On the Power of Subsumption and Context Checks

Loop checking is a mechanism used to prune infinite SLD-derivations. Here we study two classes of loop checking mechanisms subsumption checks and context checks. We analyze their soundness, completeness relative strength and related concepts. We prove their soundness (no computed answer substitution to a goal is missed) and derr~nstrate their completeness (all resulting derivations are finite) for some classes of logic programs. The completeness theorems for the subsumption checks make use of a simple version of Kruskal's Tree Theorem [K], called Higman's Lemma [H]. This paper is a sequel to Apt, Bol and Klop [ABK] where a formal framework for studying loop checking mechanisms was introduced and where so-called equality checks were studied.