Semantics and computation of the generalized modus ponens: The long paper

Abstract The generalized modus ponens is a fuzzy logic pattern of reasoning that permits inferences to be made with rules having imprecise information in both their antecedent and consequent parts. Several alternatives are available to represent the meaning one wishes to assign to a given rule. This paper first explores four of the most often encountered possibilities, in the case where a single rule is considered at a time. Second, the behavior of two of them (which seem sufficient for practical use in deduction systems) is investigated in the situation where the dependency between antecedent and consequent variables is described by a collection of rules rather than a single rule. Conjectures are made about what is semantically important in the result yielded by the exact computation of the generalized modus ponens. With these hypothesis it is shown that one can get a meaningful approximation of what is produced by the generalized modus ponens technique and also avoid the well-known inefficiency problem associated with its computation.