Metamathematics of Fuzzy Logic / Edition 1

by Petr Hïjek

Overview

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.

Product Details

ISBN-13:	9780792352389
Publisher:	Springer Netherlands
Publication date:	08/31/1998
Series:	Trends in Logic , #4
Edition description:	1998
Pages:	299
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Preface. 1. Preliminaries. 2. Many-Valued Propositional Calculi. 3. Lukasiewicz Propositional Logic. 4. Product Logic, Gödel Logic. 5. Many-Valued Predicate Logics. 6. Complexity and Undecidability. 7. On Approximate Inference. 8. Generalized Quantifiers and Modalities. 9. Miscellanea. 10. Historical Remarks. References. Index.

Editorial Reviews

"...Moreover, it can be an excellent guideline for a postgraduate course in fuzzy logic because of its clear and well-organized content. Definitively, an excellent book that we enthusiastically recommend, and that fuzzy and mathematical logic (and probably philosophical logic as well) communities have been waiting for, for a long time."
(F. Esteva, L. Godo, International Journal of General Systems, 29:5 (2000)
"On whole this book occupies a unique place in the literature on fuzzy sets and fuzzy logic and fills a substantial gap. This is the only existing monograph offering a comprehensive study of triangular norms and their interconnections. Overall the book is very well written and should become the standard reference for triangular norms."
(Mathematical Reviews, 2002a)

From the Publisher

Presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic . Some important systems of real-valued propositional and predicate calculus are defined and investigated. Discussion includes Lukasiewicz propositional logic, product logic, Godel logic, complexity and undecidability, approximate inference, quantifiers and modalities. The author aims to show that fuzzy logic as a logic of imprecise propositions does have well developed formal foundations and that most things usually named fuzzy inference can be naturally understood as logical deduction. For logicians, mathematicians, and computer scientists. Annotation c. by Book News, Inc., Portland, Or.

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