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Sample records for logic mathematics

  1. 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…

  2. 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…

  3. 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.

  4. 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

  5. The Completion of the Emergence of Modern Logic from Boole's The Mathematical Analysis of Logic to Frege's Begriffsschrift

    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.

  6. 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…

  7. 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

  8. The Contribution of Logical Reasoning to the Learning of Mathematics in Primary School

    ERIC Educational Resources Information Center

    Nunes, Terezinha; Bryant, Peter; Evans, Deborah; Bell, Daniel; Gardner, Selina; Gardner, Adelina; Carraher, Julia

    2007-01-01

    It has often been claimed that children's mathematical understanding is based on their ability to reason logically, but there is no good evidence for this causal link. We tested the causal hypothesis about logic and mathematical development in two related studies. In a longitudinal study, we showed that (a) 6-year-old children's logical abilities…

  9. Growth Processes and Formal Logic. Comments on History and Mathematics Regarded as Combined Educational Tools

    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)

  10. [Influence of music on a decision of mathematical logic tasks].

    PubMed

    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. PMID:23101361

  11. Five Departures in Logic, Mathematics, and thus—Whether We Like It, or Not—in Physics as Well...

    NASA Astrophysics Data System (ADS)

    Rosinger, Elemér E.

    2015-07-01

    Physics depends on "physical intuition", much of which is formulated in terms of Mathematics. Mathematics itself depends on Logic. The paper presents three latest novelties in Logic which have major consequences in Mathematics. Further, it presents two possible significant departures in Mathematics itself. These five departures can have major implications in Physics. Some of them are indicated, among them in Quantum Mechanics and Relativity.

  12. The Effect of Teaching Certain Concepts of Logic on Verbalization of Discovered Mathematical Generalizations.

    ERIC Educational Resources Information Center

    Retzer, Kenneth Albert

    Reported are the results of a study designed to test the effects of a programed unit in fundamentals of logic on the ability of college capable junior high school students to verbalize mathematical generalizations. The independent variables were the presence or absence of study of the logic unit, and ability level being college capable (I.Q.…

  13. Mathematical, Logical, and Formal Methods in Information Retrieval: An Introduction to the Special Issue.

    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)

  14. 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…

  15. The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory

    NASA Astrophysics Data System (ADS)

    Frey, Kimberly

    The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum

  16. Contributions from sociology of science to mathematics education in Brazil: logic as a system of beliefs

    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.

  17. Contributions from Sociology of Science to Mathematics Education in Brazil: Logic as a System of Beliefs

    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…

  18. Elements of Mathematics, Book 2: Logic and Sets.

    ERIC Educational Resources Information Center

    Exner, Robert; And Others

    One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…

  19. The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.

    PubMed

    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. PMID:26234709

  20. 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.

  1. A Generalized Instructional System for Elementary Mathematical Logic.

    ERIC Educational Resources Information Center

    Goldberg, Adele

    A computer-based instructional system for teaching the notion of mathematical proof is described. The system is capable of handling formalizations of the full predicate calculus with identity and, with minor work, definite description. Designed as an instructional device, the program is also the basis for a number of research projects involving…

  2. 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)

  3. 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…

  4. An Analysis of Mathematics Teacher Candidates' Critical Thinking Dispositions and Their Logical Thinking Skills

    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…

  5. Identification of Prospective Science Teachers' Mathematical-Logical Structures in Reference to Magnetism

    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…

  6. Mathematical modeling of the lambda switch: a fuzzy logic approach.

    PubMed

    Laschov, Dmitriy; Margaliot, Michael

    2009-10-21

    Gene regulation plays a central role in the development and functioning of living organisms. Gaining a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The Lambda switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the Lambda switch. PMID:19589343

  7. 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.

  8. The link between logic, mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children.

    PubMed

    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. PMID:23786472

  9. Causal Mathematical Logic as a guiding framework for the prediction of "Intelligence Signals" in brain simulations

    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

  10. The evolution of the human mind and logic--mathematics structures.

    PubMed

    Yunes, Rosendo A

    2005-09-01

    The evolution of the human mind is discussed based on: (i) the fact that living beings interchange matter, energy and information with their environment, (ii) an ontological interpretation of the "reality" of the quantum world, of which logic-mathematics structures are considered constitutive parts, (iii) recent theories according to which living beings are considered as dynamic complex systems organized by information, and (iv) the fact that the evolution of living beings is guided by information about the environment and by intrinsic information on living systems (auto-organization). Assuming the evolution of vision as a model we observe that the driving forces that directed the evolution of the eyes, as dynamic complex systems, are the information about the environment supplied by sunlight and the intrinsic information-gaining mechanism of living organisms. Thus, there exists a convergence toward a visual system with the greatest ability to obtain light information, like the human eye, and also a divergence that leads to the development of specific qualities in some species. As in the case of vision the evolution of the human mind-brain cannot be a consequence of factors unrelated to the object of its own functioning. The human mind was structured for the acquisition from reality of the logic-mathematics structures that underlie the whole universe and consequently of an internal representation of the external world and of its own self. Thus, these structures are, together with the intrinsic capacity for auto-organization of the human brain, the predominant driving force of the human mind evolution. Both factors are complementary. PMID:15967187

  11. From boring to scoring - a collaborative serious game for learning and practicing mathematical logic for computer science education

    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."

  12. Secondary School Mathematics, Chapter 27, Logic, Chapter 28, Applications of Probability and Statistics. Student's Text.

    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,…

  13. The Study on the Effect of Educational Games for the Development of Students’ Logic-Mathematics of Multiple Intelligence

    NASA Astrophysics Data System (ADS)

    Li, Jing; Ma, Sujuan; Ma, Linqing

    Firstly, in this article, we expound the theory of the educational games and multiple intelligence and analyze the relationship between them. Then, further, we elaborate educational games' effect on the development of students' multiple intelligence, taking logic-mathematics intelligence for example. Also, we discuss the strategies of using educational games to improve students' intelligence. In a word, we can use the computer games to develop the students' multi-intelligence.

  14. 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

  15. Carpenter, Tractors and Microbes for the Development of Logical-Mathematical Thinking--The Way 10th Graders and Pre-Service Teachers Solve Thinking Challenges

    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…

  16. The relationships between spatial ability, logical thinking, mathematics performance and kinematics graph interpretation skills of 12th grade physics students

    NASA Astrophysics Data System (ADS)

    Bektasli, Behzat

    Graphs have a broad use in science classrooms, especially in physics. In physics, kinematics is probably the topic for which graphs are most widely used. The participants in this study were from two different grade-12 physics classrooms, advanced placement and calculus-based physics. The main purpose of this study was to search for the relationships between student spatial ability, logical thinking, mathematical achievement, and kinematics graphs interpretation skills. The Purdue Spatial Visualization Test, the Middle Grades Integrated Process Skills Test (MIPT), and the Test of Understanding Graphs in Kinematics (TUG-K) were used for quantitative data collection. Classroom observations were made to acquire ideas about classroom environment and instructional techniques. Factor analysis, simple linear correlation, multiple linear regression, and descriptive statistics were used to analyze the quantitative data. Each instrument has two principal components. The selection and calculation of the slope and of the area were the two principal components of TUG-K. MIPT was composed of a component based upon processing text and a second component based upon processing symbolic information. The Purdue Spatial Visualization Test was composed of a component based upon one-step processing and a second component based upon two-step processing of information. Student ability to determine the slope in a kinematics graph was significantly correlated with spatial ability, logical thinking, and mathematics aptitude and achievement. However, student ability to determine the area in a kinematics graph was only significantly correlated with student pre-calculus semester 2 grades. Male students performed significantly better than female students on the slope items of TUG-K. Also, male students performed significantly better than female students on the PSAT mathematics assessment and spatial ability. This study found that students have different levels of spatial ability, logical thinking

  17. Dispositional logic

    SciTech Connect

    Zadeh, L.A.

    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. 7 references.

  18. Dispositional logic

    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.

  19. The Link between Logic, Mathematics and Imagination: Evidence from Children with Developmental Dyscalculia and Mathematically Gifted Children

    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…

  20. Exploring Logical Reasoning and Mathematical Proof in Grade 6 Elementary School Students

    ERIC Educational Resources Information Center

    Flegas, Konstantinos; Charalampos, Lemonidis

    2013-01-01

    Research and classroom experience reveal that the construction of mathematical proofs is difficult for all students. While many contemporary mathematics curricula recognize the importance of teaching reasoning and proof, in Greece these concepts are introduced at the secondary education level. In this study, we will attempt to investigate a group…

  1. Assessment and the Logic of Instructional Practice in Secondary 3 English and Mathematics Classrooms in Singapore

    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…

  2. Mathematical Modeling of spatial disease variables by Spatial Fuzzy Logic for Spatial Decision Support Systems

    NASA Astrophysics Data System (ADS)

    Platz, M.; Rapp, J.; Groessler, M.; Niehaus, E.; Babu, A.; Soman, B.

    2014-11-01

    A Spatial Decision Support System (SDSS) provides support for decision makers and should not be viewed as replacing human intelligence with machines. Therefore it is reasonable that decision makers are able to use a feature to analyze the provided spatial decision support in detail to crosscheck the digital support of the SDSS with their own expertise. Spatial decision support is based on risk and resource maps in a Geographic Information System (GIS) with relevant layers e.g. environmental, health and socio-economic data. Spatial fuzzy logic allows the representation of spatial properties with a value of truth in the range between 0 and 1. Decision makers can refer to the visualization of the spatial truth of single risk variables of a disease. Spatial fuzzy logic rules that support the allocation of limited resources according to risk can be evaluated with measure theory on topological spaces, which allows to visualize the applicability of this rules as well in a map. Our paper is based on the concept of a spatial fuzzy logic on topological spaces that contributes to the development of an adaptive Early Warning And Response System (EWARS) providing decision support for the current or future spatial distribution of a disease. It supports the decision maker in testing interventions based on available resources and apply risk mitigation strategies and provide guidance tailored to the geo-location of the user via mobile devices. The software component of the system would be based on open source software and the software developed during this project will also be in the open source domain, so that an open community can build on the results and tailor further work to regional or international requirements and constraints. A freely available EWARS Spatial Fuzzy Logic Demo was developed wich enables a user to visualize risk and resource maps based on individual data in several data formats.

  3. Making Sense of Student Performance Data: Data Use Logics and Mathematics Teachers' Learning Opportunities

    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.…

  4. Constrained Mathematics for Calculating Logical Safety and Reliability Probabilities with Uncertain Inputs

    SciTech Connect

    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.

  5. 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…

  6. The Effect of Scratch- and Lego Mindstorms Ev3-Based Programming Activities on Academic Achievement, Problem-Solving Skills and Logical-Mathematical Thinking Skills of Students

    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…

  7. Coordinating Mathematical Concepts with the Demands of Authority: Children's Reasoning about Conventional and Second-Order Logical Rules

    ERIC Educational Resources Information Center

    Laupa, Marta; Becker, Joe

    2004-01-01

    Arithmetic algorithms include two types of rules: conventional rules that may be changed by authority, and may legitimately vary from one classroom or country to another (e.g. putting the sum below, rather than above, the numbers added) and logical rules that involve the logic of the algorithm. Changes in the logical rules produce incorrect…

  8. 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…

  9. A Study of Students' Conceptual, Procedural Knowledge, Logical Thinking and Creativity during the First Year of Tertiary Mathematics

    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…

  10. Logical-Mathematical Constructions in an Initial Course at the University: A View of Their Syntactic, Semantic and Pragmatic Aspects

    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…

  11. Foundations of logic programming

    SciTech Connect

    Lloyd, J.W.

    1987-01-01

    This is the second edition of the first book to give an account of the mathematical foundations of Logic Programming. Its purpose is to collect the basic theoretical results of Logic Programming, which have previously only been available in widely scattered research papers. In addition to presenting the technical results, the book also contains many illustrative examples. Many of the examples and problems are part of the folklore of Logic Programming and are not easily obtainable elsewhere.

  12. Identifying Logical Necessity

    ERIC Educational Resources Information Center

    Yopp, David

    2010-01-01

    Understanding logical necessity is an important component of proof and reasoning for teachers of grades K-8. The ability to determine exactly where young students' arguments are faulty offers teachers the chance to give youngsters feedback as they progress toward writing mathematically valid deductive proofs. As defined, logical necessity is the…

  13. Mathematical Games

    ERIC Educational Resources Information Center

    Gardner, Martin

    1978-01-01

    Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)

  14. Introducing Exclusion Logic as a Deontic Logic

    NASA Astrophysics Data System (ADS)

    Evans, Richard

    This paper introduces Exclusion Logic - a simple modal logic without negation or disjunction. We show that this logic has an efficient decision procedure. We describe how Exclusion Logic can be used as a deontic logic. We compare this deontic logic with Standard Deontic Logic and with more syntactically restricted logics.

  15. Why physics needs mathematics

    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.

  16. Teaching Logic.

    ERIC Educational Resources Information Center

    Dyrud, Marilyn A.

    To make introducing logic to college students in speech and expository writing classes more interesting, letters to the editor can be used to teach logical fallacies. Letters to the editor are particularly useful because they give students a sense of the community they live in (issues, concerns, and the spectrum of opinion), they are easily…

  17. 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…

  18. Description Logics

    NASA Astrophysics Data System (ADS)

    Baader, Franz

    Description Logics (DLs) are a well-investigated family of logic-based knowledge representation formalisms, which can be used to represent the conceptual knowledge of an application domain in a structured and formally well-understood way. They are employed in various application domains, such as natural language processing, configuration, and databases, but their most notable success so far is the adoption of the DL-based language OWL as standard ontology language for the semantic web.

  19. The Logic of Life

    NASA Astrophysics Data System (ADS)

    Pascal, Robert; Pross, Addy

    2016-04-01

    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.

  20. 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)

  1. Fuzzy logic

    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.

  2. Helical logic

    NASA Astrophysics Data System (ADS)

    Merkle, Ralph C.; Drexler, K. Eric

    1996-12-01

    Helical logic is a theoretical proposal for a future computing technology using the presence or absence of individual electrons (or holes) to encode 1s and 0s. The electrons are constrained to move along helical paths, driven by a rotating electric field in which the entire circuit is immersed. The electric field remains roughly orthogonal to the major axis of the helix and confines each charge carrier to a fraction of a turn of a single helical loop, moving it like water in an Archimedean screw. Each loop could in principle hold an independent carrier, permitting high information density. One computationally universal logic operation involves two helices, one of which splits into two `descendant' helices. At the point of divergence, differences in the electrostatic potential resulting from the presence or absence of a carrier in the adjacent helix controls the direction taken by a carrier in the splitting helix. The reverse of this sequence can be used to merge two initially distinct helical paths into a single outgoing helical path without forcing a dissipative transition. Because these operations are both logically and thermodynamically reversible, energy dissipation can be reduced to extremely low levels. This is the first proposal known to the authors that combines thermodynamic reversibility with the use of single charge carriers. It is important to note that this proposal permits a single electron to switch another single electron, and does not require that many electrons be used to switch one electron. The energy dissipated per logic operation can very likely be reduced to less than 0957-4484/7/4/004/img5 at a temperature of 1 K and a speed of 10 GHz, though further analysis is required to confirm this. Irreversible operations, when required, can be easily implemented and should have a dissipation approaching the fundamental limit of 0957-4484/7/4/004/img6.

  3. Infinitesimals without logic

    NASA Astrophysics Data System (ADS)

    Giordano, P.

    2010-06-01

    We introduce a ring of the so-called Fermat reals, which is an extension of the real field containing nilpotent infinitesimals. The construction is inspired by Smooth Infinitesimal Analysis (SIA) and provides a powerful theory of actual infinitesimals without any background in mathematical logic. In particular, in contrast to SIA, which admits models in intuitionistic logic only, the theory of Fermat reals is consistent with the classical logic. We face the problem of deciding whether or not a product of powers of nilpotent infinitesimals vanishes, study the identity principle for polynomials, and discuss the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order-preserving geometrical representation. Using nilpotent infinitesimals, every smooth function becomes a polynomial because the remainder in Taylor’s formulas is now zero. Finally, we present several applications to informal classical calculations used in physics, and all these calculations now become rigorous, and at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, which clarifies how to formalize the approximations tied with Hooke’s law using the language of nilpotent infinitesimals.

  4. Indeterminacy, linguistic semantics and fuzzy logic

    SciTech Connect

    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.

  5. 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…

  6. Philosophy and mathematics: interactions.

    PubMed

    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. PMID:25029825

  7. 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.

  8. Automated deduction for first-order logic with equality

    Energy Science and Technology Software Center (ESTSC)

    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.

  9. Automated deduction for first-order logic with equality

    Energy Science and Technology Software Center (ESTSC)

    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.

  10. 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…

  11. Preservice Elementary Teachers' Understanding of Logical Inference

    ERIC Educational Resources Information Center

    Hauk, Shandy; Judd, April Brown; Tsay, Jenq Jong; Barzilai, Harel; Austin, Homer

    2009-01-01

    This article reports on the logical reasoning efforts of five prospective elementary school teachers as they responded to interview prompts involving nonsense, natural, and mathematical representations of conditional statements. The interview participants evinced various levels of reliance on personal relevance, linguistic contextualization, and…

  12. 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…

  13. The Assessment of Mathematical Abilities.

    ERIC Educational Resources Information Center

    Osborn, Herbert H.

    1983-01-01

    A test was given to 322 secondary students to develop a profile of mathematical ability based on four components: computation, pattern recognition, logical reasoning, and symbolic manipulation. These profiles were compared to mathematics test scores; the results verified hypotheses about individual differences in mental processes and knowledge…

  14. Audiovisual Materials in Mathematics.

    ERIC Educational Resources Information Center

    Raab, Joseph A.

    This pamphlet lists five thousand current, readily available audiovisual materials in mathematics. These are grouped under eighteen subject areas: Advanced Calculus, Algebra, Arithmetic, Business, Calculus, Charts, Computers, Geometry, Limits, Logarithms, Logic, Number Theory, Probability, Soild Geometry, Slide Rule, Statistics, Topology, and…

  15. Fuzzy logic controller optimization

    DOEpatents

    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.

  16. Paraconsistent quantum logics

    NASA Astrophysics Data System (ADS)

    Chiara, Maria Luisa Dalla; Giuntini, Roberto

    1989-07-01

    Paraconsistent quantum logics are weak forms of quantum logic, where the noncontradiction and the excluded-middle laws are violated. These logics find interesting applications in the operational approach to quantum mechanics. In this paper, we present an axiomatization, a Kripke-style, and an algebraic semantical characterization for two forms of paraconsistent quantum logic. Further developments are contained in Giuntini and Greuling's paper in this issue.

  17. OncoLogicTM

    EPA Science Inventory

    OncoLogicTM - A Computer System to Evaluate the Carcinogenic Potential of Chemicals
    OncoLogicTM is a software program that evaluates the likelihood that a chemical may cause cancer. OncoLogicTM has been peer reviewed and is being rele...

  18. Unified Modern Mathematics, Course 2, Part 1.

    ERIC Educational Resources Information Center

    Secondary School Mathematics Curriculum Improvement Study, New York, NY.

    This is Part 1 of the second course in a series which focuses on building fundamental mathematical structures. Topics considered in this book include: an introduction to mathematical logic and mathematical proof, a continuation of the study of groups, an introduction to axiomatic affine geometry, fields, the real number system, and coordinate…

  19. 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…

  20. 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.

  1. Digital Holographic Logic

    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.

  2. Digital Microfluidic Logic Gates

    NASA Astrophysics Data System (ADS)

    Zhao, Yang; Xu, Tao; Chakrabarty, Krishnendu

    Microfluidic computing is an emerging application for microfluidics technology. We propose microfluidic logic gates based on digital microfluidics. Using the principle of electrowetting-on-dielectric, AND, OR, NOT and XOR gates are implemented through basic droplet-handling operations such as transporting, merging and splitting. The same input-output interpretation enables the cascading of gates to create nontrivial computing systems. We present a potential application for microfluidic logic gates by implementing microfluidic logic operations for on-chip HIV test.

  3. 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.)

  4. Electrically reconfigurable logic array

    NASA Technical Reports Server (NTRS)

    Agarwal, R. K.

    1982-01-01

    To compose the complicated systems using algorithmically specialized logic circuits or processors, one solution is to perform relational computations such as union, division and intersection directly on hardware. These relations can be pipelined efficiently on a network of processors having an array configuration. These processors can be designed and implemented with a few simple cells. In order to determine the state-of-the-art in Electrically Reconfigurable Logic Array (ERLA), a survey of the available programmable logic array (PLA) and the logic circuit elements used in such arrays was conducted. Based on this survey some recommendations are made for ERLA devices.

  5. Fuzzy Logic Engine

    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.

  6. Meaning and Process in Mathematics and Programming.

    ERIC Educational Resources Information Center

    Grogono, Peter

    1989-01-01

    Trends in computer programing language design are described and children's difficulties in learning to write programs for mathematics problems are considered. Languages are compared under the headings of imperative programing, functional programing, logic programing, and pictures. (DC)

  7. 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…

  8. AROUSAL AND LOGICAL INFERENCE.

    ERIC Educational Resources Information Center

    KOEN, FRANK

    THE PURPOSE OF THE EXPERIMENT WAS TO DETERMINE THE DEGREE TO WHICH PHYSIOLOGICAL AROUSAL, AS INDEXED BY THE GRASON STADLER TYPE OPERANT CONDITIONING APPARATUS (GSR), IS RELATED TO THE ACCURACY OF LOGICAL REASONING. THE STIMULI WERE 12 SYLLOGISMS, THREE OF EACH OF FOUR DIFFERENT LOGICAL FORMS. THE 14 SUBJECTS (SS) INDICATED THEIR AGREEMENT OR…

  9. 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)…

  10. Microelectromechanical reprogrammable logic device

    PubMed Central

    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

  11. Fuzziness in abacus logic

    NASA Astrophysics Data System (ADS)

    Malhas, Othman Qasim

    1993-10-01

    The concept of “abacus logic” has recently been developed by the author (Malhas, n.d.). In this paper the relation of abacus logic to the concept of fuzziness is explored. It is shown that if a certain “regularity” condition is met, concepts from fuzzy set theory arise naturally within abacus logics. In particular it is shown that every abacus logic then has a “pre-Zadeh orthocomplementation”. It is also shown that it is then possible to associate a fuzzy set with every proposition of abacus logic and that the collection of all such sets satisfies natural conditions expected in systems of fuzzy logic. Finally, the relevance to quantum mechanics is discussed.

  12. Microelectromechanical reprogrammable logic device.

    PubMed

    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

  13. 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.

  14. 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…

  15. Uncertainty, energy, and multiple-valued logics

    SciTech Connect

    Hayes, J.P.

    1986-02-01

    The multiple-valued logics obtained by introducing uncertainty and energy considerations into classical switching theory are studied in this paper. First, the nature of uncertain or unknown signals is examined, and two general uncertainty types called U-values and P-values are identified. It is shown that multiple-valued logics composed of U/P-values can be systematically derived from 2-valued Boolean algebra. These are useful for timing and hazard analysis, and provide a rigorous framework for designing gate-level logic simulation programs. Next, signals of the form (..nu..,S) are considered where ..nu.. and S denote logic level and strength, respectively, and the product vs corresponds to energy flow or power. It is shown that these signals from a type of lattice called a Pseudo-Boolean algebra. Such algebras characterize the behavior of digital circuits at a level (the switch level) intermediate between the conventional analog and logical levels. They provide the mathematical basis for an efficient new class of switch-level simulation programs used in MOS VLSI design.

  16. 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.

  17. Applications of fuzzy logic

    SciTech Connect

    Zargham, M.R.

    1995-06-01

    Recently, fuzzy logic has been applied to many areas, such as process control, image understanding, robots, expert systems, and decision support systems. This paper will explain the basic concepts of fuzzy logic and its application in different fields. The steps to design a control system will be explained in detail. Fuzzy control is the first successful industrial application of fuzzy logic. A fuzzy controller is able to control systems which previously could only be controlled by skilled operators. In recent years Japan has achieved significant progress in this area and has applied it to variety of products such as cruise control for cars, video cameras, rice cookers, washing machines, etc.

  18. Optical logic array processor

    SciTech Connect

    Tanida, J.; Ichioka, Y.

    1983-01-01

    A simple method for optically implementing digital logic gates in parallel has been developed. Parallel logic gates can be achieved by using a lensless shadow-casting system with a light emitting diode array as an incoherent light source. All the sixteen logic functions for two binary variables, which are the fundamental computations of Boolean algebra, can be simply realised in parallel with these gates by changing the switching modes of a led array. Parallel computation structures of the developed optical digital array processor are demonstrated by implementing pattern logics for two binary images with high space-bandwidth product. Applications of the proposed method to parallel shift operation of the image, differentiation, and processing of gray-level image are shown. 9 references.

  19. Beyond Numbers: The Mathematics Literature Connection.

    ERIC Educational Resources Information Center

    Madison, John P.; Seidenstein, Roslynn

    This document is a collection of activities designed to use children's literature to introduce, reinforce or broaden mathematics skills and concepts. The mathematical topics that are addressed include: time; problem solving; logic; measurement; comparison; sets; one-to-one correspondence; fraction concepts; division; counting; averages; infinity;…

  20. Mathematics Underground

    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…

  1. Mechanical passive logic module

    NASA Astrophysics Data System (ADS)

    Chattopadhyay, Tanay; Caulfield, H. John

    2015-02-01

    Nothing from nothing gives simple simile, but something from nothing is an interesting and challenging task. Adolf Lohmann once proposed 'do nothing machine' in optics, which only copies input to output. Passive logic module (PALM) is a special type of 'do nothing machine' which can converts inputs into one of 16 possible binary outputs. This logic module is not like the conventional irreversible one. It is a simple type of reversible Turing machine. In this manuscript we discussed and demonstrated PALM using mechanical movement of plane mirrors. Also we discussed the theoretical model of micro electro mechanical system (MEMS) based PALM in this manuscript. It may have several valuable properties such as passive operation (no need for nonlinear elements as other logic device require) and modular logic (one device implementing any Boolean logic function with simple internal changes). The result is obtained from the demonstration by only looking up the output. No calculation is required to get the result. Not only that, PALM is a simple type of the famous 'billiard ball machine', which also discussed in this manuscript.

  2. 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.

  3. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

    PubMed

    Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

    2015-01-01

    Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

  4. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

    PubMed Central

    Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

    2015-01-01

    Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

  5. 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.)

  6. 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…

  7. 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…

  8. Benchmarking emerging logic devices

    NASA Astrophysics Data System (ADS)

    Nikonov, Dmitri

    2014-03-01

    As complementary metal-oxide-semiconductor field-effect transistors (CMOS FET) are being scaled to ever smaller sizes by the semiconductor industry, the demand is growing for emerging logic devices to supplement CMOS in various special functions. Research directions and concepts of such devices are overviewed. They include tunneling, graphene based, spintronic devices etc. The methodology to estimate future performance of emerging (beyond CMOS) devices and simple logic circuits based on them is explained. Results of benchmarking are used to identify more promising concepts and to map pathways for improvement of beyond CMOS computing.

  9. Logic Simulator Program

    NASA Technical Reports Server (NTRS)

    Agarwal, R. K.

    1983-01-01

    The source code for the SPICE 2 program was deblocked in order to isolate and compile the subroutine in an effort to provide a software simulation of discrete and combinatorial electronic components. Incompatibilities between the UNIVAC 1180 FORTRAN and the Sigma V CP-V FORTRAN 4 were resolved. The SPICE 2 model is to be used to determine gate and fan-out delays, logic state conditions, and signal race conditions for transistor array elements and circuit logic to be patterned in the (SPI) 7101 CMOS silicon gate semicustom array. The simulator is to be operable from the CP-V time sharing terminals.

  10. Reprint Series: What is Contemporary Mathematics. RS-3.

    ERIC Educational Resources Information Center

    Schaaf, William L., Ed.

    This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the nature of mathematics; (2) mathematical inutility and the advance of science; and (3) logic. (MP)

  11. 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…

  12. Logic production systems: Analysis and synthesis

    SciTech Connect

    Donskoi, V.I.

    1995-03-01

    Many applied systems can be described in the following terms: given is a certain number of objects and a set of rules to construct new object from the original objects and from previously constructed objects. Mathematicians call such systems deductive, or calculi. Artificial intelligence scientists subsequently improved and elaborated the notion of production, retaining the Post operator A {yields} B as a basic element or a core. Production models are generally regarded as lacking a rigorous theory and governed by heuristics. Maslov noted: {open_quotes}We may assume that the language of calculi will become in the near future as natural and as widespread in new applications of discrete mathematics as, for instance, the language of graph theory is today.{close_quotes} Studies whose results are surveyed below were triggered by the development of applications of production systems in dual expert systems and focus around the following topics: (1) formalization of logic production systems (Pospelov has noted that results in the theory of production systems can be obtained by restricting the notion of productions and production systems); (2) analysis of completeness of logic production systems as a tool for realization of Boolean functions; (3) construction of a universal algorithmic model based on a logic production system; (4) construction of algorithms that synthesize the domain of deductive derivability of a given goal fact and analysis of algorithmic complexity of the corresponding problem. It is important to note that the results obtained so far relate to a strictly defined subclass - the subclass of logic production systems and machines. They do not pretend to cover the wider domain of applicability of the apparatus of deductive systems. Classical concepts and propositions of discrete mathematics used in this paper without further explanation are defined in existing literature.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Logic and Simulation.

    ERIC Educational Resources Information Center

    Straumanis, Joan

    A major problem in teaching symbolic logic is that of providing individualized and early feedback to students who are learning to do proofs. To overcome this difficulty, a computer program was developed which functions as a line-by-line proof checker in Sentential Calculus. The program, DEMON, first evaluates any statement supplied by the student…

  19. On Mathematical Proving

    NASA Astrophysics Data System (ADS)

    Stefaneas, Petros; Vandoulakis, Ioannis M.

    2015-12-01

    This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.

  20. Sandia ATM SONET Interface Logic

    Energy Science and Technology Software Center (ESTSC)

    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.

  1. Mathematics, Anyone?

    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…

  2. Active structural control by fuzzy logic rules: An introduction

    SciTech Connect

    Tang, Yu; Wu, Kung C.

    1996-12-31

    A zeroth level introduction to fuzzy logic control applied to the active structural control to reduce the dynamic response of structures subjected to earthquake excitations is presented. It is hoped that this presentation will increase the attractiveness of the methodology to structural engineers in research as well as in practice. The basic concept of the fuzzy logic control are explained by examples and by diagrams with a minimum of mathematics. The effectiveness and simplicity of the fuzzy logic control is demonstrated by a numerical example in which the response of a single- degree-of-freedom system subjected to earthquake excitations is controlled by making use of the fuzzy logic controller. In the example, the fuzzy rules are first learned from the results obtained from linear control theory; then they are fine tuned to improve their performance. It is shown that the performance of fuzzy logic control surpasses that of the linear control theory. The paper shows that linear control theory provides experience for fuzzy logic control, and fuzzy logic control can provide better performance; therefore, two controllers complement each other.

  3. Active structural control by fuzzy logic rules: An introduction

    SciTech Connect

    Tang, Y.

    1995-07-01

    An introduction to fuzzy logic control applied to the active structural control to reduce the dynamic response of structures subjected to earthquake excitations is presented. It is hoped that this presentation will increase the attractiveness of the methodology to structural engineers in research as well as in practice. The basic concept of the fuzzy logic control are explained by examples and by diagrams with a minimum of mathematics. The effectiveness and simplicity of the fuzzy logic control is demonstrated by a numerical example in which the response of a single-degree-of-freedom system subjected to earthquake excitations is controlled by making use of the fuzzy logic controller. In the example, the fuzzy rules are first learned from the results obtained from linear control theory; then they are fine tuned to improve their performance. It is shown that the performance of fuzzy logic control surpasses that of the linear control theory. The paper shows that linear control theory provides experience for fuzzy logic control, and fuzzy logic control can provide better performance; therefore, two controllers complement each other.

  4. The mysterious connection between mathematics and physics.

    PubMed

    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. PMID:26278645

  5. 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 15-week…

  6. Logic of infinite quantum systems

    NASA Astrophysics Data System (ADS)

    Mundici, Daniele

    1993-10-01

    Limits of sequences of finite-dimensional (AF) C *-algebras, such as the CAR algebra for the ideal Fermi gas, are a standard mathematical tool to describe quantum statistical systems arising as thermodynamic limits of finite spin systems. Only in the infinite-volume limit one can, for instance, describe phase transitions as singularities in the thermodynamic potentials, and handle the proliferation of physically inequivalent Hilbert space representations of a system with infinitely many degrees of freedom. As is well known, commutative AF C *-algebras correspond to countable Boolean algebras, i.e., algebras of propositions in the classical two-valued calculus. We investigate the noncommutative logic properties of general AF C *-algebras, and their corresponding systems. We stress the interplay between Gödel incompleteness and quotient structures in the light of the “nature does not have ideals” program, stating that there are no quotient structures in physics. We interpret AF C *-algebras as algebras of the infinite-valued calculus of Lukasiewicz, i.e., algebras of propositions in Ulam's “ twenty questions” game with lies.

  7. 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.

  8. 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.

  9. A molecular logic gate

    PubMed Central

    Kompa, K. L.; Levine, R. D.

    2001-01-01

    We propose a scheme for molecule-based information processing by combining well-studied spectroscopic techniques and recent results from chemical dynamics. Specifically it is discussed how optical transitions in single molecules can be used to rapidly perform classical (Boolean) logical operations. In the proposed way, a restricted number of states in a single molecule can act as a logical gate equivalent to at least two switches. It is argued that the four-level scheme can also be used to produce gain, because it allows an inversion, and not only a switching ability. The proposed scheme is quantum mechanical in that it takes advantage of the discrete nature of the energy levels but, we here discuss the temporal evolution, with the use of the populations only. On a longer time range we suggest that the same scheme could be extended to perform quantum logic, and a tentative suggestion, based on an available experiment, is discussed. We believe that the pumping can provide a partial proof of principle, although this and similar experiments were not interpreted thus far in our terms. PMID:11209046

  10. Mathematics--Is It Any of Your Business?

    ERIC Educational Resources Information Center

    Mansfield, Ralph

    1975-01-01

    In this paper, the first section of a three-part article, the author discusses applications of mathematical theories in business situations. He explores the use of logic and networks in counting and accounting problems. (SD)

  11. A Logical Analysis of Majorana's Papers on Theoretical Physics

    NASA Astrophysics Data System (ADS)

    Drago, A.; Esposito, S.

    2006-05-01

    We study two celebrated Majorana's papers through a method of investigation which relies upon the recently recognized distinction between classical logic and several kinds of non-classical logics, i.e. the failure of the double negation law. This law fails when a double negated sentence is not equivalent to the corresponding positive sentence, owing to the lack of scientific evidence of the latter one. All recognized double negated sentences inside the text of each paper are listed; the mere sequence of such sentences giving the logical thread of Majorana's arguing. This one is recognized to be of the Lagrangian kind, which mixes logical arguing and mathematical calculation; i.e. the author puts a fundamental problem which is solved by anticipating the mathematical hypothesis able to solve it, and then by drawing from this hypothesis the mathematical consequences in order to reach to desired result. Furthermore the rethoric of presentation used by Majorana results to be a juridical one, owing to his style of presenting the laws to which an ideal theoretical physicist has to conform his mind in order to solve the problem at issue.

  12. Mathematical Geology.

    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)

  13. Mathematic Terminology.

    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)

  14. Mathematics disorder

    MedlinePlus

    ... 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 ...

  15. 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.

  16. Rainforest Mathematics

    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…

  17. 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.

  18. 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.

  19. Flexible programmable logic module

    SciTech Connect

    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.

  20. A mathematical model of a computational problem solving system

    NASA Astrophysics Data System (ADS)

    Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan

    2015-05-01

    This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.

  1. 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…

  2. Adaptive parallel logic networks

    SciTech Connect

    Martinez, T.R.; Vidal, J.J.

    1988-02-01

    This paper presents a novel class of special purpose processors referred to as ASOCS (adaptive self-organizing concurrent systems). Intended applications include adaptive logic devices, robotics, process control, system malfunction management, and in general, applications of logic reasoning. ASOCS combines massive parallelism with self-organization to attain a distributed mechanism for adaptation. The ASOCS approach is based on an adaptive network composed of many simple computing elements (nodes) which operate in a combinational and asynchronous fashion. Problem specification (programming) is obtained by presenting to the system if-then rules expressed as Boolean conjunctions. New rules are added incrementally. In the current model, when conflicts occur, precedence is given to the most recent inputs. With each rule, desired network response is simply presented to the system, following which the network adjusts itself to maintain consistency and parsimony of representation. Data processing and adaptation form two separate phases of operation. During processing, the network acts as a parallel hardware circuit. Control of the adaptive process is distributed among the network nodes and efficiently exploits parallelism.

  3. Barriers in Concurrent Separation Logic

    NASA Astrophysics Data System (ADS)

    Hobor, Aquinas; Gherghina, Cristian

    We develop and prove sound a concurrent separation logic for Pthreads-style barriers. Although Pthreads barriers are widely used in systems, and separation logic is widely used for verification, there has not been any effort to combine the two. Unlike locks and critical sections, Pthreads barriers enable simultaneous resource redistribution between multiple threads and are inherently stateful, leading to significant complications in the design of the logic and its soundness proof. We show how our logic can be applied to a specific example program in a modular way. Our proofs are machine-checked in Coq.

  4. An SEU immune logic family

    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.

  5. 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.

  6. Theoretical Mathematics

    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.

  7. The materiality of mathematics: presenting mathematics at the blackboard.

    PubMed

    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. PMID:24620862

  8. Fuzzy Logic Particle Tracking

    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

  9. 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.

  10. Reversible logic gates on Physarum Polycephalum

    SciTech Connect

    Schumann, Andrew

    2015-03-10

    In this paper, we consider possibilities how to implement asynchronous sequential logic gates and quantum-style reversible logic gates on Physarum polycephalum motions. We show that in asynchronous sequential logic gates we can erase information because of uncertainty in the direction of plasmodium propagation. Therefore quantum-style reversible logic gates are more preferable for designing logic circuits on Physarum polycephalum.

  11. The logic of deterrence

    SciTech Connect

    Kenny, A.

    1985-01-01

    In The Logic of Deterrence, Kenny presents a guide to the theory and ethics of the complicated subject of deterrence. Kenny begins by examining the necessary conditions for any war to be just and then applies these principles to the cases of limited and total nuclear war. He then critiques current deterrence policies of both East and West, concluding that they are based on a willingness to kill millions of innocent people and are morally wrong. In the final section of the book, Kenny offers proposals for nuclear disarmament. Charting a course ''between the illusory hopes of the multilateralists who seek disarmament by negotiating and the impractical idealism of those who call for immediate and total unilateral disarmament by the West,'' Kenny proposes a series of phased and partial unilateral steps by the West, coupled with pressure on the East to reciprocate.

  12. Ground State Spin Logic

    NASA Astrophysics Data System (ADS)

    Whitfield, James; Faccin, Mauro; Biamonte, Jacob

    2013-03-01

    Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin Hamiltonians. Using an approach based on group theory and symmetries, we examine the embedding of Boolean logic gates into the ground-state subspace of such spin systems. We describe parameterized families of diagonal Hamiltonians and symmetry operations which preserve the ground-state subspace encoding the truth tables of Boolean formulas. The ground-state embeddings of adder circuits are used to illustrate how gates are combined and simplified using symmetry. Our work is relevant for experimental demonstrations of ground-state embeddings found in both classical optimization as well as adiabatic quantum optimization.

  13. A Logical Process Calculus

    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.

  14. Oscillatory Threshold Logic

    PubMed Central

    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

  15. Quantificational logic of context

    SciTech Connect

    Buvac, Sasa

    1996-12-31

    In this paper we extend the Propositional Logic of Context, to the quantificational (predicate calculus) case. This extension is important in the declarative representation of knowledge for two reasons. Firstly, since contexts are objects in the semantics which can be denoted by terms in the language and which can be quantified over, the extension enables us to express arbitrary first-order properties of contexts. Secondly, since the extended language is no longer only propositional, we can express that an arbitrary predicate calculus formula is true in a context. The paper describes the syntax and the semantics of a quantificational language of context, gives a Hilbert style formal system, and outlines a proof of the system`s completeness.

  16. Partial quantum logics revisited

    NASA Astrophysics Data System (ADS)

    Vetterlein, Thomas

    2011-01-01

    Partial Boolean algebras (PBAs) were introduced by Kochen and Specker as an algebraic model reflecting the mutual relationships among quantum-physical yes-no tests. The fact that not all pairs of tests are compatible was taken into special account. In this paper, we review PBAs from two sides. First, we generalise the concept, taking into account also those yes-no tests which are based on unsharp measurements. Namely, we introduce partial MV-algebras, and we define a corresponding logic. Second, we turn to the representation theory of PBAs. In analogy to the case of orthomodular lattices, we give conditions for a PBA to be isomorphic to the PBA of closed subspaces of a complex Hilbert space. Hereby, we do not restrict ourselves to purely algebraic statements; we rather give preference to conditions involving automorphisms of a PBA. We conclude by outlining a critical view on the logico-algebraic approach to the foundational problem of quantum physics.

  17. The Logical Extension

    NASA Technical Reports Server (NTRS)

    2003-01-01

    The same software controlling autonomous and crew-assisted operations for the International Space Station (ISS) is enabling commercial enterprises to integrate and automate manual operations, also known as decision logic, in real time across complex and disparate networked applications, databases, servers, and other devices, all with quantifiable business benefits. Auspice Corporation, of Framingham, Massachusetts, developed the Auspice TLX (The Logical Extension) software platform to effectively mimic the human decision-making process. Auspice TLX automates operations across extended enterprise systems, where any given infrastructure can include thousands of computers, servers, switches, and modems that are connected, and therefore, dependent upon each other. The concept behind the Auspice software spawned from a computer program originally developed in 1981 by Cambridge, Massachusetts-based Draper Laboratory for simulating tasks performed by astronauts aboard the Space Shuttle. At the time, the Space Shuttle Program was dependent upon paper-based procedures for its manned space missions, which typically averaged 2 weeks in duration. As the Shuttle Program progressed, NASA began increasing the length of manned missions in preparation for a more permanent space habitat. Acknowledging the need to relinquish paper-based procedures in favor of an electronic processing format to properly monitor and manage the complexities of these longer missions, NASA realized that Draper's task simulation software could be applied to its vision of year-round space occupancy. In 1992, Draper was awarded a NASA contract to build User Interface Language software to enable autonomous operations of a multitude of functions on Space Station Freedom (the station was redesigned in 1993 and converted into the international venture known today as the ISS)

  18. 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…

  19. 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,…

  20. Japanese Logic Puzzles and Proof

    ERIC Educational Resources Information Center

    Wanko, Jeffrey J.

    2009-01-01

    An understanding of proof does not start in a high school geometry course. Rather, attention to logical reasoning throughout a student's school experience can help the development of proof readiness. In the spirit of problem solving, the author has begun to use some Japanese logic puzzles other than sudoku to help students develop additional…

  1. [Brunschvicg, bachelard and the internal logic of scientific discourse].

    PubMed

    Gauthier, Yvon

    2013-01-01

    Bachelard is seen as sharing with Brunschvicg an "internalist" epistemology of mathematics and exact sciences. Brunschvicg's notion of constructive idealism concurs with Bachelard's surrationalism. Both philosophers defended the idea of an internal logic of scientific discourse which discloses the dialectics inherent in the dynamics of reason. The aim of philosophy is then to emphasize the genesis and progress of rationality in the historical development of science. PMID:24091652

  2. 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.

  3. Investigating Student Use of Electronic Support Tools and Mathematical Reasoning

    ERIC Educational Resources Information Center

    Higgins, Kristina N.; Crawford, Lindy; Huscroft-D'Angelo, Jacqueline; Horney, Mark

    2016-01-01

    Mathematical reasoning involves comprehending mathematical information and concepts in a logical way and forming conclusions and generalizations based on this comprehension. Computer-based learning has been incorporated into classrooms across the country, and specific aspects of technology need to be studied to determine how programs are…

  4. A Mathematics Educator's Introduction to Rural Policy Issues

    ERIC Educational Resources Information Center

    Waters, Michael S., Ed.

    2005-01-01

    Most of the scholarship and commentary on mathematics education deals with issues of curriculum and instruction; this is understandable in a field logically belonging to the domain of curriculum and instruction. Moreover, issues of teaching and learning are compelling to people who love to learn and teach mathematics. Policy receives shorter…

  5. Teaching Mathematics from a Chemist's Viewpoint.

    ERIC Educational Resources Information Center

    DeLorenzo, Ronald A.

    This paper describes a chemistry professor's approach to teaching mathematics in the college classroom. Based on the assumption that the four main goals of the educational process in general are to teach students to communicate clearly, study regularly, master basic math skills, and think logically, a description is provided of the manner in which…

  6. 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…

  7. Killeen's (2005) p rep coefficient: logical and mathematical problems.

    PubMed

    Maraun, Michael; Gabriel, Stephanie

    2010-06-01

    In his article, "An alternative to null-hypothesis significance tests," Killeen (2005) urged the discipline to abandon the practice of p obs-based null hypothesis testing and to quantify the signal-to-noise characteristics of experimental outcomes with replication probabilities. He described the coefficient that he invented, prep, as the probability of obtaining "an effect of the same sign as that found in an original experiment" (Killeen, 2005, p. 346). The journal Psychological Science quickly came to encourage researchers to employ prep, rather than p obs, in the reporting of their experimental findings. In the current article, we (a) establish that Killeen's derivation of prep contains an error, the result of which is that prep is not, in fact, the probability that Killeen set out to derive; (b) establish that prep is not a replication probability of any kind but, rather, is a quasi-power coefficient; and (c) suggest that Killeen has mischaracterized both the relationship between replication probabilities and statistical inference, and the kinds of claims that are licensed by knowledge of the value assumed by the replication probability that he attempted to derive. PMID:20515239

  8. 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…

  9. 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…

  10. 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…

  11. 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

  12. Experimental Mathematics and Mathematical Physics

    SciTech Connect

    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.

  13. MLS, a magnetic logic simulator for magnetic bubble logic design

    NASA Astrophysics Data System (ADS)

    Kinsman, Thomas B.; Cendes, Zoltan J.

    1987-04-01

    A computer program that simulates the logic functions of magnetic bubble devices has been developed. The program uses a color graphics screen to display the locations of bubbles on a chip during operation. It complements the simulator previously developed for modeling bubble devices on the gate level [Smith et al., IEEE Trans. Magn. MAG-19, 1835 (1983); Smith and Kryder, ibid. MAG-21, 1779 (1985)]. This new tool simplifies the design and testing of bubble logic devices, and facilitates the development of complicated LSI bubble circuits. The program operation is demonstrated with the design of an in-stream faulty loop compensator using bubble logic.

  14. Mathematical opportunities in nonlinear optics

    NASA Astrophysics Data System (ADS)

    The Board on Mathematical Sciences takes as one of its functions that of identifying areas of important or emerging research activity and focusing attention on them. The Board seeks to stimulate cross-disciplinary research between mathematical sciences and disciplines. This survey notes that on the technological side nonlinear optics is likely to revolutionize future telecommunications and computer technologies, while on the mathematical side it is an ideal subject for the applied mathematician, who is particularly well positioned to make major contributions. Topics covered include wave propagation and the nonlinear Schrodinger equation; soliton propagation in the optical fibers; nonlinear waveguides; four-wave mixing, phase conjunction, and beam cleanup; lasers; optical bistability, logic elements, and information storing patterns; and spatiotemporal complexity and turbulence in nonlinear optics.

  15. A hierarchical cellular logic for pyramid computers

    SciTech Connect

    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.

  16. Mathematics Scrapbook

    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…

  17. Mathematics Education.

    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…

  18. Technical Mathematics.

    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…

  19. Innovative Mathematics.

    ERIC Educational Resources Information Center

    Siskiyou County Superintendent of Schools, Yreka, CA.

    The purpose of this project was to raise the mathematics skills of 100 mathematically retarded students in grades one through eight by one year through the development of an inservice strategy prepared by four teacher specialists. Also used in the study was a control group of 100 students chosen from the median range of stanines on pretest scores…

  20. Cognitive dynamic logic algorithms for situational awareness

    NASA Astrophysics Data System (ADS)

    Perlovsky, L. I.; Ilin, R.

    2010-04-01

    Autonomous situational awareness (SA) requires an ability to learn situations. It is mathematically difficult because in every situation there are many objects nonessential for this situation. Moreover, most objects around are random, unrelated to understanding contexts and situations. We learn in early childhood to ignore these irrelevant objects effortlessly, usually we do not even notice their existence. Here we consider an agent that can recognize a large number of objects in the world; in each situation it observes many objects, while only few of them are relevant to the situation. Most of situations are collections of random objects containing no relevant objects, only few situations "make sense," they contain few objects, which are always present in these situations. The training data contains sufficient information to identify these situations. However, to discover this information all objects in all situations should be sorted out to find regularities. This "sorting out" is computationally complex; its combinatorial complexity exceeds by far all events in the Universe. The talk relates this combinatorial complexity to Gödelian limitations of logic. We describe dynamic logic (DL) that quickly learns essential regularities-relevant, repeatable objects and situations. DL is related to mechanisms of the brain-mind and we describe brain-imaging experiments that have demonstrated these relations.

  1. Contradicting logics in everyday practice.

    PubMed

    Kristiansen, Margrethe; Obstfelder, Aud; Lotherington, Ann Therese

    2016-03-21

    Purpose - Performance management is criticised as a direct challenge to the dominant logic of professionalism in health care organisations. The purpose of this paper is to report an ethnographic study that investigates how performance management and professionalism as contradicting logics are interpreted and implemented by managers and nurses in everyday practice within Norwegian nursing homes. Design/methodology/approach - The paper presents an analysis of 18 semistructured interviews and 100 hours of observation of managers and nurses from three nursing homes. The study draws on the institutional logic perspective as a theoretical framework. In the analysis, the authors searched for patterns of activities and interactions that reflected managers and nurses' coping strategies for handling contradicting logics. Qualitative content analysis was used to systematically code the data, supported by NVIVO software. Findings - The authors identified three forms of coping strategies: the adjustment of professionalism to standards, the reinforcement of professional flexibility and problem solving, and the strategic adoption of documentation. These patterns of activities and interactions reflect new organisational structures that allowed contradicting logics to co-exist. The study demonstrates that a new complex dimension of governing processes within nursing homes is the way in which managers and nurses handle the tension between contradicting logics in their daily work and clinicians' everyday practice. Originality/value - The study provides new insight into how managers and nurses reshape internal organisational structures to cope with contradicting logics in nursing homes. PMID:26964849

  2. Fuzzy logic in control systems: Fuzzy logic controller. I, II

    NASA Technical Reports Server (NTRS)

    Lee, Chuen Chien

    1990-01-01

    Recent advances in the theory and applications of fuzzy-logic controllers (FLCs) are examined in an analytical review. The fundamental principles of fuzzy sets and fuzzy logic are recalled; the basic FLC components (fuzzification and defuzzification interfaces, knowledge base, and decision-making logic) are described; and the advantages of FLCs for incorporating expert knowledge into a control system are indicated. Particular attention is given to fuzzy implication functions, the interpretation of sentence connectives (and, also), compositional operators, and inference mechanisms. Applications discussed include the FLC-guided automobile developed by Sugeno and Nishida (1985), FLC hardware systems, FLCs for subway trains and ship-loading cranes, fuzzy-logic chips, and fuzzy computers.

  3. Suicide as social logic.

    PubMed

    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. PMID:7825197

  4. The Logic of Reachability

    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.

  5. Logic synthesis of cascade circuits

    NASA Astrophysics Data System (ADS)

    Zakrevskii, A. D.

    The work reviews aspects of the logic design of cascade circuits, particularly programmable logic matrices. Effective methods for solving various problems of the analysis and synthesis of these devices are examined; these methods are based on a matrix representation of the structure of these devices, and a vector-matrix interpretation of certain aspects of Boolean algebra. Particular consideration is given to the theory of elementary matrix circuits, methods for the minimization of Boolean functions, the synthesis of programmable logic matrices, multilevel combinational networks, and the development of automata with memory.

  6. Comparing Knowledge Bases and Reasoning Structures in Discussions of Mathematics and Pedagogy

    ERIC Educational Resources Information Center

    Steele, Michael D.

    2005-01-01

    While teaching, teachers need to access both their knowledge of mathematics and knowledge of pedagogy. Practice-based materials afford teachers opportunities to reason about both mathematics and pedagogy within the context of teaching. Accepted systems exist for explaining and reasoning in the domain of mathematics; logic, procedures, and…

  7. How Syntactic Reasoners Can Develop Understanding, Evaluate Conjectures, and Generate Counterexamples in Advanced Mathematics

    ERIC Educational Resources Information Center

    Weber, Keith

    2009-01-01

    This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…

  8. 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.

  9. Fuzzy logic and neural networks

    SciTech Connect

    Loos, J.R.

    1994-11-01

    Combine fuzzy logic`s fuzzy sets, fuzzy operators, fuzzy inference, and fuzzy rules - like defuzzification - with neural networks and you can arrive at very unfuzzy real-time control. Fuzzy logic, cursed with a very whimsical title, simply means multivalued logic, which includes not only the conventional two-valued (true/false) crisp logic, but also the logic of three or more values. This means one can assign logic values of true, false, and somewhere in between. This is where fuzziness comes in. Multi-valued logic avoids the black-and-white, all-or-nothing assignment of true or false to an assertion. Instead, it permits the assignment of shades of gray. When assigning a value of true or false to an assertion, the numbers typically used are {open_quotes}1{close_quotes} or {open_quotes}0{close_quotes}. This is the case for programmed systems. If {open_quotes}0{close_quotes} means {open_quotes}false{close_quotes} and {open_quotes}1{close_quotes} means {open_quotes}true,{close_quotes} then {open_quotes}shades of gray{close_quotes} are any numbers between 0 and 1. Therefore, {open_quotes}nearly true{close_quotes} may be represented by 0.8 or 0.9, {open_quotes}nearly false{close_quotes} may be represented by 0.1 or 0.2, and {close_quotes}your guess is as good as mine{close_quotes} may be represented by 0.5. The flexibility available to one is limitless. One can associate any meaning, such as {open_quotes}nearly true{close_quotes}, to any value of any granularity, such as 0.9999. 2 figs.

  10. 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.

  11. Optically controllable molecular logic circuits

    NASA Astrophysics Data System (ADS)

    Nishimura, Takahiro; Fujii, Ryo; Ogura, Yusuke; Tanida, Jun

    2015-07-01

    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.

  12. Optically controllable molecular logic circuits

    SciTech Connect

    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.

  13. Mathematical Geology.

    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)

  14. Mathematics disorder

    MedlinePlus

    The child may have problems in school, including behavior problems and loss of self-esteem. Some children with mathematics disorder become anxious or afraid when given math problems, making the problem even worse.

  15. Mathematics Detective.

    ERIC Educational Resources Information Center

    Johnson, Jerry

    1997-01-01

    Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)

  16. 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.

  17. Neural logic molecular, counter-intuitive.

    PubMed

    Egorov, Igor K

    2007-09-01

    A hypothesis is proposed that multiple "LOGIC" genes control Boolean logic in a neuron. Each hypothetical LOGIC gene encodes a transcription factor that regulates another LOGIC gene(s). Through transcription regulation, LOGIC genes connect into a complex circuit, such as a XOR logic gate or a two-input flip-flop logic circuit capable of retaining information. LOGIC gene duplication, mutation and recombination may result in the diversification of Boolean logic gates. Creative thinking may sometimes require counter-intuitive reasoning, rather than common sense. Such reasoning is likely to engage novel logic circuits produced by LOGIC somatic mutations. An individual's logic maturates by a mechanism of somatic hypermutation, gene conversion and recombination of LOGIC genes in precursor cells followed by selection of neurons in the brain for functional competence. In this model, a single neuron among billions in the brain may contain a unique logic circuit being the key to a hard intellectual problem. The output of a logic neuron is likely to be a neurotransmitter. This neuron is connected to other neurons in the spiking neural network. The LOGIC gene hypothesis is testable by molecular techniques. Understanding mechanisms of authentic human ingenuity may help to invent digital systems capable of creative thinking. PMID:17509937

  18. Application of linear logic to simulation

    NASA Astrophysics Data System (ADS)

    Clarke, Thomas L.

    1998-08-01

    Linear logic, since its introduction by Girard in 1987 has proven expressive and powerful. Linear logic has provided natural encodings of Turing machines, Petri nets and other computational models. Linear logic is also capable of naturally modeling resource dependent aspects of reasoning. The distinguishing characteristic of linear logic is that it accounts for resources; two instances of the same variable are considered differently from a single instance. Linear logic thus must obey a form of the linear superposition principle. A proportion can be reasoned with only once, unless a special operator is applied. Informally, linear logic distinguishes two kinds of conjunction, two kinds of disjunction, and also introduces a modal storage operator that explicitly indicates propositions that can be reused. This paper discuses the application of linear logic to simulation. A wide variety of logics have been developed; in addition to classical logic, there are fuzzy logics, affine logics, quantum logics, etc. All of these have found application in simulations of one sort or another. The special characteristics of linear logic and its benefits for simulation will be discussed. Of particular interest is a connection that can be made between linear logic and simulated dynamics by using the concept of Lie algebras and Lie groups. Lie groups provide the connection between the exponential modal storage operators of linear logic and the eigen functions of dynamic differential operators. Particularly suggestive are possible relations between complexity result for linear logic and non-computability results for dynamical systems.

  19. Pass transistor implementations of multivalued logic

    NASA Technical Reports Server (NTRS)

    Maki, G.; Whitaker, S.

    1990-01-01

    A simple straight-forward Karnaugh map logic design procedure for realization of multiple-valued logic circuits is presented in this paper. Pass transistor logic gates are used to realize multiple-valued networks. This work is an extension of pass transistor implementations for binary-valued logic.

  20. 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.

  1. Mathematical vistas

    SciTech Connect

    Malkevitch, J. ); McCarthy, D. )

    1990-01-01

    The papers in this volume represent talks given at the monthly meetings of the Mathematics Section of the New York Academy of Sciences. They reflect the operating philosophy of the Section in its efforts to make a meaningful contribution to the mathematical life of a community that is exceedingly rich in cultural resources and intellectual opportunities. Each week during the academic year a dazzling abundance of mathematical seminars and colloquia is available in the New York metropolitan area. Most of these offer highly technical treatments intended for specialists. At the New York Academy we try to provide a forum of a different sort, where interesting ideas are presented in a congenial atmosphere to a broad mathematical audience. Many of the Section talks contain substantial specialized material, but we ask our speakers to include a strong expository component aimed at working mathematicians presumed to have no expert knowledge of the topic at hand. We urge speakers to try to provide the motivating interest they themselves would like to find in an introduction to a field other than their own. The same advice has been given to the authors of the present papers, with the goal of producing a collection that will be both accessible and stimulating to mathematical minds at large. We have tried to provide variety in the mathematical vistas offered; both pure and applied mathematics are well represented. Since the papers are presented alphabetically by author, some guidance seems appropriate as to what sorts of topics are treated, and where. There are three papers in analysis: those by Engber, Narici and Beckenstein, and Todd. Engber's deals with complex analysis on compact Riemann surfaces; Narici and Beckenstein provide an introduction to analysis on non-Archimendean fields; Todd surveys an area of contemporary functional analysis.

  2. Mathematical Perspectives

    SciTech Connect

    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.

  3. 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

  4. Fuzzy logic control of the building structure with CLEMR dampers

    NASA Astrophysics Data System (ADS)

    Zhang, Xiang-Cheng; Xu, Zhao-Dong; Huang, Xing-Huai; Zhu, Jun-Tao

    2013-04-01

    The semi-active control technology has been paid more attention in the field of structural vibration control due to its high controllability, excellent control effect and low power requirement. When semi-active control device are used for vibration control, some challenges must be taken into account, such as the reliability and the control strategy of the device. This study presents a new large tonnage compound lead extrusion magnetorheological (CLEMR) damper, whose mathematical model is introduced to describe the variation of damping force with current and velocity. Then a current controller based on the fuzzy logic control strategy is designed to determine control currents of the CLEMR dampers rapidly. A ten-floor frame structure with CLEMR dampers using the fuzzy logic control strategy is built and calculated by using MATLAB. Calculation results show that CLEMR dampers can reduce the seismic responses of structures effectively. Calculation results of the fuzzy logic control strategy are compared with those of the semi-active limit Hrovat control structure, the passive-off control structure, and the uncontrolled structure. Comparison results show that the fuzzy logic control strategy can determine control currents of CLEMR dampers quickly and can reduce seismic responses of the structures more effectively than the passive-off control strategy and the uncontrolled structure.

  5. Fuzzy logic of Aristotelian forms

    SciTech Connect

    Perlovsky, L.I.

    1996-12-31

    Model-based approaches to pattern recognition and machine vision have been proposed to overcome the exorbitant training requirements of earlier computational paradigms. However, uncertainties in data were found to lead to a combinatorial explosion of the computational complexity. This issue is related here to the roles of a priori knowledge vs. adaptive learning. What is the a-priori knowledge representation that supports learning? I introduce Modeling Field Theory (MFT), a model-based neural network whose adaptive learning is based on a priori models. These models combine deterministic, fuzzy, and statistical aspects to account for a priori knowledge, its fuzzy nature, and data uncertainties. In the process of learning, a priori fuzzy concepts converge to crisp or probabilistic concepts. The MFT is a convergent dynamical system of only linear computational complexity. Fuzzy logic turns out to be essential for reducing the combinatorial complexity to linear one. I will discuss the relationship of the new computational paradigm to two theories due to Aristotle: theory of Forms and logic. While theory of Forms argued that the mind cannot be based on ready-made a priori concepts, Aristotelian logic operated with just such concepts. I discuss an interpretation of MFT suggesting that its fuzzy logic, combining a-priority and adaptivity, implements Aristotelian theory of Forms (theory of mind). Thus, 2300 years after Aristotle, a logic is developed suitable for his theory of mind.

  6. 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.

  7. Intersecting Adjectives in Syllogistic Logic

    NASA Astrophysics Data System (ADS)

    Moss, Lawrence S.

    The goal of natural logic is to present and study logical systems for reasoning with sentences of (or which are reasonably close to) ordinary language. This paper explores simple systems of natural logic which make use of intersecting adjectives; these are adjectives whose interpretation does not vary with the noun they modify. Our project in this paper is to take one of the simplest syllogistic fragments, that of all and some, and to add intersecting adjectives. There are two ways to do this, depending on whether one allows iteration or prefers a "flat" structure of at most one adjective. We present rules of inference for both types of syntax, and these differ. The main results are four completeness theorems: for each of the two types of syntax we have completeness for the all fragment and for the full language of this paper.

  8. Reversible logic gate using adiabatic superconducting devices

    PubMed Central

    Takeuchi, N.; Yamanashi, Y.; Yoshikawa, N.

    2014-01-01

    Reversible computing has been studied since Rolf Landauer advanced the argument that has come to be known as Landauer's principle. This principle states that there is no minimum energy dissipation for logic operations in reversible computing, because it is not accompanied by reductions in information entropy. However, until now, no practical reversible logic gates have been demonstrated. One of the problems is that reversible logic gates must be built by using extremely energy-efficient logic devices. Another difficulty is that reversible logic gates must be both logically and physically reversible. Here we propose the first practical reversible logic gate using adiabatic superconducting devices and experimentally demonstrate the logical and physical reversibility of the gate. Additionally, we estimate the energy dissipation of the gate, and discuss the minimum energy dissipation required for reversible logic operations. It is expected that the results of this study will enable reversible computing to move from the theoretical stage into practical usage. PMID:25220698

  9. MD-Logic Artificial Pancreas System

    PubMed Central

    Atlas, Eran; Nimri, Revital; Miller, Shahar; Grunberg, Eli A.; Phillip, Moshe

    2010-01-01

    OBJECTIVE Current state-of-the-art artificial pancreas systems are either based on traditional linear control theory or rely on mathematical models of glucose-insulin dynamics. Blood glucose control using these methods is limited due to the complexity of the biological system. The aim of this study was to describe the principles and clinical performance of the novel MD-Logic Artificial Pancreas (MDLAP) System. RESEARCH DESIGN AND METHODS The MDLAP applies fuzzy logic theory to imitate lines of reasoning of diabetes caregivers. It uses a combination of control-to-range and control-to-target strategies to automatically regulate individual glucose levels. Feasibility clinical studies were conducted in seven adults with type 1 diabetes (aged 19–30 years, mean diabetes duration 10 ± 4 years, mean A1C 6.6 ± 0.7%). All underwent 14 full, closed-loop control sessions of 8 h (fasting and meal challenge conditions) and 24 h. RESULTS The mean peak postprandial (overall sessions) glucose level was 224 ± 22 mg/dl. Postprandial glucose levels returned to <180 mg/dl within 2.6 ± 0.6 h and remained stable in the normal range for at least 1 h. During 24-h closed-loop control, 73% of the sensor values ranged between 70 and 180 mg/dl, 27% were >180 mg/dl, and none were <70 mg/dl. There were no events of symptomatic hypoglycemia during any of the trials. CONCLUSIONS The MDLAP system is a promising tool for individualized glucose control in patients with type 1 diabetes. It is designed to minimize high glucose peaks while preventing hypoglycemia. Further studies are planned in the broad population under daily-life conditions. PMID:20150292

  10. High-speed, cascaded optical logic operations using programmable optical logic gate arrays

    SciTech Connect

    Lu, B.; Lu, Y.C.; Cheng, J.; Hafich, M.J.; Klem, J.; Zolper, J.C.

    1996-01-01

    Programmable optical logic operations are demonstrated using arrays of nonlatching binary optical switches consisting of vertical-cavity surface-emitting lasers, p-i-n photodetectors and heterojunction bipolar transistors. Individual arrays can perform Boolean optical logic functions at 100 Mb/s using both optical and electrical logic inputs, while the routing and fan-out of the optical logic outputs can be controlled at the gate level. Cascaded optical logic operation is demonstrated using two programmable logic gate arrays.

  11. A Logical Approach to Entanglement

    NASA Astrophysics Data System (ADS)

    Das, Abhishek

    2016-05-01

    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.

  12. The semantics of fuzzy logic

    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.

  13. 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.

  14. Quantum Decoherence: A Logical Perspective

    NASA Astrophysics Data System (ADS)

    Fortin, Sebastian; Vanni, Leonardo

    2014-12-01

    The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have presented the possibility of studying the classical limit in terms of the decoherence of relevant observables of the system. On the basis of this approach, in this paper we introduce the classical limit from a logical perspective, by studying the way in which the logical structure of quantum properties corresponding to relevant observables acquires Boolean characteristics.

  15. 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.

  16. Relevant Mathematics.

    ERIC Educational Resources Information Center

    Catterton, Gene; And Others

    This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…

  17. Learning Mathematics.

    ERIC Educational Resources Information Center

    Lapointe, Archie E.; And Others

    In 1990-91, 20 countries (Brazil, Canada, China, England, France, Hungary, Ireland, Israel, Italy, Jordan, Korea, Mozambique, Portugal, Scotland, Slovenia, Soviet Union, Spain, Switzerland, Taiwan, and the United States) surveyed the mathematics and science performance of 13-year-old students (and 14 countries also assessed 9-year-olds in the same…

  18. Mathematical Visualization

    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…

  19. Underground Mathematics

    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…

  20. 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…

  1. 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…

  2. Test Equating Procedures: A Primer on the Logic and Applications of Test Equating.

    ERIC Educational Resources Information Center

    Buras, Avery

    The logic and uses of test equating are discussed, including three methods of test equating. The focus is on the conceptual underpinnings of each test equating method, rather than on the mathematics of the procedures. Additional consideration is given to the assumptions of each method and its respective strengths and weaknesses. A commonly…

  3. 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.

  4. 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…

  5. Miniaturization of magnetic logic circuitry

    NASA Technical Reports Server (NTRS)

    Baba, P. D.

    1969-01-01

    Magnetic logic circuit design features two ferrite materials, with different formulation and magnetic characteristics, which are bonded into a continuous structure by preparing the materials as a slurry and using the doctor blade method to form flexible ferrite sheets. After firing, the sintering process was continuous across the bond.

  6. Current Mode Logic Fan Out

    Energy Science and Technology Software Center (ESTSC)

    2011-05-07

    Current mode logic is used in high speed timing systems for particle accelerators due to the fast rise time of the electrical signal. This software provides the necessary documentation to produce multiple copies of a single input for distribution to multiple devices. This software supports the DOE mission by providing a method for producing high speed signals in accelerator timing systems.

  7. Soft computing and fuzzy logic

    SciTech Connect

    Zadeh, L.A.

    1994-12-31

    Soft computing is a collection of methodologies that aim to exploit the tolerance for imprecision and uncertainty to achieve tractability, robustness, and low solution cost. Its principal constituents are fuzzy logic, neuro-computing, and probabilistic reasoning. Soft computing is likely to play an increasingly important role in many application areas, including software engineering. The role model for soft computing is the human mind.

  8. The Temporal Logic Model Concept.

    ERIC Educational Resources Information Center

    den Heyer, Molly

    2002-01-01

    Proposes an alternative program logic model based on the concepts of learning organizations and systems theory. By redefining time as an evolutionary process, the model provides a space for stakeholders to record changes in program context, interim assessments, and program modifications. (SLD)

  9. The Logic of Research Evaluation

    ERIC Educational Resources Information Center

    Scriven, Michael; Coryn, Chris L. S.

    2008-01-01

    The authors offer suggestions about logical distinctions often overlooked in the evaluation of research, beginning with a strong plea not to treat technology as applied science, and especially not to treat research in technology as important only if it makes a contribution to scientific knowledge. They argue that the frameworks illustrated in this…

  10. Generic physical protection logic trees

    SciTech Connect

    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.

  11. Boggle Logic Puzzles: Minimal Solutions

    ERIC Educational Resources Information Center

    Needleman, Jonathan

    2013-01-01

    Boggle logic puzzles are based on the popular word game Boggle played backwards. Given a list of words, the problem is to recreate the board. We explore these puzzles on a 3 x 3 board and find the minimum number of three-letter words needed to create a puzzle with a unique solution. We conclude with a series of open questions.

  12. 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.…

  13. 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…

  14. Implementing Exclusive-OR Logic

    NASA Technical Reports Server (NTRS)

    Hough, M. E.

    1983-01-01

    Two integrated circuits, BCD-to-decimal decoder and four-input NAND gate, form basic four, input XOR circuit. Multiple-input exclusive-OR logic is implemented by combining several basic elements. 16-input XOR gate is assembled from five NAND gates and five decoders. Same principle extended to handle more inputs.

  15. Coreflections in Algebraic Quantum Logic

    NASA Astrophysics Data System (ADS)

    Jacobs, Bart; Mandemaker, Jorik

    2012-07-01

    Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.

  16. Cooperative development of logical modelling standards and tools with CoLoMoTo.

    PubMed

    Naldi, Aurélien; Monteiro, Pedro T; Müssel, Christoph; Kestler, Hans A; Thieffry, Denis; Xenarios, Ioannis; Saez-Rodriguez, Julio; Helikar, Tomas; Chaouiya, Claudine

    2015-04-01

    The identification of large regulatory and signalling networks involved in the control of crucial cellular processes calls for proper modelling approaches. Indeed, models can help elucidate properties of these networks, understand their behaviour and provide (testable) predictions by performing in silico experiments. In this context, qualitative, logical frameworks have emerged as relevant approaches, as demonstrated by a growing number of published models, along with new methodologies and software tools. This productive activity now requires a concerted effort to ensure model reusability and interoperability between tools. Following an outline of the logical modelling framework, we present the most important achievements of the Consortium for Logical Models and Tools, along with future objectives. Our aim is to advertise this open community, which welcomes contributions from all researchers interested in logical modelling or in related mathematical and computational developments. PMID:25619997

  17. 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

  18. 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…

  19. Quantitative and logic modelling of gene and molecular networks

    PubMed Central

    Le Novère, Nicolas

    2015-01-01

    Behaviours of complex biomolecular systems are often irreducible to the elementary properties of their individual components. Explanatory and predictive mathematical models are therefore useful for fully understanding and precisely engineering cellular functions. The development and analyses of these models require their adaptation to the problems that need to be solved and the type and amount of available genetic or molecular data. Quantitative and logic modelling are among the main methods currently used to model molecular and gene networks. Each approach comes with inherent advantages and weaknesses. Recent developments show that hybrid approaches will become essential for further progress in synthetic biology and in the development of virtual organisms. PMID:25645874

  20. 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.

  1. SASIL. Sandia ATM SONET Interface Logic

    SciTech Connect

    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.

  2. 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.

  3. Circulating Packet Threshold Logic To Implement Msd Logic Modules

    NASA Astrophysics Data System (ADS)

    Flannery, David L.; Vail, L. Maugh; Gustafson, Steven C.

    1986-03-01

    Threshold logic element designs in circulating packet form are presented for the implementation of addition and subtraction using modified sign digit (MSD) arithmetic. This arithmetic is attractive for digital optical computing due to its inherent parallelism and pipelining characteristics, which capitalize on natural strengths of optics. To illustrate application of these concepts, a design for CORDIC rotation modules to accomplish the complex Givens rotations required for systolic array QU matrix factorization is presented. This design accomplishes QU factorization using only threshold logic elements and bit-shift operations in a systolic configuration. Although implementable in principle by either electronic or optical means, the design is amenable to optical implementation because it involves high levels of parallelism and interconnections.

  4. 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,…

  5. 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…

  6. 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.

  7. Optimized parameter extraction using fuzzy logic

    NASA Astrophysics Data System (ADS)

    Picos, Rodrigo; Calvo, Oscar; Iñiguez, Benjamín; García-Moreno, Eugeni; García, Rodolfo; Estrada, Magali

    2007-05-01

    Precise extraction of transistor model parameters is of much importance for modeling and at the same time a difficult and time consuming task. Methods for parameter extraction can rely on purely mathematical basis, calling for intensive use of computational resources, or in human expertise to interpret results. In this work, we propose a method for parameter extraction based on fuzzy logic that includes a precise knowledge about the function of each parameter in the model to create a set of simple fitting rules that are easy to describe in human language. To simplify the computational effort, the parameter fitting rules work using only data at specific points (e.g. the distance between the calculated curve and the measured one at VDS corresponding to 50% of the maximum current). If necessary, a more accurate implementation can be used without altering the basic underlying philosophy of the method. In this work, the method is applied to extract model parameters required by Level 3 bulk MOS model and by a compact model for TFTs used in the Unified Model and Extraction Method (UMEM), which is based on an integral function. Results obtained show that the method is quite insensitive to the initial conditions and that it is also quite fast. Extension of this method for more complex models requires only the creation of the corresponding rule base, using the appropriate measurements. The method is especially useful for production testing or design.

  8. 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.

  9. 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.

  10. The Logic Behind Feynman's Paths

    NASA Astrophysics Data System (ADS)

    García Álvarez, Edgardo T.

    The classical notions of continuity and mechanical causality are left in order to reformulate the Quantum Theory starting from two principles: (I) the intrinsic randomness of quantum process at microphysical level, (II) the projective representations of symmetries of the system. The second principle determines the geometry and then a new logic for describing the history of events (Feynman's paths) that modifies the rules of classical probabilistic calculus. The notion of classical trajectory is replaced by a history of spontaneous, random and discontinuous events. So the theory is reduced to determining the probability distribution for such histories accordingly with the symmetries of the system. The representation of the logic in terms of amplitudes leads to Feynman rules and, alternatively, its representation in terms of projectors results in the Schwinger trace formula.