Non-Classical Logics and Their Applications to Fuzzy Subsets

A Handbook of the Mathematical Foundations of Fuzzy Set Theory
Herausgeber: Hc6hle, Ulrich; Klement, Erich Peter; Hahle, Ulrich; Hvhle, Ulrich; Klement, E P

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer
• Seitenzahl: 406
• Erscheinungstermin: 31. Januar 1995
• Englisch
• Abmessung: 241mm x 160mm x 28mm
• Gewicht: 770g
• ISBN-13: 9780792331940
• ISBN-10: 079233194X
• Artikelnr.: 25030230

Inhaltsangabe

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. Höhle. 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. Höhle. 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. Novák. Bibliography.
Index.