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

Abstract

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the DL $\mathcal{EL}$, which is used to define several large biomedical ontologies, unification is NP-complete. However, the unification algorithms for $\mathcal{EL}$ developed until recently could not deal with ontologies containing general concept inclusions (GCIs). In a series of recent papers we have made some progress towards addressing this problem, but the ontologies the developed unification algorithms can deal with need to satisfy a certain cycle restriction. In the present paper, we follow a different approach. Instead of restricting the input ontologies, we generalize the notion of unifiers to so-called hybrid unifiers. Whereas classical unifiers can be viewed as acyclic TBoxes, hybrid unifiers are cyclic TBoxes, which are interpreted together with the ontology of the input using a hybrid semantics that combines fixpoint and descriptive semantics. We show that hybrid unification in $\mathcal{EL}$ is NP-complete and introduce a goal-oriented algorithm for computing hybrid unifiers.