Elkan ' s theoretical argument , reconsidered q

This paper takes part in the discussion motivated by Elkan's paper ``The Paradoxical Success of Fuzzy Logic'' printed in 1993, whose main theoretical point was that Fuzzy Logic does not properly deal with a speci®c Law of Classical Logic: :…p ^ :q† ˆ q _ …:p ^ :q†. The given answer can be summarized, like in other previous cases, by the sentence ``Yes it can but, of course, at some cost''. As it is shown this cost is, basically, duality. But without De Morgan laws there are uncountable many theories of Fuzzy Sets on which that classical law holds. On the way it is observed that, this equation, is not universally veri®ed in De Morgan lattices and the solution given by Elkan, in a particular case, is incorrect. Ó 2001 Elsevier Science Inc. All rights reserved.