Residuated Lattices  An Algebraic Glimpse at Substructural Logics Book

Residuated Lattices An Algebraic Glimpse at Substructural Logics

  • Author : Nikolaos Galatos
  • Publisher : Elsevier
  • Release Date : 2007-04-25
  • Genre: Mathematics
  • Pages : 532
  • ISBN 10 : 0080489648

Residuated Lattices An Algebraic Glimpse at Substructural Logics Excerpt :

The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics. As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a cla

Hiroakira Ono on Substructural Logics Book

Hiroakira Ono on Substructural Logics

  • Author : Nikolaos Galatos
  • Publisher : Springer Nature
  • Release Date : 2021-12-13
  • Genre: Philosophy
  • Pages : 375
  • ISBN 10 : 9783030769208

Hiroakira Ono on Substructural Logics 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.

Algebraic Perspectives on Substructural Logics Book

Algebraic Perspectives on Substructural Logics

  • Author : Davide Fazio
  • Publisher : Springer Nature
  • Release Date : 2020-11-07
  • Genre: Philosophy
  • Pages : 193
  • ISBN 10 : 9783030521639

Algebraic Perspectives on Substructural Logics 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.

Mathematics  Logic  and their Philosophies Book

Mathematics Logic and their Philosophies

  • Author : Mojtaba Mojtahedi
  • Publisher : Springer Nature
  • Release Date : 2021-02-09
  • Genre: Philosophy
  • Pages : 493
  • ISBN 10 : 9783030536541

Mathematics Logic and their Philosophies Excerpt :

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

Trends in Logic Book

Trends in Logic

  • Author : Vincent F. Hendricks
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-09
  • Genre: Philosophy
  • Pages : 384
  • ISBN 10 : 9789401735988

Trends in Logic Excerpt :

In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.

Interval   Probabilistic Uncertainty and Non classical Logics Book

Interval Probabilistic Uncertainty and Non classical Logics

  • Author : Van-Nam Huynh
  • Publisher : Springer Science & Business Media
  • Release Date : 2008-01-11
  • Genre: Mathematics
  • Pages : 376
  • ISBN 10 : 9783540776642

Interval Probabilistic Uncertainty and Non classical Logics Excerpt :

This book contains the proceedings of the first International Workshop on Interval/Probabilistic Uncertainty and Non Classical Logics, Ishikawa, Japan, March 25-28, 2008. The workshop brought together researchers working on interval and probabilistic uncertainty and on non-classical logics. It is hoped this workshop will lead to a boost in the much-needed collaboration between the uncertainty analysis and non-classical logic communities, and thus, to better processing of uncertainty.

The Application of Fuzzy Logic for Managerial Decision Making Processes Book

The Application of Fuzzy Logic for Managerial Decision Making Processes

  • Author : Andreas Meier
  • Publisher : Springer
  • Release Date : 2017-03-30
  • Genre: Computers
  • Pages : 103
  • ISBN 10 : 9783319540481

The Application of Fuzzy Logic for Managerial Decision Making Processes Excerpt :

This book addresses the latest research and applications of fuzzy management methods for business decisions. It showcases a broad set of applications and discusses topics such as measures for the quality of analytics outcomes in big data environments; how fuzzy management methods support the inclusion of human thinking and human behavior in decision making processes; how to generate better results with fuzzy management methods in cases of imprecise information; new personalization concepts enabled by fuzzy logic for the offering of customized products and services especially in the electronic market; and lastly the application of fuzzy analysis for executives using natural rather than computer language. The combination of research papers and case studies makes it a valuable resource both for researchers and practitioners in the digital economy.

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

Don Pigozzi on Abstract Algebraic Logic Universal Algebra and Computer Science

  • Author : Janusz Czelakowski
  • Publisher : Springer
  • Release Date : 2018-03-20
  • Genre: Philosophy
  • Pages : 454
  • ISBN 10 : 9783319747729

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

Petr H  jek on Mathematical Fuzzy Logic Book

Petr H jek on Mathematical Fuzzy Logic

  • Author : Franco Montagna
  • Publisher : Springer
  • Release Date : 2014-09-23
  • Genre: Mathematics
  • Pages : 318
  • ISBN 10 : 9783319062334

Petr H jek on Mathematical Fuzzy Logic Excerpt :

This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.

Logic for Programming  Artificial Intelligence  and Reasoning Book

Logic for Programming Artificial Intelligence and Reasoning

  • Author : Martin Davis
  • Publisher : Springer
  • Release Date : 2015-12-01
  • Genre: Computers
  • Pages : 640
  • ISBN 10 : 9783662488997

Logic for Programming Artificial Intelligence and Reasoning Excerpt :

This book constitutes the proceedings of the 20th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR-20, held in November 2015, in Suva, Fiji. The 43 regular papers presented together with 1 invited talk included in this volume were carefully reviewed and selected from 92 submissions. The series of International Conferences on Logic for Programming, Artificial Intelligence and Reasoning, LPAR, is a forum where, year after year, some of the most renowned researchers in the areas of logic, automated reasoning, computational logic, programming languages and their applications come to present cutting-edge results, to discuss advances in these fields, and to exchange ideas in a scientifically emerging part of the world.

Logic and Implication Book

Logic and Implication

  • Author : Petr Cintula
  • Publisher : Springer Nature
  • Release Date : 2022-01-01
  • Genre: Philosophy
  • Pages : 465
  • ISBN 10 : 9783030856755

Logic and Implication Excerpt :

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.

Relational and Algebraic Methods in Computer Science Book

Relational and Algebraic Methods in Computer Science

  • Author : Uli Fahrenberg
  • Publisher : Springer Nature
  • Release Date : 2020-04-01
  • Genre: Mathematics
  • Pages : 335
  • ISBN 10 : 9783030435202

Relational and Algebraic Methods in Computer Science Excerpt :

This book constitutes the proceedings of the 18th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2020, which was due to be held in Palaiseau, France, in April 2020. The conference was cancelled due to the COVID-19 pandemic. The 20 full papers presented together with 3 invited abstracts were carefully selected from 29 submissions. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.

Modality  Semantics and Interpretations Book

Modality Semantics and Interpretations

  • Author : Shier Ju
  • Publisher : Springer
  • Release Date : 2015-07-03
  • Genre: Philosophy
  • Pages : 188
  • ISBN 10 : 9783662471975

Modality Semantics and Interpretations Excerpt :

This contributed volume includes both theoretical research on philosophical logic and its applications in artificial intelligence, mostly employing the concepts and techniques of modal logic. It collects selected papers presented at the Second Asia Workshop on Philosophical Logic, held in Guangzhou, China in 2014, as well as a number of invited papers by specialists in related fields. The contributions represent pioneering philosophical logic research in Asia.

On Logical  Algebraic  and Probabilistic Aspects of Fuzzy Set Theory Book

On Logical Algebraic and Probabilistic Aspects of Fuzzy Set Theory

  • Author : Susanne Saminger-Platz
  • Publisher : Springer
  • Release Date : 2016-01-11
  • Genre: Technology & Engineering
  • Pages : 275
  • ISBN 10 : 9783319288086

On Logical Algebraic and Probabilistic Aspects of Fuzzy Set Theory Excerpt :

The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement’s research activities, concerning copulas, measures and integrals, as well as aggregation problems. Some of the chapters reflect personal views and controversial aspects of traditional topics, while others deal with deep mathematical theories, such as the algebraic and logical foundations of fuzzy set theory and fuzzy logic. Originally thought as an homage to Peter Klement, the book also represents an advanced reference guide to the mathematical theories related to fuzzy logic and fuzzy set theory with the potential to stimulate important discussions on new research directions in the field.

The Road to Universal Logic Book

The Road to Universal Logic

  • Author : Arnold Koslow
  • Publisher : Birkhäuser
  • Release Date : 2015-06-10
  • Genre: Mathematics
  • Pages : 604
  • ISBN 10 : 9783319153681

The Road to Universal Logic Excerpt :

This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.