Description Logics for Relative Terminologies

  • Szymon Klarman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6211)

Abstract

Context-sensitivity has been for long a subject of study in linguistics, logic and computer science. Recently the problem of reasoning with contextual knowledge has been picked up also by the Semantic Web community. In this paper we introduce a conservative extension to the Description Logic \(\mathcal{ALC}\) which supports representation of ontologies containing relative terms, such as ‘big’ or ‘tall’, whose meaning depends on the choice of a particular comparison class (context). We define the language and investigate its computational properties, including the specification of a tableau-based decision procedure and complexity bounds.

Keywords

Description Logic Comparison Class Context Operator Context Structure Translation Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Shapiro, S.: Vagueness in Context. Oxford University Press, Oxford (2006)CrossRefGoogle Scholar
  2. 2.
    Gaio, S.: Granular Models for Vague Predicates. In: Proceedings of the Fifth International Conference, FOIS 2008 (2008)Google Scholar
  3. 3.
    Bouquet, P., Giunchiglia, F., van Harmelen, F., Serafini, L., Stuckenschmidt, H.: C-OWL: Contextualizing ontologies. In: Fensel, D., Sycara, K.P., Mylopoulos, J. (eds.) ISWC 2003. LNCS, vol. 2870, pp. 164–179. Springer, Heidelberg (2003)Google Scholar
  4. 4.
    Benslimane, D., Arara, A., Falquet, G., Maamar, Z., Thiran, P., Gargouri, F.: Contextual ontologies: Motivations, challenges, and solutions. In: Proceedings of the Advances in Information Systems Conference, Izmir (2006)Google Scholar
  5. 5.
    Horrocks, I., Patel-Schneider, P.F., Harmelen, F.V.: From SHIQ and RDF to OWL: The making of a Web Ontology Language. Journal of Web Semantics 1 (2003)Google Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    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
  8. 8.
    Klarman, S.: Description logics for relative terminologies or why the biggest city is not a big thing. In: Icard, T. (ed.) Proc. of the ESSLLI 2009 Student Session (2009)Google Scholar
  9. 9.
    Klarman, S., Schlobach, S.: Relativizing concept descriptions to comparison classes. In: Description Logics. CEUR Workshop Proceedings, vol. 477. CEUR-WS.org (2009)Google Scholar
  10. 10.
    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
  11. 11.
    Third, A., Bennett, B., Mallenby, D.: Architecture for a grounded ontology of geographic information. In: Fonseca, F., Rodríguez, M.A., Levashkin, S. (eds.) GeoS 2007. LNCS, vol. 4853, pp. 36–50. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Baader, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69, 5–40 (2001)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Wolter, F., Zakharyaschev, M.: Multi-dimensional description logics. In: The Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, pp. 104–109 (1999)Google Scholar
  14. 14.
    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 (1998)Google Scholar
  15. 15.
    Giunchiglia, F., Ghidini, C.: Local models semantics, or contextual reasoning = locality + compatibility. Artificial Intelligence 127 (2001)Google Scholar
  16. 16.
    Grossi, D.: Desigining Invisible Handcuffs. Formal Investigations in Institutions and Organizations for Multi-Agent Systems. PhD thesis, Utrecht University (2007)Google Scholar
  17. 17.
    Goczyla, K., Waloszek, W., Waloszek, A.: Contextualization of a DL knowledge base. In: The Proc. of the Description Logics Workshop (2007)Google Scholar
  18. 18.
    McCarthy, J.: Notes on formalizing context, pp. 555–560. Morgan Kaufmann, San Francisco (1993)Google Scholar
  19. 19.
    Guha, R.V.: Contexts: A Formalization and Some Applications. PhD thesis, Stanford University (1995)Google Scholar
  20. 20.
    Buvac, S., Mason, I.A.: Propositional logic of context. In: Proc. of the 11th National Conference on Artificial Inteligence, pp. 412–419 (1993)Google Scholar
  21. 21.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library. Springer, Heidelberg (2007)Google Scholar
  22. 22.
    Balbiani, P., Ditmarsch, H., Herzig, A., Lima, T.: A tableau method for public announcement logics. In: Olivetti, N. (ed.) TABLEAUX 2007. LNCS (LNAI), vol. 4548, pp. 43–59. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  23. 23.
    Lutz, C.: Complexity and succinctness of public announcement logic. In: AAMAS’06: Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems, pp. 137–143. ACM, New York (2006)CrossRefGoogle Scholar
  24. 24.
    Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the semantic web. Web Semantics 6(4), 291–308 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Szymon Klarman
    • 1
  1. 1.Department of Computer ScienceVrije Universiteit AmsterdamAmsterdamThe Netherlands

Personalised recommendations