Categories And Computer Science

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Author: R. F. C. Walters
Publisher: Cambridge University Press
ISBN: 9780521422260
Size: 59.60 MB
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Categories And Computer Science by R. F. C. Walters


Original Title: Categories And Computer Science

Category Theory has, in recent years, become increasingly important and popular in computer science, and many universities now introduce Category Theory as part of the curriculum for undergraduate computer science students. Here, the theory is developed in a straightforward way, and is enriched with many examples from computer science.

Categories In Computer Science And Logic

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Author: John Walker Gray
Publisher: American Mathematical Soc.
ISBN: 0821851004
Size: 40.51 MB
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Categories In Computer Science And Logic by John Walker Gray


Original Title: Categories In Computer Science And Logic

Category theory has had important uses in logic since the invention of topos theory in the early 1960s, and logic has always been an important component of theoretical computer science. A new development has been the increase in direct interactions between category theory and computer science. In June 1987, an AMS-IMS-SIAM Summer Research Conference on Categories in Computer Science and Logic was held at the University of Colorado in Boulder. The aim of the conference was to bring together researchers working on the interconnections between category theory and computer science or between computer science and logic. The conference emphasized the ways in which the general machinery developed in category theory could be applied to specific questions and be used for category-theoretic studies of concrete problems.This volume represents the proceedings of the conference. (Some of the participants' contributions have been published elsewhere.) The papers published here relate to three different aspects of the conference. The first concerns topics relevant to all three fields, including, for example, Horn logic, lambda calculus, normal form reductions, algebraic theories, and categorical models for computability theory. In the area of logic, topics include semantical approaches to proof-theoretical questions, internal properties of specific objects in (pre-) topoi and their representations, and categorical sharpening of model-theoretic notions. Finally, in the area of computer science, the use of category theory in formalizing aspects of computer programming and program design is discussed.

Category Theory And Computer Science

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Author: David H. Pitt
Publisher: Springer Science & Business Media
ISBN: 9783540544951
Size: 67.25 MB
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Category Theory And Computer Science by David H. Pitt


Original Title: Category Theory And Computer Science

The papers in this volume were presented at the fourth biennial Summer Conference on Category Theory and Computer Science, held in Paris, September3-6, 1991. Category theory continues to be an important tool in foundationalstudies in computer science. It has been widely applied by logicians to get concise interpretations of many logical concepts. Links between logic and computer science have been developed now for over twenty years, notably via the Curry-Howard isomorphism which identifies programs with proofs and types with propositions. The triangle category theory - logic - programming presents a rich world of interconnections. Topics covered in this volume include the following. Type theory: stratification of types and propositions can be discussed in a categorical setting. Domain theory: synthetic domain theory develops domain theory internally in the constructive universe of the effective topos. Linear logic: the reconstruction of logic based on propositions as resources leads to alternatives to traditional syntaxes. The proceedings of the previous three category theory conferences appear as Lecture Notes in Computer Science Volumes 240, 283 and 389.

Category Theory And Computer Science

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Author: Eugenio Moggi
Publisher: Springer Science & Business Media
ISBN: 9783540634553
Size: 47.64 MB
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Category Theory And Computer Science by Eugenio Moggi


Original Title: Category Theory And Computer Science

This book constitutes the refereed proceedings of the 7th International Conference on Category Theory and Computer Science, CTCS'97, held in Santa Margheria Ligure, Italy, in September 1997. Category theory attracts interest in the theoretical computer science community because of its ability to establish connections between different areas in computer science and mathematics and to provide a few generic principles for organizing mathematical theories. This book presents a selection of 15 revised full papers together with three invited contributions. The topics addressed include reasoning principles for types, rewriting, program semantics, and structuring of logical systems.

Applications Of Categories In Computer Science

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Author: M. P. Fourman
Publisher: Cambridge University Press
ISBN: 9780521427265
Size: 74.80 MB
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Applications Of Categories In Computer Science by M. P. Fourman


Original Title: Applications Of Categories In Computer Science

Category theory and related topics of mathematics have been increasingly applied to computer science in recent years. This book contains selected papers from the London Mathematical Society Symposium on the subject which was held at the University of Durham. Participants at the conference were leading computer scientists and mathematicians working in the area and this volume reflects the excitement and importance of the meeting. All the papers have been refereed and represent some of the most important and current ideas. Hence this book will be essential to mathematicians and computer scientists working in the applications of category theory.

Philosophy And Cognitive Science Categories Consciousness And Reasoning

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Author: A. Clark
Publisher: Springer Science & Business Media
ISBN: 9401587310
Size: 80.93 MB
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Philosophy And Cognitive Science Categories Consciousness And Reasoning by A. Clark


Original Title: Philosophy And Cognitive Science Categories Consciousness And Reasoning

PHILOSOPHY AND COGNITIVE SCIENCE: CATEGORIES, CONSCIOUSNESS, AND REASONING The individual man, since his separate existence is manifested only by ignorance and error, so far as he is anything apart from his fellows, and from what he and they are to be, is only a negation. Peirce, Some Consequences of Four Incapacities. 1868. For the second time the International Colloquium on Cognitive Science gathered at San Sebastian from May, 7-11, 1991 to discuss the following main topics: Knowledge of Categories Consciousness Reasoning and Interpretation Evolution, Biology, and Mind It is not an easy task to introduce in a few words the content of this volume. We have collected eleven invited papers presented at the Colloquium, which means the substantial part of it. Unfortunately, it has not been possible to include all the invited lectures of the meeting. Before sketching and showing the relevance of each paper, let us explain the reasons for having adopted the decision to organize each two years an international colloquium on Cognitive Science at Donostia (San Sebastian). First of all, Cognitive Science is a very active research area in the world, linking multidisciplinary efforts coming mostly from psychology, artificial intelligence, theoretical linguistics and neurobiology, and using more and more formal tools. We think that this new discipline lacks solid foundations, and in this sense philosophy, particularly knowledge theory, and logic must be called for.

A New Foundation For Representation In Cognitive And Brain Science

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Author: Jaime Gómez Ramirez
Publisher: Springer Science & Business Media
ISBN: 9400777388
Size: 57.88 MB
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A New Foundation For Representation In Cognitive And Brain Science by Jaime Gómez Ramirez


Original Title: A New Foundation For Representation In Cognitive And Brain Science

The purpose of the book is to advance in the understanding of brain function by defining a general framework for representation based on category theory. The idea is to bring this mathematical formalism into the domain of neural representation of physical spaces, setting the basis for a theory of mental representation, able to relate empirical findings, uniting them into a sound theoretical corpus. The innovative approach presented in the book provides a horizon of interdisciplinary collaboration that aims to set up a common agenda that synthesizes mathematical formalization and empirical procedures in a systemic way. Category theory has been successfully applied to qualitative analysis, mainly in theoretical computer science to deal with programming language semantics. Nevertheless, the potential of category theoretic tools for quantitative analysis of networks has not been tackled so far. Statistical methods to investigate graph structure typically rely on network parameters. Category theory can be seen as an abstraction of graph theory. Thus, new categorical properties can be added into network analysis and graph theoretic constructs can be accordingly extended in more fundamental basis. By generalizing networks using category theory we can address questions and elaborate answers in a more fundamental way without waiving graph theoretic tools. The vital issue is to establish a new framework for quantitative analysis of networks using the theory of categories, in which computational neuroscientists and network theorists may tackle in more efficient ways the dynamics of brain cognitive networks. The intended audience of the book is researchers who wish to explore the validity of mathematical principles in the understanding of cognitive systems. All the actors in cognitive science: philosophers, engineers, neurobiologists, cognitive psychologists, computer scientists etc. are akin to discover along its pages new unforeseen connections through the development of concepts and formal theories described in the book. Practitioners of both pure and applied mathematics e.g., network theorists, will be delighted with the mapping of abstract mathematical concepts in the terra incognita of cognition.

Science Of Synthesis

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Author: Dieter E. Kaufmann
Publisher: Thieme/Houben-Weyl Series
ISBN:
Size: 34.12 MB
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Science Of Synthesis by Dieter E. Kaufmann


Original Title: Science Of Synthesis

New edition of the acclaimed reference series, Houben-Weyl. This new ed. is published in English and is available in both print and electronic formats. Clear and systematic, Science of Synthesis provides practical solutions and offers a route through the mass of information available in the primary literature. This one-stop reference tool is: Comprehensive: contains synthetic models selected by world-renowned experts, with full experimental procedures and background information. Reliable: the international editorial board is made up of distinguished chemists with unparalleled experience and competence. Logical and easy-to-navigate: information is organized in a hierarchical system based on the compound or functional group to be synthesized. Authoritative: critically evaluates the preparative applicability and significance of the synthetic methods. Wide-ranging: considers methods from journals, books, and patent literature from the early 1800s up to the present day and presents important synthetic methods for all classes of compounds.

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