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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 Together with a selective bibliography and historical references it makes the work especially useful as a survey andguide in this field of logic.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 : Luis M. Augusto
Publisher :
ISBN 13 : 9781848902503
Total Pages : 342 pages
Book Rating : 4.9/5 (25 download)
Download or read book Many-Valued Logics written by Luis M. Augusto and published by . This book was released on 2017-07-31 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Robert Ackermann
Publisher : Routledge
ISBN 13 : 1000735478
Total Pages : 83 pages
Book Rating : 4.0/5 (7 download)
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 : 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 : Graham Priest
Publisher : Cambridge University Press
ISBN 13 : 9781139469678
Total Pages : pages
Book Rating : 4.4/5 (696 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 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 : 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 : 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 : Yang Xu
Publisher : Springer
ISBN 13 : 3540448470
Total Pages : 397 pages
Book Rating : 4.5/5 (44 download)
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.
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.
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 : Eric Schechter
Publisher : Princeton University Press
ISBN 13 : 9780691122793
Total Pages : 530 pages
Book Rating : 4.1/5 (227 download)
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).
Author : Lou Goble
Publisher : Wiley-Blackwell
ISBN 13 : 9780631206927
Total Pages : 510 pages
Book Rating : 4.2/5 (69 download)
Download or read book The Blackwell Guide to Philosophical Logic written by Lou Goble and published by Wiley-Blackwell. This book was released on 2001-08-30 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a definitive introduction to twenty core areas of philosophical logic including classical logic, modal logic, alternative logics and close examinations of key logical concepts. The chapters, written especially for this volume by internationally distinguished logicians, philosophers, computer scientists and linguists, provide comprehensive studies of the concepts, motivations, methods, formal systems, major results and applications of their subject areas. The Blackwell Guide to Philosophical Logic engages both general readers and experienced logicians and provides a solid foundation for further study.
Author : Anita Wasilewska
Publisher : Springer
ISBN 13 : 3319925911
Total Pages : 535 pages
Book Rating : 4.3/5 (199 download)
Download or read book Logics for Computer Science written by Anita Wasilewska and published by Springer. This book was released on 2018-11-03 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science contains intuitive introductory chapters explaining the need for logical investigations, motivations for different types of logics and some of their history. They are followed by strict formal approach chapters. All chapters contain many detailed examples explaining each of the introduced notions and definitions, well chosen sets of exercises with carefully written solutions, and sets of homework. While many logic books are available, they were written by logicians for logicians, not for computer scientists. They usually choose one particular way of presenting the material and use a specialized language. Logics for Computer Science discusses Gentzen as well as Hilbert formalizations, first order theories, the Hilbert Program, Godel's first and second incompleteness theorems and their proofs. It also introduces and discusses some many valued logics, modal logics and introduces algebraic models for classical, intuitionistic, and modal S4 and S5 logics. The theory of computation is based on concepts defined by logicians and mathematicians. Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics. Important applications derived from concepts of logic for computer technology include Artificial Intelligence and Software Engineering. In addition to Computer Science, this book may also find an audience in mathematics and philosophy courses, and some of the chapters are also useful for a course in Artificial Intelligence.
Author : Greg Restall
Publisher : Routledge
ISBN 13 : 1135111316
Total Pages : 384 pages
Book Rating : 4.1/5 (351 download)
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 384 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.
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.
