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The Equationally Defined Commutator

The Equationally Defined Commutator Author Janusz Czelakowski
ISBN-10 9783319212005
Release 2015-09-08
Pages 292
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This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic. An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebras. The author discusses the general properties of the equationally-defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally-defined commutator and its behavior in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally-Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic.

Don Pigozzi on Abstract Algebraic Logic Universal Algebra and Computer Science

Don Pigozzi on Abstract Algebraic Logic  Universal Algebra  and Computer Science Author Janusz Czelakowski
ISBN-10 9783319747729
Release 2018-03-20
Pages 454
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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.

J Michael Dunn on Information Based Logics

J  Michael Dunn on Information Based Logics Author Katalin Bimbó
ISBN-10 9783319293004
Release 2016-04-02
Pages 436
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This book celebrates and expands on J. Michael Dunn’s work on informational interpretations of logic. Dunn, in his Ph.D. thesis (1966), introduced a semantics for first-degree entailments utilizing the idea that a sentence can provide positive or negative information about a topic, possibly supplying both or neither. He later published a related interpretation of the logic R-mingle, which turned out to be one of the first relational semantics for a relevance logic. An incompatibility relation between information states lends itself to a definition of negation and it has figured into Dunn's comprehensive investigations into representations of various negations. The informational view of semantics is also a prominent theme in Dunn’s research on other logics, such as quantum logic and linear logic, and led to the encompassing theory of generalized Galois logics (or "gaggles"). Dunn’s latest work addresses informational interpretations of the ternary accessibility relation and the very nature of information. The book opens with Dunn’s autobiography, followed by a list of his publications. It then presents a series of papers written by respected logicians working on different aspects of information-based logics. The topics covered include the logic R-mingle, which was introduced by Dunn, and its applications in mathematical reasoning as well as its importance in obtaining results for other relevance logics. There are also interpretations of the accessibility relation in the semantics of relevance and other non-classical logics using different notions of information. It also presents a collection of papers that develop semantics for various logics, including certain modal and many-valued logics. The publication of this book is well timed, since we are living in an "information age.” Providing new technical findings, intellectual history and careful expositions of intriguing ideas, it appeals to a wide audience of scholars and researchers.

Lectures in Universal Algebra

Lectures in Universal Algebra Author L. Szabó
ISBN-10 9781483295404
Release 2016-01-22
Pages 655
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These 34 papers cover topics ranging from various problems on varieties and other classes of algebras including categorical aspects and duality theory to the structure of finite algebras and clones on finite (or infinite) sets. As well as survey articles by invited speakers, the papers contain full proofs of new results not published elsewhere. The volume ends with a list of problems.

Protoalgebraic Logics

Protoalgebraic Logics Author Janusz Czelakowski
ISBN-10 9789401728072
Release 2013-04-17
Pages 452
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The main aim of this book is to present recent ideas in logic centered around the notion of a consequence operation. We wish to show these ideas in a factually and materially connected way, i.e., in the form of a consistent theory derived from several simple assumptions and definitions. These ideas have arisen in many research centers. The thorough study of their history can certainly be an exciting task for the historian of logic; in the book this aspect of the theory is being played down. The book belongs to abstract algebraic logic, the area of research that explores to a large extent interconnections between algebra and logic. The results presented here concern logics defined in zero-order languages (Le., quantifier-free sentential languages without predicate symbols). The reach of the theory expounded in the book is, in fact, much wider. The theory is also valid for logics defined in languages of higer orders. The problem of transferring the theory to the level of first-order languages has been satisfactorily solved and new ideas within this area have been put forward in the work of Blok and Pigozzi [1989].

A Course in Universal Algebra

A Course in Universal Algebra Author S. Burris
ISBN-10 1461381320
Release 2011-10-21
Pages 276
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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.

Tools and Techniques in Modal Logic

Tools and Techniques in Modal Logic Author Marcus Kracht
ISBN-10 STANFORD:36105024882297
Release 1999
Pages 559
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This book treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory and transfer theory and is intended as a course in modal logic for students who have had prior contact with modal logic and who wish to study it more deeply. It presupposes training in mathematical or logic. Very little specific knowledge is presupposed, most results which are needed are proved in this book.

Algebraic Theories

Algebraic Theories Author J. Adámek
ISBN-10 9781139491884
Release 2010-11-18
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Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved very useful in various areas of mathematics and computer science. This carefully developed book gives a systematic introduction to algebra based on algebraic theories that is accessible to both graduate students and researchers. It will facilitate interactions of general algebra, category theory and computer science. A central concept is that of sifted colimits - that is, those commuting with finite products in sets. The authors prove the duality between algebraic categories and algebraic theories and discuss Morita equivalence between algebraic theories. They also pay special attention to one-sorted algebraic theories and the corresponding concrete algebraic categories over sets, and to S-sorted algebraic theories, which are important in program semantics. The final chapter is devoted to finitary localizations of algebraic categories, a recent research area.

Universal Algebra

Universal Algebra Author George Grätzer
ISBN-10 0387774874
Release 2008-12-15
Pages 583
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Universal Algebra has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well selected additional bibliography of over 1250 papers and books which makes this an indispensable new edition for students, faculty, and workers in the field.

Mathematical Reviews

Mathematical Reviews Author
ISBN-10 UVA:X006180448
Release 2003
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Mathematical Reviews has been writing in one form or another for most of life. You can find so many inspiration from Mathematical Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematical Reviews book for free.

Meaning Logic and Ludics

Meaning  Logic and Ludics Author Alain Lecomte
ISBN-10 9781908978240
Release 2011-03-22
Pages 388
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This book presents several recent advances in natural language semantics and explores the boundaries between syntax and semantics over the last two decades. It is based on some of the most recent theories in logic, such as linear logic and ludics, first created by Jean-Yves Girard, and it also provides some sharp analyses of computational semantical representations, explaining advanced theories in theoretical computer sciences, such as the lambda–mu and Lambek–Grishin calculi which were applied by Philippe de Groote and Michael Moortgat. The author also looks at Aarne Ranta's ‘proof as meaning’ approach, which was first based on Martin–Löf's Type Theory. Meaning, Logic and Ludics surveys the many solutions which have been proposed for the syntax–semantics interface, taking into account the specifications of linguistic signs (continuous or discontinuous) and the fundamental mechanisms developed by linguists and notable Generativists. This pioneering publication also presents ludics (in a chapter co-authored with Myriam Quatrini), a framework which allows us to characterize meaning as an invariant with regard to interaction between processes. It is an excellent book for advanced students, and academics alike, in the field of computational linguistics. Contents:Truth-Conditional Meaning:Compositional Approaches and BindingDerivationalismLogic:Deductive SystemsCurry–Howard CorrespondenceProof Theory Applied to Linguistics:Using the Lambek Calculus and Its VariantsGrammatical ReasoningA Type-Theoretical Version of Minimalist GrammarsGrammars in Deductive FormsContinuations and ContextsProofs as MeaningsLudics:Interaction and DialogueThe Future in Conclusion Readership: Graduates, postdoctorates, academics in the computation linguistics/logic/mathematics/bioinformatics and computational biology/genetics fields. Keywords:Natural Language;Semantics;Logic for Language;Ludics and Applications;Continuation Theory;Proof Theory and Natural Language;Linear Logic and ApplicationsKey Features:The first didactic presentation of LudicsThe first applications of Ludics to this topicThe first didactic presentation of the use of continuationsOffers well-supported philosophical viewpoint on topicsReviews:“This book presents a large part of the ongoing research on linguistics and proof theory, as developed by the author and also by some other researchers. The very interesting content, previously unavailable in book form, is made intuitive and pleasant to read. Linguists, who are familiar with the questions but not their formal treatment, will enjoy the book, especially the linguistically oriented explanations on logical systems. Logicians, and especially proof theorists, will be convinced of the relevance of their domain to natural language semantics, and at the same time, they will be offered a gentle introduction to some active topics in linguistic research.”Mathematical Reviews

Contributions to Universal Algebra

Contributions to Universal Algebra Author B. Csákány
ISBN-10 9781483103020
Release 2014-05-15
Pages 608
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Contributions to Universal Algebra focuses on the study of algebra. The compilation first discusses the congruence lattice of pseudo-simple algebras; elementary properties of limit reduced powers with applications to Boolean powers; and congruent lattices of 2-valued algebras. The book further looks at duality for algebras; weak homomorphisms of stone algebras; varieties of modular lattices not generated by their finite dimensional members; and remarks on algebraic operations of stone algebras. The text describes polynomial normal forms and the embedding of polynomial algebras; coverings in the lattice of varieties; embedding semigroups in semigroups generated by idempotents; and endomorphism semigroups and subgroupoid lattices. The book also discusses a report on sublattices of a free lattice, and then presents the cycles in finite semi-distributive lattices; cycles in S-lattices; and summary of results. The text also describes primitive subsets of algebras, ideals, normal sets, and congruences, as well as Jacobson’s density theorem. The book is a good source for readers wanting to study algebra.

Boolean Constructions in Universal Algebras

Boolean Constructions in Universal Algebras Author A.G. Pinus
ISBN-10 9789401709385
Release 2013-04-17
Pages 352
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During the last few decades the ideas, methods, and results of the theory of Boolean algebras have played an increasing role in various branches of mathematics and cybernetics. This monograph is devoted to the fundamentals of the theory of Boolean constructions in universal algebra. Also considered are the problems of presenting different varieties of universal algebra with these constructions, and applications for investigating the spectra and skeletons of varieties of universal algebras. For researchers whose work involves universal algebra and logic.

CONCUR 2007 Concurrency Theory

CONCUR 2007   Concurrency Theory Author Luís Caires
ISBN-10 9783540744061
Release 2007-08-22
Pages 506
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This book constitutes the refereed proceedings of the 17th International Conference on Concurrency Theory, CONCUR 2007, held in Lisbon, Portugal, September 3-8, 2007. The 30 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 112 submissions. The topics include model checking, process calculi, minimization and equivalence checking, types, semantics, probability, bisimulation and simulation, real time, and formal languages.

Freedom and Enforcement in Action

Freedom and Enforcement in Action Author Janusz Czelakowski
ISBN-10 9789401798556
Release 2015-06-10
Pages 261
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Action theory is the object of growing attention in a variety of scientific disciplines and this is the first volume to offer a synthetic view of the range of approaches possible in the topic. The volume focuses on the nexus of formal action theory with a startlingly diverse set of subjects, which range from logic, linguistics, artificial intelligence and automata theory to jurisprudence, deontology and economics. It covers semantic, mathematical and logical aspects of action, showing how the problem of action breaks the boundaries of traditional branches of logic located in syntactics and semantics and now lies on lies on the borderline between logical pragmatics and praxeology. The chapters here focus on specialized tasks in formal action theory, beginning with a thorough description and formalization of the language of action and moving through material on the differing models of action theory to focus on probabilistic models, the relations of formal action theory to deontic logic and its key applications in algorithmic and programming theory. The coverage thus fills a notable lacuna in the literary corpus and offers solid formal underpinning in cognitive science by approaching the problem of cognition as a composite action of mind.

The Shape of Congruence Lattices

The Shape of Congruence Lattices Author Keith Kearnes
ISBN-10 9780821883235
Release 2013-02-26
Pages 169
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This monograph is concerned with the relationships between Maltsev conditions, commutator theories and the shapes of congruence lattices in varieties of algebras. The authors develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. They prove that a residually small variety that satisfies a congruence identity is congruence modular.

Models of Computation

Models of Computation Author Maribel Fernández
ISBN-10 1848824343
Release 2009-04-14
Pages 184
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A Concise Introduction to Computation Models and Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from the standard Turing Machines and Recursive Functions, to the modern computation models inspired by quantum physics. An in-depth analysis of the basic concepts underlying each model of computation is provided. Divided into two parts, the first highlights the traditional computation models used in the first studies on computability: - Automata and Turing Machines; - Recursive functions and the Lambda-Calculus; - Logic-based computation models. and the second part covers object-oriented and interaction-based models. There is also a chapter on concurrency, and a final chapter on emergent computation models inspired by quantum mechanics. At the end of each chapter there is a discussion on the use of computation models in the design of programming languages.