Abstract
Recently, the logics of minimal knowledge and negation as failure MKNF [12] was used to introduce hybrid MKNF knowledge bases [14], a powerful formalism for combining open and closed world reasoning for the Semantic Web. We present an extension based on a new three-valued framework including an alternating fixpoint, the well-founded MKNF model. This approach, the well-founded MKNF semantics, derives its name from the very close relation to the corresponding semantics known from logic programming. We show that the well-founded MKNF model is the least model among all (three-valued) MKNF models, thus soundly approximating also the two-valued MKNF models from [14]. Furthermore, its computation yields better complexity results (up to polynomial) than the original semantics where models usually have to be guessed.
This research was partly funded by the European Commission within the 6th Framework Programme projects REWERSE number 506779 (cf. http://rewerse.net/). Pascal Hitzler is supported by the German Federal Ministry of Education and Research (BMBF) under the SmartWeb project (grant 01 IMD01 B), and by the Deutsche Forschungsgemeinschaft (DFG) under the ReaSem project.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)
de Bruijn, J., Eiter, T., Polleres, A., Tompits, H.: Embedding non-ground logic programs into autoepistemic logic for knowledge-base combination. In: IJCAI 2007. Proceedings of the Twentieth International Joint Conference on Artificial Intelligence, Hyderabad, India, January 6–12, 2007, AAAI Press, Stanford, California, USA (2007)
Eiter, T., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with description logics for the semantic web. In: Dubois, D., Welty, C., Williams, M.-A. (eds.) KR 2004, pp. 141–151. AAAI Press, Stanford, California, USA (2004)
Eiter, T., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Well-founded semantics for description logic programs in the semantic web. In: Antoniou, G., Boley, H. (eds.) RuleML 2004. LNCS, vol. 3323, pp. 81–97. Springer, Heidelberg (2004)
Fitting, M.: The family of stable models. Journal of Logic Programming 17(2/3&4), 197–225 (1993)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R.A., Bowen, K.A. (eds.) ICLP, MIT Press, Cambridge (1988)
Grimm, S., Hitzler, P.: Semantic matchmaking of web resources with local closed-world reasoning. International Journal of e-Commerce (to appear)
Grimm, S., Motik, B., Preist, C.: Matching semantic service descriptions with local closed-world reasoning. In: Sure, Y., Domingue, J. (eds.) ESWC 2006. LNCS, vol. 4011, pp. 575–589. Springer, Heidelberg (2006)
Heymans, S., Nieuwenborgh, D.V., Vermeir, D.: Guarded open answer set programming. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 92–104. Springer, Heidelberg (2005)
Horrocks, I., Motik, B., 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. (eds.) ISWC 2006. LNCS, vol. 4273, pp. 501–514. Springer, Heidelberg (2006)
Knorr, M., Alferes, J.J., Hitzler, P.: A well-founded semantics for MKNF knowledge bases. In: Calvanese, D., Franconi, E., Haarslev, V., Lembo, D., Motik, B., Turhan, A.-Y., Tessaris, S. (eds.) Description Logics 2007, CEUR–WS, pp. 417–425 (2007)
Lifschitz, V.: Nonmonotonic databases and epistemic queries. In: IJCAI 1991, pp. 381–386 (1991)
Motik, B., Rosati, R.: Closing semantic web ontologies. Technical report, University of Manchester, UK (2006)
Motik, B., Rosati, R.: A faithful integration of description logics with logic programming. In: IJCAI 2007. Proceedings of the Twentieth International Joint Conference on Artificial Intelligence, Hyderabad, India, January 6–12, 2007, pp. 477–482. AAAI Press, Stanford, California, USA (2007)
Rosati, R.: Dl+Log: A tight integration of description logics and disjunctive datalog. In: Doherty, P., Mylopoulos, J., Welty, C. (eds.) KR 2006, AAAI Press, Stanford, California, USA (2006)
van Gelder, A.: The alternating fixpoint of logic programs with negation. In: Principles of Database Systems, pp. 1–10. ACM Press, New York (1989)
van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. Journal of the ACM 38(3), 620–650 (1991)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Knorr, M., Alferes, J.J., Hitzler, P. (2007). Towards Tractable Local Closed World Reasoning for the Semantic Web. In: Neves, J., Santos, M.F., Machado, J.M. (eds) Progress in Artificial Intelligence. EPIA 2007. Lecture Notes in Computer Science(), vol 4874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77002-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-77002-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77000-8
Online ISBN: 978-3-540-77002-2
eBook Packages: Computer ScienceComputer Science (R0)