On the law [p⋀q→r]=[(p→r)V(q→r)] in fuzzy logic

Abstract

This paper deals with the logical equivalence of the classical propositional calculus [p/spl and/q/spl rarr/r]=[(p/spl rarr/r)V(q/spl rarr/r)]. This equality seems to play a central role in a recent discussion around a paper of Combs and Andrews (1998). After reconsidering the equivalence in lattices, its validity in the standard theories of fuzzy sets endowed with an implication operator is studied.