# Deciding Unifiability and Computing Local Unifiers in the Description Logic EL without Top Constructor

##### Franz BaaderFranz Baader,  Nguyen Thanh BinhNguyen Thanh Binh,  Stefan BorgwardtStefan Borgwardt,  Barbara MorawskaBarbara Morawska
Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, Barbara Morawska
Deciding Unifiability and Computing Local Unifiers in the Description Logic EL without Top Constructor
Notre Dame Journal of Formal Logic, 57(4):443–476, 2016
• KurzfassungAbstract
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 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 been shown to be NP-complete, and thus of considerably lower complexity than unification in other description logics of similarly restricted expressive 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, removing the top concept from EL makes the unification problem considerably harder. More precisely, we will show that unification in EL without the top concept is PSpace-complete. In addition to the decision problem, we also consider the problem of actually computing unifiers in EL without top.
• Bemerkung: Note: In press.
• Forschungsgruppe:Research Group: Automatentheorie
```@article{BBBM2016,
author  = {Franz Baader and Nguyen Thanh Binh and Stefan Borgwardt and Barbara
Morawska},
title   = {Deciding Unifiability and Computing Local Unifiers in the
Description Logic {EL} without Top Constructor},
journal = {Notre Dame Journal of Formal Logic},
volume  = {57},
number  = {4},
year    = {2016},
pages   = {443{\textendash}476},
doi     = {10.1215/00294527-3555507}
}
```