Don Pigozzi On Abstract Algebraic Logic Universal Algebra And Computer Science

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Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science

Author : Janusz Czelakowski
Publisher : Springer
ISBN 13 : 331974772X
Total Pages : 454 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science by : Janusz Czelakowski

Download or read book Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science written by Janusz Czelakowski and published by Springer. This book was released on 2018-03-20 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Universal Algebra and Applications in Theoretical Computer Science

Author : Klaus Denecke
Publisher : CRC Press
ISBN 13 : 1482285835
Total Pages : 396 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Universal Algebra and Applications in Theoretical Computer Science by : Klaus Denecke

Download or read book Universal Algebra and Applications in Theoretical Computer Science written by Klaus Denecke and published by CRC Press. This book was released on 2018-10-03 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the long-established work that supports them. Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core material. A leisurely pace, careful exposition, numerous examples, and exercises combine to form an introduction to the subject ideal for beginning graduate students or researchers from other areas. The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and commutators. The impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature. Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications.

Hiroakira Ono on Substructural Logics

Author : Nikolaos Galatos
Publisher : Springer Nature
ISBN 13 : 3030769208
Total Pages : 382 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Hiroakira Ono on Substructural Logics by : Nikolaos Galatos

Download or read book Hiroakira Ono on Substructural Logics written by Nikolaos Galatos and published by Springer Nature. This book was released on 2021-12-13 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science. It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions. This book will be primarily of interest to researchers working in algebraic and non-classical logic.

Janusz Czelakowski on Logical Consequence

Author : Jacek Malinowski
Publisher : Springer Nature
ISBN 13 : 3031444906
Total Pages : 473 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Janusz Czelakowski on Logical Consequence by : Jacek Malinowski

Download or read book Janusz Czelakowski on Logical Consequence written by Jacek Malinowski and published by Springer Nature. This book was released on with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Protoalgebraic Logics

Author : Janusz Czelakowski
Publisher : Springer Science & Business Media
ISBN 13 : 9401728070
Total Pages : 456 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Protoalgebraic Logics by : Janusz Czelakowski

Download or read book Protoalgebraic Logics written by Janusz Czelakowski and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].

Handbook of Logical Thought in India

Author : Sundar Sarukkai
Publisher : Springer Nature
ISBN 13 : 8132225775
Total Pages : 1339 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Handbook of Logical Thought in India by : Sundar Sarukkai

Download or read book Handbook of Logical Thought in India written by Sundar Sarukkai and published by Springer Nature. This book was released on 2022-11-04 with total page 1339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles is unique in the way it approaches established material on the various logical traditions in India. Instead of classifying these traditions within Schools as is the usual approach, the material here is classified into sections based on themes ranging from Fundamentals of ancient logical traditions to logic in contemporary mathematics and computer science. This collection offers not only an introduction to the key themes in different logical traditions such as Nyaya, Buddhist and Jaina, it also highlights certain unique characteristics of these traditions as well as contribute new material in the relationship of logic to aesthetics, linguistics, Kashmir Saivism as well as the forgotten Tamil contribution to logic.

Hajnal Andréka and István Németi on Unity of Science

Author : Judit Madarász
Publisher : Springer Nature
ISBN 13 : 3030641872
Total Pages : 517 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Hajnal Andréka and István Németi on Unity of Science by : Judit Madarász

Download or read book Hajnal Andréka and István Németi on Unity of Science written by Judit Madarász and published by Springer Nature. This book was released on 2021-05-31 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself.

Algebras, Lattices, Varieties

Author : Ralph S. Freese
Publisher : American Mathematical Society
ISBN 13 : 1470467984
Total Pages : 451 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebras, Lattices, Varieties by : Ralph S. Freese

Download or read book Algebras, Lattices, Varieties written by Ralph S. Freese and published by American Mathematical Society. This book was released on 2022-11-03 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.

Algebraic Perspectives on Substructural Logics

Author : Davide Fazio
Publisher : Springer Nature
ISBN 13 : 303052163X
Total Pages : 193 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Algebraic Perspectives on Substructural Logics by : Davide Fazio

Download or read book Algebraic Perspectives on Substructural Logics written by Davide Fazio and published by Springer Nature. This book was released on 2020-11-07 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Course in Universal Algebra

Author : S. Burris
Publisher : Springer
ISBN 13 : 9781461381327
Total Pages : 276 pages
Book Rating : 4.3/5 (813 download)

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Book Synopsis A Course in Universal Algebra by : S. Burris

Download or read book A Course in Universal Algebra written by S. Burris and published by Springer. This book was released on 2011-10-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Logic, Language, Information, and Computation

Author : Lawrence S. Moss
Publisher : Springer
ISBN 13 : 3662576694
Total Pages : 325 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis Logic, Language, Information, and Computation by : Lawrence S. Moss

Download or read book Logic, Language, Information, and Computation written by Lawrence S. Moss and published by Springer. This book was released on 2018-06-26 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 25th Workshop on Logic, Language, Information and Communication, WoLLIC 2018, held inBogota, Colombia, in July 2018. The 16 full papers together with 3 short papers and 3 invited talks presented were fully reviewed and selected from 30 submissions. The vision for the conference is to provide an annual forum which is large enough to provide meaningful interactions between logic and the sciences related to information and computation.

Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs

Author : Ivo Düntsch
Publisher : Springer Nature
ISBN 13 : 3030714306
Total Pages : 591 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs by : Ivo Düntsch

Download or read book Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs written by Ivo Düntsch and published by Springer Nature. This book was released on 2021-09-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant entailment), as well as some of their close neighbors. He proved that interpolation fails in some of those systems. Urquhart has done very important work in complexity theory, both about the complexity of proofs in classical and some nonclassical logics. In pure algebra, he has produced a representation theorem for lattices and some rather beautiful duality theorems. In addition, he has done important work in the history of logic, especially on Bertrand Russell, including editing Volume four of Russell’s Collected Papers.

Algebraizable Logics

Author : W. J. Blok
Publisher : Advanced Reasoning Forum
ISBN 13 : 1938421183
Total Pages : 90 pages
Book Rating : 4.9/5 (384 download)

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Book Synopsis Algebraizable Logics by : W. J. Blok

Download or read book Algebraizable Logics written by W. J. Blok and published by Advanced Reasoning Forum. This book was released on 2022-07-23 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: W. J. Blok and Don Pigozzi set out to try to answer the question of what it means for a logic to have algebraic semantics. In this seminal book they transformed the study of algebraic logic by giving a general framework for the study of logics by algebraic means. The Dutch mathematician W. J. Blok (1947-2003) received his doctorate from the University of Amsterdam in 1979 and was Professor of Mathematics at the University of Illinois, Chicago until his death in an automobile accident. Don Pigozzi (1935- ) grew up in Oakland, California, received his doctorate from the University of California, Berkeley in 1970, and was Professor of Mathematics at Iowa State University until his retirement in 2002. The Advanced Reasoning Forum is pleased to make available in its Classic Reprints series this exact reproduction of the 1989 text, with a new errata sheet prepared by Don Pigozzi.

Advances in Rings, Modules and Factorizations

Author : Alberto Facchini
Publisher : Springer Nature
ISBN 13 : 3030434168
Total Pages : 341 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Advances in Rings, Modules and Factorizations by : Alberto Facchini

Download or read book Advances in Rings, Modules and Factorizations written by Alberto Facchini and published by Springer Nature. This book was released on 2020-06-02 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra. A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches.

Algebraic Methods in Philosophical Logic

Author : J. Michael Dunn
Publisher : OUP Oxford
ISBN 13 : 0191589225
Total Pages : 490 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Algebraic Methods in Philosophical Logic by : J. Michael Dunn

Download or read book Algebraic Methods in Philosophical Logic written by J. Michael Dunn and published by OUP Oxford. This book was released on 2001-06-28 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Abstract Algebraic Logic. an Introductory Textbook

Author : Josep Maria Font
Publisher :
ISBN 13 : 9781848902077
Total Pages : 554 pages
Book Rating : 4.9/5 (2 download)

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Book Synopsis Abstract Algebraic Logic. an Introductory Textbook by : Josep Maria Font

Download or read book Abstract Algebraic Logic. an Introductory Textbook written by Josep Maria Font and published by . This book was released on 2016-04-11 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract algebraic logic is the more general and abstract side of algebraic logic, the branch of mathematics that studies the connections between logics and their algebra-based semantics. This emerging subfield of mathematical logic consolidated since the 1980s, and is considered as the algebraic logic of the twenty-first century; as such it is increasingly becoming an indispensable tool to approach the algebraic study of any (mainly sentential) logic in a systematic way. This book is an introductory textbook on abstract algebraic logic, and takes a bottom-up approach, treating first logics with a simpler algebraic study, such as Rasiowa's implicative logics, and then guides readers, by means of successive steps of generalization and abstraction, to meet more and more complicated algebra-based semantics. An entire chapter is devoted to Blok and Pigozzi's theory of algebraizable logics, proving the main theorems and incorporating later developments by other scholars. After a chapter with the basics of the classical theory of matrices, one chapter is devoted to an in-depth exposition of the semantics of generalized matrices. There are also two more avanced chapters providing introductions to the two hierachies that organize the logical landscape according to the criteria of abstract algebraic logic, the Leibniz hierarchy and the Frege hierarchy. All throughout the book, particular care is devoted to the presentation and classification of dozens of examples of particular logics. The book is addressed to mathematicians and logicians with little or no previous exposure to algebraic logic. Some acquaintance with examples of non-classical logics is desirable in order to appreciate the extremely general theory. The book is written with students (or beginners in the field) in mind, and combines a textbook style in its main sections, including more than 400 carefully graded exercises, with a survey style in the exposition of some research directions. The book includes scattered historical notes and numerous bibliographic references.

Algebraic Methodology and Software Technology

Author : Armando M. Haeberer
Publisher : Springer
ISBN 13 : 3540492534
Total Pages : 540 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Algebraic Methodology and Software Technology by : Armando M. Haeberer

Download or read book Algebraic Methodology and Software Technology written by Armando M. Haeberer and published by Springer. This book was released on 2003-05-20 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: AMAST’s goal is to advance awareness of algebraic and logical methodology as part of the fundamental basis of software technology. Ten years and seven conferences after the start of the AMAST movement, I believe we are attaining this. The movement has propagated throughout the world, assembling many enthusiastic specialists who have participated not only in the conferences, which are now annual, but also in the innumerable other activities that AMAST promotes and supports. We are now facing the Seventh International Conference on Algebraic Methodology and Software Technology (AMAST’98). The previous meetings were held in Iowa City, USA (1989 and 1991), in Enschede, The Netherlands (1993), in Montreal, Canada (1995), in Munich, Germany (1996), and in Sydney, Australia (1997). This time it is Brazil’s turn, in a very special part of this colorful country – Amazonia. Thus, “if we have done more it is by standing on the shoulders of giants.” The effort started by Teodor Rus, Arthur Fleck, and William A. Kirk at AMAST’89 was consolidated in AMAST'91 by Teodor Rus, Maurice Nivat, Charles Rattray, and Giuseppe Scollo. Then came modular construction of the building, wonderfully carried out by Giuseppe Scollo, Vangalur Alagar, Martin Wirsing, and Michael Johnson, as Program Chairs of the AMAST conferences held between 1993 and 1997.