Many Valued Logic
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Algebraic Foundations Of Many Valued Reasoning
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Author : R.L. Cignoli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Algebraic Foundations Of Many Valued Reasoning written by R.L. Cignoli 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.
This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics.
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.
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.
Many Valued Logics 2
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Author : Leonard Bolc
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-23
Many Valued Logics 2 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 2003-10-23 with Mathematics categories.
Many-valued logics are becoming increasingly important in all areas of computer science. This is the second volume of an authoritative two-volume handbook on many valued logics by two leading figures in the field. While the first volume was mainly concerned with theoretical foundations, this volume emphasizes automated reasoning, practical applications, and the latest developments in fuzzy logic and rough set theory. Among the applications presented are those in software specification and electronic circuit verification.
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 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.
An Introduction To Many Valued Logics
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Author : Robert Ackermann
language : en
Publisher: Routledge
Release Date : 2019-10-30
An Introduction To Many Valued Logics written by Robert Ackermann and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-30 with Philosophy categories.
Originally published in 1967. An introduction to the literature of nonstandard logic, in particular to those nonstandard logics known as many-valued logics. Part I expounds and discusses implicational calculi, modal logics and many-valued logics and their associated calculi. Part II considers the detailed development of various many-valued calculi, and some of the important metathereoms which have been proved for them. Applications of the calculi to problems in the philosophy are also surveyed. This work combines criticism with exposition to form a comprehensive but concise survey of the field.
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 : Luis M. Augusto
language : en
Publisher:
Release Date : 2017-07-31
Many Valued Logics written by Luis M. Augusto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-31 with Mathematics categories.
Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic--as well as other non-classical logics--is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize--which also means automate--decisions (i.e. reasoning) in many-valued logics. This, in turn, requires a mathematical foundation for these logics. This book provides both this mathematical foundation and this practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem(s) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing not only to learn about, but also to do something with, many-valued logics.
Many Valued Logics
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Author : Grzegorz Malinowski
language : en
Publisher: Oxford University Press on Demand
Release Date : 1993
Many Valued Logics written by Grzegorz Malinowski and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The book attempts an elementary exposition of the topics connected with many-valued logics. It gives an account of the constructions being "many-valued" at their origin, i.e. those obtained through intended introduction of logical values next to truth and falsity. To this aim, the matrixmethod has been chosen as a prevailing manner of presenting the subject. The inquiry throws light upon the profound problem of the criteria of many-valuedness and its classical characterizations. Besides, the reader can find information concerning the main systems of many-valued logic, related axiomatic constructions, and conceptions inspired by many valuedness. The examples of various applications to philosophical logic and some practical domains, as switching theory or Computer Science, helps to see many-valuedness in a wider perspective. Together with a selective bibliography and historical references it makes the work especially useful as a survey andguide in this field of logic.