Conjunctive Query Answering in Probabilistic Datalog+/– Ontologies

  • Georg Gottlob
  • Thomas Lukasiewicz
  • Gerardo I. Simari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6902)


Datalog+/– is a recently developed family of ontology languages that is especially useful for representing and reasoning over lightweight ontologies, and is set to play a central role in the context of query answering and information extraction for the Semantic Web. It has recently become apparent that it is necessary to develop a principled way to handle uncertainty in this domain; in addition to uncertainty as an inherent aspect of the Web, one must also deal with forms of uncertainty due to inconsistency and incompleteness, uncertainty resulting from automatically processing Web data, as well as uncertainty stemming from the integration of multiple heterogeneous data sources. In this paper, we present two algorithms for answering conjunctive queries over a probabilistic extension of guarded Datalog+/– that uses Markov logic networks as the underlying probabilistic semantics. Conjunctive queries ask: “what is the probability that a given set of atoms hold?”. These queries are especially relevant to Web information extraction, since extractors often work with uncertain rules and facts, and decisions must be made based on the likelihood that certain facts are inferred. The first algorithm for answering conjunctive queries is a basic one using classical forward chaining (known as the chase procedure), while the second one is a backward chaining algorithm and works on a specific subset of guarded Datalog+/–; it can be executed as an anytime algorithm for greater scalability.


Description Logic Conjunctive Query Ontology Language Probabilistic Scenario Markov Network 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  2. 2.
    Beeri, C., Vardi, M.Y.: The implication problem for data dependencies. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 73–85. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  3. 3.
    Berners-Lee, T., Hendler, J., Lassila, O.: The Semantic Web. Sci. Amer. 284, 34–43 (2002)CrossRefGoogle Scholar
  4. 4.
    Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: Query answering under expressive relational constraints. In: Proc. KR-2008, pp. 70–80. AAAI Press, Menlo Park (2008)Google Scholar
  5. 5.
    Calì, A., Gottlob, G., Lukasiewicz, T., Marnette, B., Pieris, A.: Datalog+/-: A family of logical knowledge representation and query languages for new applications. In: Proc. LICS-2010, pp. 228–242. IEEE Computer Society, Los Alamitos (2010)Google Scholar
  6. 6.
    Calì, A., Gottlob, G., Pieris, A.: Tractable query answering over conceptual schemata. In: Laender, A.H.F., Castano, S., Dayal, U., Casati, F., de Oliveira, J.P.M. (eds.) ER 2009. LNCS, vol. 5829, pp. 175–190. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Ceri, S., Gottlob, G., Tanca, L.: What you always wanted to know about Datalog (and never dared to ask). IEEE Trans. Knowl. Data Eng. 1, 146–166 (1989)CrossRefGoogle Scholar
  8. 8.
    Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational data bases. In: Proc. STOC-1977, pp. 77–90. ACM Press, New York (1977)Google Scholar
  9. 9.
    Deutsch, A., Nash, A., Remmel, J.B.: The chase revisited. In: Proc. PODS-2008, pp. 149–158. ACM Press, New York (2008)Google Scholar
  10. 10.
    Drabent, W., Eiter, T., Ianni, G., Krennwallner, T., Lukasiewicz, T., Małuszyński, J.: Hybrid reasoning with rules and ontologies. In: Bry, F., Małuszyński, J. (eds.) Semantic Techniques for the Web. LNCS, vol. 5500, pp. 1–49. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Fagin, R., Kolaitis, P.G., Miller, R.J., Popa, L.: Data exchange: Semantics and query answering. Theor. Comput. Sci. 336(1), 89–124 (2005)CrossRefzbMATHGoogle Scholar
  12. 12.
    Fink, R., Olteanu, D., Rath, S.: Providing support for full relational algebra in probabilistic databases. In: Proc. ICDE-2011, pp. 315–326. IEEE Computer Society Press, Los Alamitos (2011)Google Scholar
  13. 13.
    Heinsohn, J.: Probabilistic description logics. In: Proc. UAI-1994, pp. 311–318. Morgan Kaufmann, San Francisco (1994)Google Scholar
  14. 14.
    Huang, J., Antova, L., Koch, C., Olteanu, D.: MayBMS: A probabilistic database management system. In: Proc. SIGMOD-2009, pp. 1071–1074. ACM Press, New York (2009)Google Scholar
  15. 15.
    Johnson, D.S., Klug, A.C.: Testing containment of conjunctive queries under functional and inclusion dependencies. J. Comput. Syst. Sci. 28(1), 167–189 (1984)CrossRefzbMATHGoogle Scholar
  16. 16.
    Koch, C., Olteanu, D., Re, C., Suciu, D.: Probabilistic Databases. Morgan-Claypool, San Francisco (2011)zbMATHGoogle Scholar
  17. 17.
    Koller, D., Levy, A., Pfeffer, A.: P-Classic: A tractable probabilistic description logic. In: Proc. AAAI-1997, pp. 390–397. AAAI Press / The MIT Press (1997)Google Scholar
  18. 18.
    Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Intell. 172, 852–883 (2008)CrossRefzbMATHGoogle Scholar
  19. 19.
    Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the Semantic Web. J. Web Sem. 6, 291–308 (2008)CrossRefGoogle Scholar
  20. 20.
    Maier, D., Mendelzon, A.O., Sagiv, Y.: Testing implications of data dependencies. ACM Trans. Database Syst. 4(4), 455–469 (1979)CrossRefGoogle Scholar
  21. 21.
    Patel-Schneider, P.F., Hayes, P., Horrocks, I.: OWL Web Ontology Language. W3C Recommendation (February 10, 2004),
  22. 22.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)zbMATHGoogle Scholar
  23. 23.
    Poole, D.: Logic programming, abduction and probability: A top-down anytime algorithm for estimating prior and posterior probabilities. New Generat. Comput. 11(3/4), 377–400 (1993)CrossRefzbMATHGoogle Scholar
  24. 24.
    Richardson, M., Domingos, P.: Markov logic networks. Mach. Learn. 62, 107–136 (2006)CrossRefGoogle Scholar
  25. 25.
    Yang, Y., Calmet, J.: OntoBayes: An ontology-driven uncertainty model. In: Proc. CIMCA/ IAWTIC-2005, pp. 457–463. IEEE Computer Society Press, Los Alamitos (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Georg Gottlob
    • 1
  • Thomas Lukasiewicz
    • 1
  • Gerardo I. Simari
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordUK

Personalised recommendations