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Non-Classical Logics and their Applications to Fuzzy Subsets

A Handbook of the Mathematical Foundations of Fuzzy Set Theory

  • Ulrich Höhle
  • Erich Peter Klement

Part of the Theory and Decision Library book series (TDLB, volume 32)

Table of contents

  1. Front Matter
    Pages i-1
  2. Introduction

    1. Ulrich Höhle, Erich Peter Klement
      Pages 3-4
  3. Algebraic Foundations of Non-Classical Logics

    1. Front Matter
      Pages 5-5
    2. L. P. Belluce
      Pages 7-21
    3. A. Di Nola, S. Sessa
      Pages 23-32
    4. U. Höhle
      Pages 53-106
  4. Non-Classical Models and Topos-Like Categories

    1. Front Matter
      Pages 125-125
    2. U. Höhle
      Pages 127-157
    3. C. J. Mulvey, M. Nawaz
      Pages 159-217
  5. General Aspects of Non-Classical Logics

  6. Back Matter
    Pages 371-392

About this book

Introduction

Non-Classical Logics and their Applications to Fuzzy Subsets is the first major work devoted to a careful study of various relations between non-classical logics and fuzzy sets. This volume is indispensable for all those who are interested in a deeper understanding of the mathematical foundations of fuzzy set theory, particularly in intuitionistic logic, Lukasiewicz logic, monoidal logic, fuzzy logic and topos-like categories. The tutorial nature of the longer chapters, the comprehensive bibliography and index make it suitable as a valuable and important reference for graduate students as well as research workers in the field of non-classical logics.
The book is arranged in three parts: Part A presents the most recent developments in the theory of Heyting algebras, MV-algebras, quantales and GL-monoids. Part B gives a coherent and current account of topos-like categories for fuzzy set theory based on Heyting algebra valued sets, quantal sets of M-valued sets. Part C addresses general aspects of non-classical logics including epistemological problems as well as recursive properties of fuzzy logic.

Keywords

Heyting algebra algebra logic proof set theory ultraproduct

Editors and affiliations

  • Ulrich Höhle
    • 1
  • Erich Peter Klement
    • 2
  1. 1.Fachbereich MathematikBergische UniversitätWuppertalGermany
  2. 2.Institut für MathematikJohannes Kepler UniversitätLinzAustria

Bibliographic information

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