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Instance-Based Non-standard Inferences in \(\mathcal{EL}\) with Subjective Probabilities

  • Rafael Peñaloza
  • Anni-Yasmin Turhan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7123)

Abstract

For practical ontology-based applications representing and reasoning with probabilities is an essential task. For Description Logics with subjective probabilities reasoning procedures for testing instance relations based on the completion method have been developed.

In this paper we extend this technique to devise algorithms for solving non-standard inferences for \(\mathcal{EL}\) and its probabilistic extension Prob- \({\mathcal{EL}^{01}_c}\): computing the most specific concept of an individual and finding explanations for instance relations.

Keywords

Subjective Probability Description Logic Concept Description Instance Relation Valuation Versus 
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.

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References

  1. 1.
    Baader, F.: Least common subsumers and most specific concepts in a description logic with existential restrictions and terminological cycles. In: Gottlob, G., Walsh, T. (eds.) Proc. of the 18th Int. Joint Conf. on Artificial Intelligence, IJCAI 2003, pp. 325–330. Morgan Kaufmann (2003)Google Scholar
  2. 2.
    Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope. In: Proc. of the 19th Int. Joint Conf. on Artificial Intelligence, IJCAI 2005, Edinburgh, UK. Morgan-Kaufmann Publishers (2005)Google Scholar
  3. 3.
    Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope further. In: Clark, K., Patel-Schneider, P.F. (eds.) Proc. of the OWLED Workshop (2008)Google Scholar
  4. 4.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press (2003)Google Scholar
  5. 5.
    Baader, F., Küsters, R., Molitor, R.: Computing least common subsumers in description logics with existential restrictions. In: Dean, T. (ed.) Proc. of the 16th Int. Joint Conf. on Artificial Intelligence, IJCAI 1999, Stockholm, Sweden, pp. 96–101. Morgan Kaufmann, Los Altos (1999)Google Scholar
  6. 6.
    Baader, F., Lutz, C., Turhan, A.-Y.: Small is again Beautiful in Description Logics. KI – Künstliche Intelligenz 24(1), 25–33 (2010)CrossRefGoogle Scholar
  7. 7.
    Baader, F., Peñaloza, R.: Axiom pinpointing in general tableaux. Journal of Logic and Computation 20(1), 5–34 (2010); Special Issue: Tableaux and Analytic Proof MethodsMathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Baader, F., Peñaloza, R.: Axiom pinpointing in general tableaux. Journal of Logic and Computation 20(1), 5–34 (2010); Special Issue: Tableaux and Analytic Proof Methods MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Baader, F., Peñaloza, R., Suntisrivaraporn, B.: Pinpointing in the Description Logic \({{\mathcal{EL}}^+}\). In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007. LNCS (LNAI), vol. 4667, pp. 52–67. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Baader, F., Suntisrivaraporn, B.: Debugging SNOMED CT using axiom pinpointing in the description logic \(\mathcal{EL}^+\). In: Proceedings of the International Conference on Representing and Sharing Knowledge Using SNOMED, KR-MED 2008, Phoenix, Arizona (2008)Google Scholar
  11. 11.
    Bechhofer, S., van Harmelen, F., Hendler, J., Horrocks, I., McGuinness, D.L., Patel-Schneider, P.F., Stein, L.A.: OWL web ontology language reference. W3C Recommendation (February 2004), http://www.w3.org/TR/owl-ref/
  12. 12.
    Kalyanpur, A., Parsia, B., Horridge, M., Sirin, E.: Finding All Justifications of OWL DL Entailments. In: Aberer, K., Choi, K.-S., Noy, N., Allemang, D., Lee, K.-I., Nixon, L.J.B., Golbeck, J., Mika, P., Maynard, D., Mizoguchi, R., Schreiber, G., Cudré-Mauroux, P. (eds.) ISWC/ASWC 2007. LNCS, vol. 4825, pp. 267–280. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Küsters, R., Molitor, R.: Approximating most specific concepts in description logics with existential restrictions. AI Communications 15(1), 47–59 (2002)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the semantic web. J. Web Sem. 6(4), 291–308 (2008)CrossRefGoogle Scholar
  15. 15.
    Lutz, C., Schröder, L.: Probabilistic description logics for subjective probabilities. In: Lin, F., Sattler, U. (eds.) Proc. of the 12th Int. Conf. on the Principles of Knowledge Representation and Reasoning, KR 2010 (2010)Google Scholar
  16. 16.
    Mendez, J., Ecke, A., Turhan, A.-Y.: Implementing completion-based inferences for the \({\cal{EL}}\)-family. In: Rosati, R., Rudolph, S., Zakharyaschev, M. (eds.) Proc. of the 2011 Description Logic Workshop, DL 2011, vol. 745. CEUR (2011)Google Scholar
  17. 17.
    Peñaloza, R., Sertkaya, B.: On the complexity of axiom pinpointing in the el family of description logics. In: Lin, F., Sattler, U., Truszczynski, M. (eds.) Proceedings of the Twelfth International Conference on Principles of Knowledge Representation and Reasoning, KR 2010. AAAI Press (2010)Google Scholar
  18. 18.
    Peñaloza, R., Turhan, A.-Y.: Completion-based computation of most specific concepts with limited role-depth for \(\mathcal{EL}\) and prob-\({\mathcal{EL}^{01}}\). LTCS-Report LTCS-10-03, Chair f. Automata Theory, Inst. for Theoretical Computer Science, TU Dresden, Germany (2010)Google Scholar
  19. 19.
    Peñaloza, R., Turhan, A.-Y.: Role-depth bounded least common subsumers by completion for \(\mathcal{EL}\)- and Prob-\({\mathcal{EL}}\)-TBoxes. In: Haarslev, V., Toman, D., Weddell, G. (eds.) Proc. of the 2010 Description Logic Workshop, DL 2010 (2010)Google Scholar
  20. 20.
    Peñaloza, R., Turhan, A.-Y.: Towards approximative most specific concepts by completion for \({\mathcal{EL}^{01}}\) with subjective probabilities. In: Lukasiewicz, T., Peñaloza, R., Turhan, A.-Y. (eds.) Proceedings of the First International Workshop on Uncertainty in Description Logics, UniDL 2010 (2010)Google Scholar
  21. 21.
    Peñaloza, R., Turhan, A.-Y.: A Practical Approach for Computing Generalization Inferences in \(\mathcal{EL}\). In: Antoniou, G., Grobelnik, M., Simperl, E., Parsia, B., Plexousakis, D., De Leenheer, P., Pan, J. (eds.) ESWC 2011, Part I. LNCS, vol. 6643, pp. 410–423. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  22. 22.
    Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: Gottlob, G., Walsh, T. (eds.) Proc. of the 18th Int. Joint Conf. on Artificial Intelligence, IJCAI 2003, Acapulco, Mexico, pp. 355–362. Morgan Kaufmann, Los Altos (2003)Google Scholar
  23. 23.
    Spackman, K.: Managing clinical terminology hierarchies using algorithmic calculation of subsumption: Experience with snomed-rt. Journal of the American Medical Informatics Assoc. (2000); Fall Symposium Special IssueGoogle Scholar
  24. 24.
    Springer, T., Turhan, A.-Y.: Employing description logics in ambient intelligence for modeling and reasoning about complex situations. Journal of Ambient Intelligence and Smart Environments 1(3), 235–259 (2009)Google Scholar
  25. 25.
    W3C OWL Working Group. OWL 2 web ontology language document overview. W3C Recommendation (October 27, 2009), http://www.w3.org/TR/2009/REC-owl2-overview-20091027/

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Rafael Peñaloza
    • 1
  • Anni-Yasmin Turhan
    • 1
  1. 1.Institute for Theoretical Computer ScienceTU DresdenGermany

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