Representing Uncertain Concepts in Rough Description Logics via Contextual Indiscernibility Relations

  • Claudia d’Amato
  • Nicola Fanizzi
  • Floriana Esposito
  • Thomas Lukasiewicz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7123)

Abstract

We investigate the modeling of uncertain concepts via rough description logics (RDLs), which are an extension of traditional description logics (DLs) by a mechanism to handle approximate concept definitions via lower and upper approximations of concepts based on a rough-set semantics. This allows to apply RDLs to modeling uncertain knowledge. Since these approximations are ultimately grounded on an indiscernibility relation, we explore possible logical and numerical ways for defining such relations based on the considered knowledge. In particular, we introduce the notion of context, allowing for the definition of specific equivalence relations, which are directly used for lower and upper approximations of concepts. The notion of context also allows for defining similarity measures, which are used for introducing a notion of tolerance in the indiscernibility. Finally, we describe several learning problems in our RDL framework.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook. Cambridge University Press (2003)Google Scholar
  2. 2.
    d’Amato, C., Fanizzi, N., Esposito, F.: Query Answering and Ontology Population: An Inductive Approach. In: Bechhofer, S., Hauswirth, M., Hoffmann, J., Koubarakis, M. (eds.) ESWC 2008. LNCS, vol. 5021, pp. 288–302. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    De Comité, F., Denis, F., Gilleron, R., Letouzey, F.: Positive and Unlabeled Examples Help Learning. In: Watanabe, O., Yokomori, T. (eds.) ALT 1999. LNCS (LNAI), vol. 1720, pp. 219–230. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  4. 4.
    Doherty, P., Grabowski, M., Łukaszewicz, W., Szalas, A.: Towards a framework for approximate ontologies. Fundamenta Informaticae 57(2-4), 147–165 (2003)MathSciNetMATHGoogle Scholar
  5. 5.
    Donini, F., Lenzerini, M., Nardi, D., Nutt, W.: An epistemic operator for description logics. Artificial Intelligence 100(1/2), 225–274 (1998)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Fanizzi, N., d’Amato, C., Esposito, F.: Randomized metric induction and evolutionary conceptual clustering for semantic knowledge bases. In: Proceedings of the 16th Conference on Information and Knowledge Management, CIKM 2007, pp. 51–60. ACM Press (2007)Google Scholar
  7. 7.
    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
  8. 8.
    Fanizzi, N., d’Amato, C., Esposito, F.: Conceptual Clustering and Its Application to Concept Drift and Novelty Detection. In: Bechhofer, S., Hauswirth, M., Hoffmann, J., Koubarakis, M. (eds.) ESWC 2008. LNCS, vol. 5021, pp. 318–332. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Fanizzi, N., d’Amato, C., Esposito, F.: Statistical Learning for Inductive Query Answering on OWL Ontologies. In: Sheth, A.P., Staab, S., Dean, M., Paolucci, M., Maynard, D., Finin, T., Thirunarayan, K. (eds.) ISWC 2008. LNCS, vol. 5318, pp. 195–212. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Fanizzi, N., d’Amato, C., Esposito, F., Lukasiewicz, T.: Representing uncertain concepts in rough description logics via contextual indiscernibility relations. In: Proceedings of the 4th International Workshop on Uncertainty Reasoning for the Semantic Web, URSW 2008. CEUR Workshop Proceedings, vol. 423. CEUR-WS.org (2008)Google Scholar
  11. 11.
    Fanizzi, N., d’Amato, C., Esposito, F.: Induction of Concepts in Web Ontologies through Terminological Decision Trees. In: Balcázar, J.L., Bonchi, F., Gionis, A., Sebag, M. (eds.) ECML PKDD 2010, Part I. LNCS, vol. 6321, pp. 442–457. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Goldstone, R., Medin, D., Halberstadt, J.: Similarity in context. Memory and Cognition 25(3), 237–255 (1997)Google Scholar
  13. 13.
    Hirano, S., Tsumoto, S.: An indiscernibility-based clustering method. In: Proceedings of the 2005 IEEE International Conference on Granular Computing, pp. 468–473. IEEE Computer Society (2005)Google Scholar
  14. 14.
    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
  15. 15.
    Lehmann, J., Hitzler, P.: A Refinement Operator Based Learning Algorithm for the \({\cal ALC}\) Description Logic. In: Blockeel, H., Ramon, J., Shavlik, J., Tadepalli, P. (eds.) ILP 2007. LNCS (LNAI), vol. 4894, pp. 147–160. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Lehmann, J.: DL-Learner: Learning concepts in description logics. Journal of Machine Learning Research 10, 2639–2642 (2009)MATHGoogle Scholar
  17. 17.
    Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the Semantic Web. Journal of Web Semantics 6(4), 291–308 (2008)CrossRefGoogle Scholar
  18. 18.
    Jiang, Y., Wang, J., Tang, S., Xiao, B.: Reasoning with rough description logics: An approximate concepts approach. Information Sciences 179(5), 600–612 (2009)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Keet, C.M.: On the feasibility of description logic knowledge bases with rough concepts and vague instances. In: Proceedings of the 23rd International Workshop on Description Logics, DL 2010. CEUR Workshop Proceedings, vol. 573. CEUR-WS.org (2010)Google Scholar
  20. 20.
    Keet, C.M.: Ontology Engineering with Rough Concepts and Instances. In: Cimiano, P., Pinto, H.S. (eds.) EKAW 2010. LNCS, vol. 6317, pp. 503–513. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Mitchell, T.: Machine Learning. McGraw-Hill (1997)Google Scholar
  22. 22.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers (1991)Google Scholar
  23. 23.
    Schlobach, S., Klein, M.C.A., Peelen, L.: Description logics with approximate definitions — precise modeling of vague concepts. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence, IJCAI 2007, pp. 557–562 (2007)Google Scholar
  24. 24.
    Zezula, P., Amato, G., Dohnal, V., Batko, M.: Similarity Search — The Metric Space Approach. Advances in Database Systems. Springer (2007)Google Scholar
  25. 25.
    Zhang, B., Zuo, W.: Learning from positive and unlabeled examples: A survey. In: Proceeding of the International Symposium on Information Processing, ISP 2008, pp. 650–654 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Claudia d’Amato
    • 1
  • Nicola Fanizzi
    • 1
  • Floriana Esposito
    • 1
  • Thomas Lukasiewicz
    • 2
  1. 1.LACAM, Dipartimento di InformaticaUniversità degli Studi di BariItaly
  2. 2.Department of Computer ScienceUniversity of OxfordUK

Personalised recommendations