Metamathematics of Fuzzy Logic (Trends in Logic) [Paperback]

Petr Hájek (Author)

Book Description

ISBN-10: 1402003706 | ISBN-13: 978-1402003707 | Publication Date: November 30, 2001 | Edition: 1

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.

Editorial Reviews

Review

"...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)

Product Details

• Paperback: 312 pages
• Publisher: Springer; 1 edition (November 30, 2001)
• Language: English
• ISBN-10: 1402003706
• ISBN-13: 978-1402003707
• Product Dimensions: 8.9 x 6.1 x 0.8 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,955,465 in Books (See Top 100 in Books)

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6 of 7 people found the following review helpful:

5.0 out of 5 stars Hajek's Metamathematics of Fuzzy Logic, March 29, 2000

By 

Osher Doctorow, Ph.D. - See all my reviews

This review is from: Metamathematics of Fuzzy Logic (Trends in Logic) (Hardcover)

This is the best book on fuzzy logic that I have ever seen. Hajek and Medvedev present the latest results up to 1996 including the remarkable comparison of fuzzy logic with probability and logic. I have recently extended his results by proving that logic-based probability (LBP) given by P(A-->B) = 1 - P(A) + P(AB) where AB is the intersection or conjunction of A and B is more general than modal logic FP(RPL with product conjunction) because the conditional probability P(B/A) is related to P(A-->B) by P(A-->B) - 1 + P(A) = P(AB) = P(B/A)P(A) and replacing P(AB) and P(B/A) everywhere by P(A-->B) yields a more general logic because P(A-->B) is defined even when P(A) is 0, unlike P(B/A). I especially recommend chapter 8, Generalized Quantifiers and Modalities, which discuss crisp and fuzzy "probably" and "many" , chapter 3 which discusses Lukaciewicz propositional logic (which is closely related to LBP)and Rational Pavelka Logic (RPL) which is an extension of Lukaciewicz's logic. Chapter 1 is important for preliminaries and chapter 2 covers many-valued logics. The reader not well versed in logic and mathematics should hire a reputable consultant or tutor to translate the book into mostly ordinary English (which can be done, at the loss of some rigor). This is because fuzzy logic is entering into everything nowadays, from computers to robots to engineering and social sciences. Multivalued logics, which were for so long criticized (together with fuzzy logics) by critics except some at the University of Vienna and similar places, turn out to have important applications and properties. (I must admit that when I was working for the CSE (Center for the Study of Evaluation) at UCLA in the 1970s, I recommended against researching fuzzy logic, which was one of my worst decisions. I thought that it was insufficiently rigorous in terms of information/knowledge.)