Unification in the Description Logic $\mathcal{EL}$

Abstract

The Description Logic \(\mathcal{EL}\) has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, \(\mathcal{EL}\) 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. The main result of this paper is that unification in \(\mathcal{EL}\) is decidable. More precisely, \(\mathcal{EL}\)-unification is NP-complete, and thus has the same complexity as \(\mathcal{EL}\)-matching. We also show that, w.r.t. the unification type, \(\mathcal{EL}\) is less well-behaved: it is of type zero, which in particular implies that there are unification problems that have no finite complete set of unifiers.KeywordsModal LogicDescription LogicConcept VariableConcept ConstructorConcept TermThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.