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 demonstrate 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].

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