Relation Algebras
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Introduction To Relation Algebras
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Author : Steven Givant
language : en
Publisher: Springer
Release Date : 2017-08-29
Introduction To Relation Algebras written by Steven Givant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-29 with Mathematics categories.
The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly suited to independent study, and provide an unparalleled opportunity to learn from one of the leading authorities in the field. Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community.
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.
Relation Algebras
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Author : Roger D. Maddux
language : en
Publisher: Elsevier Science Limited
Release Date : 2006
Relation Algebras written by Roger D. Maddux and has been published by Elsevier Science Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
The modern theory of algebras of binary relations, reformulated by Tarski as an abstract, algebraic, equational theory of relation algebras, has considerable mathematical significance, with applications in various fields: e.g., in computer science---databases, specification theory, AI---and in anthropology, economics, physics, and philosophical logic. This comprehensive treatment of the theory of relation algebras and the calculus of relations is the first devoted to a systematic development of the subject. Key Features: - Presents historical milestones from a modern perspective. - Careful, thorough, detailed guide to understanding relation algebras. - Includes a wealth of scholarly material --- 100 years of work by a research community --- presented in book form for the first time. - Provides a framework and unified perspective of the subject. - Roger D. Maddux is one of the world's leading experts in the field of relation algebras. Key Features: - Presents historical milestones from a modern perspective. - Careful, thorough, detailed guide to understanding relation algebras. - Includes a wealth of scholarly material --- 100 years of work by a research community --- presented in book form for the first time. - Provides a framework and unified perspective of the subject. - Roger D. Maddux is one of the world's leading experts in the field of relation algebras.
Advanced Topics In Relation Algebras
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Author : Steven Givant
language : en
Publisher: Springer
Release Date : 2017-08-29
Advanced Topics In Relation Algebras written by Steven Givant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-29 with Mathematics categories.
The second volume of a pair that charts relation algebras from novice to expert level, this text brings the well-grounded reader to the frontiers of research. Building on the foundations established in the preceding Introduction to Relation Algebras, this volume advances the reader into the deeper mathematical results of the past few decades. Such material offers an ideal preparation for research in relation algebras and Boolean algebras with operators. Arranged in a modular fashion, this text offers the opportunity to explore any of several areas in detail; topics include canonical extensions, completions, representations, varieties, and atom structures. Each chapter offers a complete account of one such avenue of development, including a historical section and substantial number of exercises. The clarity of exposition and comprehensive nature of each module make this an ideal text for the independent reader entering the field, while researchers will value it as a reference for years to come. Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community. Note that this volume contains numerous, essential references to the previous volume, Introduction to Relation Algebras. The reader is strongly encouraged to secure at least electronic access to the first book in order to make use of the second.
The Structure Of Relation Algebras Generated By Relativizations
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Author : Steven R. Givant
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
The Structure Of Relation Algebras Generated By Relativizations written by Steven R. Givant 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 1994 with Mathematics categories.
The foundation of an algebraic theory of binary relations was laid by De Morgan, Peirce, and Schroder during the second half of the nineteenth century. Modern development of the subject as a theory of abstract algebras, called "relation algebras", was undertaken by Tarski and his students. This book aims to analyse the structure of relation algebras that are generated by relativized subalgebras. As examples of their potential for applications, the main results are used to establish representation theorems for classes of relation algebras and to prove existence and uniqueness theorems for simple closures (i.e., for minimal simple algebras containing a given family of relation algebras as relativized subalgebras). This book is well-written and accessible to those who are not specialists in this area. In particular, it contains two introductory chapters on the arithmetic and the algebraic theory of relation algebras. This book is suitable for use in graduate courses onalgebras of binary relations or algebraic logic.
Simple Relation Algebras
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Author : Steven Givant
language : en
Publisher: Springer
Release Date : 2018-01-09
Simple Relation Algebras written by Steven Givant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-09 with Mathematics categories.
This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatment in author Steven Givant’s textbook, Introduction to Relation Algebras (Springer, 2017).
Decision Problems For Equational Theories Of Relation Algebras
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Author : H. Andréka
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Decision Problems For Equational Theories Of Relation Algebras written by H. Andréka 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 1997 with Mathematics categories.
"We prove that any variety of relation algebras which contains an algebra with infinitely many elements below the identity, or which contains the full group relation algebra on some infinite group (or on arbitrarily large finite groups), must have an undecidable equational theory. Then we construct an embedding of the lattice of all subsets of the natural numbers into the lattice of varieties of relation algebras such that the variety correlated with a set [italic capital]X of natural numbers has a decidable equational theory if and only if [italic capital]X is a decidable (i.e., recursive) set. Finally, we construct an example of an infinite, finitely generated, simple, representable relation algebra that has a decidable equational theory.'' -- Abstract.
Simple Relation Algebras
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Author : Steven Givant
language : en
Publisher: Springer
Release Date : 2016-07-14
Simple Relation Algebras written by Steven Givant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-14 with Mathematics categories.
- Only book that deals specifically with simple relation algebras - Gently introduces the theory of relation algebras - Contains many new results that have never before been published - Features a large number of pictures that illustrate the main ideas and theorems
Technik Und Wissenschaftsethik
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Author : Christoph Hubig
language : en
Publisher: Springer Verlag
Release Date : 1993
Technik Und Wissenschaftsethik written by Christoph Hubig and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Philosophy categories.
Relation Algebras
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Author : Steven Givant
language : en
Publisher: Springer
Release Date : 2017-11-07
Relation Algebras written by Steven Givant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with Mathematics categories.
Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community. This set charts relation algebras from novice to expert level. The first volume, Introduction to Relation Algebras, offers a comprehensive grounding for readers new to the topic. The second, Advanced Topics in Relation Algebras, build on this foundation and advances the reader into the deeper mathematical results of the past few decades. Such material offers an ideal preparation for research in relation algebras and Boolean algebras with operators. Note that the second volume contains numerous, essential references to the first. Readers of the advanced material are encouraged to purchase the pair as a set, as access to the first book is necessary to make use of the second.