Technische Universität

In recent years, the Description Logic EL has received a significant interest. It has been shown to be useful as a knowledge representation formalism, to define large biomedical ontologies. Moreover, important inference problems like subsumption have been shown to be decidable in polynomial time in EL. In particular, unification in EL can be used to detect redundancies in big ontologies. The unification problem in EL has been shown to be an NP-complete problem even in the presence of background knowledge in the form of an acyclic TBox. Recently, the result was also extended to the case of cycle-restricted TBoxes. Unification in EL w.r.t. general TBoxes is still an open problem. Here we define a more general notion of unification problem called hybrid unification. In contrast to the usual unification problem, hybrid unification allows solutions that contain cyclic definitions of concept names. We show that hybrid unification in EL is NPcomplete. Furthermore, we provide a goal-oriented NP-decision procedure for the hybrid unification problem.