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Beyond Two: Theory and Applications of Multiple-Valued Logic

  • Book
  • © 2003

Overview

Editors:
  1. Melvin Fitting

    1. Department of Mathematics and Computer Science, Lehmann College, Bronx, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Ewa Orłowska

    1. National Institute of Telecommunications, Warsaw, Poland

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    You can also search for this editor in PubMed   Google Scholar

  • Exhaustive representation with all the relevant references
  • Current state of research
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 114)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-X
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  2. Algebras of Multiple-valued Logics and Their Applications

    1. Front Matter

      Pages 1-1
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    2. Algebras for Hazard Detection

      • Janusz Brzozowski, Zoltán Ésik, Yaacov Iland
      Pages 3-24

    3. An Abstract Algebraic Logic View of Some Mutiple-valued Logics

      • Josep Maria Font
      Pages 25-57

    4. Representation Theorems and the Semantics of Non-classical Logics, and Applications to Automated Theorem Proving

      • Viorica Sofronie-Stokkermans
      Pages 59-100

    5. An Algebraic Approach to Entropy and its Generalizations — A Survey

      • Dan A. Simovici
      Pages 101-114

  3. Proof Theory and Automated Deduction in Multiple-valued Logics

    1. Front Matter

      Pages 115-115
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    2. Classical Gentzen-type Methods in Propositional Many-valued Logics

      • Arnon Avron
      Pages 117-155

    3. Sequent of Relations Calculi: A Framework for Analytic Deduction in Many-valued Logics

      • Matthias Baaz, Agata Ciabattoni, Christian G. Fermüller
      Pages 157-180

    4. Polarity-based Stochastic Local Search Algorithms for Non-clausal Satisfiability

      • Zbigniew Stachniak
      Pages 181-192

    5. Model Checking for Multi-valued Computation Tree Logics

      • Beata Konikowska, Wojciech Penczek
      Pages 193-210

    6. Complexity of Many-valued Logics

      • Reiner Hähnle
      Pages 211-233

  4. Fuzzy Logics and Their Applications

    1. Front Matter

      Pages 235-235
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    2. Ternary Kleenean Non-additive Measures

      • Tomoyuki Araki, Masao Mukaidono, Fujio Yamamoto
      Pages 237-250

    3. On the Hierarchy of t-norm Based Residuated Fuzzy Logics

      • Francesc Esteva, Lluís Godo, Àngel García-Cerdaña
      Pages 251-272

    4. A Development of Set Theory in Fuzzy Logic

      • Petr Hájek, Zuzana Haniková
      Pages 273-285

    5. A Fuzzy Generalisation of Information Relations

      • Anna Maria Radzikowska, Etienne E. Kerre
      Pages 287-312

  5. Multiple-valued Logics for Control Theory and Rational Belief

    1. Front Matter

      Pages 313-313
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    2. Weierstrass Approximation Theorem and Łukasiewicz Formulas with one Quantified Variable

      • Stefano Aguzzoli, Daniele Mundici
      Pages 315-335

    3. A Łukasiewicz—style Many-valued Similarity Reasoning. Review

      • Esko Turunen
      Pages 337-347
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Keywords

About this book

This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.

Editors and Affiliations

  • Department of Mathematics and Computer Science, Lehmann College, Bronx, USA

    Melvin Fitting

  • National Institute of Telecommunications, Warsaw, Poland

    Ewa Orłowska

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