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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].

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.

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.

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

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.

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.

Synthetic Geometry of Manifolds

Synthetic Geometry of Manifolds Author Anders Kock
ISBN-10 9780521116732
Release 2010
Pages 302
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This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighborhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.

Lectures in General Algebra

Lectures in General Algebra Author A. G. Kurosh
ISBN-10 9781483149578
Release 2014-07-10
Pages 374
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Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.

Logic and Algebra

Logic and Algebra Author Aldo Ursini
ISBN-10 9781351434713
Release 2017-10-05
Pages 728
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""Attempts to unite the fields of mathematical logic and general algebra. Presents a collection of refereed papers inspired by the International Conference on Logic and Algebra held in Siena, Italy, in honor of the late Italian mathematician Roberto Magari, a leading force in the blossoming of research in mathematical logic in Italy since the 1960s.

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.

Categories for the Working Mathematician

Categories for the Working Mathematician Author Saunders Mac Lane
ISBN-10 9781475747218
Release 2013-04-17
Pages 317
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An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

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.