# Hybrid EL-Unification is NP-Complete

##### Franz BaaderFranz Baader,  Oliver Fernández GilOliver Fernández Gil,  Barbara MorawskaBarbara Morawska
Franz Baader, Oliver Fernández Gil, Barbara Morawska
Hybrid EL-Unification is NP-Complete
In Thomas Eiter and Birte Glimm and Yevgeny Kazakov and Markus Krötzsch, eds., Proceedings of the 26th International Workshop on Description Logics (DL-2013), volume 1014 of CEUR Workshop Proceedings, 29-40, July 2013
• KurzfassungAbstract
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 EL, which is used to define several large biomedical ontologies, unification is NP-complete. However, the unification algorithms for 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 EL is NP-complete.
• Forschungsgruppe:Research Group: Automatentheorie
@inproceedings{ BaFM-DL13,
author = {Franz {Baader} and Oliver {Fern\'andez Gil} and Barbara {Morawska}},
booktitle = {Proceedings of the 26th International Workshop on Description Logics ({DL-2013})},
editor = {Thomas {Eiter} and Birte {Glimm} and Yevgeny {Kazakov} and Markus {Kr{\"o}tzsch}},
month = {July},
pages = {29--40},
series = {CEUR Workshop Proceedings},
title = {Hybrid {$\mathcal{EL}$}-Unification is NP-Complete},
venue = {Ulm, Germany},
volume = {1014},
year = {2013},
}