Unifying cycles

Abstract

Two-literal clauses of the form L leftarrow R occur quite frequently in logic programs, deductive databases, and - disguised as an equation - in term rewriting systems. These clauses define a cycle if the atoms L and R are weakly unifiable, i.e., if L unifies with a new variant of R. The obvious problem with cycles is to control the number of iterations through the cycle. In this paper we consider the cycle unification problem of unifying two literals G and F modulo a cycle. We review the state of the art of cycle unification and give new results for a special type of cycles called unifying cycles, i.e., cycles L leftarrow R for which there exists a substitution sigma such that sigmaL = sigmaR. Altogether, these results show how the deductive process can be efficiently controlled for special classes of cycles without losing completeness.