\({\mathcal{ALC}_\mathcal{ALC}}\): A Context Description Logic

  • Szymon Klarman
  • Víctor Gutiérrez-Basulto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6341)

Abstract

We develop a novel description logic (DL) for representing and reasoning with contextual knowledge. Our approach descends from McCarthy’s tradition of treating contexts as formal objects over which one can quantify and express first-order properties. As a foundation we consider several common product-like combinations of DLs with multimodal logics and adopt the prominent \((\mathbf{K}_n)_\mathcal{ALC}\). We then extend it with a second sort of vocabulary for describing contexts, i.e., objects of the second dimension. In this way, we obtain a two-sorted, two-dimensional combination of a pair of DLs \(\mathcal{ALC}\), called \({\mathcal{ALC}_\mathcal{ALC}}\). As our main technical result, we show that the satisfiability problem in this logic, as well as in its proper fragment \((\mathbf{K}_n)_\mathcal{ALC}\) with global TBoxes and local roles, is 2ExpTime-complete. Hence, the surprising conclusion is that the significant increase in the expressiveness of \({\mathcal{ALC}_\mathcal{ALC}}\) due to adding the vocabulary comes for no substantial price in terms of its worst-case complexity.

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References

  1. 1.
    McCarthy, J.: Generality in artificial intelligence. Communications of the ACM 30, 1030–1035 (1987)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Buvač, S., Mason, I.A.: Propositional logic of context. In: Proceedings of the Eleventh National Conference on Artificial Intelligence, pp. 412–419 (1993)Google Scholar
  3. 3.
    Buvač, S., Buvac, V., Mason, I.A.: Metamathematics of contexts. Fundamenta Informaticae 23, 412–419Google Scholar
  4. 4.
    Buvač, S.: Quantificational logic of context. In: Proceedings of the Eleventh National Conference on Artificial Intelligence, pp. 412–419 (1996)Google Scholar
  5. 5.
    McCarthy, J.: Notes on formalizing context. In: Proc. of International Joint Conference on Artificial Intelligence, IJCAI 1993, pp. 555–560. Morgan Kaufmann, San Francisco (1993)Google Scholar
  6. 6.
    Guha, R.: Contexts: a formalization and some applications. PhD thesis, Stanford University (1991)Google Scholar
  7. 7.
    Guha, R., Mccool, R., Fikes, R.: Contexts for the semantic web. In: McIlraith, S.A., Plexousakis, D., van Harmelen, F. (eds.) ISWC 2004. LNCS, vol. 3298, pp. 32–46. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Nossum, R.: A decidable multi-modal logic of context. Journal of Applied Logic 1(1-2), 119–133 (2003)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Baader, F., Calvanese, D., Mcguinness, D.L., Nardi, D., Patel-Schneider, P.F.: The description logic handbook: theory, implementation, and applications. Cambridge University Press, Cambridge (2003)MATHGoogle Scholar
  10. 10.
    Borgida, A., Serafini, L.: Distributed description logics: Assimilating information from peer sources. Journal of Data Semantics 1, 2003 (2003)Google Scholar
  11. 11.
    Cuenca Grau, B., Kutz, O.: Modular ontology languages revisited. In: Proc. of the Workshop on Semantic Web for Collaborative Knowledge Acquisition (2007)Google Scholar
  12. 12.
    Goczyla, K., Waloszek, W., Waloszek, A.: Contextualization of a DL knowledge base. In: The Proceedings of the International Workshop on Description Logics, DL 2007 (2007)Google Scholar
  13. 13.
    Grossi, D.: Desigining Invisible Handcuffs. Formal Investigations in Institutions and Organizations for Multi-Agent Systems. PhD thesis, Utrecht University (2007)Google Scholar
  14. 14.
    Lutz, C., Wolter, F., Zakharyaschev, M.: Temporal description logics: A survey. In: Proceedings of the Fourteenth International Symposium on Temporal Representation and Reasoning. IEEE Computer Society Press, Los Alamitos (2008)Google Scholar
  15. 15.
    Artale, A., Lutz, C., Toman, D.: A description logic of change. In: Veloso, M. (ed.) Proceedings of IJCAI 2007, pp. 218–223 (2007)Google Scholar
  16. 16.
    Artale, A., Kontchakov, R., Lutz, C., Wolter, F., Zakharyaschev, M.: Temporalising tractable description logics. In: Proceedings of the Fourteenth International Symposium on Temporal Representation and Reasoning (2007)Google Scholar
  17. 17.
    Wolter, F., Zakharyaschev, M.: Multi-dimensional description logics. In: IJCAI 1999: Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, San Francisco, CA, USA, pp. 104–109 (1999)Google Scholar
  18. 18.
    Baader, F., Laux, A.: Terminological logics with modal operators. In: Mellish, C. (ed.) Proceedings of the 14th International Joint Conference on Artificial Intelligence, Montréal, Canada, pp. 808–814. Morgan Kaufmann, San Francisco (1995)Google Scholar
  19. 19.
    Kurucz, A., Wolter, F., Zakharyaschev, M., Gabbay, D.M.: Many-Dimensional Modal Logics: Theory and Applications. Studies in Logic and the Foundations of Mathematics, vol. 148. Elsevier, Amsterdam (2003)MATHGoogle Scholar
  20. 20.
    Wolter, F., Zakharyaschev, M.: Satisfiability problem in description logics with modal operators. In: Proceedings of the Sixth Conference on Principles of Knowledge Representation and Reasoning, pp. 512–523. Morgan Kaufman, San Francisco (1998)Google Scholar
  21. 21.
    Klarman, S., Gutiérrez-Basulto, V.: \(\mathcal{ALC}_\mathcal{ALC}\): a context description logic. Technical report, Vrije Universiteit Amsterdam (2010), http://klarman.synthasite.com/resources/JELIA2010TechRep.pdf
  22. 22.
    Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. J. ACM 28(1), 114–133 (1981)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Szymon Klarman
    • 1
  • Víctor Gutiérrez-Basulto
    • 2
  1. 1.Department of Computer ScienceVrije UniversiteitAmsterdam
  2. 2.Department of Computer ScienceUniversität BremenGermany

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