Reducing the Derivation of Redundant Clauses in Reasoning Systems

Abstract

This paper addresses two problems concerning the issue of redundant information in resolution based reasoning systems. The first one deals with the question, how the derivation of redundant clauses can be substantially reduced a priori. The second one asks for a criterion to decide, which clauses need not be tested for reduncancy. In this paper we consider a particular kind of reduncancy, which we call ancestor subsumption, that is the subsumption of a resolvent by one of its ancestors. We give a complete syntactic characterization of clause sets producing ancestor subsumed clauses. Given this characterization, a solution to the problem with generating redundant clauses is proposed. Moreover, a suitable restriction of the (usually very expensive) subsumption test is derived from this result SAM's lemma will serve as an example for demonstrating various possibilities how to avoid the derivation of redundant clauses.