Inclusive Resolution for Horn Sets

Abstract

Let L1 v C1 and L2 V Cz be two parent clauses, where L1 and Lz are positive literals, C1 and C2 are clauses. If L1 and Lz have a most general unifier U and there is the most general substitution X such that ClaX 5 C ~ U A , then CzaX is called an inclusive resolvent of L1 v Cl and L2 v C2. The problem is whether the inclusive resolution is complete. The lifting lemma for inclusive resolution is proved, then it is proved that the inclusive resolution is complete for Horn sets. The present paper gives the inclusion algorithm, and the inclusion theorem is proved.