Many-Valued Logics 1: Theoretical Foundations

Many-Valued Logics 1: Theoretical Foundations

by Leonard Bolc, Piotr Borowik
     
 

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

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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.

Editorial Reviews

Booknews
Many-valued logics were developed as an attempt to handle philosophical doubts about the "law of the excluded middle" in classical logic. This discussion, which began in the 1920s, has greatly expanded in recent years with the development of various logical systems including fuzzy and approximation logic. While acquainting the reader with the theoretical fundamentals, the text serves as a kind of compass, pointing out which logical system best answers a particular type of problem. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Product Details

ISBN-13:
9783642081453
Publisher:
Springer Berlin Heidelberg
Publication date:
12/08/2010
Edition description:
Softcover reprint of hardcover 1st ed. 1992
Pages:
288
Product dimensions:
0.65(w) x 9.21(h) x 6.14(d)

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