Learning Probabilistic Description Logics: A Framework and Algorithms

  • José Eduardo Ochoa-Luna
  • Kate Revoredo
  • Fábio Gagliardi Cozman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7094)

Abstract

Description logics have become a prominent paradigm in knowledge representation (particularly for the Semantic Web), but they typically do not include explicit representation of uncertainty. In this paper, we propose a framework for automatically learning a Probabilistic Description Logic from data. We argue that one must learn both concept definitions and probabilistic assignments. We also propose algorithms that do so and evaluate these algorithms on real data.

Keywords

Description Logic Inductive Logic Programming Probabilistic Inclusion Conditional Mutual Information Candidate Concept 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Antoniou, G., van Harmelen, F.: Semantic Web Primer. MIT Press (2008)Google Scholar
  2. 2.
    Baader, F., Nutt, W.: Basic description logics. In: Description Logic Handbook, pp. 47–100. Cambridge University Press (2002)Google Scholar
  3. 3.
    Bizer, C., Lehmann, J., Kobilarov, G., Auer, S., Becker, C., Cyganiak, R., Hellmann, S.: DBpedia - a crystallization point for the web of data. Web Semant. 7(3), 154–165 (2009)CrossRefGoogle Scholar
  4. 4.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press (2001)Google Scholar
  5. 5.
    Costa, P.C.G., Laskey, K.B.: PR-OWL: A framework for probabilistic ontologies. In: Proceeding of the 2006 Conference on Formal Ontology in Information Systems, pp. 237–249. IOS Press, Amsterdam (2006)Google Scholar
  6. 6.
    Cozman, F.G., Polastro, R.B.: Loopy Propagation in a Probabilistic Description Logic. In: Greco, S., Lukasiewicz, T. (eds.) SUM 2008. LNCS (LNAI), vol. 5291, pp. 120–133. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Cozman, F.G., Polastro, R.B.: Complexity analysis and variational inference for interpretation-based probabilistic description logics. In: Conference on Uncertainty in Artificial Intelligence (2009)Google Scholar
  8. 8.
    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
  9. 9.
    Fanizzi, N., d’Amato, C., Esposito, F.: DL-FOIL Concept Learning in Description Logics. In: Železný, F., Lavrač, N. (eds.) ILP 2008. LNCS (LNAI), vol. 5194, pp. 107–121. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Friedman, N., Geiger, D., Goldszmidt, M.: Bayesian network classifiers. Machine Learning 29, 131–163 (1997)CrossRefMATHGoogle Scholar
  11. 11.
    Heinsohn, J.: Probabilistic description logics. In: International Conf. on Uncertainty in Artificial Intelligence, pp. 311–318 (1994)Google Scholar
  12. 12.
    Iannone, L., Palmisano, I., Fanizzi, N.: An algorithm based on counterfactuals for concept learning in the semantic web. Applied Intelligence 26(2), 139–159 (2007)CrossRefGoogle Scholar
  13. 13.
    Jaeger, M.: Probabilistic reasoning in terminological logics. In: Principals of Knowledge Representation (KR), pp. 461–472 (1994)Google Scholar
  14. 14.
    Landwehr, N., Kersting, K., DeRaedt, L.: Integrating Naïve Bayes and FOIL. J. Mach. Learn. Res. 8, 481–507 (2007)MATHGoogle Scholar
  15. 15.
    Lavrac, N., Dzeroski, S.: Inductive Logic Programming: Techniques and Applications. Ellis Horwood, New York (1994)MATHGoogle Scholar
  16. 16.
    Lehmann, J.: Hybrid Learning of Ontology Classes. In: Perner, P. (ed.) MLDM 2007. LNCS (LNAI), vol. 4571, pp. 883–898. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Lehmann, J., Hitzler, P.: Foundations of Refinement Operators for Description Logics. In: Blockeel, H., Ramon, J., Shavlik, J. W., Tadepalli, P. (eds.) ILP 2007. LNCS (LNAI), vol. 4894, pp. 161–174. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Lehmann, J., Hitzler, P.: A Refinement Operator Based Learning Algorithm for the \(\mathcal{ALC}\) Description Logic. In: Blockeel, H., Ramon, J., Shavlik, J. W., Tadepalli, P. (eds.) ILP 2007. LNCS (LNAI), vol. 4894, pp. 147–160. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Intell. 172(6-7), 852–883 (2008)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Ochoa-Luna, J., Cozman, F.G.: An algorithm for learning with probabilistic description logics. In: Bobillo, F., et al. (eds.) Proceedings of the 5th International Workshop on Uncertainty Reasoning for the Semantic Web, Chantilly, USA, vol. 527, pp. 63–74. CEUR-WS.org (2009)Google Scholar
  21. 21.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: networks of plausible inference. Morgan Kaufmann (1988)Google Scholar
  22. 22.
    Polastro, R.B., Cozman, F.G.: Inference in probabilistic ontologies with attributive concept descriptions and nominals. In: 4th International Workshop on Uncertainty Reasoning for the Semantic Web (URSW) at the 7th International Semantic Web Conference (ISWC), Karlsruhe, Germany (2008)Google Scholar
  23. 23.
    Quinlan, J.R., Cameron-Jones, R.M.: FOIL: A midterm report. In: Proceedings of the European Conference on Machine Learning, pp. 3–20. Springer, Heidelberg (1993)Google Scholar
  24. 24.
    Revoredo, K., Ochoa-Luna, J.E., Cozman, F.G.: Learning Terminologies in Probabilistic Description Logics. In: da Rocha Costa, A.C., Vicari, R.M., Tonidandel, F. (eds.) SBIA 2010. LNCS, vol. 6404, pp. 41–50. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  25. 25.
    Sebastiani, F.: A probabilistic terminological logic for modelling information retrieval. In: ACM Conf. on Research and Development in Information Retrieval (SIGIR), pp. 122–130 (1994)Google Scholar
  26. 26.
    Suchanek, F.M., Kasneci, G., Weikum, G.: Yago: a core of semantic knowledge. In: WWW 2007: Proceedings of the 16th International Conference on World Wide Web, pp. 697–706. ACM, New York (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • José Eduardo Ochoa-Luna
    • 1
  • Kate Revoredo
    • 2
  • Fábio Gagliardi Cozman
    • 1
  1. 1.Escola PolitécnicaUniversidade de São PauloSão PauloBrazil
  2. 2.Departamento de Informática AplicadaUnirioRio de JaneiroBrazil

Personalised recommendations