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, such as duplicates or instances of already retained clauses, can be substantially reduced. 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. This characterization partially answers the two questions. First, if a clause set is known to exclude ancestor subsumption, linear resolution turns out to be a preferable strategy in order to reduce the generation of subsumed clauses. Concerning the second question, this result allows a suitable restriction of the (usually very expensive) subsumption test. Finally, we show that in particular cases those clauses that account for the occurrence of ancestor subsumption can be excluded from the resolution process. SAM’s lemma will serve as an example for demonstrating various possibilities to remove reduncancy-generating clauses.