Non-Classical Logics and Their Applications to Fuzzy Subsets

Non-Classical Logics and Their Applications to Fuzzy Subsets : Handbook of the Mathematical Foundations of Fuzzy Set Theory

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Description

This work is devoted to a study of various relations between non-classical logics and fuzzy sets. This volume is aimed at 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 should 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.
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Product details

  • Hardback | 400 pages
  • 177.8 x 230 x 31.75mm | 859.97g
  • Dordrecht, Netherlands, United States
  • English
  • bibliography, references, index
  • 079233194X
  • 9780792331940

Table of contents

Part A Algebraic Foundations of Non-Classical Logics: Complete MV-algebras, L.P. Belluce. On MV-algebras of continuous functions, A. Di Nola, S. Sessa. Free and projective Heyting and monadic Heyting algebras, R. Grigolia. Commutative, residuated l-monoids, U. Hohle. V. A Proof of the completeness of the infinite-valued calculus of Lukasiewicz with one variable, D. Mundici, M. Pasquetto. Part B Non-Classical Models and Topos-Like Categories: Presheaves over GL-monoids, U. Hohle. Quantales - Quantal sets, C.J. Mulvey, M. Nawaz. Categories of fuzzy sets with values in a quantale or projectale, L.N. Stout. Fuzzy logic and categories of fuzzy sets, O. Wyler. Part C General Aspects of Non-Classical Logics: Prolog extensions to many-valued logics, F. Klawonn. Epistemological aspects of many-valued logics and fuzzy structures, L.J. Kohout. Ultraproduct theorem and recursive properties of fuzzy logic, V. Novak.
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