Understanding a Probabilistic Description Logic via Connections to First-Order Logic of Probability

  • Pavel Klinov
  • Bijan Parsia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7123)

Abstract

This paper analyzes the probabilistic description logic P-\(\mathcal{SROIQ}\) as a fragment of well-known first-order probabilistic logic (FOPL).P-\(\mathcal{SROIQ}\) was suggested as a language that is capable of representing and reasoning about different kinds of uncertainty in ontologies, namely generic probabilistic relationships between concepts and probabilistic facts about individuals. However, some semantic properties of P-\(\mathcal{SROIQ}\) have been unclear which raised concerns regarding whether it could be used for representing probabilistic ontologies. In this paper we provide an insight into its semantics by translating P-\(\mathcal{SROIQ}\) into FOPL with a specific subjective semantics based on possible worlds. We prove faithfulness of the translation and demonstrate the fundamental nature of some limitations of P-\(\mathcal{SROIQ}\). Finally, we briefly discuss the implications of the exposed semantic properties of the logic on probabilistic modeling.

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References

  1. 1.
    Lukasiewicz, T.: Expressive probabilistic description logics. Artificial Intelligence 172(6-7), 852–883 (2008)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Klinov, P., Parsia, B.: A Hybrid Method for Probabilistic Satisfiability. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 354–368. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Bacchus, F.: Representing and reasoning with probabilistic knowledge. MIT Press (1990)Google Scholar
  4. 4.
    Halpern, J.Y.: An analysis of first-order logics of probability. Artificial Intelligence 46, 311–350 (1990)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\mathcal{SROIQ}\). In: Knowledge Representation and Reasoning, pp. 57–67 (2006)Google Scholar
  6. 6.
    Lutz, C., Sattler, U., Tendera, L.: The complexity of finite model reasoning in description logics. Information and Computation 199(1-2), 132–171 (2005)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Klinov, P.: Practical Reasoning in Probabilistic Description Logic. PhD thesis, The University of Manchester (2011)Google Scholar
  8. 8.
    Abadi, M., Halpern, J.Y.: Decidability and expressiveness for first-order logics of probability. Information and Computation 112(1), 1–36 (1994)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Koller, D., Halpern, J.Y.: Irrelevance and conditioning in first-order probabilistic logic. In: Advances in Artificial Intelligence Conference, pp. 569–576 (1996)Google Scholar
  10. 10.
    Borgida, A.: On the relationship between description logic and predicate logic. In: International Conference on Information and Knowledge Management, pp. 219–225 (1994)Google Scholar
  11. 11.
    Klinov, P., Parsia, B., Sattler, U.: On correspondences between probabilistic first-order and description logics. In: International Workshop on Description Logic (2009)Google Scholar
  12. 12.
    Geffner, H., Pearl, J.: A framework for reasoning with defaults. In: Kyburg, H., Loui, R., Carlson, G. (eds.) Knowledge Representation and Defeasible Reasoning, pp. 69–87. Kluwer Academic Publishers (1990)Google Scholar
  13. 13.
    Lukasiewicz, T.: Nonmonotonic probabilistic logics under variable-strength inheritance with overriding: Complexity, algorithms, and implementation. International Journal of Approximate Reasoning 44(3), 301–321 (2007)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Cheeseman, P.: An inquiry into computer understanding. Computational Intelligence 4, 58–66 (1988)CrossRefGoogle Scholar
  15. 15.
    Bacchus, F.: Lp, a logic for representing and reasoning with statistical knowledge. Computational Intelligence 6, 209–231 (1990)CrossRefGoogle Scholar
  16. 16.
    Klinov, P., Parsia, B.: Relationships between probabilistic description and first-order logics. In: International Workshop on Uncertainty in Description Logics (2010)Google Scholar
  17. 17.
    Giugno, R., Lukasiewicz, T.: P-\(\mathcal{SHOQ}({\bf D})\): A Probabilistic Extension of \(\mathcal{SHOQ}({\bf D})\) 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)CrossRefGoogle Scholar
  18. 18.
    Lutz, C., Schröder, L.: Probabilistic description logics for subjective uncertainty. In: International Conference on the Principles of Knowledge Representation and Reasoning (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pavel Klinov
    • 1
  • Bijan Parsia
    • 2
  1. 1.Institute of Artificial IntelligenceUniversity of UlmGermany
  2. 2.School of Computer ScienceUniversity of ManchesterUnited Kingdom

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