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International Conference on Scalable Uncertainty Management

SUM 2008: Scalable Uncertainty Management pp 120–133Cite as

Loopy Propagation in a Probabilistic Description Logic

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

Abstract

This paper introduces a probabilistic description logic that adds probabilistic inclusions to the popular logic \(\mathcal{ALC}\), and derives inference algorithms for inference in the logic. The probabilistic logic, referred to as cr \(\mathcal{ALC}\) (“credal” \(\mathcal{ALC}\)), combines the usual acyclicity condition with a Markov condition; in this context, inference is equated with calculation of (bounds on) posterior probability in relational credal/Bayesian networks. As exact inference does not seem scalable due to the presence of quantifiers, we present first-order loopy propagation methods that seem to behave appropriately for non-trivial domain sizes.

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References

  1. Andersen, K.A., Hooker, J.N.: Bayesian logic. Decision Support Systems 11, 191–210 (1994)

    Article  Google Scholar 

  2. Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F.: Description Logic Handbook. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  3. Bacchus, F.: Representing and Reasoning with Probabilistic Knowledge: A Logical Approach. MIT Press, Cambridge (1990)

    Google Scholar 

  4. Berners-Lee, T., Hendlers, J., Lassila, O.: The semantic web. In: Scientific American, pp. 34–43 (2001)

    Google Scholar 

  5. Borgida, A.: On the relative expressiveness of description logics and predicate logics. Artificial Intelligence 82(1-2), 353–367 (1996)

    Article  MathSciNet  Google Scholar 

  6. Costa, P.C.G., Laskey, K.B.: PR-OWL: A framework for probabilistic ontologies. In: Conf. on Formal Ontology in Information Systems (2006)

    Google Scholar 

  7. da Costa, P.C.G., Laskey, K.B.: Of Klingons and starships: Bayesian logic for the 23rd century. In: Conf. on Uncertainty in Artificial Intelligence (2005)

    Google Scholar 

  8. Cozman, F.G.: Credal networks. Artificial Intelligence 120, 199–233 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Cozman, F.G., de Campos, C.P., Ferreira da Rocha, J.C.: Probabilistic logic with independence. Int. Journal of Approximate Reasoning (in press, September 7, 2007) doi: 10.1016/j.ijar.2007.08.002

    Google Scholar 

  10. Polpo de Campos, C., Cozman, F.G., Luna, J.E.O.: Assessing a consistent set of sentences in relational probabilistic logic with stochastic independence. Journal of Applied Logic (to appear)

    Google Scholar 

  11. de Salvo Braz, R., Amir, E., Roth, D.: Lifted first-order probabilistic inference. In: Int. Joint Conf. in Artificial Intelligence (IJCAI) (2005)

    Google Scholar 

  12. de Salvo Braz, R., Amir, E., Roth, D.: MPE and partial inversion in lifted probabilistic variable elimination. AAAI (2006)

    Google Scholar 

  13. Ding, Z., Peng, Y., Pan, R.: BayesOWL: Uncertainty modeling in semantic web ontologies. In: Soft Computing in Ontologies and Semantic Web. Studies in Fuzziness and Soft Computing, vol. 204. Springer, Berlin (2006)

    Chapter  Google Scholar 

  14. Dürig, M., Studer, T.: Probabilistic ABox reasoning: preliminary results. In: Description Logics, pp. 104–111 (2005)

    Google Scholar 

  15. Gaifman, H.: Concerning measures on first-order calculi. Israel Journal of Mathematics 2, 1–18 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  16. Getoor, L., Friedman, N., Koller, D., Taskar, B.: Learning probabilistic models of relational structure. In: Int. Conf. on Machine Learning, pp. 170–177 (2001)

    Google Scholar 

  17. Getoor, L., Taskar, B.: Introduction to Statistical Relational Learning. MIT Press, Cambridge (2007)

    MATH  Google Scholar 

  18. Lukasiewicz, T., Giugno, R.: P-SHOQ(D): A probabilistic extension of 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 

  19. Halpern, J.Y.: Reasoning about Uncertainty. MIT Press, Cambridge (2003)

    MATH  Google Scholar 

  20. Heinsohn, J.: Probabilistic description logics. In: Conf. on Uncertainty in Artificial Intelligence, pp. 311–318 (1994)

    Google Scholar 

  21. Horrocks, I., Patel-Schneider, P.F., van Harmelen, F.: From SHIQ and RDF to OWL: The making of a web ontology language. Journal of Web Semantics 1(1), 7–26 (2003)

    Google Scholar 

  22. Hung, E., Getoor, L., Subrahmanian, V.S.: Probabilistic interval XML. ACM Transactions on Computational Logic 8(4) (2007)

    Google Scholar 

  23. Ide, J.S., Cozman, F.G.: Approximate algorithms for credal networks with binary variables. Int. Journal of Approximate Reasoning 48(1), 275–296 (2008)

    Article  Google Scholar 

  24. Jaeger, M.: Probabilistic reasoning in terminological logics. Principles of Knowledge Representation (KR), pp. 461–472 (1994)

    Google Scholar 

  25. Jaeger, M.: Relational Bayesian networks. In: Uncertainty in Artificial Intelligence, pp. 266–273. Morgan Kaufmann, San Francisco (1997)

    Google Scholar 

  26. Jaeger, M.: Convergence results for relational Bayesian networks. LICS (1998)

    Google Scholar 

  27. Jaeger, M.: Reasoning about infinite random structures with relational Bayesian networks. In: Knowledge Representation. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  28. Jaimovich, A., Meshi, O., Friedman, N.: Template based inference in symmetric relational Markov random fields. Uncertainty in Artificial Intelligence, Canada. AUAI Press (2007)

    Google Scholar 

  29. Jordan, M.I., Ghahramani, Z., Jaakkola, T.S.: An introduction to variational methods for graphical models. Machine Learning 37, 183–233 (1999)

    Article  MATH  Google Scholar 

  30. Koller, D., Pfeffer, A.: Object-oriented Bayesian networks. In: Conf. on Uncertainty in Artificial Intelligence, pp. 302–313 (1997)

    Google Scholar 

  31. Kyburg Jr., H.E., Teng, C.M.: Uncertain Inference. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  32. Lukasiewicz, T.: Probabilistic logic programming. In: European Conf. on Artificial Intelligence, pp. 388–392 (1998)

    Google Scholar 

  33. Lukasiewicz, T.: Expressive probabilistic description logics. Artificial Intelligence (to appear)

    Google Scholar 

  34. Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the semantic web (submitted, 2008)

    Google Scholar 

  35. Milch, B., Marthi, B., Sontag, D., Russell, S., Ong, D.L., Kolobov, A.: BLOG: Probabilistic models with unknown objects. In: IJCAI (2005)

    Google Scholar 

  36. Milch, B., Russell, S.: First-order probabilistic languages: into the unknown. In: Int. Conf. on Inductive Logic Programming (2007)

    Google Scholar 

  37. Motik, B., Horrocks, I., Rosati, R., Sattler, U.: Can OWL and logic programming live together happily ever after? In: Cruz, I., Decker, S., Allemang, D., Preist, C., Schwabe, D., Mika, P., Uschold, M., Aroyo, L.M. (eds.) ISWC 2006. LNCS, vol. 4273, pp. 501–514. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  38. Moussouris, J.: Gibbs and Markov random systems with constraints. Journal of Statistical Physics 10(1), 11–33 (1974)

    Article  MathSciNet  Google Scholar 

  39. Murphy, K.P., Weiss, Y., Jordan, M.I.: Loopy belief propagation for approximate inference: An empirical study. In: Uncertainty in Artificial Intelligence, pp. 467–475 (1999)

    Google Scholar 

  40. Nottelmann, H., Fuhr, N.: Adding probabilities and rules to OWL lite subsets based on probabilistic datalog. Int. Journal of Uncertainty, Fuzziness and Knowledge-based Systems 14(1), 17–42 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  41. Pfeffer, A., Koller, D.: Semantics and inference for recursive probability models. In: AAAI, pp. 538–544 (2000)

    Google Scholar 

  42. Poole, D.: First-order probabilistic inference. In: Int. Joint Conf. on Artificial Intelligence (IJCAI), pp. 985–991 (2003)

    Google Scholar 

  43. Richardson, M., Domingos, P.: Markov logic networks. Machine Learning 62(1-2), 107–136 (2006)

    Article  Google Scholar 

  44. Schild, K.: A correspondence theory for terminological logics: Preliminary report. In: Int. Joint Conf. on Artificial Intelligence, pp. 466–471 (1991)

    Google Scholar 

  45. Schmidt-Schauss, M., Smolka, G.: Attributive concept descriptions with complements. Artificial Intelligence 48, 1–26 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  46. Sebastiani, F.: A probabilistic terminological logic for modelling information retrieval. In: Int. ACM Conf. on Research and Development in Information Retrieval (SIGIR), Dublin, Ireland, pp. 122–130. Springer, Heidelberg (1994)

    Google Scholar 

  47. Sigla, P., Domingos, P.: Markov logic in infinite domains. In: Uncertainty in Artificial Intelligence, pp. 368–375. AUAI Press (2007)

    Google Scholar 

  48. Sigla, P., Domingos, P.: Lifted first-order belief propagation. AAAI (2008)

    Google Scholar 

  49. Staker, R.: Reasoning in expressive description logics using belief networks. In: Int. Conf. on Information and Knowledge Engineering, Las Vegas, USA, pp. 489–495 (2002)

    Google Scholar 

  50. Taskar, B., Abbeel, P., Koller, D.: Discriminative probabilistic models for relational data. In: Conf. on Uncertainty in Artificial Intelligence, Edmonton, Canada (2002)

    Google Scholar 

  51. Ycart, B., Rousset, M.-C.: A zero-one law for random sentences in description logics. Colloquium on Mathematics and Computer Science (2000)

    Google Scholar 

  52. Yelland, P.M.: Market analysis using a combination of Bayesian networks and description logics. Technical Report SMLI TR-99-78, Sun Microsystems Laboratories (1999)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Escola Politécnica, Universidade de São Paulo, São Paulo, SP, Brazil

    Fabio Gagliardi Cozman & Rodrigo Bellizia Polastro

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  1. Fabio Gagliardi Cozman
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  2. Rodrigo Bellizia Polastro
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Editors and Affiliations

  1. DEIS, Univ. della Calabria, 87036, Rende, Italy

    Sergio Greco

  2. Computing Laboratory, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Thomas Lukasiewicz

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Cozman, F.G., Polastro, R.B. (2008). Loopy Propagation in a Probabilistic Description Logic. 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_11

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  • DOI: https://doi.org/10.1007/978-3-540-87993-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87992-3

  • Online ISBN: 978-3-540-87993-0

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