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An Introduction To Many Valued Logics
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Book Synopsis An Introduction to Many-Valued and Fuzzy Logic by : Merrie Bergmann
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.
Book Synopsis An Introduction to Many-valued Logics by : Robert Ackermann
Download or read book An Introduction to Many-valued Logics written by Robert Ackermann and published by Routledge. This book was released on 2019-10-30 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Grzegorz Malinowski Publisher :Oxford University Press on Demand ISBN 13 :9780198537878 Total Pages :131 pages Book Rating :4.5/5 (378 download)
Book Synopsis Many-valued Logics by : Grzegorz Malinowski
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.
Book Synopsis Many-valued Logic by : Nicholas Rescher
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:
Book Synopsis Algebraic Foundations of Many-Valued Reasoning by : R.L. Cignoli
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.
Book Synopsis Possibilities and Paradox by : J. C. Beall
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.
Book Synopsis Many-Valued Logics 1 by : Leonard Bolc
Download or read book Many-Valued Logics 1 written by Leonard Bolc and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Non-Classical Logic by : Graham Priest
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.
Book Synopsis A Treatise on Many-valued Logics by : Siegfried Gottwald
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.
Book Synopsis Multiple-Valued Logic by : D. Michael Miller
Download or read book Multiple-Valued Logic written by D. Michael Miller and published by Springer Nature. This book was released on 2022-05-31 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Valued Logic: Concepts and Representations begins with a survey of the use ofmultiple-valued logic in several modern application areas including electronic design automation algorithms and circuit design. The mathematical basis and concepts of various algebras and systems of multiple valued logic are provided including comparisons among various systems and examples of their application. The book also provides an examination of alternative representations of multiple-valued logic suitable for implementation as data structures in automated computer applications. Decision diagram structures for multiple valued applications are described in detail with particular emphasis on the recently developed quantum multiple valued decision diagram. Table of Contents: Multiple Valued Logic Applications / MVL Concepts and Algebra / Functional Representations / Reversible andQuantum Circuits / Quantum Multiple-Valued Decision Diagrams / Summary / Bibliography
Book Synopsis The Many Valued and Nonmonotonic Turn in Logic by : Dov M. Gabbay
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.
Download or read book Lattice-Valued Logic written by Yang Xu and published by Springer. This book was released on 2012-11-02 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice-valued Logic aims at establishing the logical foundation for uncertain information processing routinely performed by humans and artificial intelligence systems. In this textbook for the first time a general introduction on lattice-valued logic is given. It systematically summarizes research from the basic notions up to recent results on lattice implication algebras, lattice-valued logic systems based on lattice implication algebras, as well as the corresponding reasoning theories and methods. The book provides the suitable theoretical logical background of lattice-valued logic systems and supports newly designed intelligent uncertain-information-processing systems and a wide spectrum of intelligent learning tasks.
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.
Book Synopsis Classical and Nonclassical Logics by : Eric Schechter
Download or read book Classical and Nonclassical Logics written by Eric Schechter and published by Princeton University Press. This book was released on 2005-08-28 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).
Book Synopsis Modal Logic by : Nino B. Cocchiarella
Download or read book Modal Logic written by Nino B. Cocchiarella and published by Oxford University Press. This book was released on 2008 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction. 2. The Syntax of Modal Sentential Calculi. 4. Semantics for Logical Necessity. 5. Semantics for S5. 6. Relational World Systems. 7. Quantified Modal Logic. 8. The Semantics of Quantified Modal Logic. 9. Second-Order Modal Logic. 10. Semantics of Second-Order Modal Logic. Afterword. Bibliography. Index.
Book Synopsis Automated Deduction in Multiple-valued Logics by : Reiner Hähnle
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
Book Synopsis An Introduction to Substructural Logics by : Greg Restall
Download or read book An Introduction to Substructural Logics written by Greg Restall and published by Routledge. This book was released on 2002-09-11 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.
