An Introduction To Many Valued Logics
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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.
An Introduction To Many Valued And Fuzzy Logic
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Author : Merrie Bergmann
language : en
Publisher: Cambridge University Press
Release Date : 2008-01-14
An Introduction To Many Valued And Fuzzy Logic written by Merrie Bergmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-14 with Mathematics categories.
Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.
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.
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 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.
Possibilities And Paradox
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Author : J. C. Beall
language : en
Publisher: Oxford University Press, USA
Release Date : 2003
Possibilities And Paradox written by J. C. Beall and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Philosophy categories.
"The book opens up topics to debate, suitable for an intermediate course in logic. Each chapter contains innovative features that guide us through the subject: exercises to give students hands-on experience, examples to demonstrate the application of concepts, and lists of further reading."--Jacket.
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.
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.
An Introduction To Non Classical Logic
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Author : Graham Priest
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-10
An Introduction To Non Classical Logic written by Graham Priest and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-10 with Science categories.
This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.
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 Many-valued logic 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.