A Disjunctive Positive Refinement of Model Elimination and its Application to Subsumption Deletion

Abstract

The Model Elimination (ME) calculus is a refutationally complete, goal-oriented calculus for first-order clause logic. In this article, we introduce a new variant called disjunctive positive ME (DPME); it improves on Plaisted’s positive refinement of ME in that reduction steps are allowed only with positive literals stemming from clauses having at least two positive literals (so-called disjunctive clauses). DPME is motivated by its application to various kinds of subsumption deletion: in order to apply subsumption deletion in ME equally successful as in resolution, it is crucial to employ a version of ME that minimizes ancestor context (i.e., the necessary A-literals to find a refutation). DPME meets this demand. We describe several variants of ME with subsumption, the most important ones being ME with backward and forward subsumption and the Ta-Context Check. We compare their pruning power, also taking into consideration the well-known regularity restriction. All proofs are supplied. The practicability of our approach is demonstrated with experiments.