Optimizing Horn-\(\mathcal {SHIQ}\) Reasoning for OBDA

  • Labinot BajraktariEmail author
  • Magdalena Ortiz
  • Guohui Xiao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11778)


The ontology-based data access (OBDA) paradigm can ease access to heterogeneous and incomplete data sources in many application domains. However, state-of-the-art tools are still based on the DL-Lite family of description logics (DLs) that underlies OWL 2 QL, which despite its usefulness is not sufficiently expressive for many domains. Accommodating more expressive ontology languages remains an open challenge, and the consensus is that Horn DLs like Horn-\(\mathcal {SHIQ}\) are particularly promising. Query answering in Horn-\(\mathcal {SHIQ}\), a prerequisite for OBDA, is supported in existing reasoners, but many ontologies cannot be handled. This is largely because algorithms build on an ABox-independent approach to ontological reasoning that easily incurs in an exponential behaviour. As an alternative to full ABox-independence, in this paper we advocate taking into account general information about the structure of the ABoxes of interest. This is especially natural in the setting of OBDA, where ABoxes are generated via mappings, and thus have a predictable structure. We present a simple yet effective approach that guides ontological reasoning using the possible combinations of concepts that may occur in the ABox, which can be obtained from the mappings of an OBDA specification. We implemented and tested our optimization in the Clipper reasoner with encouraging results.


  1. 1.
    Baader, F., Bienvenu, M., Lutz, C., Wolter, F.: Query and predicate emptiness in ontology-based data access. J. Artif. Intell. Res. 56, 1–59 (2016)MathSciNetCrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    Bienvenu, M., Ortiz, M.: Ontology-mediated query answering with data-tractable description logics. In: Faber, W., Paschke, A. (eds.) Reasoning Web 2015. LNCS, vol. 9203, pp. 218–307. Springer, Cham (2015). Scholar
  4. 4.
    Botoeva, E., Calvanese, D., Santarelli, V., Savo, D.F., Solimando, A., Xiao, G.: Beyond OWL 2 QL in OBDA: rewritings and approximations. In: Proceedings of of AAAI, pp. 921–928. AAAI Press (2016)Google Scholar
  5. 5.
    Botoeva, E., Kontchakov, R., Ryzhikov, V., Wolter, F., Zakharyaschev, M.: Games for query inseparability of description logic knowledge bases. Artif. Intell. 234, 78–119 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Botoeva, E., Lutz, C., Ryzhikov, V., Wolter, F., Zakharyaschev, M.: Query inseparability for ALC ontologies. CoRR abs/1902.00014 (2019)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: the DL-Lite family. J. Autom. Reas. 39(3), 385–429 (2007)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Carral, D., Dragoste, I., Krötzsch, M.: The combined approach to query answering in Horn-ALCHOIQ. In: Proceedings of KR, pp. 339–348. AAAI Press (2018)Google Scholar
  9. 9.
    Carral, D., González, L., Koopmann, P.: From Horn-SRIQ to datalog: a data-independent transformation that preserves assertion entailment. In: Proceedings of AAAI. AAAI Press (2019)Google Scholar
  10. 10.
    Das, S., Sundara, S., Cyganiak, R.: R2RML: RDB to RDF mapping language. In: W3C Recommendation, W3C (2012)Google Scholar
  11. 11.
    Eiter, T., Ortiz, M., Simkus, M., Tran, T., Xiao, G.: Query rewriting for Horn-SHIQ plus rules. In: Proceedings of AAAI, pp. 726–733. AAAI Press (2012)Google Scholar
  12. 12.
    Hovland, D., Kontchakov, R., Skjæveland, M.G., Waaler, A., Zakharyaschev, M.: Ontology-based data access to Slegge. In: d’Amato, C., et al. (eds.) ISWC 2017. LNCS, vol. 10588, pp. 120–129. Springer, Cham (2017). Scholar
  13. 13.
    Kazakov, Y.: Consequence-driven reasoning for Horn SHIQ ontologies. In: Proceedings of IJCAI, pp. 2040–2045 (2009)Google Scholar
  14. 14.
    Krötzsch, M., Rudolph, S., Hitzler, P.: Complexity boundaries for Horn description logics. In: Proceedings of AAAI, pp. 452–457. AAAI Press (2007)Google Scholar
  15. 15.
    Lanti, D., Rezk, M., Xiao, G., Calvanese, D.: The NPD benchmark: reality check for OBDA systems. In: Proceedings of EDBT. ACM Press (2015)Google Scholar
  16. 16.
    Leone, N., Manna, M., Terracina, G., Veltri, P.: Fast query answering over existential rules. ACM Trans. Comput. Log. 20(2), 1–48 (2019). Scholar
  17. 17.
    Lutz, C., Walther, D., Wolter, F.: Conservative extensions in expressive description logics. In: Proceedings of IJCAI, pp. 453–458 (2007)Google Scholar
  18. 18.
    Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Semant. 10, 133–173 (2008)zbMATHGoogle Scholar
  19. 19.
    Ren, Y., Pan, J.Z., Zhao, Y.: Soundness preserving approximation for TBox reasoning. In: Proceedings of AAAI, pp. 351–356. AAAI Press (2010)Google Scholar
  20. 20.
    Rodriguez-Muro, M., Rezk, M.: Efficient SPARQL-to-SQL with R2RML mappings. J. Web Semant. 33, 141–169 (2015)CrossRefGoogle Scholar
  21. 21.
    Shi, L., Cai, X.: An exact fast algorithm for minimum hitting set. In: Third International Joint Conference on Computational Science and Optimization, vol. 1, pp. 64–67 (2010)Google Scholar
  22. 22.
    Xiao, G., et al.: Ontology-based data access: a survey. In: Proceedings of IJCAI, pp. 5511–5519 (2018)Google Scholar
  23. 23.
    Xiao, G., Ding, L., Cogrel, B., Calvanese, D.: Virtual knowledge graphs: an overview of systems and use cases. Data Intell. 1, 201–223 (2019)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Labinot Bajraktari
    • 1
    Email author
  • Magdalena Ortiz
    • 1
  • Guohui Xiao
    • 2
  1. 1.Faculty of InformaticsVienna University of TechnologyViennaAustria
  2. 2.Faculty of Computer ScienceFree University of Bozen-BolzanoBolzanoItaly

Personalised recommendations