A Resolution Procedure for Description Logics with Nominal Schemas

  • Cong Wang
  • Pascal Hitzler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7774)

Abstract

We present a polynomial resolution-based decision procedure for the recently introduced description logic \(\mathcal{ELHOV}_{n}(\sqcap)\) , which features nominal schemas as new language construct. Our algorithm is based on ordered resolution and positive superposition, together with a lifting lemma. In contrast to previous work on resolution for description logics, we have to overcome the fact that \(\mathcal{ELHOV}_{n}(\sqcap)\) does not allow for a normalization resulting in clauses of globally limited size.

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References

  1. 1.
    Baader, F., Brandt, S., Lutz, C.: Pushing the el envelope. In: Kaelbling, L.P., Saffiotti, A. (eds.) IJCAI, pp. 364–369. Professional Book Center (2005)Google Scholar
  2. 2.
    Bachmair, L., Ganzinger, H.: Ordered chaining for total orderings. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 435–450. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  3. 3.
    Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 19–99. Elsevier, MIT Press (2001)Google Scholar
  4. 4.
    Boley, H., Hallmark, G., Kifer, M., Paschke, A., Polleres, A., Reynolds, D. (eds.): RIF Core Dialect. W3C Recommendation (June 22, 2010), http://www.w3.org/TR/rif-core/
  5. 5.
    Horrocks, I., Patel-Schneider, P., Boley, H., Tabet, S., Grosof, B., Dean, M.: SWRL: A Semantic Web Rule Language. W3C Member Submission (May 21, 2004), http://www.w3.org/Submission/SWRL/
  6. 6.
    Hustadt, U., Motik, B., Sattler, U.: Reasoning for Description Logics around SHIQ in a Resolution Framework. Tech. Rep. 3-8-04/04, FZI, Germany (2004)Google Scholar
  7. 7.
    Kazakov, Y.: Saturation-based decision procedures for extensions of the guarded fragment. Ph.D. thesis, Saarländische Universitäts- und Landesbibliothek, Postfach 151141, 66041 Saarbrücken (2005), http://scidok.sulb.uni-saarland.de/volltexte/2007/1137
  8. 8.
    Kazakov, Y., Krötzsch, M., Simančík, F.: Practical reasoning with nominals in the \(\mathcal{EL}\) family of description logics. In: Brewka, G., Eiter, T., McIlraith, S.A. (eds.) Proceedings of the 13th International Conference on Principles of Knowledge Representation and Reasoning (KR 2012), pp. 264–274. AAAI Press (2012)Google Scholar
  9. 9.
    Kazakov, Y., Krötzsch, M., Simančík, F.: Concurrent classification of el ontologies (2011) (to appear)Google Scholar
  10. 10.
    Kazakov, Y., Motik, B.: A resolution-based decision procedure for \(\mathcal{SHOIQ}\). In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 662–677. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Knorr, M., Alferes, J.J., Hitzler, P.: Local closed world reasoning with description logics under the well-founded semantics. Artif. Intell. 175(9-10), 1528–1554 (2011)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Knorr, M., Martínez, D.C., Hitzler, P., Krisnadhi, A.A., Maier, F., Wang, C.: Recent advances in integrating owl and rules (technical communication). In: Krötzsch, Straccia (eds.) [18], pp. 225–228Google Scholar
  13. 13.
    Krisnadhi, A., Hitzler, P.: A tableau algorithm for description logics with nominal schema. In: Krötzsch, Straccia (eds.) [18], pp. 234–237Google Scholar
  14. 14.
    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
  15. 15.
    Krötzsch, M.: Efficient inferencing for OWL EL. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS (LNAI), vol. 6341, pp. 234–246. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Krötzsch, M., Maier, F., Krisnadhi, A., Hitzler, P.: A better uncle for owl: nominal schemas for integrating rules and ontologies. In: Srinivasan, S., Ramamritham, K., Kumar, A., Ravindra, M.P., Bertino, E., Kumar, R. (eds.) WWW, pp. 645–654. ACM (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.
    Krötzsch, M., Straccia, U. (eds.): RR 2012. LNCS, vol. 7497. Springer, Heidelberg (2012)MATHGoogle Scholar
  19. 19.
    Martinezi, D.C., Krisnadhi, A., Maier, F., Sengupta, K., Hitzler, P.: Reconciling owl and rules. Tech. rep. Kno.e.sis Center, Wright State University, Dayton, OH, U.S.A. (2011), http://www.pascal-hitzler.de/
  20. 20.
    Motik, B.: Reasoning in Description Logics using Resolution and Deductive Databases. Ph.D. thesis, Universität Karlsruhe (TH), Karlsruhe, Germany (January 2006)Google Scholar
  21. 21.
    Motik, B., Sattler, U., Studer, R.: Query answering for owl-dl with rules. In: McIlraith, S.A., Plexousakis, D., van Harmelen, F. (eds.) ISWC 2004. LNCS, vol. 3298, pp. 549–563. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  22. 22.
    Motik, B., Shearer, R., Horrocks, I.: Hypertableau reasoning for description logics. J. Artif. Intell. Res. (JAIR) 36, 165–228 (2009)Google Scholar
  23. 23.
    Dal Palù, A., Dovier, A., Pontelli, E., Rossi, G.: Answer set programming with constraints using lazy grounding. In: Hill, P.M., Warren, D.S. (eds.) ICLP 2009. LNCS, vol. 5649, pp. 115–129. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  24. 24.
    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
  25. 25.
    Simancik, F., Kazakov, Y., Horrocks, I.: Consequence-based reasoning beyond horn ontologies. In: Walsh, T. (ed.) IJCAI, pp. 1093–1098. IJCAI/AAAI (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Cong Wang
    • 1
  • Pascal Hitzler
    • 1
  1. 1.Kno.e.sis CenterWright State UniversityDaytonUSA

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