Advertisement

Probabilistic Query Answering in the Bayesian Description Logic \(\mathcal {BE{}L}\)

  • İsmail İlkan Ceylan
  • Rafael Peñaloza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9310)

Abstract

\(\mathcal {BE{}L}\) is a probabilistic description logic (DL) that extends the light-weight DL \(\mathcal {E{}L}\) with a joint probability distribution over the axioms, expressed with the help of a Bayesian network (BN). In recent work it has been shown that the complexity of standard logical reasoning in \(\mathcal {BE{}L}\) is the same as performing probabilistic inferences over the BN.

In this paper we consider conjunctive query answering in \(\mathcal {BE{}L}\). We study the complexity of the three main problems associated to this setting: computing the probability of a query entailment, computing the most probable answers to a query, and computing the most probable context in which a query is entailed. In particular, we show that all these problems are tractable w.r.t. data and ontology complexity.

Keywords

Bayesian Network Description Logic Reasoning Task Conjunctive Query Query Answering 
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.

References

  1. 1.
    Abiteboul, S., Senellart, P.: Querying and updating probabilistic information in XML. In: Ioannidis, Y., Scholl, M.H., Schmidt, J.W., Matthes, F., Hatzopoulos, M., Böhm, K., Kemper, A., Grust, T., Böhm, C. (eds.) EDBT 2006. LNCS, vol. 3896, pp. 1059–1068. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  2. 2.
    Baader, F., Brandt, S., Lutz, C.: Pushing the EL. In: Proceedings of the IJCAI 2005. Morgan Kaufmann Publishers (2005)Google Scholar
  3. 3.
    Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications, 2nd edn. Cambridge University Press, Cambridge (2007) Google Scholar
  4. 4.
    Beigel, R., Nick, R., Spielman, D.A.: PP Is closed under intersection. J. Comput. Syst. Sci. 50(2), 191–202 (1995)zbMATHCrossRefGoogle Scholar
  5. 5.
    Bienvenu, M., Ortiz, M., Šimkus, M., Xiao, G.: Tractable queries for lightweight description logics. In: Proceedings of the IJCAI 2013. AAAI (2013)Google Scholar
  6. 6.
    Brandt, S.: Polynomial time reasoning in a description logic with existential restrictions, GCI axioms, and–what else? In: Proceedings of the ECAI 2004, vol. 110. IOS Press (2004)Google Scholar
  7. 7.
    Ceylan, İ.İ.: Query answering in Bayesian description logics. In: Proceedings of the DL 2015. CEUR Workshop Proceedings, vol. 1350. CEUR-WS (2015)Google Scholar
  8. 8.
    Ceylan, İ.İ., Mendez, J., Peñaloza, R.: The Bayesian ontology reasoner is BORN! In: Proceedings of ORE 2015. CEUR Workshop Proceedings, vol. 1387. CEUR-WS (2015)Google Scholar
  9. 9.
    Ceylan, İ.İ., Peñaloza, R.: Bayesian description logics. In: Proceedings of DL 2014. CEUR Workshop Proceedings, vol. 1193. CEUR-WS (2014)Google Scholar
  10. 10.
    Ceylan, İ.İ., Peñaloza, R.: Reasoning in the description logic \({\cal BEL}\) using Bayesian networks. In: Proceedings of StarAI 2014. AAAI Workshops, vol. WS-14-13. AAAI (2014)Google Scholar
  11. 11.
    Ceylan, İİ., Peñaloza, R.: The Bayesian description logic \({\cal BEL}\). In: Demri, S., Kapur, D., Weidenbach, C. (eds.) VSL 2014. LNCS, vol. 8562, pp. 480–494. Springer, Heidelberg (2014) Google Scholar
  12. 12.
    Ceylan, İİ., Peñaloza, R.: Tight complexity bounds for reasoning in the description logic \({\cal BEL}\). In: Fermé, E., Leite, J. (eds.) Logics in Artificial Intelligence. LNCS, vol. 8761, pp. 77–91. Springer, Heidelberg (2014) Google Scholar
  13. 13.
    Ceylan, İ.İ., Peñaloza, R.: Dynamic Bayesian ontology languages. CoRR abs/1506.08030 (2015)Google Scholar
  14. 14.
    Chavira, M., Darwiche, A.: On probabilistic inference by weighted model counting. Artif. Intell. 172(6–7), 772–799 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Dalvi, N., Suciu, D.: Efficient query evaluation on probabilistic databases. VLDB J. 16(4), 523–544 (2007)CrossRefGoogle Scholar
  16. 16.
    d’Amato, C., Fanizzi, N., Lukasiewicz, T.: Tractable reasoning with Bayesian description logics. In: Greco, S., Lukasiewicz, T. (eds.) SUM 2008. LNCS (LNAI), vol. 5291, pp. 146–159. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  17. 17.
    Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press, Cambridge (2009)zbMATHCrossRefGoogle Scholar
  18. 18.
    Fuhr, N., Rölleke, T.: A probabilistic relational algebra for the integration of information retrieval and database systems. ACM TOIS 15(1), 32–66 (1997)CrossRefGoogle Scholar
  19. 19.
    Gottlob, G., Lukasiewicz, T., Martinez, M.V., Simar, G.L.: Query answering under probabilistic uncertainty in datalog +/- ontologies. Ann. Math. AI 69(1), 131–159 (2013)Google Scholar
  20. 20.
    Grädel, E., Gurevich, Y., Hirsch, C.: The complexity of query reliability. In: Proceedings of the ACM SIGACT-SIGMOD-SIGART 1998 (1998)Google Scholar
  21. 21.
    Huang, H., Liu, C.: Query evaluation on probabilistic RDF databases. In: Vossen, G., Long, D.D.E., Yu, J.X. (eds.) WISE 2009. LNCS, vol. 5802, pp. 307–320. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  22. 22.
    Hung, E., Getoor, L., Subrahmanian, V.S.: PXML: a probabilistic semistructured data model and algebra. In: Proceedings of the ICDE 2003 (2003)Google Scholar
  23. 23.
    Joseph, H.: An analysis of first - order logics of probability. In: Proceedings of the IJCAI 1989. Morgan Kaufmann Publishers (1989)Google Scholar
  24. 24.
    Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the semantic web. Web Semant. Sci. Serv. Agents World Wide Web 6(4), 291–308 (2008)CrossRefGoogle Scholar
  25. 25.
    Lutz, C., Schröder, L.: Probabilistic description logics for subjective uncertainty. In: Proceedings of the KR 2010. AAAI (2010)Google Scholar
  26. 26.
    Lutz, C., Toman, D., Wolter, F.: Conjunctive query answering in the description logic calel using a relational database system. In: Proceedings of the IJCAI 2009. AAAI (2009)Google Scholar
  27. 27.
    Rosati, R.: On conjunctive query answering in EL. In: Proceedings of the DL 2007. CEUR Workshop Proceedings, vol. 250. CEUR-WS (2007)Google Scholar
  28. 28.
    Roth, D.: On the hardness of approximate reasoning. Artif. Intell. 82(1–2), 273–302 (1996)CrossRefGoogle Scholar
  29. 29.
    Schulz, S., Suntisrivaraporn, B., Baader, F., Boeker, M.: SNOMED reaching its adolescence: ontologists’ and logicians’ health check. Int. J. Med. Inf. 78(Supplement 1), 86–94 (2009)CrossRefGoogle Scholar
  30. 30.
    Toda, S.: On the Computational power of PP and +P. In: Proceedings of the SFCS 1989, pp. 514–519. IEEE (1989)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Theoretical Computer ScienceTU DresdenDresdenGermany
  2. 2.KRDB Research CentreFree University of Bozen-BolzanoBolzanoItaly

Personalised recommendations