Ebook: Non-Classical Logics and their Applications to Fuzzy Subsets: A Handbook of the Mathematical Foundations of Fuzzy Set Theory
- Tags: Mathematical Logic and Foundations, Order Lattices Ordered Algebraic Structures, Logic
- Series: Theory and Decision Library 32
- Year: 1995
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-1
Introduction....Pages 3-4
Front Matter....Pages 5-5
?-Complete MV-Algebras....Pages 7-21
On MV-algebras of continuous functions....Pages 23-32
Free and projective Heyting and monadic Heyting algebras....Pages 33-52
Commutative, residuated 1—monoids....Pages 53-106
A proof of the completeness of the infinite-valued calculus of ?ukasiewicz with one variable....Pages 107-123
Front Matter....Pages 125-125
Presheaves over GL-monoids....Pages 127-157
Quantales: Quantal sets....Pages 159-217
Categories of fuzzy sets with values in a quantale or projectale....Pages 219-234
Fuzzy logic and categories of fuzzy sets....Pages 235-268
Front Matter....Pages 269-269
Prolog extensions to many-valued logics....Pages 271-289
Epistemological aspects of many-valued logics and fuzzy structures....Pages 291-339
Ultraproduct theorem and recursive properties of fuzzy logic....Pages 341-370
Back Matter....Pages 371-392
Content:
Front Matter....Pages i-1
Introduction....Pages 3-4
Front Matter....Pages 5-5
?-Complete MV-Algebras....Pages 7-21
On MV-algebras of continuous functions....Pages 23-32
Free and projective Heyting and monadic Heyting algebras....Pages 33-52
Commutative, residuated 1—monoids....Pages 53-106
A proof of the completeness of the infinite-valued calculus of ?ukasiewicz with one variable....Pages 107-123
Front Matter....Pages 125-125
Presheaves over GL-monoids....Pages 127-157
Quantales: Quantal sets....Pages 159-217
Categories of fuzzy sets with values in a quantale or projectale....Pages 219-234
Fuzzy logic and categories of fuzzy sets....Pages 235-268
Front Matter....Pages 269-269
Prolog extensions to many-valued logics....Pages 271-289
Epistemological aspects of many-valued logics and fuzzy structures....Pages 291-339
Ultraproduct theorem and recursive properties of fuzzy logic....Pages 341-370
Back Matter....Pages 371-392
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