Many-Valued Logics 1: Theoretical Foundations / Edition 1

Many-Valued Logics 1: Theoretical Foundations / Edition 1

by Leonard Bolc, Piotr Borowik
     
 

ISBN-10: 3540559264

ISBN-13: 9783540559269

Pub. Date: 12/03/1992

Publisher: Springer Berlin Heidelberg

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

Overview

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.

Product Details

ISBN-13:
9783540559269
Publisher:
Springer Berlin Heidelberg
Publication date:
12/03/1992
Edition description:
1992
Pages:
288
Product dimensions:
6.10(w) x 9.25(h) x 0.03(d)

Related Subjects

Table of Contents

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.

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