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Fuzzy Sets, Logics and Reasoning about Knowledge

  • Book
  • © 1999

Overview

Editors:
  1. Didier Dubois

    1. I.R.I.T., C.N.R.S., University of Toulouse-III, France

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  2. Henri Prade

    1. I.R.I.T., C.N.R.S., University of Toulouse-III, France

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  3. Erich Peter Klement

    1. Johannes Kepler Universität, Linz, Austria

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Part of the book series: Applied Logic Series (APLS, volume 15)

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction: Bridging the Gap between Multiple-Valued Logics, Fuzzy Logic, Uncertain Reasoning and Reasoning about Knowledge

    1. Introduction: Bridging the Gap between Multiple-Valued Logics, Fuzzy Logic, Uncertain Reasoning and Reasoning about Knowledge

      • Didier Dubois, Henri Prade, Erich Peter Klement
      Pages 1-6

  3. Advances in Mutiple-valued Logics

    1. The Poincaré Paradox and Non-Classical Logics

      • Ulrich Höhle
      Pages 7-16

    2. Propositional Fuzzy Logics Based on Frank T-Norms: A Comparison

      • Erich Peter Klement, Mirko Navara
      Pages 17-38

    3. A Resolution-Based Axiomatisation of ‘Bold’ Propositional Fuzzy Logic

      • Stephan Lehmke
      Pages 39-50

    4. How to Make Your Logic Fuzzy: Fibred Semantics and the Weaving of Logics

      • Dov M. Gabbay
      Pages 51-83

    5. Introducing Grade to Some Metalogical Notions

      • Mihir K. Chakraborty, Sanjukta Basu
      Pages 85-99

    6. Closure Operators, Fuzzy Logic and Constraints

      • Giangiacomo Gerla
      Pages 101-120

  4. Algebraic Aspects of Multiple-valued Logics

    1. Ulam Game, the Logic of Maxsat, and Many-Valued Partitions

      • Daniele Mundici
      Pages 121-137

    2. A Many-Valued Generalization of the Ultrapower Construction

      • Costas A. Drossos
      Pages 139-150

    3. Gabriel Filters and the Spectrum of an MV-Algebra

      • Panagis Karazeris
      Pages 151-160

    4. Conditional States in Finite-Valued Logics

      • Antonio Di Nola, George Georgescu, Ada Lettieri
      Pages 161-174

    5. Conditioning on MV-Algebras and Additive Measures, Further Results

      • Siegfried Weber
      Pages 175-199

  5. Advances in Approximate Reasoning

    1. Toward Adequacy Conditions for Inference Schemata in Approximate Reasoning: The Case of the Rule of Syllogism

      • Siegfried Gottwald
      Pages 201-211

    2. Formal Theories in Fuzzy Logic

      • Vilém Novák
      Pages 213-235

    3. A Note on Fuzzy Inference as Deduction

      • Lluís Godo, Petr Hájek
      Pages 237-241

    4. The Role of Similarity in Fuzzy Reasoning

      • Frank Klawonn
      Pages 243-253

    5. T-indistinguishability Operators and Approximate Reasoning via CRI

      • Dionis Boixader, Joan Jacas
      Pages 255-268

    6. About Similarity-Based Logical Systems

      • Francesco Esteva, Pere Garcia, Lluís Godo
      Pages 269-287

    7. On Similarity-Based Fuzzy Clusterings

      • Helmut Thiele
      Pages 289-299
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Keywords

About this book

Fuzzy Sets, Logics and Reasoning about Knowledge reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning. It takes a state-of-the-art look at multiple-valued and fuzzy set-based logics, in an artificial intelligence perspective. The papers, all of which are written by leading contributors in their respective fields, are grouped into four sections.
The first section presents a panorama of many-valued logics in connection with fuzzy sets. The second explores algebraic foundations, with an emphasis on MV algebras. The third is devoted to approximate reasoning methods and similarity-based reasoning. The fourth explores connections between fuzzy knowledge representation, especially possibilistic logic and prioritized knowledge bases.
Readership: Scholars and graduate students in logic, algebra, knowledge representation, and formal aspects of artificial intelligence.

Editors and Affiliations

  • I.R.I.T., C.N.R.S., University of Toulouse-III, France

    Didier Dubois, Henri Prade

  • Johannes Kepler Universität, Linz, Austria

    Erich Peter Klement

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