Abstract
Based on the first order predicate logic, in this paper, we present a new approach to generalizing the syntax of ordinary Horn clause rules to establish a fuzzy proof theory. First of all, each Horn clause rule is associated with a numerical implication strengthf. Therefore we obtainf-Horn clause rules. Secondly, Herbrand interpretations 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 way forf-Horm clause rules.
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