Toposes And Local Set Theories
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Toposes And Local Set Theories
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Author : John L. Bell
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
Toposes And Local Set Theories written by John L. Bell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.
Toposes And Local Set Theories
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Author : John Lane Bell
language : en
Publisher: Oxford University Press, USA
Release Date : 1988
Toposes And Local Set Theories written by John Lane Bell and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Logic, Symbolic and mathematical. categories.
The author introduces Lawvere and Tierney's concept of topos theory, a striking development in category theory that unites a number of important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topos theory has led to the forging of surprising new links between classical and constructive mathematics. Bell presents toposes as the models of theories--the so-called local set theories--formulated within a typed intuitionistic logic.
Fibring Logics
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Author : Dov M. Gabbay
language : en
Publisher: Clarendon Press
Release Date : 1998-11-05
Fibring Logics written by Dov M. Gabbay and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-05 with Mathematics categories.
Modern applications of logic, in mathematics, theoretical computer science, and linguistics, require combined systems involving many different logics working together. In this book the author offers a basic methodology for combining-or fibring-systems. This means that many existing complex systems can be broken down into simpler components, hence making them much easier to manipulate. Using this methodology the book discusses ways of obtaining a wide variety of multimodal, modal intuitionistic, modal substructural and fuzzy systems in a uniform way. It also covers self-fibred languages which allow formulae to apply to themselves. The book also studies sufficient conditions for transferring properties of the component logics into properties of the combined system.
Change Choice And Inference
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Author : Hans Rott
language : en
Publisher: Clarendon Press
Release Date : 2001
Change Choice And Inference written by Hans Rott and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Language Arts & Disciplines categories.
Change, Choice and Inference unifies lively and significant strands of research in logic, philosophy, economics and artificial intelligence.
Foundational Theories Of Classical And Constructive Mathematics
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Author : Giovanni Sommaruga
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-24
Foundational Theories Of Classical And Constructive Mathematics written by Giovanni Sommaruga and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-24 with Mathematics categories.
The book "Foundational Theories of Classical and Constructive Mathematics" is a book on the classical topic of foundations of mathematics. Its originality resides mainly in its treating at the same time foundations of classical and foundations of constructive mathematics. This confrontation of two kinds of foundations contributes to answering questions such as: Are foundations/foundational theories of classical mathematics of a different nature compared to those of constructive mathematics? Do they play the same role for the resp. mathematics? Are there connections between the two kinds of foundational theories? etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time more subtle and more differentiated. Another important aspect of the book is that some of its contributions are of a more philosophical, others of a more technical nature. This double face is emphasized, since foundations of mathematics is an eminent topic in the philosophy of mathematics: hence both sides of this discipline ought to be and are being paid due to.
Logic From Computer Science
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Author : Yiannis N. Moschovakis
language : en
Publisher: Springer Science & Business Media
Release Date : 1992
Logic From Computer Science written by Yiannis N. Moschovakis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computers categories.
The volume is the outgrowth of a workshop with the same title held at MSRI in the week of November 13-17, 1989, and for those who did not get it, Logic from Computer Science is the converse of Logic in Computer Science, the full name of the highly successful annual LICS conferences. We meant to have a conference which would bring together the LICS commu nity with some of the more traditional "mathematical logicians" and where the emphasis would be on the flow of ideas from computer science to logic rather than the other way around. In a LICS talk, sometimes, the speaker presents a perfectly good theorem about (say) the A-calculus or finite model theory in terms of its potential applications rather than its (often more ob vious) intrinsic, foundational interest and intricate proof. This is not meant to be a criticism; the LICS meetings are, after all, organized by the IEEE Computer Society. We thought, for once, it would be fun to see what we would get if we asked the speakers to emphasize the relevance of their work for logic rather than computer science and to point out what is involved in the proofs. I think, mostly, it worked. In any case, the group of people represented as broad a selection of logicians as I have seen in recent years, and the quality of the talks was (in my view) exceptionally, unusually high. I learned a lot and (I think) others did too.
Categories For The Working Philosopher
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Author : Elaine M. Landry
language : en
Publisher: Oxford University Press
Release Date : 2017
Categories For The Working Philosopher written by Elaine M. Landry and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.
Database Theory Icdt 2007
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Author : Thomas Schwentick
language : en
Publisher: Springer
Release Date : 2006-12-08
Database Theory Icdt 2007 written by Thomas Schwentick and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Computers categories.
This book constitutes the refereed proceedings of the 11th International Conference on Database Theory, ICDT 2007, held in Spain in January 2007. The papers are organized in topical sections on information integration and peer to peer, axiomatizations for XML, expressive power of query languages, incompleteness, inconsistency, and uncertainty, XML schemas and typechecking, stream processing and sequential query processing, ranking, XML update and query, as well as query containment.
Introduction To Logic And To The Methodology Of The Deductive Sciences
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Author : Alfred Tarski
language : en
Publisher: Oxford University Press
Release Date : 1994-01-06
Introduction To Logic And To The Methodology Of The Deductive Sciences written by Alfred Tarski and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-06 with Mathematics categories.
Now in its fourth edition, this classic work clearly and concisely introduces the subject of logic and its applications. The first part of the book explains the basic concepts and principles which make up the elements of logic. The author demonstrates that these ideas are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The second part of the book shows the applications of logic in mathematical theory building with concrete examples that draw upon the concepts and principles presented in the first section. Numerous exercises and an introduction to the theory of real numbers are also presented. Students, teachers and general readers interested in logic and mathematics will find this book to be an invaluable introduction to the subject.
Godel S Incompleteness Theorems
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Author : Raymond M. Smullyan
language : en
Publisher: Oxford University Press
Release Date : 1992-08-20
Godel S Incompleteness Theorems written by Raymond M. Smullyan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-20 with Mathematics categories.
Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.