Non-Classical Logics and their Applications to Fuzzy Subsets

A Handbook of the Mathematical Foundations of Fuzzy Set Theory
Softcover Nachdruck of the original 1. Auflage 1995
ISBN: 978-94-010-4096-9
Verlag: Springer Netherlands

Buch, Englisch, Band 32, 392 Seiten, Format (B × H): 160 mm x 240 mm, Gewicht: 643 g

Reihe: Theory and Decision Library B

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.

Zielgruppe

Research

Autoren/Hrsg.

Klement, Erich Peter

Höhle, Ulrich

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

A Algebraic Foundations of Non-Classical Logics.- I ?-Complete MV-algebras.- II On MV-algebras of continuous functions.- III Free and projective Heyting and monadic Heyting algebras.- IV Commutative, residuated 1—monoids.- V A Proof of the completeness of the infinite-valued calculus of Lukasiewicz with one varibale.- B Non-Classical Models and Topos-Like Categories.- VI Presheaves Over GL-monoide.- VII Quantales: Quantal sets.- VIII Categories of fuzzy sets with values in a quantale or project ale.- IX Fuzzy logic and categories of fuzzy sets.- C General Aspects of Non-Classical Logics 269.- X Prolog extensions to many-valued logics.- XI Epistemological aspects of many-valued logics and fuzzy structures.- XII Ultraproduct theorem and recursive properties of fuzzy logic.