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＜電子ブック＞
Many-Valued Logics 1 : Theoretical Foundations / by Leonard Bolc, Piotr Borowik

版	1st ed. 1992.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1992
本文言語	英語
大きさ	XII, 288 p : online resource
著者標目	*Bolc, Leonard author Borowik, Piotr author SpringerLink (Online service)
件　名	LCSH:Mathematical logic LCSH:Computer science LCSH:Artificial intelligence LCSH:Machine theory FREE:Mathematical Logic and Foundations FREE:Computer Science Logic and Foundations of Programming FREE:Artificial Intelligence FREE:Formal Languages and Automata Theory
一般注記	1 Preliminaries -- 2 Many-Valued Propositional Calculi -- 3 Survey of Three-Valued Propositional Calculi -- 4 Some n-valued Propositional Calculi: A Selection -- 5 Intuitionistic Propositional Calculus -- 6 First-Order Predicate Calculus for Many-Valued Logics -- 7 The Method of Finitely Generated Trees in n-valued Logical Calculi -- 8 Fuzzy Propositional Calculi -- 9 Approximation Logics -- 10 Probability Logics -- References -- Index of Symbols -- Author Index 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 HTTP:URL=https://doi.org/10.1007/978-3-662-08494-6

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