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Author : Nicholas Rescher
Publisher : McGraw-Hill Companies
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.:/5 (319 download)
Download or read book Many-valued Logic written by Nicholas Rescher and published by McGraw-Hill Companies. This book was released on 1969 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Grzegorz Malinowski
Publisher : Oxford University Press on Demand
ISBN 13 : 9780198537878
Total Pages : 131 pages
Book Rating : 4.5/5 (378 download)
Download or read book Many-valued Logics written by Grzegorz Malinowski and published by Oxford University Press on Demand. This book was released on 1993 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Together with a selective bibliography and historical references it makes the work especially useful as a survey andguide in this field of logic.
Author : Merrie Bergmann
Publisher : Cambridge University Press
ISBN 13 : 1139468782
Total Pages : 7 pages
Book Rating : 4.1/5 (394 download)
Download or read book An Introduction to Many-Valued and Fuzzy Logic written by Merrie Bergmann and published by Cambridge University Press. This book was released on 2008-01-14 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Siegfried Gottwald
Publisher :
ISBN 13 :
Total Pages : 624 pages
Book Rating : 4.:/5 (321 download)
Download or read book A Treatise on Many-valued Logics written by Siegfried Gottwald and published by . This book was released on 2001 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : R.L. Cignoli
Publisher : Springer Science & Business Media
ISBN 13 : 9401594805
Total Pages : 238 pages
Book Rating : 4.4/5 (15 download)
Download or read book Algebraic Foundations of Many-Valued Reasoning written by R.L. Cignoli and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : J. C. Beall
Publisher : Oxford University Press, USA
ISBN 13 : 9780199259878
Total Pages : 233 pages
Book Rating : 4.2/5 (598 download)
Download or read book Possibilities and Paradox written by J. C. Beall and published by Oxford University Press, USA. This book was released on 2003 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Author : Dov M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 9781402005831
Total Pages : 428 pages
Book Rating : 4.0/5 (58 download)
Download or read book Handbook of Philosophical Logic written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2002-05-31 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: such questions for centuries (unrestricted by the capabilities of any hard ware). The principles governing the interaction of several processes, for example, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based effective but rigid bureaucracy is very much similar to a complex computer program handling and manipulating data. My guess is that the principles underlying one are very much the same as those underlying the other. I believe the day is not far away in the future when the computer scientist will wake up one morning with the realisation that he is actually a kind of formal philosopher! The projected number of volumes for this Handbook is about 18. The subject has evolved and its areas have become interrelated to such an extent that it no longer makes sense to dedicate volumes to topics. However, the volumes do follow some natural groupings of chapters. I would like to thank our authors are readers for their contributions and their commitment in making this Handbook a success. Thanks also to our publication administrator Mrs J. Spurr for her usual dedication and excellence and to Kluwer Academic Publishers for their continuing support for the Handbook.
Author : Reiner Hähnle
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.3/5 (91 download)
Download or read book Automated Deduction in Multiple-valued Logics written by Reiner Hähnle and published by . This book was released on 1993 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: A notation called sets-as-signs is developed, and then it is demonstrated how it can be used to modify any known inference method to handle many-valued logics. Applications are discussed, both in pure mathematics, and in hardware verification and interval arithmetic. Concludes with a historical overview of activities in many-valued theorem proving. Annotation copyright by Book News, Inc., Portland, OR
Author :
Publisher : Elsevier
ISBN 13 : 008046663X
Total Pages : 1219 pages
Book Rating : 4.0/5 (84 download)
Download or read book Philosophy of Logic written by and published by Elsevier. This book was released on 2006-11-29 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter
Author : Graham Priest
Publisher : Cambridge University Press
ISBN 13 : 1139469673
Total Pages : 582 pages
Book Rating : 4.1/5 (394 download)
Download or read book An Introduction to Non-Classical Logic written by Graham Priest and published by Cambridge University Press. This book was released on 2008-04-10 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Yaroslav Shramko
Publisher : Springer Science & Business Media
ISBN 13 : 9400709072
Total Pages : 254 pages
Book Rating : 4.4/5 (7 download)
Download or read book Truth and Falsehood written by Yaroslav Shramko and published by Springer Science & Business Media. This book was released on 2011-09-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi.
Author : D.M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 1402035217
Total Pages : 371 pages
Book Rating : 4.4/5 (2 download)
Download or read book Handbook of Philosophical Logic written by D.M. Gabbay and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ninth volume of the Second Edition contains major contributions on Rewriting Logic as a Logical and Semantic Framework, Logical Frameworks, Proof Theory and Meaning, Goal Directed Deductions, Negations, Completeness and Consistency as well as Logic as General Rationality. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.
Author : Dov M. Gabbay
Publisher : Elsevier
ISBN 13 : 008054939X
Total Pages : 691 pages
Book Rating : 4.0/5 (85 download)
Download or read book The Many Valued and Nonmonotonic Turn in Logic written by Dov M. Gabbay and published by Elsevier. This book was released on 2007-08-13 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence.The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called "left non-monotonicity, it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called "right non-monotonicity, limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained.In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs.The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. - Detailed and comprehensive chapters covering the entire range of modal logic. - Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.
Author : D. J. Shoesmith
Publisher : CUP Archive
ISBN 13 : 9780521217651
Total Pages : 426 pages
Book Rating : 4.2/5 (176 download)
Download or read book Multiple-Conclusion Logic written by D. J. Shoesmith and published by CUP Archive. This book was released on 1978-07-06 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a sustained study of the subject and is certain to stimulate further research.
Author : Sandra Lapointe
Publisher : Springer Science & Business Media
ISBN 13 : 9048124018
Total Pages : 251 pages
Book Rating : 4.0/5 (481 download)
Download or read book The Golden Age of Polish Philosophy written by Sandra Lapointe and published by Springer Science & Business Media. This book was released on 2009-05-19 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jan Wolenski ́ and Sandra Lapointe Polish philosophy goes back to the 13th century, when Witelo, famous for his works in optics and the metaphysics of light, lived and worked in Silesia. Yet, Poland’s academic life only really began after the University of Cracow was founded in 1364 – its development was interrupted by the sudden death of King Kazimierz III, but it was re-established in 1400. The main currents of classical scholastic thought like Thomism, Scottism or Ockhamism had been late – about a century – to come to Poland and they had a considerable impact on the budding Polish philosophical scene. The controversy between the via antiqua and the via moderna was hotly 1 debated. Intellectuals deliberated on the issues of concilliarism (whether the C- mon Council has priority over the Pope) and curialism (whether the Bishop of Rome has priority over the Common Council). On the whole, the situation had at least two remarkable features. Firstly, Polish philosophy was pluralistic, and remained so, since its very beginning. But it was also eclectic, which might explain why it aimed to a large extent at achieving a compromise between rival views. Secondly, given the shortcomings of the political system of the time as well as external pr- sure by an increasingly hegemonic Germany, thinkers were very much interested in political matters. Poland was a stronghold of political thought (mostly inclined towards concilliarism) and Polish political thought distinguished itself in Europe J.
Author : Petr Hájek
Publisher : Springer Science & Business Media
ISBN 13 : 9401153000
Total Pages : 304 pages
Book Rating : 4.4/5 (11 download)
Download or read book Metamathematics of Fuzzy Logic written by Petr Hájek and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.
Author : John L. Bell
Publisher : Broadview Press
ISBN 13 : 1551112973
Total Pages : 313 pages
Book Rating : 4.5/5 (511 download)
Download or read book Logical Options written by John L. Bell and published by Broadview Press. This book was released on 2001-03-30 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work.
