Skip to main content

A Resolution Procedure for Description Logics with Nominal Schemas

  • Conference paper
Semantic Technology (JIST 2012)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7774))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. Bachmair, L., Ganzinger, H.: Ordered chaining for total orderings. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 435–450. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  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. 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. 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. 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. 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. 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. Kazakov, Y., Krötzsch, M., Simančík, F.: Concurrent classification of el ontologies (2011) (to appear)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 225–228

    Google Scholar 

  13. Krisnadhi, A., Hitzler, P.: A tableau algorithm for description logics with nominal schema. In: Krötzsch, Straccia (eds.) [18], pp. 234–237

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  18. Krötzsch, M., Straccia, U. (eds.): RR 2012. LNCS, vol. 7497. Springer, Heidelberg (2012)

    MATH  Google Scholar 

  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. Motik, B.: Reasoning in Description Logics using Resolution and Deductive Databases. Ph.D. thesis, Universität Karlsruhe (TH), Karlsruhe, Germany (January 2006)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  22. Motik, B., Shearer, R., Horrocks, I.: Hypertableau reasoning for description logics. J. Artif. Intell. Res. (JAIR) 36, 165–228 (2009)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, C., Hitzler, P. (2013). A Resolution Procedure for Description Logics with Nominal Schemas. In: Takeda, H., Qu, Y., Mizoguchi, R., Kitamura, Y. (eds) Semantic Technology. JIST 2012. Lecture Notes in Computer Science, vol 7774. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37996-3_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-37996-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37995-6

  • Online ISBN: 978-3-642-37996-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics