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The Structure Of Relation Algebras Generated By Relativizations
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Book Synopsis The Structure of Relation Algebras Generated by Relativizations by : Steven R. Givant
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.
Book Synopsis Simple Relation Algebras by : Steven Givant
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 629 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).
Book Synopsis Decision Problems for Equational Theories of Relation Algebras by : H. Andréka
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.
Book Synopsis Relations: Concrete, Abstract, And Applied - An Introduction by : Herbert Toth
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:
Book Synopsis Relational Methods in Computer Science by : Chris Brink
Download or read book Relational Methods in Computer Science written by Chris Brink and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of relations has been an important component of the development of logic and algebra since the middle of the nineteenth century, when Augustus De Morgan observed that since a horse is an animal we should be able to infer that the head of a horse is the head of an animal. For this, Aristotelian syllogistic does not suffice: We require relational reasoning. George Boole, in his Mathematical Analysis of Logic of 1847, initiated the treatment of logic as part of mathematics, specifically as part of algebra. Quite the opposite conviction was put forward early this century by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica (1910 - 1913): that mathematics was essentially grounded in logic. Logic thus developed in two streams. On the one hand algebraic logic, in which the calculus of relations played a particularly prominent part, was taken up from Boole by Charles Sanders Peirce, who wished to do for the "calculus of relatives" what Boole had done for the calculus of sets. Peirce's work was in turn taken up by Schroder in his Algebra und Logik der Relative of 1895 (the third part of a massive work on the algebra of logic). Schroder's work, however, lay dormant for more than 40 years, until revived by Alfred Tarski in his seminal paper "On the calculus of binary relations" of 1941 (actually his presidential address to the Association for Symbolic Logic).
Book Synopsis Handbook of Philosophical Logic by : Dov M. Gabbay
Download or read book Handbook of Philosophical Logic written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2001-07-31 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as weIl as to consumers of logic in many applied areas. The main logic artiele in the Encyelopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ Philosophical Logic, published 1983-1989 came at a fortunate at the evolution of logic. This was the time when logic temporal junction was gaining ground in computer science and artificial intelligence cireles. These areas were under increasing commercial pressure to provide devices which help andjor replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.
Book Synopsis A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences by : K. Glazek
Download or read book A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences written by K. Glazek and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).
Download or read book $C^*$-Algebras: 1943-1993 written by and published by American Mathematical Soc.. This book was released on 1994 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lie Algebras, Cohomology, and New Applications to Quantum Mechanics by : Niky Kamran
Download or read book Lie Algebras, Cohomology, and New Applications to Quantum Mechanics written by Niky Kamran and published by American Mathematical Soc.. This book was released on 1994 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.
Book Synopsis Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra by : William J. Heinzer
Download or read book Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra written by William J. Heinzer and published by American Mathematical Soc.. This book was released on 1994 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains refereed papers on themes explored at the AMS-IMS-SIAM Summer Research Conference, Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, held at Mount Holyoke College in 1992. The conference featured a series of one-hour invited lectures on recent advances in commutative algebra and interactions with such areas as algebraic geometry, representation theory, and combinatorics. The major themes of the conference were tight closure Hilbert functions, birational algebra, free resolutions and the homological conjectures, Rees algebras, and local cohomology. With contributions by several leading experts in the field, this volume provides an excellent survey of current research in commutative algebra.
Download or read book Logic as Algebra written by Paul Halmos and published by American Mathematical Soc.. This book was released on 2019-01-29 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed to understand the book is some basic acquaintance with algebra.
Book Synopsis Second International Conference on Algebra by : Leonid Arkadʹevich Bokutʹ
Download or read book Second International Conference on Algebra written by Leonid Arkadʹevich Bokutʹ and published by American Mathematical Soc.. This book was released on 1995 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented at the Second International Conference on Algebra, held in Barnaul in August 1991 in honour of the memory of A. I. Shirshov (1921--1981). Many of the results presented here have not been published elsewhere in the literature. The collection provides a panorama of current research in PI-, associative, Lie, and Jordan algebras and discusses the interrelations of these areas with geometry and physics. Other topics in group theory and homological algebra are also covered.
Book Synopsis Applications of Hypergroups and Related Measure Algebras by :
Download or read book Applications of Hypergroups and Related Measure Algebras written by and published by American Mathematical Soc.. This book was released on 1995-02-28 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: `The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks.' - from the Introduction. Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work.
Book Synopsis Differential Geometry and Mathematical Physics by : John K. Beem
Download or read book Differential Geometry and Mathematical Physics written by John K. Beem and published by American Mathematical Soc.. This book was released on 1994 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Special Session, Geometric Methods in Mathematical Physics, held at the joint AMS-CMS meeting in Vancouver in August 1993. The papers collected here contain a number of new results in differential geometry and its applications to physics. The major themes include black holes, singularities, censorship, the Einstein field equations, geodesics, index theory, submanifolds, CR-structures, and space-time symmetries. In addition, there are papers on Yang-Mills fields, geometric techniques in control theory, and equilibria. Containing new results by established researchers in the field, this book provides a look at developments in this exciting area of research.
Book Synopsis Finite Fields: Theory, Applications, and Algorithms by : Gary L. Mullen
Download or read book Finite Fields: Theory, Applications, and Algorithms written by Gary L. Mullen and published by American Mathematical Soc.. This book was released on 1994 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.
Book Synopsis Chaotic Numerics by : Peter E. Kloeden
Download or read book Chaotic Numerics written by Peter E. Kloeden and published by American Mathematical Soc.. This book was released on 1994 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much of what is known about specific dynamical systems is obtained from numerical experiments. Although the discretization process usually has no significant effect on the results for simple, well-behaved dynamics, acute sensitivity to changes in initial conditions is a hallmark of chaotic behavior. How confident can one be that the numerical dynamics reflects that of the original system? Do numerically calculated trajectories always shadow a true one? What role does numerical analysis play in the study of dynamical systems? And conversely, can advances in dynamical systems provide new insights into numerical algorithms? These and related issues were the focus of the workshop on Chaotic Numerics, held at Deakin University in Geelong, Australia, in July 1993. The contributions to this book are based on lectures presented during the workshop and provide a broad overview of this area of research.
Book Synopsis Mathematical Problems in the Theory of Water Waves by : Frederic Dias
Download or read book Mathematical Problems in the Theory of Water Waves written by Frederic Dias and published by American Mathematical Soc.. This book was released on 1996 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings featured in this book grew out of a conference attended by 40 applied mathematicians and physicists which was held at the International Center for Research in Mathematics in Luminy, France, in May 1995. This volume reviews recent developments in the mathematical theory of water waves. The following aspects are considered: modeling of various wave systems, mathematical and numerical analysis of the full water wave problem (the Euler equations with a free surface) and of asymptotic models (Korteweg-de Vries, Boussinesq, Benjamin-Ono, Davey-Stewartson, Kadomtsev-Petviashvili, etc.), and existence and stability of solitary waves.
