Cylindric Like Algebras And Algebraic Logic
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Cylindric Like Algebras And Algebraic Logic
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Author : Hajnal Andréka
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-27
Cylindric Like Algebras And Algebraic Logic written by Hajnal Andréka 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 2014-01-27 with Mathematics categories.
Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.
Cylindric Like Algebras And Algebraic Logic
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Author : Hajnal Andréka
language : en
Publisher:
Release Date : 2012
Cylindric Like Algebras And Algebraic Logic written by Hajnal Andréka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Algebraic logic categories.
Cylindric Algebras
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Author : Leon Henkin
language : en
Publisher: North Holland
Release Date : 1971
Cylindric Algebras written by Leon Henkin and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Computers categories.
Volume I provides a detailed analysis of cylindric algebras, starting with a formulation of their axioms and a development of their elementary properties, and proceeding to a deeper study of their interrelationships by means of general algebraic notions such as subalgebras, homomorphisms, direct products, free algebras, reducts and relativized algebras.
Cylindric Algebras
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Author : Bozzano G Luisa
language : en
Publisher: Elsevier
Release Date : 1985-02-01
Cylindric Algebras written by Bozzano G Luisa and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-02-01 with Mathematics categories.
Volume II completes the description of the main aspects of the theory, covering representation questions, model theory and decision problems for them, translations from logic to algebra and vice-versa, and relationships with other algebraic versions of logic.
Universal Algebraic Logic
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Author : Hajnal Andréka
language : en
Publisher: Springer Nature
Release Date : 2022-11-01
Universal Algebraic Logic written by Hajnal Andréka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-01 with Mathematics categories.
This book gives a comprehensive introduction to Universal Algebraic Logic. The three main themes are (i) universal logic and the question of what logic is, (ii) duality theories between the world of logics and the world of algebra, and (iii) Tarskian algebraic logic proper including algebras of relations of various ranks, cylindric algebras, relation algebras, polyadic algebras and other kinds of algebras of logic. One of the strengths of our approach is that it is directly applicable to a wide range of logics including not only propositional logics but also e.g. classical first order logic and other quantifier logics. Following the Tarskian tradition, besides the connections between logic and algebra, related logical connections with geometry and eventually spacetime geometry leading up to relativity are also part of the perspective of the book. Besides Tarskian algebraizations of logics, category theoretical perspectives are also touched upon. This book, apart from being a monograph containing state of the art results in algebraic logic, can be used as the basis for a number of different courses intended for both novices and more experienced students of logic, mathematics, or philosophy. For instance, the first two chapters can be used in their own right as a crash course in Universal Algebra.
Studies In Algebraic Logic
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Author : Aubert Daigneault
language : en
Publisher: Mathematical Association of America (MAA)
Release Date : 1974
Studies In Algebraic Logic written by Aubert Daigneault and has been published by Mathematical Association of America (MAA) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
As will be seen in the four papers brought under this cover algebraic logic did not stop with the invention of polyadic and cylindric algebras and the development of their theory. These papers which were all written especially for this study present rather different facets of contemporary concepts and results in the subject.
Cylindric Set Algebras
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Author : L. Henkin
language : en
Publisher: Springer
Release Date : 2006-11-14
Cylindric Set Algebras written by L. Henkin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Algebraic Logic
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Author : H. Andréka
language : en
Publisher: North Holland
Release Date : 1991
Algebraic Logic written by H. Andréka and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Algebraic logic categories.
Relation Algebras By Games
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Author : Robin Hirsch
language : en
Publisher: Elsevier
Release Date : 2002-08-15
Relation Algebras By Games written by Robin Hirsch and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-15 with Mathematics categories.
Relation algebras are algebras arising from the study of binary relations. They form a part of the field of algebraic logic, and have applications in proof theory, modal logic, and computer science. This research text uses combinatorial games to study the fundamental notion of representations of relation algebras. Games allow an intuitive and appealing approach to the subject, and permit substantial advances to be made. The book contains many new results and proofs not published elsewhere. It should be invaluable to graduate students and researchers interested in relation algebras and games. After an introduction describing the authors' perspective on the material, the text proper has six parts. The lengthy first part is devoted to background material, including the formal definitions of relation algebras, cylindric algebras, their basic properties, and some connections between them. Examples are given. Part 1 ends with a short survey of other work beyond the scope of the book. In part 2, games are introduced, and used to axiomatise various classes of algebras. Part 3 discusses approximations to representability, using bases, relation algebra reducts, and relativised representations. Part 4 presents some constructions of relation algebras, including Monk algebras and the 'rainbow construction', and uses them to show that various classes of representable algebras are non-finitely axiomatisable or even non-elementary. Part 5 shows that the representability problem for finite relation algebras is undecidable, and then in contrast proves some finite base property results. Part 6 contains a condensed summary of the book, and a list of problems. There are more than 400 exercises. The book is generally self-contained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of first-order logic and set theory is assumed, though many of the definitions are given. Chapter 2 introduces the necessary universal algebra and model theory, and more specific model-theoretic ideas are explained as they arise.
Algebraic Logic
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Author : Paul R. Halmos
language : en
Publisher:
Release Date : 2014-05
Algebraic Logic written by Paul R. Halmos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05 with Mathematics categories.
2014 Reprint of 1962 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. In "Algebraic Logic" Halmos devised polyadic algebras, an algebraic version of first-order logic differing from the better known cylindric algebras of Alfred Tarski and his students. An elementary version of polyadic algebra is described in monadic Boolean algebra. This book addresses some of the problems of mathematical logic and the theory of polyadic Boolean algebras in particular. It is intended to be an efficient way of treating algebraic logic in a unified manner.