SAT Encoding of Unification in EL

Abstract

The Description Logic EL is an inexpressive knowledge representation language, which nevertheless has recently drawn considerable attention in the knowledge representation and the ontology community since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. In a recent paper, we have shown that unification in EL is NP-complete, and thus of a complexity that is considerably lower than in other Description Logics of comparably restricted expressive power. In this paper, we introduce a new NP-algorithm for solving unification problem in EL, which is based on a reduction to satisfiability in propositional logic (SAT). The advantage of this new algorithm is, on the one hand, that it allows us to employ highly optimized state of the art SAT solverswhen implementing an EL-unification algorithm. On the other hand, this reduction provides us with a proof of the fact that EL-unification is in NP that is much simpler than the one given in our previous paper on EL-unification.