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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Baral, C., Subrahmanian, V.S.: Dualities between alternative semantics for logic programming and nonmonotonic reasoning. J. Autom. Reasoning 10(3), 399–420 (1993)
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)
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)
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)
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)
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)
Castano, S., Ferrara, A., Messa, G.: ISLab HMatch Results for OAEI 2006. In: Proc. International Workshop on Ontology Matching (2006)
da Costa, P.C.G.: Bayesian semantics for the Semantic Web. Doctoral dissertation, George Mason University, Fairfax, VA, USA (2005)
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)
Dantsin, E., Eiter, T., Gottlob, G., Voronkov, A.: Complexity and expressive power of logic programming. ACM Comput. Surv. 33(3), 374–425 (2001)
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)
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)
Drabent, W., Małuszyński, J.: Well-founded semantics for hybrid rules. In: Proc. RR-2007, pp. 1–15. LNCS 4524. Springer, New York (2007)
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)
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)
Euzenat, J., Shvaiko, P.: Ontology Matching. Springer, Heidelberg (2007)
Euzenat, J., Stuckenschmidt, H., Yatskevich, M.: Introduction to the ontology alignment evaluation 2005. In: Proc. K-CAP-2005 Workshop on Integrating Ontologies (2005)
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)
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)
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)
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)
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)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9(3/4), 365–386 (1991)
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)
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)
Hu, W., Qu, Y., Cheng, G.: Matching large ontologies: a divide-and-conquer approach. Data Knowl. Eng. 67(1), 140–160 (2008)
Hustadt, U., Motik, B., Sattler, U.: Data complexity of reasoning in very expressive description logics. In: Proc. IJCAI-2005, pp. 466–471 (2005)
Kifer, M., Lausen, G., Wu, J.: Logical foundations of object-oriented and frame-based languages. J. ACM 42(4), 741–843 (1995)
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)
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)
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)
Lukasiewicz, T.: Probabilistic description logic programs. Int. J. Approx. Reason. 45(2), 288–307 (2007)
Lukasiewicz, T.: Tractable probabilistic description logic programs. In: Proc. SUM-2007, pp. 143–156. LNCS 4772. Springer, New York (2007)
Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Intell. 172(6/7), 852–883 (2008)
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)
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)
Meilicke, C., Stuckenschmidt, H., Tamilin, A.: Repairing ontology mappings. In: Proc. AAAI-2007, pp. 1408–1413. AAAI Press, Menlo Park (2007)
Motik, B., Rosati, R.: A faithful integration of description logics with logic programming. In: Proc. IJCAI-2007, pp. 477–482. AAAI Press/IJCAI (2007)
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)
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)
Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Sem. 10, 133–173 (2008)
Poole, D.: The independent choice logic for modelling multiple agents under uncertainty. Artif. Intell. 94(1/2), 7–56 (1997)
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)
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)
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)
Rosati, R.: On the decidability and complexity of integrating ontologies and rules. J. Web Sem. 3(1), 61–73 (2005)
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)
Scharffe, F., Fensel, D.: Correspondence patterns for ontology alignment. In: Proc. EKAW-2008, pp. 83–92. LNCS 5268. Springer, New York (2008)
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)
Serafini, L., Stuckenschmidt, H., Wache, H.: A formal investigation of mapping languages for terminological knowledge. In: Proc. IJCAI-2005, pp. 576–581 (2005)
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)
van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10472-012-9280-3
Keywords
- Description logics
- Ontologies
- Logic programs
- Description logic programs
- Ontology mappings
- Semantic Web
- Probabilistic logics
- Uncertainty
- Inconsistency
- Well-founded semantics
- Answer set semantics
- Data integration
- Databases