Journal on Data Semantics XII pp 95-130

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5480) | Cite as

Tightly Coupled Probabilistic Description Logic Programs for the Semantic Web

  • Andrea Calì
  • Thomas Lukasiewicz
  • Livia Predoiu
  • Heiner Stuckenschmidt

Abstract

We present a novel approach to probabilistic description logic programs for the Semantic Web in which disjunctive logic programs under the answer set semantics are tightly coupled with description logics and Bayesian probabilities. The approach has several nice features. In particular, it is a logic-based representation formalism that naturally fits into the landscape of Semantic Web languages. Tightly coupled probabilistic description logic programs can especially be used for representing mappings between ontologies, which are a common way of approaching the semantic heterogeneity problem on the Semantic Web. In this application, they allow in particular for resolving inconsistencies and for merging mappings from different matchers based on the level of confidence assigned to different rules. Furthermore, tightly coupled probabilistic description logic programs also provide a natural integration of ontologies, action languages, and Bayesian probabilities towards Web Services. We explore the computational aspects of consistency checking and query processing in tightly coupled probabilistic description logic programs. We show that these problems are decidable and computable, respectively, and that they can be reduced to consistency checking and cautious/brave reasoning, respectively, in tightly coupled disjunctive description logic programs. Using these results, we also provide an anytime algorithm for tight query processing. Furthermore, we analyze the complexity of consistency checking and query processing in the new probabilistic description logic programs, and we present a special case of these problems with polynomial data complexity.

Keywords

Probabilistic description logic programs Semantic Web disjunctive logic programs answer set semantics description logics Bayesian probabilities ontology mapping inconsistency handling merging ontology mappings Web Services algorithms complexity data tractability 

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References

  1. 1.
    Calì, A., Lukasiewicz, T.: Tightly integrated probabilistic description logic programs for the semantic web. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 428–429. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Calì, A., Lukasiewicz, T., Predoiu, L., Stuckenschmidt, H.: A framework for representing ontology mappings under probabilities and inconsistency. In: Proceedings URSW 2007. CEUR Workshop Proceedings, vol. 327 (2008) CEUR-WS.orgGoogle Scholar
  3. 3.
    Calì, A., Lukasiewicz, T., Predoiu, L., Stuckenschmidt, H.: Tightly integrated probabilistic description logic programs for representing ontology mappings. In: Hartmann, S., Kern-Isberner, G. (eds.) FoIKS 2008. LNCS, vol. 4932, pp. 178–198. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Berners-Lee, T.: Weaving the Web. Harper, San Francisco (1999)Google Scholar
  5. 5.
    Fensel, D., Wahlster, W., Lieberman, H., Hendler, J. (eds.): Spinning the Semantic Web: Bringing the World Wide Web to Its Full Potential. MIT Press, Cambridge (2002)Google Scholar
  6. 6.
    W3C: OWL Web Ontology Language Overview (2004) W3C Recommendation (February 10, 2004), http://www.w3.org/TR/2004/REC-owl-features-20040210/
  7. 7.
    Horrocks, I., Patel-Schneider, P.F.: Reducing OWL entailment to description logic satisfiability. In: Fensel, D., Sycara, K.P., Mylopoulos, J. (eds.) ISWC 2003. LNCS, vol. 2870, pp. 17–29. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Eiter, T., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with description logics for the Semantic Web. In: Proceedings KR 2004, pp. 141–151. AAAI Press, Menlo Park (2004)Google Scholar
  9. 9.
    Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with description logics for the Semantic Web. Artif. Intell. 172(12/13), 1495–1539 (2008)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Lukasiewicz, T.: A novel combination of answer set programming with description logics for the semantic web. In: Franconi, E., Kifer, M., May, W. (eds.) ESWC 2007. LNCS, vol. 4519, pp. 384–398. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Heymans, S., de Bruijn, J., Predoiu, L., Feier, C., Van Nieuwenborgh, D.: Guarded hybrid knowledge bases (2007)Google Scholar
  13. 13.
    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, vol. 2424, pp. 86–97. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Intell. 172(6/7), 852–883 (2008)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    da Costa, P.C.G.: Bayesian Semantics for the Semantic Web. PhD thesis, George Mason University, Fairfax, VA, USA (2005)Google Scholar
  16. 16.
    da Costa, P.C.G., Laskey, K.B.: PR-OWL: A framework for probabilistic ontologies. In: Proceedings FOIS 2006, pp. 237–249. IOS Press, Amsterdam (2006)Google Scholar
  17. 17.
    Lukasiewicz, T.: Probabilistic description logic programs. Int. J. Approx. Reasoning 45(2), 288–307 (2007)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Lukasiewicz, T.: Tractable probabilistic description logic programs. In: Prade, H., Subrahmanian, V.S. (eds.) SUM 2007. LNCS, vol. 4772, pp. 143–156. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Poole, D.: The independent choice logic for modelling multiple agents under uncertainty. Artif. Intell. 94(1/2), 7–56 (1997)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Finzi, A., Lukasiewicz, T.: Structure-based causes and explanations in the independent choice logic. In: Proceedings UAI 2003, pp. 225–232. Morgan Kaufmann, San Francisco (2003)Google Scholar
  21. 21.
    Serafini, L., Stuckenschmidt, H., Wache, H.: A formal investigation of mapping language for terminological knowledge. In: Proceedings IJCAI 2005, Professional Book Center, pp. 576–581 (2005)Google Scholar
  22. 22.
    Predoiu, L., Stuckenschmidt, H.: A probabilistic framework for information integration and retrieval on the Semantic Web. In: Proceedings InterDB 2007 Workshop on Database Interoperability (2007)Google Scholar
  23. 23.
    Euzenat, J., Shvaiko, P.: Ontology Matching. Springer, Heidelberg (2007)MATHGoogle Scholar
  24. 24.
    Euzenat, J., Mochol, M., Shvaiko, P., Stuckenschmidt, H., Svab, O., Svatek, V., van Hage, W.R., Yatskevich, M.: First results of the ontology alignment evaluation initiative 2006. In: Cruz, I., Decker, S., Allemang, D., Preist, C., Schwabe, D., Mika, P., Uschold, M., Aroyo, L.M. (eds.) ISWC 2006. LNCS, vol. 4273. Springer, Heidelberg (2006)Google Scholar
  25. 25.
    Euzenat, J., Stuckenschmidt, H., Yatskevich, M.: Introduction to the ontology alignment evaluation, In: Proceedings K-CAP 2005 Workshop on Integrating Ontologies (2005)Google Scholar
  26. 26.
    Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for expressive description logics. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol. 1705, pp. 161–180. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  27. 27.
    Faber, W., Leone, N., Pfeifer, G.: Recursive aggregates in disjunctive logic programs: Semantics and complexity. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS, vol. 3229, pp. 200–212. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  28. 28.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Comput. 9(3/4), 365–386 (1991)CrossRefMATHGoogle Scholar
  29. 29.
    Poole, D.: Probabilistic Horn abduction and Bayesian networks. Artif. Intell. 64(1), 81–129 (1993)CrossRefMATHGoogle Scholar
  30. 30.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)MATHGoogle Scholar
  31. 31.
    Frisch, A.M., Haddawy, P.: Anytime deduction for probabilistic logic. Artif. Intell. 69(1/2), 93–122 (1994)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Prentice Hall, San Francisco (2002)MATHGoogle Scholar
  33. 33.
    Meilicke, C., Stuckenschmidt, H., Tamilin, A.: Repairing ontology mappings. In: Proceedings AAAI 2007, pp. 1408–1413. AAAI Press, Menlo Park (2007)Google Scholar
  34. 34.
    Wang, P., Xu, B.: Debugging ontology mapping: A static method. Computing and Informatics 27(1), 21–36 (2008)Google Scholar
  35. 35.
    McIlraith, S.A., Son, T.C., Zeng, H.: Semantic Web Services. IEEE Intelligent Systems 16(2), 46–53 (2001)CrossRefGoogle Scholar
  36. 36.
    McIlraith, S.A., Son, T.C.: Adapting Golog for composition of Semantic Web Services. In: Proceedings KR 2002, pp. 482–496. Morgan Kaufmann, San Francisco (2002)Google Scholar
  37. 37.
    Narayanan, S., McIlraith, S.A.: Simulation, verification and automated composition of Web Services. In: Proceedings WWW 2002, pp. 77–88. ACM Press, New York (2002)Google Scholar
  38. 38.
    McIlraith, S.A., Martin, D.L.: Bringing semantics to Web Services. IEEE Intelligent Systems 18(1), 90–93 (2003)CrossRefGoogle Scholar
  39. 39.
    McCarthy, J., Hayes, P.J.: Some philosophical problems from the standpoint of Artificial Intelligence. In: Machine Intelligence, vol. 4, pp. 463–502. Edinburgh University Press (1969)Google Scholar
  40. 40.
    Reiter, R.: Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems. MIT Press, Cambridge (2001)MATHGoogle Scholar
  41. 41.
    Levesque, H.J., Reiter, R., Lespérance, Y., Lin, F., Scherl, R.: GOLOG: A logic programming language for dynamic domains. J. Logic Program. 31(1–3), 59–84 (1997)MathSciNetCrossRefMATHGoogle Scholar
  42. 42.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: DL-Lite: Tractable description logics for ontologies. In: Proceedings AAAI 2005, pp. 602–607. AAAI Press MIT Press (2005)Google Scholar
  43. 43.
    Donini, F.M., Lenzerini, M., Nardi, D., Schaerf, A.: \({\cal AL}\)-log: Integrating Datalog and description logics. J. Intell. Inf. Syst. 10(3), 227–252 (1998)CrossRefGoogle Scholar
  44. 44.
    Levy, A.Y., Rousset, M.C.: Combining Horn rules and description logics in CARIN. Artif. Intell. 104(1/2), 165–209 (1998)MathSciNetCrossRefMATHGoogle Scholar
  45. 45.
    Grosof, B.N., Horrocks, I., Volz, R., Decker, S.: Description logic programs: Combining logic programs with description logics. In: Proceedings WWW 2003, pp. 48–57. ACM Press, New York (2003)Google Scholar
  46. 46.
    Motik, B., Sattler, U., Studer, R.: Query answering for OWL-DL with rules. J. Web Sem. 3(1), 41–60 (2005)CrossRefGoogle Scholar
  47. 47.
    Heymans, S., Van Nieuwenborgh, D., Vermeir, D.: Nonmonotonic ontological and rule-based reasoning with extended conceptual logic programs. In: Gómez-Pérez, A., Euzenat, J. (eds.) ESWC 2005. LNCS, vol. 3532, pp. 392–407. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  48. 48.
    Rosati, R.: On the decidability and complexity of integrating ontologies and rules. J. Web Sem. 3(1), 61–73 (2005)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Rosati, R.: DL+log: Tight integration of description logics and disjunctive Datalog. In: Proceedings KR 2006, pp. 68–78. AAAI Press, Menlo Park (2006)Google Scholar
  50. 50.
    Horrocks, I., Patel-Schneider, P.F., Boley, H., Tabet, S., Grosof, B., Dean, M.: SWRL: A Semantic Web rule language combining OWL and RuleML, W3C Member Submission (May 2004), http://www.w3.org/Submission/SWRL/
  51. 51.
    Angele, J., Boley, H., de Bruijn, J., Fensel, D., Hitzler, P., Kifer, M., Krummenacher, R., Lausen, H., Polleres, A., Studer, R.: Web Rule Language (WRL), W3C Member Submission (September 2005), http://www.w3.org/Submission/WRL/
  52. 52.
    Heymans, S., Van Nieuwenborgh, D., Vermeir, D.: Guarded open answer set programming. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS, vol. 3662, pp. 92–104. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  53. 53.
    Motik, B., Sattler, U.: A comparison of reasoning techniques for querying large description logic aBoxes. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS, vol. 4246, pp. 227–241. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  54. 54.
    Predoiu, L., Stuckenschmidt, H.: Probabilistic extensions of Semantic Web languages — a survey. In: The Semantic Web for Knowledge and Data Management: Technologies and Practices. Idea Group (to appear)Google Scholar
  55. 55.
    Koller, D., Levy, A.Y., Pfeffer, A.: P-CLASSIC: A tractable probabilistic description logic. In: Proceedings AAAI 2007, pp. 390–397. AAAI Press, Menlo Park (1997)Google Scholar
  56. 56.
    Ding, Z., Peng, Y., Pan, R.: BayesOWL: Uncertainty modeling in Semantic Web ontologies. In: Soft Computing in Ontologies and Semantic Web, pp. 3–28. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  57. 57.
    Nottelmann, H., Fuhr, N.: Adding probabilities and rules to OWL Lite subsets based on probabilistic Datalog. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 14(1), 17–42 (2006)MathSciNetCrossRefMATHGoogle Scholar
  58. 58.
    De Giacomo, G., Iocchi, L., Nardi, D., Rosati, R.: Moving a robot: The KR&R approach at work. In: Proceedings KR 1996, pp. 198–209. Morgan Kaufmann, San Francisco (1996)Google Scholar
  59. 59.
    Iocchi, L., Lukasiewicz, T., Nardi, D., Rosati, R.: Reasoning about actions with sensing under qualitative and probabilistic uncertainty. ACM Trans. Computat. Logic (in press)Google Scholar
  60. 60.
    Baader, F., Lutz, C., Milicic, M., Sattler, U., Wolter, F.: Integrating description logics and action formalisms: First results. In: Proceedings AAAI 2005, pp. 572–577. AAAI Press/ MIT Press (2005)Google Scholar
  61. 61.
    Milicic, M.: Planning in action formalisms based on DLs: First results. In: Proceedings DL 2007. CEUR Workshop Proceedings, vol. 250 (2007) CEUR-WS.orgGoogle Scholar
  62. 62.
    Drescher, C., Thielscher, M.: Integrating action calculi and description logics. In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007. LNCS, vol. 4667, pp. 68–83. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andrea Calì
    • 1
    • 2
  • Thomas Lukasiewicz
    • 1
  • Livia Predoiu
    • 3
  • Heiner Stuckenschmidt
    • 3
  1. 1.Computing LaboratoryUniversity of OxfordOxfordUK
  2. 2.Oxford-Man Institute of Quantitative FinanceUniversity of OxfordOxfordUK
  3. 3.Institut für InformatikUniversität MannheimMannheimGermany

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