Unification in the Description Logic EL without the Top Concept

Abstract. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundan-cies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has recently been shown to be NP-complete, and thus of considerably lower complexity than unification in other DLs of similarly restricted expres-sive power. However, EL allows the use of the top concept (>), which represents the whole interpretation domain, whereas the large medical ontology SNOMED CT makes no use of this feature. Surprisingly, remov-ing the top concept from EL makes the unification problem considerably harder. More precisely, we will show in this paper that unification in EL without the top concept is PSpace-complete.