The presentation of Elkan's AAAI-93 paper Charles Elkan, "The Paradoxical Success of Fuzzy Logic", in Proceedings of the Eleventh National Conference on Artificial Intelligence, 698-703, 1993. has generated much controversy. The fuzzy logic community claims that the paper is based on some common misunderstandings about fuzzy logic, but Elkan still maintains the correctness of his proof. (See, for instance, AI Magazine 15(1):6-8, Spring 1994.) Elkan proves that for a particular set of axiomatizations of fuzzy logic, fuzzy logic collapses to two-valued logic. The proof is correct in the sense that the conclusion follows from the premises. The disagreement concerns the relevance of the premises to fuzzy logic. At issue are the logical equivalence axioms. Elkan has shown that if you include any of several plausible equivalences, such as not(A and not B) == (not A and not B) or B with the min, max, and 1- axioms of fuzzy logic, then fuzzy logic reduces to binary logic. The fuzzy logic community states that these logical equivalence axioms are not required in fuzzy logic, and that Elkan's proof requires the excluded middle law, a law that is commonly rejected in fuzzy logic. Fuzzy logic researchers must simply take care to avoid using any of these equivalences in their work. It is difficult to do justice to the issues in so short a summary. Readers of this FAQ should not assume that this summary is the last word on this topic, but should read Elkan's paper and some of the other correspondence on this topic (some of which has appeared in the comp.ai.fuzzy newsgroup). Two responses to Elkan's paper, one by Enrique Ruspini and the other by Didier Dubois and Henri Prade, may be found as ftp.cs.cmu.edu:/user/ai/areas/fuzzy/doc/elkan/response.txt A final version of Elkan's paper, together with responses from members of the fuzzy logic community, will appear in an issue of IEEE Expert sometime in 1994. A paper by Dubois and Prade will be presented at AAAI-94. ================================================================Go Back Up