Advertisement

Journal of Automated Reasoning

, Volume 47, Issue 4, pp 427–450 | Cite as

Tractable Extensions of the Description Logic \({\mathcal{EL}}\) with Numerical Datatypes

  • Despoina MagkaEmail author
  • Yevgeny Kazakov
  • Ian Horrocks
Article

Abstract

We consider extensions of the lightweight description logic (DL) \(\mathcal{EL}\) with numerical datatypes such as naturals, integers, rationals and reals equipped with relations such as equality and inequalities. It is well-known that the main reasoning problems for such DLs are decidable in polynomial time provided that the datatypes enjoy the so-called convexity property. Unfortunately many combinations of the numerical relations violate convexity, which makes the usage of these datatypes rather limited in practice. In this paper, we make a more fine-grained complexity analysis of these DLs by considering restrictions not only on the kinds of relations that can be used in ontologies but also on their occurrences, such as allowing certain relations to appear only on the left-hand side of the axioms. To this end, we introduce a notion of safety for a numerical datatype with restrictions (NDR) which guarantees tractability, extend the \(\mathcal{EL}\) reasoning algorithm to these cases, and provide a complete classification of safe NDRs for natural numbers, integers, rationals and reals.

Keywords

Description logic Computational complexity Datatypes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F.: The Description Logic Handbook: Theory, Implementation, and Applications, 2nd edn. Cambridge University Press, Cambridge (2007)CrossRefzbMATHGoogle Scholar
  2. 2.
    Grau, B.C., Horrocks, I., Motik, B., Parsia, B., Patel-Schneider, P.F., Sattler, U.: OWL 2: the next step for OWL. J. Web Semantics 6(4), 309–322 (2008)CrossRefGoogle Scholar
  3. 3.
    Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope. In: IJCAI, pp. 364–369. Professional Book Center, London (2005)Google Scholar
  4. 4.
    Spackman, K.: Managing clinical terminology hierarchies using algorithmic calculation of subsumption: experience with SNOMED-RT. J. Am. Med. Inform. Assoc. (2000)Google Scholar
  5. 5.
    The Gene Ontology Consortium: Gene ontology: tool for the unification of biology. Nat. Genet. 25, 25–29 (2000)CrossRefGoogle Scholar
  6. 6.
    Motik, B., Grau, B.C., Horrocks, I., Wu, Z., Fokoue, A., Lutz, C.: OWL 2 Web Ontology Language Profiles. http://www.w3.org/TR/owl2-profiles/ (27 October 2009)
  7. 7.
    Magka, D., Kazakov, Y., Horrocks, I.: Tractable extensions of the description logic \(\mathcal{EL}\) with numerical datatypes. In: Proc. of the Int. Joint Conf. on Automated Reasoning (IJCAR 2010), 16–19 July. LNAI, vol. 6173, pp. 61–75. Springer (2010)Google Scholar
  8. 8.
    Lutz, C.: Description logics with concrete domains—a survey. In: Advances in Modal Logic, pp. 265–296. King’s College Publications, London (2002)Google Scholar
  9. 9.
    Haase, C., Lutz, C.: Complexity of subsumption in the \(\mathcal{EL}\) family of description logics: acyclic and cyclic Tboxes. In: ECAI, vol. 178, pp. 25–29. IOS Press, Amstderdam (2008)Google Scholar
  10. 10.
    Sofronie-Stokkermans, V.: Locality and subsumption testing in \(\mathcal{EL}\) and some of its extensions. In: Advances in Modal Logic, pp. 315–339. College Publications, London (2008)Google Scholar
  11. 11.
    Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope further. In: Proceedings of the OWLED 2008 DC Workshop on OWL: Experiences and Directions (2008)Google Scholar
  12. 12.
    Kazakov, Y.: Consequence-driven reasoning for horn \(\mathcal{SHIQ}\) ontologies. In: IJCAI, pp. 2040–2045 (2009)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of OxfordOxfordUK

Personalised recommendations