics, teach them how to solve mathematical problems related to current global issues, provide coherence to mathematical studies through a focus on issues of human…
ERIC Educational Resources Information Center
Martin, Tami S.; Speer, William R.
2009-01-01
This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…
Modern Versus Traditional Mathematics
ERIC Educational Resources Information Center
Roberts, A. M.
1974-01-01
The effect of different secondary school mathematics syllabi on first-year performance in college-level mathematics was studied in an attempt to evaluate the syllabus change. Students with a modern mathematics background performed sigficantly better on most first-year units. A topic-by-topic analysis of results is included. (DT)
The purpose of this book is to familiarize the reader with how mathematics can solve important problems in modern military affairs. The authors discuss and explain, without resorting to complex mathematical calculations, the essence of the basic methods which modern mathematics makes available to military problems, design and combat deployment of modern weapons.
ERIC Educational Resources Information Center
Henson, R.; Stumbles, A.
1977-01-01
The relationship between mathematics and chemistry has been changing rapidly in recent years. Some chemistry teachers have experienced difficulties in their teaching with the introduction of modern mathematics in the schools. Some suggestions for reinforcing the concepts and language of modern mathematics are put forth. (Author/MA)
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY. Bureau of Curriculum Development.
The Materials in this bulletin indicate suggested teaching procedures needed to implement the teaching of "mathematics, 9th Year" as outlined in Curriculum Bulletin No. 3, 1958-59 series, Course of Study Mathematics 7-8-9. Whereas the course of study suggests the application of mathematical principles such as commutativity,…
Abraham, Ralph
2015-12-01
Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination.
ERIC Educational Resources Information Center
Galligan, Linda
2016-01-01
A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…
NASA Astrophysics Data System (ADS)
Sommer, Hanns; Schreiber, Lothar
2012-05-01
Dreyfus' call ‘to make artificial intelligence (AI) more Heideggerian‘ echoes Heidegger's affirmation that pure calculations produce no ‘intelligence’ (Dreyfus, 2007). But what exactly is it that AI needs more than mathematics? The question in the title gives rise to a reexamination of the basic principles of cognition in Husserl's Phenomenology. Using Husserl's Phenomenological Method, a formalization of these principles is presented that provides the principal idea of cognition, and as a consequence, a ‘natural logic’. Only in a second step, mathematics is obtained from this natural logic by abstraction. The limitations of pure reasoning are demonstrated for fundamental considerations (Hilbert's ‘finite Einstellung’) as well as for the task of solving practical problems. Principles will be presented for the design of general intelligent systems, which make use of a natural logic.
Consciousness and Logic in a Quantum-Computing Universe
NASA Astrophysics Data System (ADS)
Zizzi, Paola
of the quantum mind, which are not algorithmic in the usual sense: the self, and mathematical intuition. The self is due to a reversible self-measurement of a quantum state of superposed tubulins. Mathematical intuition is due to the paraconsistent logic of the internal observer in a quantum-computing universe.
The Tower of Hanoi and Inductive Logic
ERIC Educational Resources Information Center
Merrotsy, Peter
2015-01-01
In the "Australian Curriculum," the concept of mathematical induction is first met in the senior secondary subject Specialist Mathematics. This article details an example, the Tower of Hanoi problem, which provides an enactive introduction to the inductive process before moving to more abstract and cognitively demanding representations.…
NASA Astrophysics Data System (ADS)
Bogdanov, Alexander; Khramushin, Vasily
2016-02-01
The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.
Young Children's Comprehension of Logical Connectives.
ERIC Educational Resources Information Center
Suppes, Patrick; Feldman, Shirley
To determine to what extent children of preschool age comprehend the meaning of logical connectives, 64 5- and 6-year-olds were told to hand differently colored and shaped wooden blocks to an experimenter. The commands involved various English idioms used for conjunction (e.g. both black and round), disjunction (either black or round), and…
On Logical Error Underlying Classical Mechanics
NASA Astrophysics Data System (ADS)
Kalanov, Temur Z.
2012-03-01
The logical analysis of the general accepted description of mechanical motion of material point M in classical mechanics is proposed. The key idea of the analysis is as follows. Let point M be moved in the positive direction of the axis O 1ptx. Motion is characterized by a change of coordinate x,( t ) -- continuous function of time t(because motion is a change in general). If δ,->;0;δ,;=;0, then δ,;->;0δ,;=;0, i.e., according to practice and formal logic, value of coordinate does not change and, hence, motion does not exist. But, contrary to practice and formal logic, differential calculus and classical mechanics contain the assertion that velocity δ,;->;0;δ,δ,;exists without motion. Then velocity δ,;->;0;δ,δ,;is not real (i.e. not physical) quantity, but fictitious quantity. Therefore, use of non-physical (unreal) quantity (i.e. the first and second derivatives of function) in classical mechanics is a logic error.
Demonstrating Boolean Logic Using Simple Electrical Circuits
ERIC Educational Resources Information Center
McElhaney, Kevin W.
2004-01-01
While exploring the subject of geometric proofs, boolean logic operators AND and OR can be used to allow students to visualize their true-or-false patterns. An activity in the form of constructing electrical circuits is illustrated to explain the concept.
Fuzzy logic program at SGS-Thomson
NASA Astrophysics Data System (ADS)
Pagni, Andrea; Poluzzi, Rinaldo; Rizzotto, GianGuido
1993-12-01
From its conception by Professor Lotfi A. Zadeh in the early '60s, Fuzzy Logic has slowly won acceptance, first in the academic world, then in industry. Its success is mainly due to the different perspective with which problems are tackled. Thanks to Fuzzy Logic we have moved from a numerical/analytical description to a quantitative/qualitative one. It is important to stress that this different perspective not only allows us to solve analysis/control problems at lower costs but can also allow otherwise insoluble problems to be solved at acceptable costs. Of course, it must be stressed that Fuzzy Systems cannot match the computational precision of traditional techniques but seek, instead, to find acceptable solutions in shorter times. Recognizing the enormous importance of fuzzy logic in the markets of the future, SGS-THOMSON intends to produce devices belonging to a new class of machines: Fuzzy Computational Machines. For this purpose a major research project has been established considering the architectural aspects and system implications of fuzzy logic, the development of dedicated VLSI components and supporting software.
Logical Structure of a Hypermedia Newspaper.
ERIC Educational Resources Information Center
Saarela, Janne; Turpeinen, Marko; Puskala, Tuomas; Korkea-aho, Mari; Sulonen, Reijo
1997-01-01
Describes an object-oriented approach which implements the logical model of a hypermedia newspaper based on experiences with the OtaOnline project at the Helsinki University of Technology (Finland.) Highlights include presentation formats, a semantical rating system, distribution schemes, metadata, and added-value features facilitated by the…
New Logic Circuit with DC Parametric Excitation
NASA Astrophysics Data System (ADS)
Sugahara, Masanori; Kaneda, Hisayoshi
1982-12-01
It is shown that dc parametric excitation is possible in a circuit named JUDO, which is composed of two resistively-connected Josephson junctions. Simulation study proves that the circuit has large gain and properties suitable for the construction of small, high-speed logic circuits.
ERIC Educational Resources Information Center
Molnar, Jane
The logical mysteries in this book are designed to develop critical thinking and deductive reasoning skills, motivate children to read carefully, and develop memory skills. The mystery solutions are explained at the end of the book. The first nine mysteries are intended for third grade students to work on with their teacher or parents. The second…
Optical logic array processor using shadowgrams
NASA Astrophysics Data System (ADS)
Tanida, J.; Ichioka, Y.
1983-06-01
On the basis of a lensless shadow-casting technique, a new, simple method of optically implementing digital logic gates has been developed. These gates are capable of performimg a complete set of logical operations on a large array of binary variables in parallel, i.e., the pattern logics. A light-emitting diode (LED) array is used as an incoherent light source in the lensless shadow-casting system. Sixteen possible functions of two binary variables are simply realizable with these gates in parallel by controlling the switching modes of the LEDs. Experimental results demonstrate the feasibility of various gate arrays, such as AND, OR, NOR, XOR, and NAND. As an example of application of the proposed method, an optical logic array processor is constructed that can implement parallel operations of addition or subtraction for two binary variables without considering the carry mechanisms. Use of the light-modulated LED array means that the proposed method can be applied to combinational circuits.
Logical Access Control Mechanisms in Computer Systems.
ERIC Educational Resources Information Center
Hsiao, David K.
The subject of access control mechanisms in computer systems is concerned with effective means to protect the anonymity of private information on the one hand, and to regulate the access to shareable information on the other hand. Effective means for access control may be considered on three levels: memory, process and logical. This report is a…
Interacting institutional logics in general dental practice☆
Harris, Rebecca; Holt, Robin
2013-01-01
We investigate the organisational field of general dental practice and how agents change or maintain the institution of values associated with the everyday work of health care provision. Our dataset comprise archival literature and policy documents, interview data from field level actors, as well as service delivery level interview data and secondary data gathered (2011–12) from 16 English dental practices. Our analysis provides a typology of institutional logics (prevailing systems of value) experienced in the field of dental practice. Confirming current literature, we find two logics dominate how care is assessed: business-like health care and medical professionalism. We advance the literature by finding the business-like health care logic further distinguished by values of commercialism on the one hand and those of accountability and procedural diligence on the other. The logic of professionalism we also find is further distinguished into a commitment to clinical expertise and independence in delivering patient care on the one hand, and concerns for the autonomy and sustainability of a business enterprise on the other. PMID:23931946
Children's Acquisition of Conditional Logic Structure: Teachable?
ERIC Educational Resources Information Center
Lee, Seong-Soo
1985-01-01
To assess the teachability of conditional logic structure, the commonly used syllogistic conditional reasoning task was divided into three main components: (1) inductive rule learning; (2) induction of conditional language; and (3) deductive interpretation. When trained on all components, fifth and seventh graders became very competent in dealing…
Evolutionary program induction directed by logic grammars
Wong; Leung
1997-01-01
Program induction generates a computer program that can produce the desired behavior for a given set of situations. Two of the approaches in program induction are inductive logic programming (ILP) and genetic programming (GP). Since their formalisms are so different, these two approaches cannot be integrated easily, although they share many common goals and functionalities. A unification will greatly enhance their problem-solving power. Moreover, they are restricted in the computer languages in which programs can be induced. In this paper, we present a flexible system called LOGENPRO (The LOgic gramar-based GENetic PROgramming system) that uses some of the techniques of GP and ILP. It is based on a formalism of logic grammars. The system applies logic grammars to control the evolution of programs in various programming languages and represent context-sensitive information and domain-dependent knowledge. Experiments have been performed to demonstrate that LOGENPRO can emulate GP and GP with automatically defined functions (ADFs). Moreover, LOGENPRO can employ knowledge such as argument types in a unified framework. The experiments show that LOGENPRO has superior performance to that of GP and GP with ADFs when more domain-dependent knowledge is available. We have applied LOGENPRO to evolve general recursive functions for the even-n-parity problem from noisy training examples. A number of experiments have been performed to determine the impact of domain-specific knowledge and noise in training examples on the speed of learning.
Mapping individual logical processes in information searching
NASA Technical Reports Server (NTRS)
Smetana, F. O.
1974-01-01
An interactive dialog with a computerized information collection was recorded and plotted in the form of a flow chart. The process permits one to identify the logical processes employed in considerable detail and is therefore suggested as a tool for measuring individual thought processes in a variety of situations. A sample of an actual test case is given.
Teleology as Logical Phenomenology: Some Therapeutic Implications.
ERIC Educational Resources Information Center
Rychlak, Joseph F.
Phenomenology is an important force in the development of psychological theory, rather than a variant type of counseling method. A distinction must be drawn between the sensory phenomenology in which gestaltists focus on sensory receptors, and logical pheomenology in which the grounding of belief or self-identity is viewed as a prediction or…
The music of morality and logic.
Mesz, Bruno; Rodriguez Zivic, Pablo H; Cecchi, Guillermo A; Sigman, Mariano; Trevisan, Marcos A
2015-01-01
Musical theory has built on the premise that musical structures can refer to something different from themselves (Nattiez and Abbate, 1990). The aim of this work is to statistically corroborate the intuitions of musical thinkers and practitioners starting at least with Plato, that music can express complex human concepts beyond merely "happy" and "sad" (Mattheson and Lenneberg, 1958). To do so, we ask whether musical improvisations can be used to classify the semantic category of the word that triggers them. We investigated two specific domains of semantics: morality and logic. While morality has been historically associated with music, logic concepts, which involve more abstract forms of thought, are more rarely associated with music. We examined musical improvisations inspired by positive and negative morality (e.g., good and evil) and logic concepts (true and false), analyzing the associations between these words and their musical representations in terms of acoustic and perceptual features. We found that music conveys information about valence (good and true vs. evil and false) with remarkable consistency across individuals. This information is carried by several musical dimensions which act in synergy to achieve very high classification accuracy. Positive concepts are represented by music with more ordered pitch structure and lower harmonic and sensorial dissonance than negative concepts. Music also conveys information indicating whether the word which triggered it belongs to the domains of logic or morality (true vs. good), principally through musical articulation. In summary, improvisations consistently map logic and morality information to specific musical dimensions, testifying the capacity of music to accurately convey semantic information in domains related to abstract forms of thought.
The music of morality and logic
Mesz, Bruno; Rodriguez Zivic, Pablo H.; Cecchi, Guillermo A.; Sigman, Mariano; Trevisan, Marcos A.
2015-01-01
Musical theory has built on the premise that musical structures can refer to something different from themselves (Nattiez and Abbate, 1990). The aim of this work is to statistically corroborate the intuitions of musical thinkers and practitioners starting at least with Plato, that music can express complex human concepts beyond merely “happy” and “sad” (Mattheson and Lenneberg, 1958). To do so, we ask whether musical improvisations can be used to classify the semantic category of the word that triggers them. We investigated two specific domains of semantics: morality and logic. While morality has been historically associated with music, logic concepts, which involve more abstract forms of thought, are more rarely associated with music. We examined musical improvisations inspired by positive and negative morality (e.g., good and evil) and logic concepts (true and false), analyzing the associations between these words and their musical representations in terms of acoustic and perceptual features. We found that music conveys information about valence (good and true vs. evil and false) with remarkable consistency across individuals. This information is carried by several musical dimensions which act in synergy to achieve very high classification accuracy. Positive concepts are represented by music with more ordered pitch structure and lower harmonic and sensorial dissonance than negative concepts. Music also conveys information indicating whether the word which triggered it belongs to the domains of logic or morality (true vs. good), principally through musical articulation. In summary, improvisations consistently map logic and morality information to specific musical dimensions, testifying the capacity of music to accurately convey semantic information in domains related to abstract forms of thought. PMID:26191020
The connection between logical and thermodynamic irreversibility
NASA Astrophysics Data System (ADS)
Ladyman, James; Presnell, Stuart; Short, Anthony J.; Groisman, Berry
There has recently been a good deal of controversy about Landauer's Principle, which is often stated as follows: the erasure of one bit of information in a computational device is necessarily accompanied by a generation of kT ln 2 heat. This is often generalised to the claim that any logically irreversible operation cannot be implemented in a thermodynamically reversible way. Norton [2005. Eaters of the lotus: Landauer's principle and the return of Maxwell's demon. Studies in History and Philosophy of Modern Physics, 36, 375-411] and Maroney [2005. The (absence of a) relationship between thermodynamic and logical reversibility. Studies in History and Philosophy of Modern Physics, 36, 355-374] both argue that Landauer's Principle has not been shown to hold in general, and Maroney offers a method that he claims instantiates the operation Reset in a thermodynamically reversible way. In this paper we defend the qualitative form of Landauer's Principle, and clarify its quantitative consequences (assuming the second law of thermodynamics). We analyse in detail what it means for a physical system to implement a logical transformation L, and we make this precise by defining the notion of an L-machine. Then we show that logical irreversibility of L implies thermodynamic irreversibility of every corresponding L-machine. We do this in two ways. First, by assuming the phenomenological validity of the Kelvin statement of the second law, and second, by using information-theoretic reasoning. We illustrate our results with the example of the logical transformation 'Reset', and thereby recover the quantitative form of Landauer's Principle.
Fuzzy Logic Based Controller for a Grid-Connected Solid Oxide Fuel Cell Power Plant.
Chatterjee, Kalyan; Shankar, Ravi; Kumar, Amit
2014-10-01
This paper describes a mathematical model of a solid oxide fuel cell (SOFC) power plant integrated in a multimachine power system. The utilization factor of a fuel stack maintains steady state by tuning the fuel valve in the fuel processor at a rate proportional to a current drawn from the fuel stack. A suitable fuzzy logic control is used for the overall system, its objective being controlling the current drawn by the power conditioning unit and meet a desirable output power demand. The proposed control scheme is verified through computer simulations.
The History of Mathematics and Mathematical Education
ERIC Educational Resources Information Center
Grattan-Guinness, I.
1977-01-01
Answers to questions which were asked after the author's various lectures in Australia are gathered here. Topics touched upon include "new" mathematics, unknown constants and free variables, propositional functions, linear algebra, arithmetic and geometry, and student assessment. (MN)
Exclusive-or logic circuit has useful properties
NASA Technical Reports Server (NTRS)
Batte, W. G.
1966-01-01
Single, simple exclusive-or logic connective eliminates excessive hardware and the number of interconnections between logic modules. This circuit performs the necessary switching for the exclusive-or operation and amplifies, restores, and inverts the signal.
The Three Rs of Teaching Logic: Revelation, Relevance, and Reinforcement
ERIC Educational Resources Information Center
Covel, Robert C.
2010-01-01
Covel offers a primer on logic and describes how students react when they realize what a useful resource it can be in their real lives. His article includes useful definitions of critical concepts and logical fallacies. (Contains 2 figures.)
A biochemical logic gate using an enzyme and its inhibitor. Part II: The logic gate.
Sivan, Sarit; Tuchman, Samuel; Lotan, Noah
2003-06-01
Enzyme-Based Logic Gates (ENLOGs) are key components in bio-molecular systems for information processing. This report and the previous one in this series address the characterization of two bio-molecular switching elements, namely the alpha-chymotrypsin (alphaCT) derivative p-phenylazobenzoyl-alpha-chymotrypsin (PABalphaCT) and its inhibitor (proflavine), as well as their assembly into a logic gate. The experimental output of the proposed system is expressed in terms of enzymic activity and this was translated into logic output (i.e. "1" or "0") relative to a predetermined threshold value. We have found that an univalent link exists between the dominant isomers of PABalphaCT (cis or trans), the dominant form of either acridine (proflavine) or acridan and the logic output of the system. Thus, of all possible combinations, only the trans-PABalphaCT and the acridan lead to an enzymic activity that can be defined as logic output "1". The system operates under the rules of Boolean algebra and performs as an "AND" logic gate.
Application of temporal LNC logic in artificial intelligence
NASA Astrophysics Data System (ADS)
Adamek, Marek; Mulawka, Jan
2016-09-01
This paper presents the temporal logic inference engine developed in our university. It is an attempt to demonstrate implementation and practical application of temporal logic LNC developed in Cardinal Stefan Wyszynski University in Warsaw.1 The paper describes the fundamentals of LNC logic, architecture and implementation of inference engine. The practical application is shown by providing the solution for popular in Artificial Intelligence problem of Missionaries and Cannibals in terms of LNC logic. Both problem formulation and inference engine are described in details.
Institutional Logics, Indie Software Developers and Platform Governance
ERIC Educational Resources Information Center
Qiu, Yixin
2013-01-01
This two-essay dissertation aims to study institutional logics in the context of Apple's independent third-party software developers. In essay 1, I investigate the embedded agency aspect of the institutional logics theory. It builds on the premise that logics constrain preferences, interests and behaviors of individuals and organizations, thereby…
Electronics. Module 3: Digital Logic Application. Instructor's Guide.
ERIC Educational Resources Information Center
Carter, Ed; Murphy, Mark
This guide contains instructor's materials for a 10-unit secondary school course on digital logic application. The units are introduction to digital, logic gates, digital integrated circuits, combination logic, flip-flops, counters and shift registers, encoders and decoders, arithmetic circuits, memory, and analog/digital and digital/analog…
George Pierce Baker's "Principles of Argumentation": "Completely Logical"?
ERIC Educational Resources Information Center
Bordelon, Suzanne
2006-01-01
The article contends that previous scholars have misread George Pierce Baker's efforts by focusing primarily on "The Principles of Argumentation" and the role of logic. Baker's view of logic was more complex than scholars have claimed. He challenged traditional concepts of formal logic, highlighting only those aspects that would help students…
15 CFR 970.601 - Logical mining unit.
Code of Federal Regulations, 2010 CFR
2010-01-01
... ENVIRONMENTAL DATA SERVICE DEEP SEABED MINING REGULATIONS FOR EXPLORATION LICENSES Resource Development Concepts § 970.601 Logical mining unit. (a) In the case of an exploration license, a logical mining unit is an... 15 Commerce and Foreign Trade 3 2010-01-01 2010-01-01 false Logical mining unit. 970.601...
43 CFR 3487.1 - Logical mining units.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Logical mining units. 3487.1 Section 3487..., DEPARTMENT OF THE INTERIOR MINERALS MANAGEMENT (3000) COAL EXPLORATION AND MINING OPERATIONS RULES Logical Mining Unit § 3487.1 Logical mining units. (a) An LMU shall become effective only upon approval of...
43 CFR 3487.1 - Logical mining units.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Logical mining units. 3487.1 Section 3487..., DEPARTMENT OF THE INTERIOR MINERALS MANAGEMENT (3000) COAL EXPLORATION AND MINING OPERATIONS RULES Logical Mining Unit § 3487.1 Logical mining units. (a) An LMU shall become effective only upon approval of...
15 CFR 970.601 - Logical mining unit.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 15 Commerce and Foreign Trade 3 2012-01-01 2012-01-01 false Logical mining unit. 970.601 Section... ENVIRONMENTAL DATA SERVICE DEEP SEABED MINING REGULATIONS FOR EXPLORATION LICENSES Resource Development Concepts § 970.601 Logical mining unit. (a) In the case of an exploration license, a logical mining unit is...
15 CFR 970.601 - Logical mining unit.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 15 Commerce and Foreign Trade 3 2014-01-01 2014-01-01 false Logical mining unit. 970.601 Section... ENVIRONMENTAL DATA SERVICE DEEP SEABED MINING REGULATIONS FOR EXPLORATION LICENSES Resource Development Concepts § 970.601 Logical mining unit. (a) In the case of an exploration license, a logical mining unit is...
43 CFR 3487.1 - Logical mining units.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Logical mining units. 3487.1 Section 3487..., DEPARTMENT OF THE INTERIOR MINERALS MANAGEMENT (3000) COAL EXPLORATION AND MINING OPERATIONS RULES Logical Mining Unit § 3487.1 Logical mining units. (a) An LMU shall become effective only upon approval of...
43 CFR 3487.1 - Logical mining units.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Logical mining units. 3487.1 Section 3487..., DEPARTMENT OF THE INTERIOR MINERALS MANAGEMENT (3000) COAL EXPLORATION AND MINING OPERATIONS RULES Logical Mining Unit § 3487.1 Logical mining units. (a) An LMU shall become effective only upon approval of...
15 CFR 970.601 - Logical mining unit.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 15 Commerce and Foreign Trade 3 2013-01-01 2013-01-01 false Logical mining unit. 970.601 Section... ENVIRONMENTAL DATA SERVICE DEEP SEABED MINING REGULATIONS FOR EXPLORATION LICENSES Resource Development Concepts § 970.601 Logical mining unit. (a) In the case of an exploration license, a logical mining unit is...
15 CFR 970.601 - Logical mining unit.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 15 Commerce and Foreign Trade 3 2011-01-01 2011-01-01 false Logical mining unit. 970.601 Section... ENVIRONMENTAL DATA SERVICE DEEP SEABED MINING REGULATIONS FOR EXPLORATION LICENSES Resource Development Concepts § 970.601 Logical mining unit. (a) In the case of an exploration license, a logical mining unit is...
Logic system aids in evaluation of project readiness
NASA Technical Reports Server (NTRS)
Maris, S. J.; Obrien, T. J.
1966-01-01
Measurement Operational Readiness Requirements /MORR/ assignments logic is used for determining the readiness of a complex project to go forward as planned. The system used logic network which assigns qualities to all important criteria in a project and establishes a logical sequence of measurements to determine what the conditions are.
NASA Technical Reports Server (NTRS)
Lennington, R. K.; Rassbach, M. E.
1979-01-01
Discussed in this report is the clustering algorithm CLASSY, including detailed descriptions of its general structure and mathematical background and of the various major subroutines. The report provides a development of the logic and equations used with specific reference to program variables. Some comments on timing and proposed optimization techniques are included.
Mathematics Curriculum Outline and Sample Activities for Gifted Students Grades 2 through 8.
ERIC Educational Resources Information Center
Barson, Alan; And Others
This document includes a statement of 11 basic considerations for a mathematics curriculum for the gifted in grades two through eight and a series of activities appropriate for such a curriculum. The activities are grouped under five strands: (1) logic; (2) combinations (combinatorics), probability, introduction to statistics; (3) geometry,…
Studying the Mathematical Concept of Implication through a Problem on Written Proofs
ERIC Educational Resources Information Center
Deloustal-Jorrand, Virginie
2004-01-01
In this paper, we present a didactic analysis of the mathematical concept of implication under three points of view: sets, formal logic, deductive reasoning. For this study, our hypothesis is that most of the difficulties and mistakes, as well in the use of implication as in its understanding, are due to the lack of links in education between…
NASA Technical Reports Server (NTRS)
Merticaru, V.
1974-01-01
An original mathematical model is proposed to derive equations for calculation of gear noise. These equations permit the acoustic pressure level to be determined as a function of load. Application of this method to three parallel gears is reported. The logical calculation scheme is given, as well as the results obtained.
Teaching the Blue-Eyed Islanders Puzzle in a Liberal Arts Mathematics Course
ERIC Educational Resources Information Center
Shea, Stephen
2012-01-01
The blue-eyed islanders puzzle is an old and challenging logic puzzle. This is a narrative of an experience introducing a variation of this puzzle on the first day of classes in a liberal arts mathematics course for non-majors. I describe an exercise that was used to facilitate the class's understanding of the puzzle.
Geometry Students' Hedged Statements and Their Self-Regulation of Mathematics
ERIC Educational Resources Information Center
Kosko, Karl W.
2012-01-01
Statements conveying a degree of certainty or doubt, in the form of hedging, have been linked with logical inference in students' talk (Rowland, 2000). Considering the current emphasis on increasing student autonomy for effective mathematical discourse, I posit a relationship between hedging and student autonomy. In the current study, high school…
Photonic encryption using all optical logic.
Blansett, Ethan L.; Schroeppel, Richard Crabtree; Tang, Jason D.; Robertson, Perry J.; Vawter, Gregory Allen; Tarman, Thomas David; Pierson, Lyndon George
2003-12-01
With the build-out of large transport networks utilizing optical technologies, more and more capacity is being made available. Innovations in Dense Wave Division Multiplexing (DWDM) and the elimination of optical-electrical-optical conversions have brought on advances in communication speeds as we move into 10 Gigabit Ethernet and above. Of course, there is a need to encrypt data on these optical links as the data traverses public and private network backbones. Unfortunately, as the communications infrastructure becomes increasingly optical, advances in encryption (done electronically) have failed to keep up. This project examines the use of optical logic for implementing encryption in the photonic domain to achieve the requisite encryption rates. In order to realize photonic encryption designs, technology developed for electrical logic circuits must be translated to the photonic regime. This paper examines two classes of all optical logic (SEED, gain competition) and how each discrete logic element can be interconnected and cascaded to form an optical circuit. Because there is no known software that can model these devices at a circuit level, the functionality of the SEED and gain competition devices in an optical circuit were modeled in PSpice. PSpice allows modeling of the macro characteristics of the devices in context of a logic element as opposed to device level computational modeling. By representing light intensity as voltage, 'black box' models are generated that accurately represent the intensity response and logic levels in both technologies. By modeling the behavior at the systems level, one can incorporate systems design tools and a simulation environment to aid in the overall functional design. Each black box model of the SEED or gain competition device takes certain parameters (reflectance, intensity, input response), and models the optical ripple and time delay characteristics. These 'black box' models are interconnected and cascaded in an
Mobile Health in Maternal and Newborn Care: Fuzzy Logic
Premji, Shahirose
2014-01-01
Whether mHealth improves maternal and newborn health outcomes remains uncertain as the response is perhaps not true or false but lies somewhere in between when considering unintended harmful consequences. Fuzzy logic, a mathematical approach to computing, extends the traditional binary “true or false” (one or zero) to exemplify this notion of partial truths that lies between completely true and false. The commentary explores health, socio-ecological and environmental consequences–positive, neutral or negative. Of particular significance is the negative influence of mHealth on maternal care-behaviors, which can increase stress reactivity and vulnerability to stress-induced illness across the lifespan of the child and establish pathways for intergenerational transmission of behaviors. A mHealth “fingerprinting” approach is essential to monitor psychosocial, economic, cultural, environmental and physical impact of mHealth intervention and make evidence-informed decision(s) about use of mHealth in maternal and newborn care. PMID:25003177
NASA Technical Reports Server (NTRS)
Wong, J. T.; Andre, W. L.
1981-01-01
A recent result shows that, for a certain class of systems, the interdependency among the elements of such a system together with the elements constitutes a mathematical structure a partially ordered set. It is called a loop free logic model of the system. On the basis of an intrinsic property of the mathematical structure, a characterization of system component failure in terms of maximal subsets of bad test signals of the system was obtained. Also, as a consequence, information concerning the total number of failure components in the system was deduced. Detailed examples are given to show how to restructure real systems containing loops into loop free models for which the result is applicable.
Conceptual and logical level of database modeling
NASA Astrophysics Data System (ADS)
Hunka, Frantisek; Matula, Jiri
2016-06-01
Conceptual and logical levels form the top most levels of database modeling. Usually, ORM (Object Role Modeling) and ER diagrams are utilized to capture the corresponding schema. The final aim of business process modeling is to store its results in the form of database solution. For this reason, value oriented business process modeling which utilizes ER diagram to express the modeling entities and relationships between them are used. However, ER diagrams form the logical level of database schema. To extend possibilities of different business process modeling methodologies, the conceptual level of database modeling is needed. The paper deals with the REA value modeling approach to business process modeling using ER-diagrams, and derives conceptual model utilizing ORM modeling approach. Conceptual model extends possibilities for value modeling to other business modeling approaches.
Voltage controlled spintronic devices for logic applications
You, Chun-Yeol; Bader, Samuel D.
2001-01-01
A reprogrammable logic gate comprising first and second voltage-controlled rotation transistors. Each transistor comprises three ferromagnetic layers with a spacer and insulating layer between the first and second ferromagnetic layers and an additional insulating layer between the second and third ferromagnetic layers. The third ferromagnetic layer of each transistor is connected to each other, and a constant external voltage source is applied to the second ferromagnetic layer of the first transistor. As input voltages are applied to the first ferromagnetic layer of each transistor, the relative directions of magnetization of the ferromagnetic layers and the magnitude of the external voltage determines the output voltage of the gate. By altering these parameters, the logic gate is capable of behaving as AND, OR, NAND, or NOR gates.
Spin wave nonreciprocity for logic device applications
Jamali, Mahdi; Kwon, Jae Hyun; Seo, Soo-Man; Lee, Kyung-Jin; Yang, Hyunsoo
2013-01-01
The utilization of spin waves as eigenmodes of the magnetization dynamics for information processing and communication has been widely explored recently due to its high operational speed with low power consumption and possible applications for quantum computations. Previous proposals of spin wave Mach-Zehnder devices were based on the spin wave phase, a delicate entity which can be easily disrupted. Here, we propose a complete logic system based on the spin wave amplitude utilizing the nonreciprocal spin wave behavior excited by microstrip antennas. The experimental data reveal that the nonreciprocity of magnetostatic surface spin wave can be tuned by the bias magnetic field. Furthermore, engineering of the device structure could result in a high nonreciprocity factor for spin wave logic applications. PMID:24196318
Optical design of programmable logic arrays
NASA Astrophysics Data System (ADS)
Murdocca, Miles J.; Huang, Alan; Jahns, Jurgen; Streibl, Norbert
1988-05-01
Regular free-space interconnects such as the perfect shuffle and banyan provided by beam splitters, lenses, and mirrors connect optical logic gates arranged in two-dimensional arrays. An algorithmic design technique transforms arbitrary logic equations into a near-optimal depth circuit. Analysis shows that an arbitrary interconnect makes little or no improvement in circuit depth and can even reduce throughput. Gate count is normally higher with a regular interconnect, and cost bounds are shown. It is concluded that regularly interconnected circuits will have a higher gate count compared with arbitrarily interconnected circuits using the design techniques presented here and that regular free-space interconnects are comparable with arbitrary interconnects in terms of circuit depth and are preferred to arbitrary interconnects for maximizing throughput.
Logic gates based on ion transistors.
Tybrandt, Klas; Forchheimer, Robert; Berggren, Magnus
2012-05-29
Precise control over processing, transport and delivery of ionic and molecular signals is of great importance in numerous fields of life sciences. Integrated circuits based on ion transistors would be one approach to route and dispense complex chemical signal patterns to achieve such control. To date several types of ion transistors have been reported; however, only individual devices have so far been presented and most of them are not functional at physiological salt concentrations. Here we report integrated chemical logic gates based on ion bipolar junction transistors. Inverters and NAND gates of both npn type and complementary type are demonstrated. We find that complementary ion gates have higher gain and lower power consumption, as compared with the single transistor-type gates, which imitates the advantages of complementary logics found in conventional electronics. Ion inverters and NAND gates lay the groundwork for further development of solid-state chemical delivery circuits.
Program Logics for Homogeneous Meta-programming
NASA Astrophysics Data System (ADS)
Berger, Martin; Tratt, Laurence
A meta-program is a program that generates or manipulates another program; in homogeneous meta-programming, a program may generate new parts of, or manipulate, itself. Meta-programming has been used extensively since macros were introduced to Lisp, yet we have little idea how formally to reason about meta-programs. This paper provides the first program logics for homogeneous meta-programming - using a variant of MiniML_e^{square} by Davies and Pfenning as underlying meta-programming language. We show the applicability of our approach by reasoning about example meta-programs from the literature. We also demonstrate that our logics are relatively complete in the sense of Cook, enable the inductive derivation of characteristic formulae, and exactly capture the observational properties induced by the operational semantics.
Neurocontrol and fuzzy logic: Connections and designs
NASA Technical Reports Server (NTRS)
Werbos, Paul J.
1991-01-01
Artificial neural networks (ANNs) and fuzzy logic are complementary technologies. ANNs extract information from systems to be learned or controlled, while fuzzy techniques mainly use verbal information from experts. Ideally, both sources of information should be combined. For example, one can learn rules in a hybrid fashion, and then calibrate them for better whole-system performance. ANNs offer universal approximation theorems, pedagogical advantages, very high-throughput hardware, and links to neurophysiology. Neurocontrol - the use of ANNs to directly control motors or actuators, etc. - uses five generalized designs, related to control theory, which can work on fuzzy logic systems as well as ANNs. These designs can copy what experts do instead of what they say, learn to track trajectories, generalize adaptive control, and maximize performance or minimize cost over time, even in noisy environments. Design tradeoffs and future directions are discussed throughout.
Logic circuits based on molecular spider systems.
Mo, Dandan; Lakin, Matthew R; Stefanovic, Darko
2016-08-01
Spatial locality brings the advantages of computation speed-up and sequence reuse to molecular computing. In particular, molecular walkers that undergo localized reactions are of interest for implementing logic computations at the nanoscale. We use molecular spider walkers to implement logic circuits. We develop an extended multi-spider model with a dynamic environment wherein signal transmission is triggered via localized reactions, and use this model to implement three basic gates (AND, OR, NOT) and a cascading mechanism. We develop an algorithm to automatically generate the layout of the circuit. We use a kinetic Monte Carlo algorithm to simulate circuit computations, and we analyze circuit complexity: our design scales linearly with formula size and has a logarithmic time complexity.
DNA strand displacement system running logic programs.
Rodríguez-Patón, Alfonso; Sainz de Murieta, Iñaki; Sosík, Petr
2014-01-01
The paper presents a DNA-based computing model which is enzyme-free and autonomous, not requiring a human intervention during the computation. The model is able to perform iterated resolution steps with logical formulae in conjunctive normal form. The implementation is based on the technique of DNA strand displacement, with each clause encoded in a separate DNA molecule. Propositions are encoded assigning a strand to each proposition p, and its complementary strand to the proposition ¬p; clauses are encoded comprising different propositions in the same strand. The model allows to run logic programs composed of Horn clauses by cascading resolution steps. The potential of the model is demonstrated also by its theoretical capability of solving SAT. The resulting SAT algorithm has a linear time complexity in the number of resolution steps, whereas its spatial complexity is exponential in the number of variables of the formula.
Noise-free logical stochastic resonance.
Gupta, Animesh; Sohane, Aman; Kohar, Vivek; Murali, K; Sinha, Sudeshna
2011-11-01
The phenomena of logical stochastic resonance (LSR) was demonstrated recently [Phys. Rev. Lett. 102, 104101 (2009)]: namely, when a bistable system is driven by two inputs it consistently yields a response mirroring a logic function of the two inputs in an optimal window of moderate noise. Here we examine the intriguing possibility of obtaining dynamical behavior equivalent to LSR in a noise-free bistable system, subjected only to periodic forcing, such as sinusoidal driving or rectangular pulse trains. We find that such a system, despite having no stochastic influence, also yields phenomena analogous to LSR, in an appropriate window of frequency and amplitude of the periodic forcing. The results are corroborated by circuit experiments.
Nanoeletromechanical switch and logic circuits formed therefrom
Nordquist, Christopher D.; Czaplewski, David A.
2010-05-18
A nanoelectromechanical (NEM) switch is formed on a substrate with a source electrode containing a suspended electrically-conductive beam which is anchored to the substrate at each end. This beam, which can be formed of ruthenium, bows laterally in response to a voltage applied between a pair of gate electrodes and the source electrode to form an electrical connection between the source electrode and a drain electrode located near a midpoint of the beam. Another pair of gate electrodes and another drain electrode can be located on an opposite side of the beam to allow for switching in an opposite direction. The NEM switch can be used to form digital logic circuits including NAND gates, NOR gates, programmable logic gates, and SRAM and DRAM memory cells which can be used in place of conventional CMOS circuits, or in combination therewith.
The nonequivalence of behavioral and mathematical equivalence.
Saunders, R R; Green, G
1992-03-01
Sidman and his colleagues derived behavioral tests for stimulus equivalence from the axiom in logic and mathematics that defines a relation of equivalence. The analogy has generated abundant research in which match-to-sample methods have been used almost exclusively to study interesting and complex stimulus control phenomena. It has also stimulated considerable discussion regarding interpretation of the analogy and speculation as to its validity and generality. This article reexamines the Sidman stimulus equivalence analogy in the context of a broader consideration of the mathematical axiom than was included in the original presentation of the analogy and some of the data that have accumulated in the interim. We propose that (a) mathematical and behavioral examples of equivalence relations differ substantially, (b) terminology is being used in ways that can lead to erroneous conclusions about the nature of the stimulus control that develops in stimulus equivalence experiments, and (c) complete analyses of equivalence and other types of stimulus-stimulus relations require more than a simple invocation of the analogy. Implications of our analysis for resolving current issues and prompting new research are discussed.
Early childhood mathematics intervention.
Clements, Douglas H; Sarama, Julie
2011-08-19
Preschool and primary grade children have the capacity to learn substantial mathematics, but many children lack opportunities to do so. Too many children not only start behind their more advantaged peers, but also begin a negative trajectory in mathematics. Interventions designed to facilitate their mathematical learning during ages 3 to 5 years have a strong positive effect on these children's lives for many years thereafter.
Plastic Logic quits e-reader market
NASA Astrophysics Data System (ADS)
Perks, Simon
2012-07-01
A UK firm spun out from the University of Cambridge that sought to be a world leader in flexible organic electronic circuits and displays has pulled out of the competitive e-reader market as it struggles to find a commercial outlet for its technology. Plastic Logic announced in May that it is to close its development facility in Mountain View, California, with the loss of around 40 jobs.
Reconfigurable Optical Directed-Logic Circuits
2015-11-20
advantage of the fast and low-loss propagation of light . DL can enhance the performance of digital systems for real-time applications that are... light . For instance, directed-logic architectures could find applications in packet-switched optical interconnect networks by providing fast...a) The transmission spectra of a switch in block/pass mode for light at working wavelength λL. The red dashed line and the black solid line are the
Logic Functions for Cryptography - A Tutorial
2009-05-01
Logic Functions for Cryptography - A Tutorial Jon T. Butler Tsutomu Sasao Department of Electrical Department of Computer Science and Computer ... of Computer Programming, Vol- ume 4” [9]. Definition 2.1 A linear function is the constant 0 function or the Exclusive OR of one or more variables...S) AND ADDRESS(ES) Naval Postgraduate School,Department of Electrical and Computer Engineering,Monterey,CA,93943 8. PERFORMING ORGANIZATION REPORT
Designing for Reuse of Configurable Logic
2005-07-01
include high-level abstractions of " source code " artifacts such as hardware description language rep- resentations (such as VHDL ) and logic/function/state...assist with debugging the resultant FPGA firmware, analogous to the tools that exist for simulating, testing, and debugging software source code . The FPGA ...may be provided as VHDL or Verilog files, enabling their inclusion with the user’s source code . Embedded processors, with their more stringent timing
The Family of Concurrent Logic Programming Languages
1989-05-01
nature , such as the solution of large numerical problems. Following Harel [70], we call concurrent systems that are transforma- tional as a whole parallel...nondeterminitic finite mtompla, and logic programs. Reactive systems are also nondeter- ministic. However, the nature of nondetaminism in the former is very...0l) Im(EXIXs],S) fail Figure 4: Examples of input matching of goals with clause heads The dataflow nature of matching is evident: an "instruction
Modeling anatomical spatial relations with description logics.
Schulz, S.; Hahn, U.; Romacker, M.
2000-01-01
Although spatial relations are essential for the anatomy domain, spatial reasoning is only weakly supported by medical knowledge representation systems. To remedy this shortcoming we express spatial relations that can intuitively be applied to anatomical objects (such as 'disconnected', 'externally connected', 'partial overlap' and 'proper part') within the formal framework of description logics. A special encoding of concept descriptions (in terms of SEP triplets) allows us to emulate spatial reasoning by classification-based reasoning. PMID:11079990
Fuzzy logic controller to improve powerline communication
NASA Astrophysics Data System (ADS)
Tirrito, Salvatore
2015-12-01
The Power Line Communications (PLC) technology allows the use of the power grid in order to ensure the exchange of data information among devices. This work proposes an approach, based on Fuzzy Logic, that dynamically manages the amplitude of the signal, with which each node transmits, by processing the master-slave link quality measured and the master-slave distance. The main objective of this is to reduce both the impact of communication interferences induced and power consumption.
Mixed wasted integrated program: Logic diagram
Mayberry, J.; Stelle, S.; O`Brien, M.; Rudin, M.; Ferguson, J.; McFee, J.
1994-11-30
The Mixed Waste Integrated Program Logic Diagram was developed to provide technical alternative for mixed wastes projects for the Office of Technology Development`s Mixed Waste Integrated Program (MWIP). Technical solutions in the areas of characterization, treatment, and disposal were matched to a select number of US Department of Energy (DOE) treatability groups represented by waste streams found in the Mixed Waste Inventory Report (MWIR).
The Focused Inverse Method for Linear Logic
2006-12-04
accomplishes this unifying view by providing logical connectives whose behaviour is closely tied to the precise collection of resources. The...interaction of the rules for multiplicative, additive and exponential connectives gives rise to a wide and expressive array of behaviours . This expressivity...also for providing an extraordinarily supportive enviroment where the students can truly pursue their work free of any worries. I would also like to
The Propositional Logic Induced by Means of Basic Algebras
NASA Astrophysics Data System (ADS)
Chajda, I.
2015-12-01
A propositional logic induced by means of commutative basic algebras was already described by M. Botur and R. Halaš. It turns out that this is a kind of non-associative fuzzy logic which can be used e.g. in expert systems. Unfortunately, there are other important classes of basic algebras which are not commutative, e.g. orthomodular lattices which are used as an axiomatization of the logic of quantum mechanics. This motivated us to develop another axioms and derivation rules which form a propositional logic induced by basic algebras in general. We show that this logic is algebraizable in the sense of W. J. Blok and D. Pigozzi.
CMAT non-volatile spintronic computing: complementary MTJ logic
NASA Astrophysics Data System (ADS)
Friedman, Joseph S.
2016-10-01
Magnetic tunnel junctions (MTJs) have thoroughly demonstrated their utility as a non-volatile memory storage element, inspiring their application to a memory-in-logic computer that would overcome the von Neumann bottleneck. However, MTJ logic gates must be able to cause other MTJs to switch, thus ensuring the cascading capability fundamental to efficient computing. Complementary MTJ logic (CMAT) provides a simple circuit structure through which MTJs can be cascaded directly to perform logic operations. In this novel logic family, charge pulses resulting from MTJ switching create magnetic fields that switch other MTJs, providing impetus for further development of MTJs for computing applications.
An interval logic for higher-level temporal reasoning
NASA Technical Reports Server (NTRS)
Schwartz, R. L.; Melliar-Smith, P. M.; Vogt, F. H.; Plaisted, D. A.
1983-01-01
Prior work explored temporal logics, based on classical modal logics, as a framework for specifying and reasoning about concurrent programs, distributed systems, and communications protocols, and reported on efforts using temporal reasoning primitives to express very high level abstract requirements that a program or system is to satisfy. Based on experience with those primitives, this report describes an Interval Logic that is more suitable for expressing such higher level temporal properties. The report provides a formal semantics for the Interval Logic, and several examples of its use. A description of decision procedures for the logic is also included.
A parity checker circuit based on microelectromechanical resonator logic elements
NASA Astrophysics Data System (ADS)
Hafiz, Md Abdullah Al; Li, Ren; Younis, Mohammad I.; Fariborzi, Hossein
2017-03-01
Micro/nano-electromechanical resonator based logic computation has attracted significant attention in recent years due to its dynamic mode of operation, ultra-low power consumption, and potential for reprogrammable and reversible computing. Here we demonstrate a 4-bit parity checker circuit by utilizing recently developed logic gates based on MEMS resonators. Toward this, resonance frequencies of shallow arch shaped micro-resonators are electrothermally tuned by the logic inputs to constitute the required logic gates for the proposed parity checker circuit. This study demonstrates that by utilizing MEMS resonator based logic elements, complex digital circuits can be realized.
The (absence of a) relationship between thermodynamic and logical reversibility
NASA Astrophysics Data System (ADS)
Maroney, O. J. E.
Landauer erasure seems to provide a powerful link between thermodynamics and information processing (logical computation). The only logical operations that require a generation of heat are logically irreversible ones, with the minimum heat generation being kT ln 2 per bit of information lost. Nevertheless, it will be shown that logical reversibility neither implies, nor is implied by thermodynamic reversibility. By examining thermodynamically reversible operations which are logically irreversible, it is possible to show that information and entropy, while having the same form, are conceptually different.
Cognitive and brain systems underlying early mathematical development.
Geary, D C; Moore, A M
2016-01-01
We review current debate regarding the core competencies that support early mathematics learning, focusing on the contributions of the inherent system for representing approximate magnitudes, and domain-general systems that facilitate learning across academic domains. The latter include the executive control system that enables explicit processing of quantitative symbols, such as Arabic numerals, and the logical problem-solving abilities (intelligence) that facilitate learning the relations among numerals. The neural systems that underlie these abilities, as related to mathematical learning, are also discussed, albeit briefly. We place the contributions of inherent quantitative abilities and domain-general mechanisms in an evolutionary context and provide some discussion as to how they interact during the learning of evolutionarily novel mathematics.
Finite Mathematics and Discrete Mathematics: Is There a Difference?
ERIC Educational Resources Information Center
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers
ERIC Educational Resources Information Center
Cai, Jinfa; Ding, Meixia
2017-01-01
Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…
Mathematics for Teaching: A Form of Applied Mathematics
ERIC Educational Resources Information Center
Stylianides, Gabriel J.; Stylianides, Andreas J.
2010-01-01
In this article we elaborate a conceptualisation of "mathematics for teaching" as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design…
Exploring Differential Effects of Mathematics Courses on Mathematics Achievement
ERIC Educational Resources Information Center
Ma, Xin; McIntyre, Laureen J.
2005-01-01
Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…
A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa
2012-01-01
This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…
Using Mathematics Literature with Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Jett, Christopher C.
2014-01-01
Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…
Design of a Ferroelectric Programmable Logic Gate Array
NASA Technical Reports Server (NTRS)
MacLeod, Todd C.; Ho, Fat Duen
2003-01-01
A programmable logic gate array has been designed utilizing ferroelectric field effect transistors. The design has only a small number of gates, but this could be scaled up to a more useful size. Using FFET's in a logic array gives several advantages. First, it allows real-time programmability to the array to give high speed reconfiguration. It also allows the array to be configured nearly an unlimited number of times, unlike a FLASH FPGA. Finally, the Ferroelectric Programmable Logic Gate Array (FPLGA) can be implemented using a smaller number of transistors because of the inherent logic characteristics of an FFET. The device was only designed and modeled using Spice models of the circuit, including the FFET. The actual device was not produced. The design consists of a small array of NAND and NOR logic gates. Other gates could easily be produced. They are linked by FFET's that control the logic flow. Timing and logic tables have been produced showing the array can produce a variety of logic combinations at a real time usable speed. This device could be a prototype for a device that could be put into imbedded systems that need the high speed of hardware implementation of logic and the complexity to need to change the logic algorithm. Because of the non-volatile nature of the FFET, it would also be useful in situations that needed to program a logic array once and use it repeatedly after the power has been shut off.
Realization of Functional Complete Stateful Boolean Logic in Memristive Crossbar.
Li, Yi; Zhou, Ya-Xiong; Xu, Lei; Lu, Ke; Wang, Zhuo-Rui; Duan, Nian; Jiang, Lei; Cheng, Long; Chang, Ting-Chang; Chang, Kuan-Chang; Sun, Hua-Jun; Xue, Kan-Hao; Miao, Xiang-Shui
2016-12-21
Nonvolatile stateful logic computing in memristors is a promising paradigm with which to realize the unity of information storage and processing in the same physical location that has shown great feasibility for breaking the von Neumann bottleneck in traditional computing architecture. How to reduce the computational complexity of memristor-based logic functions is a matter of concern. Here, based on a general logic expression, we proposed a method to implement the arbitrary logic of complete 16 Boolean logic in two steps with one memristor in the crossbar architecture. A representative functional complete NAND logic is successfully experimentally demonstrated in the filamentary Ag-AgGeTe-Ta memristors to prove the validity of our method. We believe our work may promote the development of the revolutionary logic in memory architectures.
Constructing a logical, regular axis topology from an irregular topology
Faraj, Daniel A.
2014-07-01
Constructing a logical regular topology from an irregular topology including, for each axial dimension and recursively, for each compute node in a subcommunicator until returning to a first node: adding to a logical line of the axial dimension a neighbor specified in a nearest neighbor list; calling the added compute node; determining, by the called node, whether any neighbor in the node's nearest neighbor list is available to add to the logical line; if a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, adding, by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line; and, if no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, returning to the calling compute node.
Constructing a logical, regular axis topology from an irregular topology
Faraj, Daniel A.
2014-07-22
Constructing a logical regular topology from an irregular topology including, for each axial dimension and recursively, for each compute node in a subcommunicator until returning to a first node: adding to a logical line of the axial dimension a neighbor specified in a nearest neighbor list; calling the added compute node; determining, by the called node, whether any neighbor in the node's nearest neighbor list is available to add to the logical line; if a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, adding, by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line; and, if no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, returning to the calling compute node.
Sub-kBT micro-electromechanical irreversible logic gate.
López-Suárez, M; Neri, I; Gammaitoni, L
2016-06-28
In modern computers, computation is performed by assembling together sets of logic gates. Popular gates like AND, OR and XOR, processing two logic inputs and yielding one logic output, are often addressed as irreversible logic gates, where the sole knowledge of the output logic value is not sufficient to infer the logic value of the two inputs. Such gates are usually believed to be bounded to dissipate a finite minimum amount of energy determined by the input-output information difference. Here we show that this is not necessarily the case, by presenting an experiment where a OR logic gate, realized with a micro-electromechanical cantilever, is operated with energy well below the expected limit, provided the operation is slow enough and frictional phenomena are properly addressed.
Sub-kBT micro-electromechanical irreversible logic gate
López-Suárez, M.; Neri, I.
2016-01-01
In modern computers, computation is performed by assembling together sets of logic gates. Popular gates like AND, OR and XOR, processing two logic inputs and yielding one logic output, are often addressed as irreversible logic gates, where the sole knowledge of the output logic value is not sufficient to infer the logic value of the two inputs. Such gates are usually believed to be bounded to dissipate a finite minimum amount of energy determined by the input–output information difference. Here we show that this is not necessarily the case, by presenting an experiment where a OR logic gate, realized with a micro-electromechanical cantilever, is operated with energy well below the expected limit, provided the operation is slow enough and frictional phenomena are properly addressed. PMID:27350333
Logic Models for Program Design, Implementation, and Evaluation: Workshop Toolkit. REL 2015-057
ERIC Educational Resources Information Center
Shakman, Karen; Rodriguez, Sheila M.
2015-01-01
The Logic Model Workshop Toolkit is designed to help practitioners learn the purpose of logic models, the different elements of a logic model, and the appropriate steps for developing and using a logic model for program evaluation. Topics covered in the sessions include an overview of logic models, the elements of a logic model, an introduction to…
Gómez, Antonio; Cedano, Juan; Espadaler, Jordi; Hermoso, Antonio; Piñol, Jaume; Querol, Enrique
2008-02-01
The functional annotation of the new protein sequences represents a major drawback for genomic science. The best way to suggest the function of a protein from its sequence is by finding a related one for which biological information is available. Current alignment algorithms display a list of protein sequence stretches presenting significant similarity to different protein targets, ordered by their respective mathematical scores. However, statistical and biological significance do not always coincide, therefore, the rearrangement of the program output according to more biological characteristics than the mathematical scoring would help functional annotation. A new method that predicts the putative function for the protein integrating the results from the PSI-BLAST program and a fuzzy logic algorithm is described. Several protein sequence characteristics have been checked in their ability to rearrange a PSI-BLAST profile according more to their biological functions. Four of them: amino acid content, matched segment length and hydropathic and flexibility profiles positively contributed, upon being integrated by a fuzzy logic algorithm into a program, BYPASS, to the accurate prediction of the function of a protein from its sequence.
The Strengths and Weaknesses of Logic Formalisms to Support Mishap Analysis
NASA Technical Reports Server (NTRS)
Johnson, C. W.; Holloway, C. M.
2002-01-01
The increasing complexity of many safety critical systems poses new problems for mishap analysis. Techniques developed in the sixties and seventies cannot easily scale-up to analyze incidents involving tightly integrated software and hardware components. Similarly, the realization that many failures have systemic causes has widened the scope of many mishap investigations. Organizations, including NASA and the NTSB, have responded by starting research and training initiatives to ensure that their personnel are well equipped to meet these challenges. One strand of research has identified a range of mathematically based techniques that can be used to reason about the causes of complex, adverse events. The proponents of these techniques have argued that they can be used to formally prove that certain events created the necessary and sufficient causes for a mishap to occur. Mathematical proofs can reduce the bias that is often perceived to effect the interpretation of adverse events. Others have opposed the introduction of these techniques by identifying social and political aspects to incident investigation that cannot easily be reconciled with a logic-based approach. Traditional theorem proving mechanisms cannot accurately capture the wealth of inductive, deductive and statistical forms of inference that investigators routinely use in their analysis of adverse events. This paper summarizes some of the benefits that logics provide, describes their weaknesses, and proposes a number of directions for future research.
The Characteristics of Mathematical Creativity
ERIC Educational Resources Information Center
Sriraman, Bharath
2004-01-01
Mathematical creativity ensures the growth of mathematics as a whole. However, the source of this growth, the creativity of the mathematician, is a relatively unexplored area in mathematics and mathematics education. In order to investigate how mathematicians create mathematics, a qualitative study involving five creative mathematicians was…
Remedial Mathematics for Quantum Chemistry
ERIC Educational Resources Information Center
Koopman, Lodewijk; Brouwer, Natasa; Heck, Andre; Buma, Wybren Jan
2008-01-01
Proper mathematical skills are important for every science course and mathematics-intensive chemistry courses rely on a sound mathematical pre-knowledge. In the first-year quantum chemistry course at this university, it was noticed that many students lack basic mathematical knowledge. To tackle the mathematics problem, a remedial mathematics…
NASA Astrophysics Data System (ADS)
Dari, Anna; Kia, Behnam; Bulsara, Adi R.; Ditto, William L.
2011-12-01
Following the advent of synthetic biology, several gene networks have been engineered to emulate digital devices, with the ability to program cells for different applications. In this work, we adapt the concept of logical stochastic resonance to a synthetic gene network derived from a bacteriophage λ. The intriguing results of this study show that it is possible to build a biological logic block that can emulate or switch from the AND to the OR gate functionalities through externally tuning the system parameters. Moreover, this behavior and the robustness of the logic gate are underpinned by the presence of an optimal amount of random fluctuations. We extend our earlier work in this field, by taking into account the effects of correlated external (additive) and internal (multiplicative or state-dependent) noise. Results obtained through analytical calculations as well as numerical simulations are presented.
Astronomy and Mathematics Education
NASA Astrophysics Data System (ADS)
Ros, Rosa M.
There are many European countries where Astronomy does not appear as a specific course on the secondary school. In these cases Astronomy content can be introduced by means of other subjects. There are some astronomical topics within the subject of Physics but this talk concerns introducing Astronomy in Mathematics classes. Teaching Astronomy through Mathematics would result in more exposure than through Physics as Mathematics is more prevalent in the curriculum. Generally it is not easy to motivate students in Mathematics but they are motivated to find out more about the universe and Astronomy current events than appears in the media. This situation can be an excellent introduction to several mathematics topics. The teachers in secondary and high school can use this idea in order to present more attractive mathematics courses. In particular some different examples will be offered regarding * Angles and spherical coordinates considering star traces * Logarithms and visual magnitudes * Plane trigonometry related orbital movements * Spherical trigonometry in connection with ecliptic obliquity * Conic curves related to sundial at several latitudes Some students do not enjoy studying Mathematics but they can be attracted by practical situations using Applied Mathematics: Astronomy is always very attractive to teenagers.
Mathematical techniques: A compilation
NASA Technical Reports Server (NTRS)
1975-01-01
Articles on theoretical and applied mathematics are introduced. The articles cover information that might be of interest to workers in statistics and information theory, computational aids that could be used by scientists and engineers, and mathematical techniques for design and control.
[Collected Papers on Mathematics.
ERIC Educational Resources Information Center
Connell, Michael L., Ed.
This document contains the following papers on issues related to mathematics in technology and teacher education: "A Case for Strong Conceptualization in Technology Enhanced Mathematics Instruction" (Michael L. Connell and Delwyn L. Harnisch); "Faculty/Student Collaboration in Education and Math--Using the Web To Improve Student…
The Applied Mathematics Laboratory.
ERIC Educational Resources Information Center
Siegel, Martha J.
This report describes the Applied Mathematics Laboratory (AML) operated by the Department of Mathematics at Towson State University, Maryland. AML is actually a course offered to selected undergraduates who are given the opportunity to apply their skills in investigating industrial and governmental problems. By agreement with sponsoring…
Mathematics. [SITE 2002 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…
Developing Mathematically Promising Students.
ERIC Educational Resources Information Center
Sheffield, Linda Jensen, Ed.
This book, written on the recommendation of the Task Force on Mathematically Promising Students, investigates issues involving the development of promising mathematics students. Recommendations are made concerning topics such as the definition of promising students; the identification of such students; appropriate curriculum, instruction, and…
Learning Together: Mathematics
ERIC Educational Resources Information Center
Her Majesty's Inspectorate of Education, 2010
2010-01-01
This guide is intended to stimulate professional reflection, dialogue and debate about mathematics and how to improve it. It draws together themes, features and characteristics of effective improvement in mathematics and descriptions of good practice. It offers a reference point for staff and teachers who are working together to improve…
ERIC Educational Resources Information Center
Carr, Martha, Ed.
The purpose of this book is to bring together research and theory about motivation for mathematics from different perspectives. Chapters are included that present theory and research on the influence of gender, culture, the classroom environment, and curriculum on children's mathematical performance and motivation. Chapters are: (1) "Sociocultural…
Mathematics across the Curriculum.
ERIC Educational Resources Information Center
Kleiman, Glenn M.
1991-01-01
Except for its relationship to science, mathematics is the forgotten cousin in interdisciplinary teaching and learning. In the Journeys in Mathematics project, teachers engage children in imaginative activities that inspire them to identify patterns and relationships, solve problems, and communicate accurately, using Jonathan Swift's…
Experimenting with Mathematical Biology
ERIC Educational Resources Information Center
Sanft, Rebecca; Walter, Anne
2016-01-01
St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…
Mathematics in Power Technology.
ERIC Educational Resources Information Center
Trombley, Carl; And Others
This mathematics curriculum is designed to be taught by the technology education teacher during the power technology class over a period of 2 years. It is intended to be elective in nature; upon successful completion of both years, one-half credit in mathematics is to be awarded. A list of the academic competencies contained in the curriculum…