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Absorption-Based Query Answering for Expressive Description Logics

  • Andreas SteigmillerEmail author
  • Birte Glimm
Conference paper
  • 1.2k Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11778)

Abstract

Conjunctive query answering is an important reasoning task for logic-based knowledge representation formalisms, such as Description Logics, to query for instance data that is related in certain ways. Although many knowledge bases use language features of more expressive Description Logics, there are hardly any systems that support full conjunctive query answering for these logics. In fact, existing systems usually impose restrictions on the queries or only compute incomplete results.

In this paper, we present a new approach for answering conjunctive queries that can directly be integrated into existing reasoning systems for expressive Description Logics. The approach reminds of absorption, a well-known preprocessing step that rewrites axioms such that they can be handled more efficiently. In this sense, we rewrite the query such that entailment can dynamically be checked in the dominantly used tableau calculi with minor extensions. Our implementation in the reasoning system Konclude outperforms existing systems even for queries that are restricted to the capabilities of these other systems.

References

  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, Cambridge (2007)zbMATHGoogle Scholar
  2. 2.
    Blackburn, P., Seligman, J.: Hybrid languages. J. Logic Lang. Inf. 4(3), 251–272 (1995)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Calvanese, D., Eiter, T., Ortiz, M.: Answering regular path queries in expressive description logics: an automata-theoretic approach. In: Proceedings of National Conference on Artificial Intelligence (2007)Google Scholar
  4. 4.
    Glimm, B., Horrocks, I., Motik, B., Stoilos, G., Wang, Z.: HermiT: an OWL 2 reasoner. J. Autom. Reasoning 53(3), 1–25 (2014)CrossRefGoogle Scholar
  5. 5.
    Glimm, B., Horrocks, I., Sattler, U.: Unions of conjunctive queries in SHOQ. In: Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (2008)Google Scholar
  6. 6.
    Glimm, B., Kazakov, Y., Kollia, I., Stamou, G.: Lower and upper bounds for SPARQL queries over OWL ontologies. In: Proceedings of National Conference on Artificial Intelligence (2015)Google Scholar
  7. 7.
    Glimm, B., Lutz, C., Horrocks, I., Sattler, U.: Conjunctive query answering for the description logic SHIQ. J. Artif. Intell. Res. 31, 157–204 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Grädel, E.: Why are modal logics so robustly decidable? In: Current Trends in Theoretical Computer Science, Entering the 21th Century, vol. 2, pp. 393–408. World Scientific (2001)Google Scholar
  9. 9.
    Haarslev, V., Möller, R., Wessel, M.: Querying the semantic web with Racer+nRQL. In: Proceedings of KI-2004 International Workshop on Applications of Description Logics (2004)Google Scholar
  10. 10.
    Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible SROIQ. In: Proceedings International Conference on Principles of Knowledge Representation and Reasoning. AAAI Press (2006)Google Scholar
  11. 11.
    Horrocks, I., Tessaris, S.: Querying the semantic web: a formal approach. In: Horrocks, I., Hendler, J. (eds.) ISWC 2002. LNCS, vol. 2342, pp. 177–191. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-48005-6_15CrossRefzbMATHGoogle Scholar
  12. 12.
    Hudek, A.K., Weddell, G.E.: Binary absorption in tableaux-based reasoning for description logics. In: Proceedings of International Workshop on Description Logics, vol. 189. CEUR (2006)Google Scholar
  13. 13.
    Kollia, I., Glimm, B.: Optimizing SPARQL query answering over OWL ontologies. J. Artif. Intell. Res. 48, 253–303 (2013)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ma, L., Yang, Y., Qiu, Z., Xie, G., Pan, Y., Liu, S.: Towards a complete OWL ontology benchmark. In: Sure, Y., Domingue, J. (eds.) ESWC 2006. LNCS, vol. 4011, pp. 125–139. Springer, Heidelberg (2006).  https://doi.org/10.1007/11762256_12CrossRefGoogle Scholar
  15. 15.
    Ortiz, M., Calvanese, D., Eiter, T.: Data complexity of query answering in expressive description logics via tableaux. J. Autom. Reasoning 41(1), 61–98 (2008)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Pan, J.Z., Thomas, E., Zhao, Y.: Completeness guaranteed approximation for OWL-DL query answering. In: Proceedings of International Workshop on Description Logics, vol. 477. CEUR (2009)Google Scholar
  17. 17.
    Parsia, B., Matentzoglu, N., Gonçalves, R.S., Glimm, B., Steigmiller, A.: The OWL reasoner evaluation (ORE) 2015 competition report. J. Autom. Reasoning 59(4), 455–482 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Rudolph, S., Glimm, B.: Nominals, inverses, counting, and conjunctive queries or: why infinity is your friend!. J. Artif. Intell. Res. 39, 429–481 (2010)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Sirin, E., Parsia, B., Cuenca Grau, B., Kalyanpur, A., Katz, Y.: Pellet: a practical OWL-DL reasoner. J. Web Semant. 5(2), 51–53 (2007)CrossRefGoogle Scholar
  20. 20.
    Steigmiller, A., Glimm, B.: Absorption-based query answering for expressive description logics - technical report. Technical report, Ulm University, Ulm, Germany (2019). https://www.uni-ulm.de/fileadmin/website_uni_ulm/iui.inst.090/Publikationen/2019/StGl2019-ABQA-TR-ISWC.pdf
  21. 21.
    Steigmiller, A., Glimm, B., Liebig, T.: Reasoning with nominal schemas through absorption. J. Autom. Reason. 53(4), 351–405 (2014)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Steigmiller, A., Liebig, T., Glimm, B.: Konclude: system description. J. Web Semantics 27(1), 78–85 (2014)CrossRefGoogle Scholar
  23. 23.
    Stoilos, G., Stamou, G.: Hybrid query answering over OWL ontologies. In: Proceedings of European Conference on Artificial Intelligence (2014)Google Scholar
  24. 24.
    Vardi, M.Y.: Why is modal logic so robustly decidable? In: Proceedings of DIMACS Workshop on Descriptive Complexity and Finite Models, vol. 31. American Mathematical Society (1997)Google Scholar
  25. 25.
    Zhou, Y., Cuenca Grau, B., Nenov, Y., Kaminski, M., Horrocks, I.: PAGOdA: pay-as-you-go ontology query answering using a datalog reasoner. J. Artif. Intell. Res. 54, 309–367 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Ulm UniversityUlmGermany

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