Journal of Automated Reasoning

, Volume 53, Issue 4, pp 351–405 | Cite as

Reasoning with Nominal Schemas through Absorption

  • Andreas Steigmiller
  • Birte Glimm
  • Thorsten Liebig
Article

Abstract

Nominal schemas have recently been introduced as a new approach for the integration of DL-safe rules into the Description Logic framework. The efficient processing of knowledge bases with nominal schemas remains, however, challenging. We address this by extending the well-known optimisation of absorption as well as the standard tableau calculus to directly handle the (absorbed) nominal schema axioms. We implement the resulting extension of standard tableau calculi in the novel reasoning system Konclude and present further optimisations. In our empirical evaluation, we show the effect of these optimisations and we find that the proposed nominal schema handling performs well even when compared to (hyper)tableau systems with dedicated rule support.

Keywords

Description logics Nominal schemas Tableau theorem proving Absorption Implementation and optimisation techniques 

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References

  1. 1.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications, 2nd edn. Cambridge University Press (2007)Google Scholar
  2. 2.
    Baader, F., Hollunder, B., Nebel, B., Profitlich, H.J., Franconi, E.: An empirical analysis of optimization techniques for terminological representation systems. J. Appl. Intell. 4(2), 109–132 (1994)CrossRefGoogle Scholar
  3. 3.
    Blackburn, P., Tzakova, M.: Hybridizing concept languages. Ann. Math. Artif. Intell. 24(1–4), 23–49 (1998)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Demri, S., Nivelle, H.: Deciding regular grammar logics with converse through first-order logic. J. Logic Lang. Inf. 14(3), 289–329 (2005)CrossRefMATHGoogle Scholar
  5. 5.
    Forgy, C.L.: Rete: A fast algorithm for the many pattern/many object pattern match problem. Artif. Int. 19(1), 17–37 (1982)CrossRefGoogle Scholar
  6. 6.
    Glimm, B., Horrocks, I., Motik, B., Shearer, R., Stoilos, G.: A novel approach to ontology classification. J. Web Semant. Sci. Serv. Agents World Wide Web 14, 84–101 (2012)CrossRefGoogle Scholar
  7. 7.
    Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\mathcal {SROIQ}\). In: Proceedings 10th International Conference on Principles of Knowledge Representation and Reasoning (KR’06), pp. 57–67. AAAI Press (2006)Google Scholar
  8. 8.
    Horrocks, I., Patel-Schneider, P.F., Boley, H., Tabet, S., Grosof, B.N., Dean, M.: SWRL: A Semantic Web Rule Language. W3C Member Submission. Available at http://www.w3.org/Submission/SWRL/ (2004)
  9. 9.
    Horrocks, I., Sattler, U.: A description logic with transitive and inverse roles and role hierarchies. J. Logic Comput. 9(3), 385–410 (1999)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Horrocks, I., Sattler, U.: A tableau decision procedure for \(\mathcal {SHOIQ}\). J. Autom. Reason. 39(3), 249–276 (2007)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Horrocks, I., Sattler, U., Tobies, S.: Reasoning with individuals for the description logic \(\mathcal {SHIQ}\). In: McAllester D.A., (ed.) Proceedings 17th International Conference on Automated Deduction (CADE’00), LNCS, vol. 1831, pp. 482–496. Springer (2000)Google Scholar
  12. 12.
    Horrocks, I., Tobies, S.: Reasoning with axioms: Theory and practice. In: Proceedings 7th International Conference on Principles of Knowledge Representation and Reasoning (KR’00), pp. 285–296. Morgan Kaufmann (2000)Google Scholar
  13. 13.
    Hudek, A.K., Weddell, G.E.: Binary absorption in tableaux-based reasoning for description logics. In: Proceedings 19th International Workshop on Description Logics (DL’06), vol. 189. CEUR (2006)Google Scholar
  14. 14.
    Kazakov, Y: \(\mathcal {RIQ}\) and \(\mathcal {SROIQ}\) are harder than \(\mathcal {SHOIQ}\). In: Brewka, G., Lang, J. (eds.) Proceedings 11th International Conference on Principles of Knowledge Representation and Reasoning (KR’08), pp. 274–284. AAAI Press (2008)Google Scholar
  15. 15.
    Kifer, M., Boley, H. (eds.): RIF Overview. W3C Working Group Note (2010). Available at http://www.w3.org/TR/rif-overview/. Accessed 20 June 2010
  16. 16.
    Krisnadhi, A., Hitzler, P.: A tableau algorithm for description logics with nominal schema. In: Proceedings 6th International Conference on Web Reasoning and Rule Systems (RR’12), LNCS, vol. 7497, pp. 234–237 (2012)Google Scholar
  17. 17.
    Krötzsch, M., Maier, F., Krisnadhi, A., Hitzler, P.: A better uncle for OWL: Nominal schemas for integrating rules and ontologies. In: Proceedings 20th International Conference on World Wide Web (WWW’11), pp. 645–654. ACM (2011)Google Scholar
  18. 18.
    Krötzsch, M., Rudolph, S.: Nominal schemas in description logics: Complexities clarified. In: Proceedings 14th International Conference on Principles of Knowledge Representation and Reasoning (KR’14). AAAI Press. Accepted, http://korrekt.org/page/Nominal_Schemas_in_Description_Logics:_Complexities_Clarified (2014)
  19. 19.
    Liang, S., Fodor, P., Wan, H., Kifer, M.: Openrulebench: an analysis of the performance of rule engines. In: Proceedings 18th International Conference on World wide web (WWW’09), pp. 601–610. ACM, New York (2009)Google Scholar
  20. 20.
    Ma, L., Yang, Y., Qiu, Z., Xie, G., Pan, Y., Liu, S.: Towards a complete OWL ontology benchmark. In: Proceedings 3rd European Semantic Web Conference (ESWC’06), LNCS, vol. 4011, pp. 125–139. Springer (2006)Google Scholar
  21. 21.
    Martínez, D.C., Wang, C., Hitzler, P.: Towards an efficient algorithm to reason over description logics extended with nominal schemas. In: Proceedings 7th International Conference on Web Reasoning and Rule Systems (RR’13), LNCS, vol. 7994, pp. 65–79. Springer (2013)Google Scholar
  22. 22.
    Motik, B., Shearer, R., Horrocks, I.: Hypertableau reasoning for description logics. J. Artif. Intell. Res. 36, 165–228 (2009)MATHMathSciNetGoogle Scholar
  23. 23.
    Simančík, F.: Elimination of complex RIAs without automata. In: Proceedings 25th International Workshop on Description Logics (DL’12), vol. 846. CEUR (2012)Google Scholar
  24. 24.
    Sirin, E., Parsia, B., Cuenca Grau, B., Kalyanpur, A., Katz, Y.: Pellet: A practical OWL-DL reasoner. J. Web Semant. 5(2), 51–53 (2007)CrossRefGoogle Scholar
  25. 25.
    Steigmiller, A., Glimm, B., Liebig, T.: Extending absorption to nominal schemas. In: Proceedings 26th International Workshop on Description Logics (DL’13), vol. 1014. CEUR (2013)Google Scholar
  26. 26.
    Steigmiller, A., Glimm, B., Liebig, T.: Nominal schema absorption. In: Proceedings 23rd International Joint Conference on Artificial Intelligence (IJCAI’13), pp. 1104–1110. AAAI Press/The MIT Press (2013)Google Scholar
  27. 27.
    Steigmiller, A., Glimm, B., Liebig, T.: Optimised absorption for expressive description logics. In: Proceedings 27th International Workshop on Description Logics (DL’14). Accepted (2014)Google Scholar
  28. 28.
    Steigmiller, A., Liebig, T., Glimm, B.: Extended caching, backjumping and merging for expressive description logics. In: Proceedings 6th International Joint Conference on Automated Reasoning (IJCAR’12), LNCS, vol. 7364, pp. 514–529. Springer (2012)Google Scholar
  29. 29.
    Steigmiller, A., Liebig, T., Glimm, B.: Konclude: System description. J. Web Semant. Accepted (2014)Google Scholar
  30. 30.
    Tsarkov, D., Horrocks, I.: Efficient reasoning with range and domain constraints. In: Proceedings 17th International Workshop on Description Logics (DL’04), vol. 104. CEUR (2004)Google Scholar
  31. 31.
    Tsarkov, D., Horrocks, I., Patel-Schneider, P.F.: Optimizing terminological reasoning for expressive description logics. J. Autom. Reas. 39, 277–316 (2007)CrossRefMATHMathSciNetGoogle Scholar
  32. 32.
    W3C OWL Working Group: OWL 2 Web Ontology Language: Document Overview. W3C Recommendation (2009). Available at http://www.w3.org/TR/owl2-overview/. Accessed 27 Oct 2009
  33. 33.
    Wang, C., Hitzler, P.: A resolution procedure for description logics with nominal schemas. In: Proceedings 2nd Joint International Semantic Technology Conf. (JIST’12), LNCS, vol. 7774, pp. 1–16. Springer (2012)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Andreas Steigmiller
    • 1
  • Birte Glimm
    • 1
  • Thorsten Liebig
    • 2
  1. 1.Institute of Artificial IntelligenceUniversity of UlmUlmGermany
  2. 2.derivo GmbHUlmGermany

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