Local Closed World Semantics: Grounded Circumscription for OWL

  • Kunal Sengupta
  • Adila Alfa Krisnadhi
  • Pascal Hitzler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7031)

Abstract

We present a new approach to adding closed world reasoning to the Web Ontology Language OWL. It transcends previous work on circumscriptive description logics which had the drawback of yielding an undecidable logic unless severe restrictions were imposed. In particular, it was not possible, in general, to apply local closure to roles.

In this paper, we provide a new approach, called grounded circumscription, which is applicable to \(\mathcal{SROIQ}\) and other description logics around OWL without these restrictions. We show that the resulting language is decidable, and we derive an upper complexity bound. We also provide a decision procedure in the form of a tableaux algorithm.

References

  1. 1.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.: The Description Logic Handbook: Theory, Implementation, and Applications, 2nd edn. Cambridge University Press (2007)Google Scholar
  2. 2.
    Bonatti, P.A., Lutz, C., Wolter, F.: Expressive Non-Monotonic Description Logics Based on Circumscription. In: Proc. of the 10th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 2006), pp. 400–410. AAAI Press (2009)Google Scholar
  3. 3.
    Bonatti, P.A., Lutz, C., Wolter, F.: The Complexity of Circumscription in Description Logic. Journal of Artificial Intelligence Research 35, 717–773 (2009)MathSciNetMATHGoogle Scholar
  4. 4.
    Carral Martínez, D., Krisnadhi, A., Maier, F., Sengupta, K., Hitzler, P.: Reconciling OWL and rules. Tech. rep., Kno.e.sis Center, Wright State University, Dayton, Ohio, USA (2011), http://www.pascal-hitzler.de/
  5. 5.
    Donini, F.M., Nardi, D., Rosati, R.: Description Logics of Minimal Knowledge and Negation as Failure. ACM Trans. on Computational Logic (TOCL) 3(2), 177–225 (2002)CrossRefGoogle Scholar
  6. 6.
    Grimm, S., Hitzler, P.: Semantic Matchmaking of Web Resources with Local Closed-World Reasoning. International Journal of Electronic Commerce 12(2), 89–126 (2007)CrossRefGoogle Scholar
  7. 7.
    Grimm, S., Hitzler, P.: A Preferential Tableaux Calculus for Circumscriptive \({\mathcal ALCO}\). In: Polleres, A., Swift, T. (eds.) RR 2009. LNCS, vol. 5837, pp. 40–54. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    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/
  9. 9.
    Hitzler, P., Krötzsch, M., Rudolph, S.: Foundations of Semantic Web Technologies. Chapman & Hall/CRC (2009)Google Scholar
  10. 10.
    Hitzler, P., Seda, A.K.: Mathematical Aspects of Logic Programming Semantics. CRC Press (2010)Google Scholar
  11. 11.
    Horrocks, I., Sattler, U.: Ontology reasoning in the SHOQ(D) description logic. In: Proc. IJCAI-2001, pp. 199–204 (2001)Google Scholar
  12. 12.
    Knorr, M., Alferes, J.J., Hitzler, P.: Local Closed-World Reasoning with Description Logics under the Well-founded Semantics. Artificial Intelligence 175(9-10), 1528–1554 (2011)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    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. Frontiers in Artificial Intelligence and Applications, Patras, Greece, July 21-25, vol. 178, pp. 99–103. IOS Press, Amsterdam (2008)Google Scholar
  14. 14.
    Krisnadhi, A., Sengupta, K., Hitzler, P.: Local closed world semantics: Keep it simple, stupid! In: Rosati, R., Rudolph, S., Zakharyaschev, M. (eds.) 2011 International Workshop on Description Logics. CEUR Workshop Proceedings, vol. 745. CEUR-WS.org (2011)Google Scholar
  15. 15.
    Krisnadhi, A., Maier, F., Hitzler, P.: OWL and Rules. In: Polleres, A., d’Amato, C., Arenas, M., Handschuh, S., Kroner, P., Ossowski, S., Patel-Schneider, P. (eds.) Reasoning Web 2011. LNCS, vol. 6848, pp. 382–415. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  16. 16.
    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.P., Bertino, E., Kumar, R. (eds.) Proceedings of the 20th International World Wide Web Conference, WWW 2011, Hyderabad, India, pp. 645–654. ACM, New York (2011)Google Scholar
  17. 17.
    Krötzsch, M., Rudolph, S., Hitzler, P.: ELP: Tractable Rules for OWL 2. In: Sheth, A.P., Staab, S., Dean, M., Paolucci, M., Maynard, D., Finin, T., Thirunarayan, K. (eds.) ISWC 2008. LNCS, vol. 5318, pp. 649–664. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Makinson, D.: Bridges from Classical to Nonomonotonic Logic, Texts in Computing, vol. 5. King’s College Publications (2005)Google Scholar
  19. 19.
    McCarthy, J.: Circumscription – A Form of Non-Monotonic Reasoning. Artificial Intelligence 13(1-2), 27–39 (1980)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Moore, R.: Possible-worlds Semantics for Autoepistemic Logic. In: Proceedings of the 1984 Non-monotonic Reasoning Workshop. AAAI, Menlo Park (1984)Google Scholar
  21. 21.
    Motik, B., Rosati, R.: Reconciling Description Logics and Rules. Journal of the ACM 57(5), 1–62 (2010)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Motik, B., Sattler, U., Studer, R.: Query Answering for OWL-DL with Rules. Journal of Web Semantics 3, 41–60 (2005)CrossRefGoogle Scholar
  23. 23.
    Patel, C., Cimino, J.J., Dolby, J., Fokoue, A., Kalyanpur, A., Kershenbaum, A., Ma, L., Schonberg, E., Srinivas, K.: Matching Patient Records to Clinical Trials Using Ontologies. In: Aberer, K., Choi, K.S., Noy, N.F., Allemang, D., Lee, K.I., Nixon, L.J.B., Golbeck, J., Mika, P., Maynard, D., Mizoguchi, R., Schreiber, G., Cudré-Mauroux, P. (eds.) ASWC 2007 and ISWC 2007. LNCS, vol. 4825, pp. 816–829. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  24. 24.
    Reiter, R.: A Logic for Default Reasoning. Artificial Intelligence 13, 81–132 (1980)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Rudolph, S., Krötzsch, M., Hitzler, P.: Cheap Boolean Role Constructors for Description Logics. In: Hölldobler, S., Lutz, C., Wansing, H. (eds.) JELIA 2008. LNCS (LNAI), vol. 5293, pp. 362–374. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  26. 26.
    Rudolph, S., Krötzsch, M., Hitzler, P.: All Elephants are Bigger than All Mice. In: Baader, F., Lutz, C., Motik, B. (eds.) Proceedings of the 21st International Workshop on Description Logics (DL 2008), Dresden, Germany, May 13-16. CEUR Workshop Proceedings, vol. 353 (2008)Google Scholar
  27. 27.
    Seylan, I., Franconi, E., de Bruijn, J.: Effective query rewriting with ontologies over DBoxes. In: Boutilier, C. (ed.) IJCAI 2009, Proceedings of the 21st International Joint Conference on Artificial Intelligence, Pasadena, California, USA, July 11-17, pp. 923–925 (2009)Google Scholar
  28. 28.
    Tobies, S.: Complexity Results and Practical Algorithms for Logics in Knowledge Representation. Ph.D. thesis, RWTH Aachen, Germany (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kunal Sengupta
    • 1
  • Adila Alfa Krisnadhi
    • 1
  • Pascal Hitzler
    • 1
  1. 1.Wright State UniversityDaytonUSA

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