A Fuzzy Proof Theory

Based on the first order predicate logic, in this paper, we present a new approach to generalizing the syn- tax of ordinary Horn clause rules to establish a fuzzy proof theory. First of all, each Horn clause rule is associ- ated with a numerical implication strength f. Therefore we obtain f-Horn clause rules. Secondly, Herbrand in- terpretations can be generalized to fuzzy subsets of the Herbrand base in the sense of Zadeh. As a result the proof theory for Horn clause rules can be developed in much the same…