Many Valued Logics 1
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Many Valued Logics 1
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Author : Leonard Bolc
language : en
Publisher: Springer
Release Date : 2014-03-12
Many Valued Logics 1 written by Leonard Bolc and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Mathematics categories.
Many-valued logics were developed as an attempt to handle philosophical doubts about the "law of excluded middle" in classical logic. The first many-valued formal systems were developed by J. Lukasiewicz in Poland and E.Post in the U.S.A. in the 1920s, and since then the field has expanded dramatically as the applicability of the systems to other philosophical and semantic problems was recognized. Intuitionisticlogic, for example, arose from deep problems in the foundations of mathematics. Fuzzy logics, approximation logics, and probability logics all address questions that classical logic alone cannot answer. All these interpretations of many-valued calculi motivate specific formal systems thatallow detailed mathematical treatment. In this volume, the authors are concerned with finite-valued logics, and especially with three-valued logical calculi. Matrix constructions, axiomatizations of propositional and predicate calculi, syntax, semantic structures, and methodology are discussed. Separate chapters deal with intuitionistic logic, fuzzy logics, approximation logics, and probability logics. These systems all find application in practice, in automatic inference processes, which have been decisive for the intensive development of these logics. This volume acquaints the reader with theoretical fundamentals of many-valued logics. It is intended to be the first of a two-volume work. The second volume will deal with practical applications and methods of automated reasoning using many-valued logics.
Many Valued Logics 1
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Author : Leonard Bolc
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Many Valued Logics 1 written by Leonard Bolc and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Many-valued logics were developed as an attempt to handle philosophical doubts about the "law of excluded middle" in classical logic. The first many-valued formal systems were developed by J. Lukasiewicz in Poland and E.Post in the U.S.A. in the 1920s, and since then the field has expanded dramatically as the applicability of the systems to other philosophical and semantic problems was recognized. Intuitionisticlogic, for example, arose from deep problems in the foundations of mathematics. Fuzzy logics, approximation logics, and probability logics all address questions that classical logic alone cannot answer. All these interpretations of many-valued calculi motivate specific formal systems thatallow detailed mathematical treatment. In this volume, the authors are concerned with finite-valued logics, and especially with three-valued logical calculi. Matrix constructions, axiomatizations of propositional and predicate calculi, syntax, semantic structures, and methodology are discussed. Separate chapters deal with intuitionistic logic, fuzzy logics, approximation logics, and probability logics. These systems all find application in practice, in automatic inference processes, which have been decisive for the intensive development of these logics. This volume acquaints the reader with theoretical fundamentals of many-valued logics. It is intended to be the first of a two-volume work. The second volume will deal with practical applications and methods of automated reasoning using many-valued logics.
Neutrality And Many Valued Logics
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Author : Andrew Schumann
language : en
Publisher: Infinite Study
Release Date : 2007
Neutrality And Many Valued Logics written by Andrew Schumann and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. Recall that hypersequents are a natural generalization of Gentzen's style sequents that was introduced independently by Avron and Pottinger. In particular, we consider Hilbert's style, sequent, and hypersequent calculi for infinite-valued logics based on the three fundamental continuous t-norms: Lukasiewicz's, Godel?s, and Product logics. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Godel?s, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. We consider two cases of non-Archimedean multi-valued logics: the first with many-validity in the interval [0,1] of hypernumbers and the second with many-validity in the ring of p-adic integers. Notice that in the second case we set discrete infinite-valued logics. Logics investigated: 1. hyperrational valued Lukasiewicz's, Godel?s, and Product logics, 2. hyperreal valued Lukasiewicz's, Godel?s, and Product logics, 3. p-adic valued Lukasiewicz's, Godel?s, and Post's logics.
A Treatise On Many Valued Logics
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Author : Siegfried Gottwald
language : en
Publisher:
Release Date : 2001
A Treatise On Many Valued Logics written by Siegfried Gottwald and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
A growing interest in many-valued logic has developed which to a large extent is based on applications, intended as well as already realised ones. These applications range from the field of computer science, e.g. in the areas of automated theorem proving, approximate reasoning, multi-agent systems, switching theory, and program verification, through the field of pure mathematics, e.g. in independence of consistency proofs, in generalized set theories, or in the theory of particular algebraic structures, into the fields of humanities, linguistics and philosophy.
Many Valued Logics
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Author : John Barkley Rosser
language : en
Publisher: Greenwood
Release Date : 1977
Many Valued Logics written by John Barkley Rosser and has been published by Greenwood this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Philosophy categories.
Many Valued Logic
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Author : Nicholas Rescher
language : en
Publisher: McGraw-Hill Companies
Release Date : 1969
Many Valued Logic written by Nicholas Rescher and has been published by McGraw-Hill Companies this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Philosophy categories.
Many Valued Logics
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Author : Leonard Bolc
language : en
Publisher:
Release Date : 1992
Many Valued Logics written by Leonard Bolc and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
The Twenty Third International Symposium On Multiple Valued Logic May 24 27 1993 Sacramento California
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Author : IEEE Computer Society
language : en
Publisher: Los Alamitos, Calif. : IEEE Computer Society Press
Release Date : 1993
The Twenty Third International Symposium On Multiple Valued Logic May 24 27 1993 Sacramento California written by IEEE Computer Society and has been published by Los Alamitos, Calif. : IEEE Computer Society Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Computers categories.
The proceedings of the symposium held in Sacramento, California, May 1993, include sessions on algebra, logic, circuits, logic minimization, fuzzy logic, testing, function decomposition, learning, reasoning, logic design, and special applications. In addition to 41 contributed papers, three invited
Beyond Two Theory And Applications Of Multiple Valued Logic
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Author : Melvin Fitting
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-09
Beyond Two Theory And Applications Of Multiple Valued Logic written by Melvin Fitting and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-09 with Mathematics categories.
This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.
Proceedings
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Author :
language : en
Publisher:
Release Date : 1969
Proceedings written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Philosophy categories.