UID:
almahu_9949198410502882
Umfang:
VIII, 392 p.
,
online resource.
Ausgabe:
1st ed. 1995.
ISBN:
9789401102155
Serie:
Theory and Decision Library B, Mathematical and Statistical Methods ; 32
Inhalt:
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.
Anmerkung:
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.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9780792331940
Weitere Ausg.:
Printed edition: ISBN 9789401040969
Weitere Ausg.:
Printed edition: ISBN 9789401102162
Sprache:
Englisch
DOI:
10.1007/978-94-011-0215-5
URL:
https://doi.org/10.1007/978-94-011-0215-5
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