Open Access
2016 Deciding Unifiability and Computing Local Unifiers in the Description Logic EL without Top Constructor
Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, Barbara Morawska
Notre Dame J. Formal Logic 57(4): 443-476 (2016). DOI: 10.1215/00294527-3555507


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 EL-unifiers.


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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 J. Formal Logic 57 (4) 443 - 476, 2016.


Received: 10 January 2012; Accepted: 21 August 2013; Published: 2016
First available in Project Euclid: 19 July 2016

zbMATH: 1358.68272
MathSciNet: MR3565533
Digital Object Identifier: 10.1215/00294527-3555507

Primary: 68Q17 , 68Q25 , 68Q45
Secondary: 03B45 , 03B70 , 68T27 , 68T30

Keywords: description logics , unification

Rights: Copyright © 2016 University of Notre Dame

Vol.57 • No. 4 • 2016
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