Abstract
Hybrid MKNF knowledge bases, originally based on the stable model semantics, is a mature method of combining rules and Description Logics (DLs). The well-founded semantics for such knowledge bases has been proposed subsequently for better efficiency of reasoning. However, integration of rules and DLs may give rise to inconsistencies, even if they are respectively consistent. Accordingly, reasoning systems based on the previous two semantics will break down. In this paper, we employ the four-valued logic proposed by Belnap, and present a paraconsistent semantics for Hybrid MKNF knowledge bases, which can detect inconsistencies and handle it effectively. Besides, we transform our proposed semantics to the stable model semantics via a linear transformation operator, which indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide a fixpoint algorithm for computing paraconsistent MKNF models.
This work is supported by the National Natural Science Foundation of China (No. 11071061) and National Basic Research Program of China (No. 2010CB334706). The last named author acknowledges support by the National Science Foundation under award 1017225 ”III: Small: TROn - Tractable Reasoning with Ontologies.”
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., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, Cambridge (2003)
Belnap, N.D.: A useful four-valued logic. Modern uses of multiple-valued logics, 7–73 (1977)
Berners-Lee, T., Hendler, J., Lassila, O.: The Semantic Web. Scientific American 284(5), 35–43 (2001)
Donini, F.M., Lenzerini, M., Nardi, D., Schaerf, A.: AL-log: Integrating Datalog and Description Logics. Journal of Intelligent Information Systems (JIIS) 10(3), 227–252 (1998)
Eiter, T., Ianni, G., Schindlauer, R., Tompits, H.: Effective Integration of Declarative Rules with External Evaluations for Semantic-Web Reasoning. In: Sure, Y., Domingue, J. (eds.) ESWC 2006. LNCS, vol. 4011, pp. 273–287. Springer, Heidelberg (2006)
Fitting, M.: First-Order Logic and Automated Theorem Proving, 2nd edn. Texts in Computer Science. Springer, Heidelberg (1996)
Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programming. In: Proceedings of the 5th International Conference and Symposium on Logic Programming (ICLP/SLP), pp. 1070–1080. MIT Press, Cambridge (1988)
Grosof, B.N., Horrocks, I., Volz, R., Decker, S.: Description Logic Programs: Combining Logic Programs with Description Logic. In: Proceedings of the 12th International World Wide Web Conference (WWW), pp. 48–57. ACM, New York (2003)
Haase, P., van Harmelen, F., Huang, Z., Stuckenschmidt, H., Sure, Y.: A framework for handling inconsistency in changing ontologies. In: Gil, Y., Motta, E., Benjamins, V.R., Musen, M.A. (eds.) ISWC 2005. LNCS, vol. 3729, pp. 353–367. Springer, Heidelberg (2005)
Hitzler, P., Krötzsch, M., Parsia, B., Patel-Schneider, P.F., Rudolph, S. (eds.): OWL 2 Web Ontology Language: Primer. W3C Recommendation (October 27, 2009), http://www.w3.org/TR/owl2-primer/
Hitzler, P., Krötzsch, M., Rudolph, S.: Foundations of Semantic Web Technologies. Chapman & Hall/CRC (2009)
Knorr, M., Alferes, J.J., Hitzler, P.: A Coherent Well-founded Model for Hybrid MKNF Knowledge Bases. In: Ghallab, M., Spyropoulos, C.D., Fakotakis, N., Avouris, N.M. (eds.) Proceedings of the 18th European Conference on Artificial Intelligence (ECAI 2008), vol. 178, pp. 99–103. IOS Press, Patras (2008)
Knorr, M., Alferes, J., Hitzler, P.: Local closed-world reasoning with description logics under the well-founded semantics. Artificial Intelligence 175(9–10), 1528–1554 (2011)
Krisnadhi, A., Maier, F., Hitzler, P.: OWL and Rules. In: Reasoning Web 2011. LNCS, Springer, Heidelberg ( to appear 2011)
Krötzsch, M., Maier, F., Krisnadhi, A.A., Hitzler, P.: A better uncle for OWL: Nominal schemas for integrating rules and ontologies. In: Sadagopan, S., Ramamritham, K., Kumar, A., Ravindra, M., Bertino, E., Kumar, R. (eds.) Proceedings of the 20th International World Wide Web Conference, WWW 2011, Hyderabad, India, March/April 2011, pp. 645–654. ACM, New York (2011)
Levy, A.Y., Rousset, M.-C.: Combining Horn Rules and Description Logics in CARIN. Artifician Intelligence 104(1-2), 165–209 (1998)
Lifschitz, V.: Nonmonotonic Databases and Epistemic Queries. In: Mylopoulos, J., Reiter, R. (eds.) Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI 1991), pp. 381–386. Morgan Kaufmann Publishers, San Francisco (1991)
Ma, Y., Hitzler, P., Lin, Z.: Algorithms for paraconsistent reasoning with OWL. In: Franconi, E., Kifer, M., May, W. (eds.) ESWC 2007. LNCS, vol. 4519, pp. 399–413. Springer, Heidelberg (2007)
Motik, B., Rosati, R.: Reconciling Description Logics and Rules. Journal of the ACM 57(5), 1–61 (2010)
Motik, B., Sattler, U., Studer, R.: Query Answering for OWL-DL with rules. Journal of Web Semantics 3(1), 41–60 (2005)
Patel-Schneider, P.F.: A four-valued semantics for terminological logics. Artificial Intelligence 38, 319–351 (1989)
Rosati, R.: DL+log: Tight Integration of Description Logics and Disjunctive Datalog. In: Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning (KR), pp. 68–78. AAAI Press, Menlo Park (2006)
Sakama, C., Inoue, K.: Paraconsistent Stable Semantics for extended disjunctive programs. Journal of Logic and Computation 5, 265–285 (1995)
Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: Gottlob, G., Walsh, T. (eds.) Proceedings of the 18th International Conference on Artificial Intelligence (IJCAI 2003), pp. 355–362. Morgan Kaufmann Publishers, San Francisco (2003)
Van Gelder, A., Ross, K., Schlipf, J.S.: The Well-Founded Semantics for General Logic Programs. Journal of the ACM 38(3), 620–650 (1991)
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 21, 2004), http://www.w3.org/Submission/SWRL/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Huang, S., Li, Q., Hitzler, P. (2011). Paraconsistent Semantics for Hybrid MKNF Knowledge Bases. In: Rudolph, S., Gutierrez, C. (eds) Web Reasoning and Rule Systems. RR 2011. Lecture Notes in Computer Science, vol 6902. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23580-1_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-23580-1_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23579-5
Online ISBN: 978-3-642-23580-1
eBook Packages: Computer ScienceComputer Science (R0)