[21] Elkan's "The Paradoxical Success of Fuzzy Logic" paper

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

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.

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