Advertisement

Query Answering in the Description Logic Horn-\(\mathcal{SHIQ}\)

  • Thomas Eiter
  • Georg Gottlob
  • Magdalena Ortiz
  • Mantas Šimkus
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5293)

Abstract

We provide an ExpTime algorithm for answering conjunctive queries (CQs) in Horn-\(\mathcal{SHIQ}\), a Horn fragment of the well-known Description Logic \(\mathcal{SHIQ}\) underlying the OWL-Lite standard. The algorithm employs a domino system for model representation, which is constructed via a worst-case optimal tableau algorithm for Horn-\(\mathcal{SHIQ}\); the queries are answered by reasoning over the domino system. Our algorithm not only shows that CQ answering in Horn-\(\mathcal{SHIQ}\) is not harder than satisfiability testing, but also that it is polynomial in data complexity, making Horn-\(\mathcal{SHIQ}\) an attractive expressive Description Logic.

Keywords

Data Complexity Description Logic Conjunctive Query Query Answering Standard Reasoning 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baader, F.: Terminological cycles in a description logic with existential restrictions. In: IJCAI 2003, pp. 325–330 (2003)Google Scholar
  2. 2.
    Cali, A., Gottlob, G., Kifer, M.: Taming the Infinite Chase: Query Answering under Expressive Relational Constraints. In: KR 2008 (to appear, 2008)Google Scholar
  3. 3.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. In: KR 2006 (2006)Google Scholar
  4. 4.
    Calvanese, D., De Giacomo, G., Lenzerini, M.: On the decidability of query containment under constraints. In: PODS 1998, pp. 149–158 (1998)Google Scholar
  5. 5.
    Calvanese, D., Giacomo, G.D., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: The DL-lite family. J. Autom. Reasoning 39(3), 385–429 (2007)zbMATHCrossRefGoogle Scholar
  6. 6.
    Glimm, B., Horrocks, I., Lutz, C., Sattler, U.: Conjunctive Query Answering for the Description Logic \(\mathcal{SHIQ}\). In: IJCAI 2007, pp. 399–404 (2007)Google Scholar
  7. 7.
    Horrocks, I.: Optimising Tableaux Decision Procedures for Description Logics. PhD thesis, University of Manchester (1997)Google Scholar
  8. 8.
    Horrocks, I., Sattler, U.: A tableaux decision procedure for \(\mathcal{SHOIQ}\). In: IJCAI 2005, pp. 448–453 (2005)Google Scholar
  9. 9.
    Hustadt, U., Motik, B., Sattler, U.: Data complexity of reasoning in very expressive description logics. In: IJCAI 2005, pp. 466–471 (2005)Google Scholar
  10. 10.
    Krisnadhi, A., Lutz, C.: Data complexity in the \(\mathcal{EL}\) family of description logics. In: DL 2007, Bressanone, Italy. CEUR-WS, vol. 250, pp. 88–99 (2007)Google Scholar
  11. 11.
    Krötzsch, M., Rudolph, S., Hitzler, P.: Complexity boundaries for Horn description logics. In: AAAI 2007, pp. 452–457 (2007)Google Scholar
  12. 12.
    Krötzsch, M., Rudolph, S., Hitzler, P.: Conjunctive queries for a tractable fragment of OWL 1.1. In: Aberer, K., Choi, K.-S., Noy, N., Allemang, D., Lee, K.-I., Nixon, L., Golbeck, J., Mika, P., Maynard, D., Mizoguchi, R., Schreiber, G., Cudré-Mauroux, P. (eds.) ASWC 2007/ISWC 2007. LNCS, vol. 4825, pp. 310–323. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Lutz, C.: Inverse roles make conjunctive queries hard. In: DL 2007 (2007)Google Scholar
  14. 14.
    Lutz, C.: Two upper bounds for conjunctive query answering in \(\mathcal{SHIQ}\). In: DL 2008 (2008)Google Scholar
  15. 15.
    Motik, B., Shearer, R., Horrocks, I.: Optimized reasoning in description logics using hypertableaux. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 67–83. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Ortiz, M., Šimkus, M., Eiter, T.: Worst-case optimal conjunctive query answering in description logics without inverses. In: AAAI 2008 (to appear, 2008)Google Scholar
  17. 17.
    Rosati, R.: On conjunctive query answering in \(\mathcal{EL}\). In: DL 2007 (2007)Google Scholar
  18. 18.
    Rudolph, S., Krötzsch, M., Hitzler, P.: Terminological reasoning in \(\mathcal{SHIQ}\) with ordered binary decision diagrams. In: AAAI 2008 (to appear, 2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Thomas Eiter
    • 1
  • Georg Gottlob
    • 2
  • Magdalena Ortiz
    • 1
  • Mantas Šimkus
    • 1
  1. 1.Institute of Information SystemsTU ViennaAustria
  2. 2.Computing LaboratoryOxford UniversityUnited Kingdom

Personalised recommendations