Skip to main content

Tractable Reasoning with Bayesian Description Logics

  • Conference paper
Scalable Uncertainty Management (SUM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5291))

Included in the following conference series:

Abstract

The DL-Lite family of tractable description logics lies between the semantic web languages RDFS and OWL Lite. In this paper, we present a probabilistic generalization of the DL-Lite description logics, which is based on Bayesian networks. As an important feature, the new probabilistic description logics allow for flexibly combining terminological and assertional pieces of probabilistic knowledge. We show that the new probabilistic description logics are rich enough to properly extend both the DL-Lite description logics as well as Bayesian networks. We also show that satisfiability checking and query processing in the new probabilistic description logics is reducible to satisfiability checking and query processing in the DL-Lite family. Furthermore, we show that satisfiability checking and answering unions of conjunctive queries in the new logics can be done in LogSpace in the data complexity. For this reason, the new probabilistic description logics are very promising formalisms for data-intensive applications in the Semantic Web involving probabilistic uncertainty.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  2. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: DL-Lite: Tractable description logics for ontologies. In: Proceedings AAAI 2005, pp. 602–607. AAAI Press/MIT Press (2005)

    Google Scholar 

  3. da Costa, P.C.G., Laskey, K.B.: PR-OWL: A framework for probabilistic ontologies. In: Proceedings FOIS 2006, pp. 237–249. IOS Press, Amsterdam (2006)

    Google Scholar 

  4. da Costa, P.C.G., Laskey, K.B., Laskey, K.J.: PR-OWL: A Bayesian ontology language for the Semantic Web. In: Proceedings URSW 2005, pp. 23–33 (2005)

    Google Scholar 

  5. Dantsin, E., Eiter, T., Gottlob, G., Voronkov, A.: Complexity and expressive power of logic programming. ACM Comput. Surv. 33(3), 374–425 (2001)

    Article  Google Scholar 

  6. d’Amato, C., Staab, S., Fanizzi, N., Esposito, F.: Efficient discovery of services specified in description logics languages. In: Proceedings of the ISWC-2007 Workshop on Service Matchmaking and Resource Retrieval in the Semantic Web (SMR2 2007) (2007)

    Google Scholar 

  7. Ding, Z., Peng, Y.: A probabilistic extension to ontology language OWL. In: Proceedings HICSS 2004 (2004)

    Google Scholar 

  8. Ding, Z., Peng, Y., Pan, R.: BayesOWL: Uncertainty modeling in Semantic Web ontologies. In: Ma, Z. (ed.) Soft Computing in Ontologies and Semantic Web. Studies in Fuzziness and Soft Computing, vol. 204, Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Fukushige, Y.: Representing probabilistic knowledge in the Semantic Web. In: Proceedings of the W3C Workshop on Semantic Web for Life Sciences, Cambridge, MA, USA (2004)

    Google Scholar 

  10. Lukasiewicz, T., Giugno, R.: P-\(\mathcal{SHOQ}({ D})\): A Probabilistic Extension of \(\mathcal{SHOQ}({ D})\) for probabilistic ontologies in the Semantic Web. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 86–97. Springer, Heidelberg (2002)

    Google Scholar 

  11. Grimm, S., Motik, B., Preist, C.: Variance in e-business service discovery. In: Proceedings of the ISWC 2004 Workshop on Semantic Web Services (2004)

    Google Scholar 

  12. Heinsohn, J.: Probabilistic description logics. In: Proceedings UAI 1994, pp. 311–318. Morgan Kaufmann, San Francisco (1994)

    Google Scholar 

  13. Jaeger, M.: Probabilistic reasoning in terminological logics. In: Proceedings KR 1994, pp. 305–316. Morgan Kaufmann, San Francisco (1994)

    Google Scholar 

  14. Jaeger, M.: Probabilistic role models and the guarded fragment. In: Proc. IPMU 2004, pp. 235–242 (2004); Extended version in Int. J. Uncertain. Fuzz., 14(1), 43–60 (2006)

    Google Scholar 

  15. Jensen, F.V.: Bayesian Networks and Decision Graphs. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  16. Klinov, P.: Pronto: A non-monotonic probabilistic description logic reasoner. In: System demo at ESWC 2008 (2008)

    Google Scholar 

  17. Koller, D., Levy, A., Pfeffer, A.: P-Classic: A tractable probabilistic description logic. In: Proceedings AAAI 1997, pp. 390–397. AAAI Press/MIT Press (1997)

    Google Scholar 

  18. Lukasiewicz, T.: Probabilistic deduction with conditional constraints over basic events. J. Artif. Intell. Res. 10, 199–241 (1999)

    MATH  MathSciNet  Google Scholar 

  19. Lukasiewicz, T.: Probabilistic default reasoning with conditional constraints. Ann. Math. Artif. Intell. 34(1–3), 35–88 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Intell. 172(6/7), 852–883 (2008)

    Article  MathSciNet  Google Scholar 

  21. Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the Semantic Web. J. Web Sem. (in press)

    Google Scholar 

  22. Mitra, P., Noy, N.F., Jaiswal, A.: OMEN: A probabilistic ontology mapping tool. In: Gil, Y., Motta, E., Benjamins, V.R., Musen, M.A. (eds.) ISWC 2005. LNCS, vol. 3729, pp. 537–547. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Nilsson, N.J.: Probabilistic logic. Artif. Intell. 28(1), 71–88 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  24. Nottelmann, H., Fuhr, N.: Adding probabilities and rules to OWL Lite subsets based on probabilistic Datalog. Int. J. Uncertain. Fuzz. 14(1), 17–42 (2006)

    MATH  MathSciNet  Google Scholar 

  25. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)

    Google Scholar 

  26. Pool, M., Aikin, J.: KEEPER and Protégé: An elicitation environment for Bayesian inference tools. In: Proceedings of the Workshop on Protégé and Reasoning held at the 7th International Protégé Conference (2004)

    Google Scholar 

  27. Smyth, C., Poole, D.: Qualitative probabilistic matching with hierarchical descriptions. In: Proceedings KR 2004, pp. 479–487. AAAI Press, Menlo Park (2004)

    Google Scholar 

  28. Yang, Y., Calmet, J.: OntoBayes: An ontology-driven uncertainty model. In: Proceedings IAWTIC 2005, pp. 457–463. IEEE Computer Society Press, Los Alamitos (2005)

    Google Scholar 

  29. Yelland, P.M.: An alternative combination of Bayesian networks and description logics. In: Proceedings KR 2000, pp. 225–234. Morgan Kaufmann, San Francisco (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

d’Amato, C., Fanizzi, N., Lukasiewicz, T. (2008). Tractable Reasoning with Bayesian Description Logics. In: Greco, S., Lukasiewicz, T. (eds) Scalable Uncertainty Management. SUM 2008. Lecture Notes in Computer Science(), vol 5291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87993-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-87993-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87992-3

  • Online ISBN: 978-3-540-87993-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics