Decidability of Unification in EL without Top Constructor

  • Nguyen Thanh Binh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6902)

Abstract

In recent years, the description logic \(\cal{EL}\) has received a significant interest. The description logic \(\cal{EL}\) is a knowledge representation formalism used e.g in natural language processing, configuration of technical systems, databases and biomedical ontologies. Unification is used there as a tool to recognize equivalent concepts. It has been proven that unification in \(\cal{EL}\) is NP-complete. This result was based on a locality property of certain \(\cal{EL}\) unifiers. In fact, the large medical ontology SNOMED CT was built on a subset of \({\cal{EL}}\)++ formalism, however, without top-concept. It would be interesting to investigate decidability of unification in extensions of \(\cal{EL}\) without using top-concept. In this paper, we look at decidability of unification in \(\cal{EL}\) without top (\(\cal{EL}^{- \top}\)). We show that a similar locality holds for \(\cal{EL}^{- \top}\), but decidability of \(\cal{EL}^{- \top}\) unification does not follow immediately from locality as it does in the case of unification in \(\cal{EL}\). However, by restricting further the locality property, we prove that \(\cal{EL}^{- \top}\) unification is decidable and construct an NExpTime decision procedure for the problem. Moreover, the procedure allows us to compute a specific set of solutions to the unification problem.

Keywords

Description Logic Dependency Path Dependency Order Biomedical Ontology Concept Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Nguyen Thanh Binh
    • 1
  1. 1.ETH ZurichSwitzerland

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