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Non-Classical Logics and their Applications to Fuzzy Subsets

A Handbook of the Mathematical Foundations of Fuzzy Set Theory

  • Book
  • © 1995

Overview

Editors:
  1. Ulrich Höhle

    1. Fachbereich Mathematik, Bergische Universität, Wuppertal, Germany

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    You can also search for this editor in PubMed   Google Scholar

  2. Erich Peter Klement

    1. Institut für Mathematik, Johannes Kepler Universität, Linz, Austria

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    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-1
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  2. Introduction

    1. Introduction

      • Ulrich Höhle, Erich Peter Klement
      Pages 3-4

  3. Algebraic Foundations of Non-Classical Logics

    1. Front Matter

      Pages 5-5
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    2. α-Complete MV-Algebras

      • L. P. Belluce
      Pages 7-21

    3. On MV-algebras of continuous functions

      • A. Di Nola, S. Sessa
      Pages 23-32

    4. Free and projective Heyting and monadic Heyting algebras

      • R. Grigolia
      Pages 33-52

    5. Commutative, residuated 1—monoids

      • U. Höhle
      Pages 53-106

    6. A proof of the completeness of the infinite-valued calculus of Łukasiewicz with one variable

      • D. Mundici, M. Pasquetto
      Pages 107-123

  4. Non-Classical Models and Topos-Like Categories

    1. Front Matter

      Pages 125-125
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    2. Presheaves over GL-monoids

      • U. Höhle
      Pages 127-157

    3. Quantales: Quantal sets

      • C. J. Mulvey, M. Nawaz
      Pages 159-217

    4. Categories of fuzzy sets with values in a quantale or projectale

      • L. N. Stout
      Pages 219-234

    5. Fuzzy logic and categories of fuzzy sets

      • O. Wyler
      Pages 235-268

  5. General Aspects of Non-Classical Logics

    1. Front Matter

      Pages 269-269
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    2. Prolog extensions to many-valued logics

      • F. Klawonn
      Pages 271-289

    3. Epistemological aspects of many-valued logics and fuzzy structures

      • L. J. Kohout
      Pages 291-339

    4. Ultraproduct theorem and recursive properties of fuzzy logic

      • V. Novák
      Pages 341-370

  6. Back Matter

    Pages 371-392
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Keywords

About this book

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.

Editors and Affiliations

  • Fachbereich Mathematik, Bergische Universität, Wuppertal, Germany

    Ulrich Höhle

  • Institut für Mathematik, Johannes Kepler Universität, Linz, Austria

    Erich Peter Klement

Bibliographic Information

  • Book Title: Non-Classical Logics and their Applications to Fuzzy Subsets

  • Book Subtitle: A Handbook of the Mathematical Foundations of Fuzzy Set Theory

  • Editors: Ulrich Höhle, Erich Peter Klement

  • Series Title: Theory and Decision Library B

  • DOI: https://doi.org/10.1007/978-94-011-0215-5

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1995

  • Hardcover ISBN: 978-0-7923-3194-0Published: 31 January 1995

  • Softcover ISBN: 978-94-010-4096-9Published: 20 October 2012

  • eBook ISBN: 978-94-011-0215-5Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: VIII, 392

  • Topics: Mathematical Logic and Foundations, Order, Lattices, Ordered Algebraic Structures, Logic

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