Many-Valued Logics

1: Theoretical Foundations

  • Leonard Bolc
  • Piotr Borowik

Table of contents

  1. Front Matter
    Pages I-XII
  2. Leonard Bolc, Piotr Borowik
    Pages 1-21
  3. Leonard Bolc, Piotr Borowik
    Pages 23-61
  4. Leonard Bolc, Piotr Borowik
    Pages 63-77
  5. Leonard Bolc, Piotr Borowik
    Pages 79-94
  6. Leonard Bolc, Piotr Borowik
    Pages 95-103
  7. Leonard Bolc, Piotr Borowik
    Pages 105-122
  8. Leonard Bolc, Piotr Borowik
    Pages 123-141
  9. Leonard Bolc, Piotr Borowik
    Pages 143-207
  10. Leonard Bolc, Piotr Borowik
    Pages 209-230
  11. Leonard Bolc, Piotr Borowik
    Pages 231-254
  12. Back Matter
    Pages 255-292

About this book

Introduction

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.

Keywords

Approximation Logic Intuitionistic Logic Many-valued Logic Philosophical Logic Probability Logic fuzzy logic logic propositional calculus

Authors and affiliations

  • Leonard Bolc
    • 1
  • Piotr Borowik
    • 2
  1. 1.Institute of Computer SciencePolish Academy of SciencesWarszawaPoland
  2. 2.Institute of MathematicsUniversity of CzestochowaCzestochowaPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-08494-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08145-3
  • Online ISBN 978-3-662-08494-6
  • About this book