Metamathematics of Fuzzy Logic (Trends in Logic)

Rating:
Summary: Hajek's Metamathematics of Fuzzy Logic
Review: 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.)

Rating:
Summary: Hajek's Metamathematics of Fuzzy Logic
Review: 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.)