Download or read book Simple Relation Algebras written by Steven Givant and published by Springer. This book was released on 2018-01-09 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Simple Relation Algebras written by Steven Givant and published by Springer. This book was released on 2016-07-14 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: - 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
Download or read book Technik und Wissenschaftsethik written by Christoph Hubig and published by Springer Verlag. This book was released on 1993 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relation Algebras by Games written by Robin Hirsch and published by Elsevier. This book was released on 2002-08-15 with total page 711 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advanced Topics in Relation Algebras written by Steven Givant and published by Springer. This book was released on 2017-08-29 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Relation Algebras written by Steven Givant and published by Springer. This book was released on 2017-08-29 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Structure of Relation Algebras Generated by Relativizations written by Steven R. Givant and published by American Mathematical Soc.. This book was released on 1994 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Semi Simple Lie Algebras and Their Representations written by Robert N. Cahn and published by Courier Corporation. This book was released on 2014-06-10 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed to acquaint students of particle physiME already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Author Robert N. Cahn, who is affiliated with the Lawrence Berkeley National Laboratory in Berkeley, California, has provided a new preface for this edition. Subjects include the killing form, the structure of simple Lie algebras and their representations, simple roots and the Cartan matrix, the classical Lie algebras, and the exceptional Lie algebras. Additional topiME include Casimir operators and Freudenthal's formula, the Weyl group, Weyl's dimension formula, reducing product representations, subalgebras, and branching rules. 1984 edition.
Download or read book Decision Problems for Equational Theories of Relation Algebras written by H. Andréka and published by American Mathematical Soc.. This book was released on 1997 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Relation Algebras by Games written by Robin Hirsch and published by Gulf Professional Publishing. This book was released on 2002-08-15 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. P 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.-
Download or read book Relation Algebras written by Roger D. Maddux and published by Elsevier Science Limited. This book was released on 2006 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Basic Algebra written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
Download or read book Function Algebras on Finite Sets written by Dietlinde Lau and published by Springer Science & Business Media. This book was released on 2006-11-23 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras. The second part covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, and clone theory.
Download or read book Relation Algebras written by Steven Givant and published by Springer. This book was released on 2017-11-07 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fork Algebras in Algebra Logic and Computer Science written by Marcelo Fabi n Frias and published by World Scientific. This book was released on 2002 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fork algebras are a formalism based on the relational calculus, with interesting algebraic and metalogical properties. Their representability is especially appealing in computer science, since it allows a closer relationship between their language and models. This book gives a careful account of the results and presents some applications of Fork algebras in computer science, particularly in system specification and program construction. Many applications of Fork algebras in formal methods can be applied in many ways, and the book covers all the essentials in order to provide the reader with a better understanding.
Download or read book Relations and Kleene Algebra in Computer Science written by Renate Schmidt and published by Springer. This book was released on 2006-10-04 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book constitutes the joint refereed proceedings of the 9th International Conference on Relational Methods in Computer Science, RelMiCS 2006, and the 4th International Workshop on Applications of Kleene Algebras, AKA 2006, held in Manchester, UK in August/September 2006. The 25 revised full papers presented together with two invited papers and the abstract of an invited talk were carefully reviewed and selected from 44 submissions.
Download or read book Relations Concrete Abstract And Applied An Introduction written by Herbert Toth and published by World Scientific. This book was released on 2020-06-22 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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:
