Duality And Definability In First Order Logic
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Duality And Definability In First Order Logic
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Author : Michael Makkai
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Duality And Definability In First Order Logic written by Michael Makkai and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Using the theory of categories as a framework, this book develops a duality theory for theories in first order logic in which the dual of a theory is the category of its models with suitable additional structure. This duality theory resembles and generalizes M. H. Stone's famous duality theory for Boolean algebras. As an application, the author derives a result akin to the well-known definability theorem of E. W. Beth. This new definability theorem is related to theorems of descent in category theory and algebra and can also be stated as a result in pure logic without reference to category theory. Containing novel techniques as well as applications of classical methods, this carefuly written book shows an attention to both organization and detail and will appeal to mathematicians and philosophers interested in category theory.
Duality And Definability In First Order Logic
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Author : Mihály Makkai
language : en
Publisher: Oxford University Press, USA
Release Date : 2014-08-31
Duality And Definability In First Order Logic written by Mihály Makkai 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 2014-08-31 with Duality theory categories.
Using the theory of categories as a framework, this book develops a duality theory for theories in first order logic in which the dual of a theory is the category of its models with suitable additional structure. This duality theory resembles and generalizes M. H. Stone's famous duality theory for Boolean algebras. As an application, the author derives a result akin to the well-known definability theorem of E. W. Beth. This new definability theorem is related to theorems of descent in category theory and algebra and can also be stated as a result in pure logic without reference to category theory. Containing novel techniques as well as applications of classical methods, this carefuly written book shows an attention to both organization and detail and will appeal to mathematicians and philosophers interested in category theory.
Topological Duality For Distributive Lattices
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Author : Mai Gehrke
language : en
Publisher: Cambridge University Press
Release Date : 2024-02-29
Topological Duality For Distributive Lattices written by Mai Gehrke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-29 with Computers categories.
Introducing Stone-Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.
Models Logics And Higher Dimensional Categories
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Author : Bradd T. Hart
language : en
Publisher: American Mathematical Soc.
Release Date :
Models Logics And Higher Dimensional Categories written by Bradd T. Hart and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Proceedings of a conference held at Centre de recherches mathematiques of the Universite de Montreal, June 18-20, 2009.
Qu Bec Studies In The Philosophy Of Science
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Author : Mathieu Marion
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Qu Bec Studies In The Philosophy Of Science written by Mathieu Marion 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 2012-12-06 with Science categories.
By North-American standards, philosophy is not new in Quebec: the first men tion of philosophy lectures given by a Jesuit in the College de Quebec (founded 1635) dates from 1665, and the oldest logic manuscript dates from 1679. In English-speaking universities such as McGill (founded 1829), philosophy began to be taught later, during the second half of the 19th century. The major influence on English-speaking philosophers was, at least initially, that of Scottish Empiricism. On the other hand, the strong influence of the Catholic Church on French-Canadian society meant that the staff of the facultes of the French-speaking universities consisted, until recently, almost entirely of Thomist philosophers. There was accordingly little or no work in modem Formal Logic and Philosophy of Science and precious few contacts between the philosophical communities. In the late forties, Hugues Leblanc was a young student wanting to learn Formal Logic. He could not find anyone in Quebec to teach him and he went to study at Harvard University under the supervision of W. V. Quine. His best friend Maurice L' Abbe had left, a year earlier, for Princeton to study with Alonzo Church. After receiving his Ph. D from Harvard in 1948, Leblanc started his profes sional career at Bryn Mawr College, where he stayed until 1967. He then went to Temple University, where he taught until his retirement in 1992, serving as Chair of the Department of Philosophy from 1973 until 1979.
The Logic In Philosophy Of Science
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Author : Hans Halvorson
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-11
The Logic In Philosophy Of Science written by Hans Halvorson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-11 with Philosophy categories.
Reconsiders the role of formal logic in the analytic approach to philosophy, using cutting-edge mathematical techniques to elucidate twentieth-century debates.
Complexity Of Constraints
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Author : Nadia Creignou
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-18
Complexity Of Constraints written by Nadia Creignou 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 2008-12-18 with Computers categories.
Nowadays constraint satisfaction problems (CSPs) are ubiquitous in many different areas of computer science, from artificial intelligence and database systems to circuit design, network optimization, and theory of programming languages. Consequently, it is important to analyze and pinpoint the computational complexity of certain algorithmic tasks related to constraint satisfaction. The complexity-theoretic results of these tasks may have a direct impact on, for instance, the design and processing of database query languages, or strategies in data-mining, or the design and implementation of planners. This state-of-the-art survey contains the papers that were invited by the organizers after conclusion of an International Dagstuhl-Seminar on Complexity of Constraints, held in Dagstuhl Castle, Germany, in October 2006. A number of speakers were solicited to write surveys presenting the state of the art in their area of expertise. These contributions were peer-reviewed by experts in the field and revised before they were collated to the 9 papers of this volume. In addition, the volume contains a reprint of a survey by Kolaitis and Vardi on the logical approach to constraint satisfaction that first appeared in 'Finite Model Theory and its Applications', published by Springer in 2007.
Handbook Of Philosophical Logic
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Author : D.M. Gabbay
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-15
Handbook Of Philosophical Logic written by D.M. Gabbay 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 2005-12-15 with Philosophy categories.
The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications
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 book on category theory for a broad philosophical readership. There is no other discussion of category theory comparable in its scope. It is designed to show the interest and significant of category theory for philosophers working in a range of areas, including mathematics, proof theory, computer science, ontology, physics, biology, cognition, mathematical modelling, the structure of scientific theories, and the structure of the world. Moreover, it does this in a way that is accessible to non specialists. Each chapter is written by either a category-theorist or a philosopher working in one of the represented fields, in a way that builds on the concepts already familiar to philosophers working in these areas. The book is split into two halves. The 'pure' chapters focus on the use of category theory for mathematical, foundational, and logical purposes, while the 'applied' chapters consider the use of category theory for representational purposes, investigating category theory as a framework for theories of physics and biology, for mathematical modelling more generally, and for the structure of scientific theories. Book jacket.
Sketches Of An Elephant A Topos Theory Compendium
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Author : P. T. Johnstone
language : en
Publisher: Oxford University Press
Release Date : 2002-09-12
Sketches Of An Elephant A Topos Theory Compendium written by P. T. Johnstone 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 2002-09-12 with Computers categories.
Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and to thereby demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.