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Reasoning with Nominal Schemas through Absorption

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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.

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References

  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)

  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)

    Article  Google Scholar 

  3. Blackburn, P., Tzakova, M.: Hybridizing concept languages. Ann. Math. Artif. Intell. 24(1–4), 23–49 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Demri, S., Nivelle, H.: Deciding regular grammar logics with converse through first-order logic. J. Logic Lang. Inf. 14(3), 289–329 (2005)

    Article  MATH  Google Scholar 

  5. Forgy, C.L.: Rete: A fast algorithm for the many pattern/many object pattern match problem. Artif. Int. 19(1), 17–37 (1982)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  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. Horrocks, I., Sattler, U.: A description logic with transitive and inverse roles and role hierarchies. J. Logic Comput. 9(3), 385–410 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Horrocks, I., Sattler, U.: A tableau decision procedure for \(\mathcal {SHOIQ}\). J. Autom. Reason. 39(3), 249–276 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  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)

  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)

  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)

  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. 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)

  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)

  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. 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)

  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)

  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)

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

    MATH  MathSciNet  Google Scholar 

  23. Simančík, F.: Elimination of complex RIAs without automata. In: Proceedings 25th International Workshop on Description Logics (DL’12), vol. 846. CEUR (2012)

  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)

    Article  Google Scholar 

  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)

  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)

  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)

  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)

  29. Steigmiller, A., Liebig, T., Glimm, B.: Konclude: System description. J. Web Semant. Accepted (2014)

  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)

  31. Tsarkov, D., Horrocks, I., Patel-Schneider, P.F.: Optimizing terminological reasoning for expressive description logics. J. Autom. Reas. 39, 277–316 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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)

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Authors and Affiliations

  1. Institute of Artificial Intelligence, University of Ulm, Ulm, Germany

    Andreas Steigmiller & Birte Glimm

  2. derivo GmbH, Ulm, Germany

    Thorsten Liebig

Authors
  1. Andreas Steigmiller
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  2. Birte Glimm
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  3. Thorsten Liebig
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Correspondence to Andreas Steigmiller.

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Steigmiller, A., Glimm, B. & Liebig, T. Reasoning with Nominal Schemas through Absorption. J Autom Reasoning 53, 351–405 (2014). https://doi.org/10.1007/s10817-014-9310-4

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  • DOI: https://doi.org/10.1007/s10817-014-9310-4

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