Description
Book Synopsis
This work is a study of the relations between non-classical logics and fuzzy sets. It is aimed at all those who are interested in a deeper understanding of the mathematical foundations of fuzzy set theory, including intuitionistic logic, Lukasiewicz logic and monoidal logic.
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.
