Abstract
Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic \(\mathcal{EL}\) is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using \(\mathcal{EL}\). On the other hand, unification in \(\mathcal{EL}\) has recently been shown to be NP-complete, and thus of considerably lower complexity than unification in other DLs of similarly restricted expressive power. However, \(\mathcal{EL}\) 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, removing the top concept from \(\mathcal{EL}\) makes the unification problem considerably harder. More precisely, we will show in this paper that unification in \(\mathcal{EL}\) without the top concept is PSpace-complete.
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Baader, F., Binh, N.T., Borgwardt, S., Morawska, B. (2011). Unification in the Description Logic \(\mathcal{EL}\) without the Top Concept. In: Bjørner, N., Sofronie-Stokkermans, V. (eds) Automated Deduction – CADE-23. CADE 2011. Lecture Notes in Computer Science(), vol 6803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22438-6_8
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DOI: https://doi.org/10.1007/978-3-642-22438-6_8
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