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Tightly integrated probabilistic description logic programs for representing ontology mappings

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Abstract

Creating mappings between ontologies is a common way of approaching the semantic heterogeneity problem on the Semantic Web. To fit into the landscape of Semantic Web languages, a suitable, logic-based representation formalism for mappings is needed. We argue that such a formalism has to be able to deal with uncertainty and inconsistencies in automatically created mappings. We analyze the requirements for such a formalism, and we propose a novel approach to probabilistic description logic programs as such a formalism, which tightly combines normal logic programs under the well-founded semantics with both tractable ontology languages and Bayesian probabilities. We define the language, and we show that it can be used to resolve inconsistencies and merge mappings from different matchers based on the level of confidence assigned to different rules. Furthermore, we explore the semantic and computational aspects of probabilistic description logic programs under the well-founded semantics. In particular, we show that the well-founded semantics approximates the answer set semantics. We also describe algorithms for consistency checking and tight query processing, and we analyze the data and general complexity of these two central computational problems. As a crucial property, the novel tightly integrated probabilistic description logic programs under the well-founded semantics allow for tractable consistency checking and for tractable tight query processing in the data complexity, and they even have a first-order rewritable (and thus LogSpace data complexity) special case, which is especially interesting for representing ontology mappings.

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References

  1. Baral, C., Subrahmanian, V.S.: Dualities between alternative semantics for logic programming and nonmonotonic reasoning. J. Autom. Reasoning 10(3), 399–420 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Calì, A., Lukasiewicz, T., Predoiu, L., Stuckenschmidt, H.: A framework for representing ontology mappings under probabilities and inconsistency. In: Proc. URSW-2007. CEUR Workshop Proceedings 327, CEUR-WS.org (2008)

  3. Calì, A., Lukasiewicz, T., Predoiu, L., Stuckenschmidt, H.: Tightly integrated probabilistic description logic programs for representing ontology mappings. In: Proc. FoIKS-2008, pp. 178–198. LNCS 4932. Springer, New York (2008)

    Google Scholar 

  4. Calì, A., Lukasiewicz, T., Predoiu, L., Stuckenschmidt, H.: Tightly coupled probabilistic description logic programs for the Semantic Web. J. Data Sem. 12, 95–130 (2009)

    Article  Google Scholar 

  5. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: The DL-Lite family. J. Autom. Reason. 39(3), 385–429 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Caracciolo, C., Euzenat, J., Hollink, L., Ichise, R., Isaac, A., Malaise, V., Meilicke, C., Pane, J., Shvaiko, P., Stuckenschmidt, H., Svab-Zamazal, O., Svatek, V.: Results of the ontology alignment evaluation initiative 2008. In: Proc. ISWC-2008 Workshop on Ontology Matching (2008)

  7. Castano, S., Ferrara, A., Messa, G.: ISLab HMatch Results for OAEI 2006. In: Proc. International Workshop on Ontology Matching (2006)

  8. da Costa, P.C.G.: Bayesian semantics for the Semantic Web. Doctoral dissertation, George Mason University, Fairfax, VA, USA (2005)

  9. da Costa, P.C.G., Laskey, K.B.: PR-OWL: a framework for probabilistic ontologies. In: Proc. FOIS-2006, pp. 237–249. IOS Press, Amsterdam (2006)

    Google Scholar 

  10. Dantsin, E., Eiter, T., Gottlob, G., Voronkov, A.: Complexity and expressive power of logic programming. ACM Comput. Surv. 33(3), 374–425 (2001)

    Article  Google Scholar 

  11. de Bruijn, J., Lausen, H., Polleres, A., Fensel, D.: The Web service modeling language WSML: an overview. In: Proc. ESWC-2006, pp. 590–604. LNCS 4011. Springer, New York (2006)

    Google Scholar 

  12. 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, New York (2006)

    Chapter  Google Scholar 

  13. Drabent, W., Małuszyński, J.: Well-founded semantics for hybrid rules. In: Proc. RR-2007, pp. 1–15. LNCS 4524. Springer, New York (2007)

    Google Scholar 

  14. 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)

    Article  MathSciNet  MATH  Google Scholar 

  15. Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R.: Well-founded semantics for description logic programs in the Semantic Web. ACM Trans. Comput. Log. 12(2), Article 11 (2011)

    Google Scholar 

  16. Euzenat, J., Shvaiko, P.: Ontology Matching. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  17. Euzenat, J., Stuckenschmidt, H., Yatskevich, M.: Introduction to the ontology alignment evaluation 2005. In: Proc. K-CAP-2005 Workshop on Integrating Ontologies (2005)

  18. 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: Proc. ISWC-2006 Workshop on Ontology Matching (2006)

  19. Euzenat, J., Isaac, A., Meilicke, C., Shvaiko, P., Stuckenschmidt, H., Svab, O., Svatek, V., van Hage, W.R., Yatskevich, M.: Results of the ontology alignment evaluation initiative 2007. In: Proc. ISWC-2007 Workshop on Ontology Matching (2007)

  20. Euzenat, J., Ferrara, A., Hollink, L., Isaac, A., Joslyn, C., Malaise, V., Meilicke, C., Nikolov, A., Pane, J., Sabou, M., Scharffe, F., Shvaiko, P., Spiliopoulos, V., Stuckenschmidt, H., Svab-Zamazal, O., Svatek, V., Trojahn dos Santos, C., Vouros, G., Wang, S.: Results of the ontology alignment evaluation initiative 2009. In: Proc. ISWC-2009 Workshop on Ontology Matching (2009)

  21. Faber, W., Leone, N., Pfeifer, G.: Recursive aggregates in disjunctive logic programs: semantics and complexity. In: Proc. JELIA-2004, pp. 200–212. LNCS 3229. Springer, New York (2004)

    Google Scholar 

  22. Finzi, A., Lukasiewicz, T.: Structure-based causes and explanations in the independent choice logic. In: Proc. UAI-2003, pp. 225–232. Morgan Kaufmann, San Mateo (2003)

    Google Scholar 

  23. Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9(3/4), 365–386 (1991)

    Article  Google Scholar 

  24. 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: Proc. JELIA-2002, pp. 86–97. LNCS 2424. Springer, New York (2002)

    Google Scholar 

  25. Grosof, B.N., Horrocks, I., Volz, R., Decker, S.: Description logic programs: combining logic programs with description logics. In: Proc. WWW-2003, pp. 48–57. ACM Press, New York (2003)

    Chapter  Google Scholar 

  26. Hu, W., Qu, Y., Cheng, G.: Matching large ontologies: a divide-and-conquer approach. Data Knowl. Eng. 67(1), 140–160 (2008)

    Article  Google Scholar 

  27. Hustadt, U., Motik, B., Sattler, U.: Data complexity of reasoning in very expressive description logics. In: Proc. IJCAI-2005, pp. 466–471 (2005)

  28. Kifer, M., Lausen, G., Wu, J.: Logical foundations of object-oriented and frame-based languages. J. ACM 42(4), 741–843 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  29. Knorr, M., Alferes, J.J., Hitzler, P.: A coherent well-founded model for hybrid MKNF knowledge bases. In: Proc. ECAI-2008, pp. 99–103. Frontiers in Artificial Intelligence and Applications 178. IOS Press, Amsterdam (2008)

    Google Scholar 

  30. Koller, D., Levy, A.Y., Pfeffer, A.: P-CLASSIC: a tractable probabilistic description logic. In: Proc. AAAI-2007, pp. 390–397. AAAI Press, Menlo Park (1997)

    Google Scholar 

  31. Lukasiewicz, T.: A novel combination of answer set programming with description logics for the Semantic Web. In: Proc. ESWC-2007, pp. 384–398. LNCS 4519. Springer, New York (2007)

    Google Scholar 

  32. Lukasiewicz, T.: Probabilistic description logic programs. Int. J. Approx. Reason. 45(2), 288–307 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  33. Lukasiewicz, T.: Tractable probabilistic description logic programs. In: Proc. SUM-2007, pp. 143–156. LNCS 4772. Springer, New York (2007)

    Google Scholar 

  34. Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Intell. 172(6/7), 852–883 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  35. Lukasiewicz, T.: A novel combination of answer set programming with description logics for the Semantic Web. IEEE Trans. Knowl. Data Eng. 22(11), 1577–1592 (2010)

    Article  Google Scholar 

  36. Lukasiewicz, T., Straccia, U.: Top-k retrieval in description logic programs under vagueness for the Semantic Web. In: Proc. SUM-2007, pp. 16–30. LNCS 4772. Springer, New York (2007)

    Google Scholar 

  37. Meilicke, C., Stuckenschmidt, H., Tamilin, A.: Repairing ontology mappings. In: Proc. AAAI-2007, pp. 1408–1413. AAAI Press, Menlo Park (2007)

    Google Scholar 

  38. Motik, B., Rosati, R.: A faithful integration of description logics with logic programming. In: Proc. IJCAI-2007, pp. 477–482. AAAI Press/IJCAI (2007)

  39. Motik, B., Horrocks, I., Rosati, R., Sattler, U.: Can OWL and logic programming live together happily ever after? In: Proc. ISWC-2006, pp. 501–514. LNCS 4273. Springer, New York (2006)

    Google Scholar 

  40. Nottelmann, H., Fuhr, N.: Adding probabilities and rules to OWL Lite subsets based on probabilistic Datalog. Int. J. Uncertain. Fuzziness Knowledge-Based Syst. 14(1), 17–42 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  41. Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Sem. 10, 133–173 (2008)

    Google Scholar 

  42. Poole, D.: The independent choice logic for modelling multiple agents under uncertainty. Artif. Intell. 94(1/2), 7–56 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  43. Predoiu, L.: Probabilistic models for the Semantic Web. In: Ma, Z., Wang, H. (eds.) The Semantic Web for Knowledge and Data Management: Technologies and Practices, pp. 74–105. Information Science Reference (2009)

  44. Predoiu, L., Stuckenschmidt, H.: A probabilistic framework for information integration and retrieval on the Semantic Web. In: Proc. InterDB-2007 Workshop on Database Interoperability (2007)

  45. Ritze, D., Meilicke, C., Svab-Zamazal, O., Stuckenschmidt, H.: A pattern-based ontology matching approach for detecting complex correspondences. In: Proc. ISWC-2009 Workshop on Ontology Matching (2009)

  46. Rosati, R.: On the decidability and complexity of integrating ontologies and rules. J. Web Sem. 3(1), 61–73 (2005)

    Article  Google Scholar 

  47. Rosati, R.: \(\mathcal{DL}{+}\mathit{log}\): tight integration of description logics and disjunctive Datalog. In: Proc. KR-2006, pp. 68–78. AAAI Press, Menlo Park (2006)

    Google Scholar 

  48. Scharffe, F., Fensel, D.: Correspondence patterns for ontology alignment. In: Proc. EKAW-2008, pp. 83–92. LNCS 5268. Springer, New York (2008)

    Google Scholar 

  49. Scharffe, F., de Bruijn, J., Foxvog, D.: Ontology mediation patterns library, V2. Deliverable D4.3.2, EU-IST Integrated Project (IP) IST-2003-506826 SEKT (2006)

  50. Serafini, L., Stuckenschmidt, H., Wache, H.: A formal investigation of mapping languages for terminological knowledge. In: Proc. IJCAI-2005, pp. 576–581 (2005)

  51. Straccia, U.: Towards top-k query answering in description logics: the case of DL-Lite. In: Proc. JELIA-2006, pp. 439–451. LNCS 4160. Springer, New York (2006)

    Google Scholar 

  52. van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, UK

    Thomas Lukasiewicz

  2. Institut für Technische und Betriebliche Informationssysteme, Universität Magdeburg, Magdeburg, Germany

    Livia Predoiu

  3. Institut für Informatik, Universität Mannheim, Mannheim, Germany

    Heiner Stuckenschmidt

Authors
  1. Thomas Lukasiewicz
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  2. Livia Predoiu
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  3. Heiner Stuckenschmidt
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Corresponding author

Correspondence to Thomas Lukasiewicz.

Additional information

This article is a significantly extended and revised version of two papers that appeared in Proc. URSW-2007 [2] and Proc. FoIKS-2008 [3].

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Lukasiewicz, T., Predoiu, L. & Stuckenschmidt, H. Tightly integrated probabilistic description logic programs for representing ontology mappings. Ann Math Artif Intell 63, 385–425 (2011). https://doi.org/10.1007/s10472-012-9280-3

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