Extended Caching, Backjumping and Merging for Expressive Description Logics

  • Andreas Steigmiller
  • Thorsten Liebig
  • Birte Glimm
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)


With this contribution we push the boundary of some known optimisations such as caching to the very expressive Description Logic \(\mathcal{SROIQ}\). The developed method is based on a sophisticated dependency management and a precise unsatisfiability caching technique, which further enables better informed tableau backtracking and more efficient pruning. Additionally, we optimise the handling of cardinality restrictions, by introducing a strategy called pool-based merging.

We empirically evaluate the proposed optimisations within the novel reasoning system Konclude and show that the proposed optimisations indeed result in significant performance improvements.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications, 2nd edn. Cambridge University Press (2007)Google Scholar
  2. 2.
    Ding, Y., Haarslev, V.: Tableau caching for description logics with inverse and transitive roles. In: Proc. 2006 Int. Workshop on Description Logics, pp. 143–149 (2006)Google Scholar
  3. 3.
    Ding, Y., Haarslev, V.: A procedure for description logic \(\mathcal{ALCFI}\). In: Proc. 16th European Conf. on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2007 (2007)Google Scholar
  4. 4.
    Donini, F.M., Massacci, F.: EXPTIME tableaux for \(\mathcal{ALC}\). J. of Artificial Intelligence 124(1), 87–138 (2000)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Faddoul, J., Farsinia, N., Haarslev, V., Möller, R.: A hybrid tableau algorithm for \(\mathcal{ALCQ}\). In: Proc 18th European Conf. on Artificial Intelligence (ECAI 2008), pp. 725–726 (2008)Google Scholar
  6. 6.
    Goré, R., Widmann, F.: Sound Global State Caching for ALC with Inverse Roles. In: Giese, M., Waaler, A. (eds.) TABLEAUX 2009. LNCS, vol. 5607, pp. 205–219. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Haarslev, V., Möller, R.: Consistency Testing: The RACE Experience. In: Dyckhoff, R. (ed.) TABLEAUX 2000. LNCS (LNAI), vol. 1847, pp. 57–61. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Haarslev, V., Möller, R.: High performance reasoning with very large knowledge bases: A practical case study. In: Proc. 17th Int. Joint Conf. on Artificial Intelligence (IJCAI 2001), pp. 161–168. Morgan Kaufmann (2001)Google Scholar
  9. 9.
    Haarslev, V., Sebastiani, R., Vescovi, M.: Automated Reasoning in \(\mathcal{ALCQ}\) via SMT. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 283–298. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Hoffmann, J., Koehler, J.: A new method to index and query sets. In: Proc. 16th Int. Conf. on Artificial Intelligence (IJCAI 1999), pp. 462–467. Morgan Kaufmann (1999)Google Scholar
  11. 11.
    Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\mathcal{SROIQ}\). In: Proc.10th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 2006), pp. 57–67. AAAI Press (2006)Google Scholar
  12. 12.
    Horrocks, I., Patel-Schneider, P.F.: DL systems comparison. In: Proc. 1998 Int. Workshop on Description Logics (DL 1998), vol. 11, pp. 55–57 (1998)Google Scholar
  13. 13.
    Horrocks, I., Patel-Schneider, P.F.: Optimizing description logic subsumption. J. of Logic and Computation 9(3), 267–293 (1999)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Liebig, T.: Reasoning with OWL – system support and insights –. Tech. Rep. TR-2006-04, Ulm University, Ulm, Germany (September 2006)Google Scholar
  15. 15.
    Liebig, T., Steigmiller, A., Noppens, O.: Scalability via parallelization of OWL reasoning. In: Proc. Workshop on New Forms of Reasoning for the Semantic Web: Scalable & Dynamic (NeFoRS 2010) (2010)Google Scholar
  16. 16.
    OWL Working Group, W.: OWL 2 Web Ontology Language: Document Overview. W3C Recommendation (October 27, 2009), http://www.w3.org/TR/owl2-overview/
  17. 17.
    Sirin, E., Parsia, B., Grau, B.C., Kalyanpur, A., Katz, Y.: Pellet: A practical OWL-DL reasoner. J. of Web Semantics 5(2), 51–53 (2007)CrossRefGoogle Scholar
  18. 18.
    Steigmiller, A., Liebig, T., Glimm, B.: Extended caching, backjumping and merging for expressive description logics. Tech. Rep. TR-2012-01, Ulm University, Ulm, Germany (2012), http://www.uni-ulm.de/fileadmin/website_uni_ulm/iui/Ulmer_Informatik_Berichte/2012/UIB-2012-01.pdf
  19. 19.
    Tsarkov, D., Horrocks, I.: FaCT++ Description Logic Reasoner: System Description. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 292–297. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Tsarkov, D., Horrocks, I., Patel-Schneider, P.F.: Optimizing terminological reasoning for expressive description logics. J. of Automated Reasoning 39, 277–316 (2007)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andreas Steigmiller
    • 1
  • Thorsten Liebig
    • 2
  • Birte Glimm
    • 1
  1. 1.Ulm UniversityUlmGermany
  2. 2.derivo GmbHUlmGermany

Personalised recommendations