Notre Dame Journal of Formal Logic

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

Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, and Barbara Morawska

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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 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.

Article information

Source
Notre Dame J. Formal Logic, Volume 57, Number 4 (2016), 443-476.

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1468952202

Digital Object Identifier
doi:10.1215/00294527-3555507

Mathematical Reviews number (MathSciNet)
MR3565533

Zentralblatt MATH identifier
1358.68272

Subjects
Primary: 68Q17: Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) [See also 68Q15] 68Q25: Analysis of algorithms and problem complexity [See also 68W40] 68Q45: Formal languages and automata [See also 03D05, 68Q70, 94A45]
Secondary: 68T27: Logic in artificial intelligence 68T30: Knowledge representation 03B70: Logic in computer science [See also 68-XX] 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}

Keywords
unification description logics

Citation

Baader, Franz; Binh, Nguyen Thanh; Borgwardt, Stefan; Morawska, Barbara. Deciding Unifiability and Computing Local Unifiers in the Description Logic $\mathcal{E\!L}$ without Top Constructor. Notre Dame J. Formal Logic 57 (2016), no. 4, 443--476. doi:10.1215/00294527-3555507. https://projecteuclid.org/euclid.ndjfl/1468952202


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