Non-Classical Logics and their Applications to Fuzzy Subsets: A Handbook of the Mathematical Foundations of Fuzzy Set Theory (Theory and Decision Library B)

Editore

Springer

Data di pubblicazione

2012

Lingua

Inglese

ISBN 10

9401040966

ISBN 13

9789401040969

Rilegatura

Brossura

Condizione

New

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Riassunto

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.

Contenuti

Preface. Introduction. Part A: Algebraic Foundations of Non-Classical Logics. I. alpha-Complete MV-algebras; L.P. Belluce. II. On MV-algebras of continuous functions; A. Di Nola, S. Sessa. III. Free and projective Heyting and monadic Heyting algebras; R. Grigolia. IV. Commutative, residuated l-monoids; U. H�hle. 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. VI. Presheaves over GL-monoids; U. H�hle. VII. Quantales: Quantal sets; C.J. Mulvey, M. Nawaz. VIII. Categories of fuzzy sets with values in a quantale or projectale; L.N. Stout. IX. Fuzzy logic and categories of fuzzy sets; O. Wyler. Part C: General Aspects of Non-Classical Logics. X. Prolog extensions to many-valued logics; F. Klawonn. XI. Epistemological aspects of many-valued logics and fuzzy structures; L.J. Kohout. XII. Ultraproduct theorem and recursive properties of fuzzy logic; V. Nov�k. Bibliography. Index.

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