Simple Relation Algebras

Author : Steven Givant,Hajnal Andréka
Publisher : Springer
Page : 622 pages
File Size : 47,7 Mb
Release : 2018-01-09
Category : Mathematics
ISBN : 9783319676968

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Simple Relation Algebras by Steven Givant,Hajnal Andréka Pdf

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).

Author : Steven Givant
Publisher : Springer
Page : 128 pages
File Size : 49,7 Mb
Release : 2016-07-14
Category : Mathematics
ISBN : 0387753605

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Simple Relation Algebras by Steven Givant Pdf

- 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

Author : Christoph Hubig
Publisher : Springer Verlag
Page : 192 pages
File Size : 52,7 Mb
Release : 1993
Category : Philosophy
ISBN : 0387567194

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Technik- und Wissenschaftsethik by Christoph Hubig Pdf

Author : Robin Hirsch,Ian Hodkinson
Publisher : Elsevier
Page : 710 pages
File Size : 40,7 Mb
Release : 2002-08-15
Category : Mathematics
ISBN : 0080540457

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Relation Algebras by Games by Robin Hirsch,Ian Hodkinson Pdf

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.

Author : Steven Givant
Publisher : Springer
Page : 605 pages
File Size : 45,7 Mb
Release : 2017-08-29
Category : Mathematics
ISBN : 9783319659459

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Advanced Topics in Relation Algebras by Steven Givant Pdf

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.

Author : Steven R. Givant
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 45,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851777

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The Structure of Relation Algebras Generated by Relativizations by Steven R. Givant Pdf

The foundation for 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 analyze 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 on algebras of binary relations or algebraic logic.

Author : Steven Givant
Publisher : Springer
Page : 572 pages
File Size : 53,7 Mb
Release : 2017-08-29
Category : Mathematics
ISBN : 9783319652351

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Introduction to Relation Algebras by Steven Givant Pdf

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.

Author : H. Andréka,Steven R. Givant,I. Németi
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 53,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805954

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Decision Problems for Equational Theories of Relation Algebras by H. Andréka,Steven R. Givant,I. Németi Pdf

This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. They provide researchers in algebra and logic with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic.

Author : Roger D. Maddux
Publisher : Elsevier Science Limited
Page : 731 pages
File Size : 49,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9780444520135

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Relation Algebras by Roger D. Maddux Pdf

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.

Author : Herbert Toth
Publisher : World Scientific
Page : 573 pages
File Size : 42,8 Mb
Release : 2020-06-22
Category : Mathematics
ISBN : 9789811220364

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Relations: Concrete, Abstract, And Applied - An Introduction by Herbert Toth Pdf

The book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.This book is unique by the spectrum of the topics it handles. As indicated in its title these are:

Author : Ivo G. Rosenberg,Gert Sabidussi
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 45,8 Mb
Release : 1993-02-28
Category : Mathematics
ISBN : 079232143X

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Algebras and Orders by Ivo G. Rosenberg,Gert Sabidussi Pdf

In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.

Author : Steven Givant
Publisher : Springer
Page : 128 pages
File Size : 47,6 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 3319685805

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Relation Algebras by Steven Givant Pdf

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.

Author : James Arthur,Laurent Clozel
Publisher : Princeton University Press
Page : 248 pages
File Size : 42,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882403

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Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120 by James Arthur,Laurent Clozel Pdf

A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.

Author : Louise Hoy Chin,Alfred Tarski
Publisher : Unknown
Page : 54 pages
File Size : 40,6 Mb
Release : 1951
Category : Algebra, Abstract
ISBN : UVA:X001180934

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Distributive and Modular Laws in the Arithmetic of Relation Algebras by Louise Hoy Chin,Alfred Tarski Pdf

Author : Anonim
Publisher : Unknown
Page : 1022 pages
File Size : 54,7 Mb
Release : 1952
Category : Mathematics
ISBN : UCAL:B3635396

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American Journal of Mathematics by Anonim Pdf