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

Authors:
E. Trillas;C. Alsina
Affiliations:
Departamento de Inteligencia Artificial, Univ. Politecnica de Madrid;-
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2002

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Abstract

This paper deals with the logical equivalence of the classical propositional calculus [p∧q→r]=[(p→r)V(q→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