Beyond Two: Theory and Applications of Multiple-Valued Logic / Edition 1

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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.

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Product Details

  • ISBN-13: 9783790815412
  • Publisher: Physica-Verlag HD
  • Publication date: 2/12/2003
  • Series: Studies in Fuzziness and Soft Computing Series, #114
  • Edition description: 2003
  • Edition number: 1
  • Pages: 374
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.88 (d)

Table of Contents

Pt. I Algebras of Multiple-valued Logics and Their Applications 1
Ch. 1 Algebras for Hazard Detection 3
Ch. 2 An Abstract Algebraic Logic View of Some Multiple-valued Logics 25
Ch. 3 Representation Theorems and the Semantics of Non-classical Logics, and Applications to Automated Theorem Proving 59
Ch. 4 An Algebraic Approach to Entropy and its Generalizations - A Survey 101
Pt. II Proof Theory and Automated Deduction in Multiple-valued Logics 115
Ch. 5 Classical Gentzen-type Methods in Propositional Many-valued Logics 117
Ch. 6 Sequent of Relations Calculi: A Framework for Analytic Deduction in Many-valued Logics 157
Ch. 7 Polarity-based Stochastic Local Search Algorithms for Non-clausal Satisfiability 181
Ch. 8 Model Checking for Multi-valued Computation Tree Logics 193
Ch. 9 Complexity of Many-valued Logics 211
Pt. III Fuzzy Logics and Their Applications 235
Ch. 10 Ternary Kleenean Non-additive Measures 237
Ch. 11 On the Hierarchy of t-norm Based Residuated Fuzzy Logics 251
Ch. 12 A Development of Set Theory in Fuzzy Logic 273
Ch. 13 A Fuzzy Generalisation of Information Relations 287
Pt. IV Multiple-valued Logics for Control Theory and Rational Belief 313
Ch. 14 Weierstrass Approximation Theorem and Lukasiewicz Formulas with one Quantified Variable 315
Ch. 15 A Lukasiewicz-style Many-valued Similarity Reasoning. Review 337
Ch. 16 Two Values, Three Values, Many Values, No Values 349
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