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  • © 1995

Non-Classical Logics and their Applications to Fuzzy Subsets

A Handbook of the Mathematical Foundations of Fuzzy Set Theory

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
  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
    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. Commutative, residuated 1—monoids

      • U. Höhle
      Pages 53-106
  4. Non-Classical Models and Topos-Like Categories

    1. Front Matter

      Pages 125-125
    2. Presheaves over GL-monoids

      • U. Höhle
      Pages 127-157
    3. Quantales: Quantal sets

      • C. J. Mulvey, M. Nawaz
      Pages 159-217
  5. General Aspects of Non-Classical Logics

    1. Front Matter

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

      • F. Klawonn
      Pages 271-289
  6. Back Matter

    Pages 371-392

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

  • Industry Sectors: IT & Software

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access