Universal Algebraic Logic

Author : Hajnal Andréka,Zalán Gyenis,István Németi,Ildikó Sain
Publisher : Springer Nature
Page : 337 pages
File Size : 49,7 Mb
Release : 2022-11-01
Category : Mathematics
ISBN : 9783031148873

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Universal Algebraic Logic by Hajnal Andréka,Zalán Gyenis,István Németi,Ildikó Sain Pdf

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.

Author : B. Plotkin
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401108201

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Universal Algebra, Algebraic Logic, and Databases by B. Plotkin Pdf

Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills.

Author : Janusz Czelakowski
Publisher : Springer
Page : 454 pages
File Size : 53,5 Mb
Release : 2018-03-20
Category : Philosophy
ISBN : 9783319747729

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Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science by Janusz Czelakowski Pdf

This book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life. It reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.

Author : J. Michael Dunn,Gary Hardegree
Publisher : OUP Oxford
Page : 490 pages
File Size : 42,7 Mb
Release : 2001-06-28
Category : Electronic
ISBN : 9780191589225

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Algebraic Methods in Philosophical Logic by J. Michael Dunn,Gary Hardegree Pdf

This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily for logisticians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic, but is also accessible to those from a non-logistics background. It is suitable for researchers, graduates and advanced undergraduates who have an introductory knowledge of algebraic logic providing more advanced concepts, as well as more theoretical aspects. The main theme is that standard algebraic results (representations) translate into standard logical results (completeness). Other themes involve identification of a class of algebras appropriate for classical and non-classical logic studies, including: gaggles, distributoids, partial- gaggles, and tonoids. An imporatant sub title is that logic is fundamentally information based, with its main elements being propositions, that can be understood as sets of information states. Logics are considered in various senses e.g. systems of theorems, consequence relations and, symmetric consequence relations.

Author : Wolfgang Wechler
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642767715

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Universal Algebra for Computer Scientists by Wolfgang Wechler Pdf

A new model-theoretic approach to universal algebra is offered in this book. Written for computer scientists, it presents a systematic development of the methods and results of universal algebra that are useful in a variety of applications in computer science. The notation is simple and the concepts are clearly presented. The book concerns the algebraic characterization of axiomatic classes of algebras (equational, implicational, and universal Horn classes) by closure operators generalizing the famous Birkhoff Variety Theorem, and the algebraic characterization of the related theories. The book also presents a thorough study of term rewriting systems. Besides basic notions, the Knuth-Bendix completion procedure and termination proof methods are considered. A third main topic is that of fixpoint techniques and complete ordered algebras. Algebraic specifications of abstract data types and algebraic semantics of recursive program schemes are treated as applications. The book is self-contained and suitable both as a textbook for graduate courses and as a reference for researchers.

Author : Clifford H. Bergman
Publisher : Unknown
Page : 292 pages
File Size : 55,9 Mb
Release : 1990
Category : Electronic
ISBN : OCLC:658622946

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Algebraic Logic and Universal Algebra in Computer Science by Clifford H. Bergman Pdf

Author : J. Y. Beziau,Alexandre Costa-Leite
Publisher : Polimetrica s.a.s.
Page : 442 pages
File Size : 54,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9788876990779

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Perspectives on Universal Logic by J. Y. Beziau,Alexandre Costa-Leite Pdf

Author : United States. Securities and Exchange Commission
Publisher : Unknown
Page : 300 pages
File Size : 46,9 Mb
Release : 1988
Category : Securities
ISBN : MINN:30000007281623

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Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935 by United States. Securities and Exchange Commission Pdf

Author : H. Andréka,James Donald Monk,I. Németi
Publisher : North Holland
Page : 768 pages
File Size : 44,8 Mb
Release : 1991
Category : Algebraic logic
ISBN : UCSD:31822007943160

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Algebraic Logic by H. Andréka,James Donald Monk,I. Németi Pdf

Author : Hiroakira Ono
Publisher : Springer
Page : 160 pages
File Size : 41,8 Mb
Release : 2019-08-02
Category : Philosophy
ISBN : 9789811379970

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Proof Theory and Algebra in Logic by Hiroakira Ono Pdf

This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.

Author : S. Burris,H. P. Sankappanavar
Publisher : Springer
Page : 276 pages
File Size : 49,5 Mb
Release : 2011-10-21
Category : Mathematics
ISBN : 1461381320

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A Course in Universal Algebra by S. Burris,H. P. Sankappanavar Pdf

Universal algebra has enjoyed a particularly explosive growth in the last twenty years, and a student entering the subject now will find a bewildering amount of material to digest. This text is not intended to be encyclopedic; rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests. Chapter I contains a brief but substantial introduction to lattices, and to the close connection between complete lattices and closure operators. In particular, everything necessary for the subsequent study of congruence lattices is included. Chapter II develops the most general and fundamental notions of uni versal algebra-these include the results that apply to all types of algebras, such as the homomorphism and isomorphism theorems. Free algebras are discussed in great detail-we use them to derive the existence of simple algebras, the rules of equational logic, and the important Mal'cev conditions. We introduce the notion of classifying a variety by properties of (the lattices of) congruences on members of the variety. Also, the center of an algebra is defined and used to characterize modules (up to polynomial equivalence). In Chapter III we show how neatly two famous results-the refutation of Euler's conjecture on orthogonal Latin squares and Kleene's character ization of languages accepted by finite automata-can be presented using universal algebra. We predict that such "applied universal algebra" will become much more prominent.

Author : George M. Bergman
Publisher : Springer
Page : 572 pages
File Size : 44,9 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9783319114781

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An Invitation to General Algebra and Universal Constructions by George M. Bergman Pdf

Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.

Author : D.W. Barnes,J.M. Mack
Publisher : Springer Science & Business Media
Page : 129 pages
File Size : 40,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475744897

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An Algebraic Introduction to Mathematical Logic by D.W. Barnes,J.M. Mack Pdf

This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a substantial course on abstract algebra. Consequently, our treatment of the subject is algebraic. Although we assume a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of the exercises. We also assume a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model of logic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based--rather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory.

Author : Davide Fazio,Antonio Ledda,Francesco Paoli
Publisher : Springer Nature
Page : 193 pages
File Size : 40,6 Mb
Release : 2020-11-07
Category : Philosophy
ISBN : 9783030521639

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Algebraic Perspectives on Substructural Logics by Davide Fazio,Antonio Ledda,Francesco Paoli Pdf

This volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics. Substructural logics are usually formulated as Gentzen systems that lack one or more structural rules. They have been intensively studied over the past two decades by logicians of various persuasions. These researchers include mathematicians, philosophers, linguists, and computer scientists. Substructural logics are applicable to the mathematical investigation of such processes as resource-conscious reasoning, approximate reasoning, type-theoretical grammar, and other focal notions in computer science. They also apply to epistemology, economics, and linguistics. The recourse to algebraic methods -- or, better, the fecund interplay of algebra and proof theory -- has proved useful in providing a unifying framework for these investigations. The AsubL series of conferences, in particular, has played an important role in these developments. This collection will appeal to students and researchers with an interest in substructural logics, abstract algebraic logic, residuated lattices, proof theory, universal algebra, and logical semantics.

Author : Steven Givant,Hajnal Andréka
Publisher : Springer
Page : 622 pages
File Size : 52,7 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).