Fuzzy reasoning based on f-horn clause rules

Abstract

Based on the first order predicate logic, in this paper, we present an approach to generalizing the syntax and semantics of ordinary Horn clause rules to establish the fuzzy proof theory. First of all, each Horn clause rule is associated with a numerical implication strength f, therefore we obtain f-Horn clause rules. Secondly, Herbrand interpretations can be generalized to fuzzy subsets of the Herbrand base in the sense of Zadeh. We show that as a result the procedural interpretation for Horn clause rules presented by R. A. Kowalski can be developed in much the same way for f-Horn clause rules. Hence, we obtain the fuzzy logic program system