Merging Qualitative Constraint Networks Defined on Different Qualitative Formalisms

  • Jean-François Condotta
  • Souhila Kaci
  • Pierre Marquis
  • Nicolas Schwind
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5756)

Abstract

This paper addresses the problem of merging qualitative constraint networks (QCNs) defined on different qualitative formalisms. Our model is restricted to formalisms where the entities and the relationships between these entities are defined on the same domain. The method is an upstream step to a previous framework dealing with a set of QCNs defined on the same formalism. It consists of translating the input QCNs into a well-chosen common formalism. Two approaches are investigated: in the first one, each input QCN is translated to an equivalent QCN; in the second one, the QCNs are translated to approximations. These approaches take advantage of two dual notions that we introduce, the ones of refinement and abstraction between qualitative formalisms.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allen, J.-F.: An interval-based representation of temporal knowledge. In: Proc. of 7th the International Joint Conference on Artificial Intelligence (IJCAI), pp. 221–226 (1981)Google Scholar
  2. 2.
    Cholvy, L.: Reasoning about merging information. Handbook of Defeasible Reasoning and Uncertainty Management Systems 3, 233–263 (1998)MathSciNetMATHGoogle Scholar
  3. 3.
    Condotta, J.-F., Kaci, S., Marquis, P., Schwind, N.: Merging qualitative constraints networks using propositional logic. In: Proc. of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU), pp. 347–358 (2009)Google Scholar
  4. 4.
    Condotta, J.-F., Kaci, S., Schwind, N.: A Framework for Merging Qualitative Constraints Networks. In: Proc. of the 21th FLAIRS Conference, pp. 586–591 (2008)Google Scholar
  5. 5.
    Condotta, J.-F., Ligozat, G., Saade, M.: A qualitative algebra toolkit. In: Proc. of the 2nd IEEE International Conference on Information Technologies: from Theory to Applications, ICTTA (2006)Google Scholar
  6. 6.
    Egenhofer, M.-J.: Reasoning about binary topological relations. In: Günther, O., Schek, H.-J. (eds.) SSD 1991. LNCS, vol. 525, pp. 143–160. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  7. 7.
    Frank, A.U.: Qualitative spatial reasoning about cardinal directions. In: Proc. of the 7th Austrian Conference on Artificial Intelligence, pp. 157–167 (1991)Google Scholar
  8. 8.
    Gerevini, A., Renz, J.: Combining topological and size information for spatial reasoning. Artificial Intelligence 137(1-2), 1–42 (2002)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Jonsson, P., Drakengren, T.: A complete classification of tractability in RCC-5. Journal of Artificial Intelligence Research 6, 211–221 (1997)MathSciNetMATHGoogle Scholar
  10. 10.
    Konieczny, S., Lang, J., Marquis, P.: DA2 merging operators. Artificial Intelligence 157(1-2), 49–79 (2004)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Li, S.: Combining topological and directional information for spatial reasoning. In: Proc. of the 20th International Joint Conference on Artificial Intelligence (IJCAI), pp. 435–440 (2007)Google Scholar
  12. 12.
    Ligozat, G.: Reasoning about cardinal directions. Journal of Visual Languages and Computing 9(1), 23–44 (1998)CrossRefGoogle Scholar
  13. 13.
    Ligozat, G., Renz, J.: What Is a Qualitative Calculus? A General Framework. In: Zhang, C., Guesgen, H.W., Yeap, W.-K. (eds.) PRICAI 2004. LNCS, vol. 3157, pp. 53–64. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Lin, J.: Integration of weighted knowledge bases. Artificial Intelligence 83, 363–378 (1996)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Pujari, A.K., Kumari, G.V., Sattar, A.: \(\mathcal{INDU}\): An interval duration network. In: Proc. of the 16th Australian Joint Conference on Artificial Intelligence (AI), pp. 291–303 (2000)Google Scholar
  16. 16.
    Ragni, M., Wölfl, S.: Reasoning about topological and positional information in dynamic settings. In: Proc. of the 21th FLAIRS Conference, pp. 606–611 (2008)Google Scholar
  17. 17.
    Randell, D.-A., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: Proc. of the 3rd International Conference on Principles of Knowledge Representation and Reasoning (KR), pp. 165–176 (1992)Google Scholar
  18. 18.
    Renz, J.: Qualitative spatial reasoning with topological information. Springer, Heidelberg (2002)CrossRefMATHGoogle Scholar
  19. 19.
    Renz, J., Ligozat, G.: Weak Composition for Qualitative Spatial and Temporal Reasoning. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 534–548. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    Renz, J., Mitra, D.: Qualitative direction calculi with arbitrary granularity. In: Zhang, C., Guesgen, H.W., Yeap, W.-K. (eds.) PRICAI 2004. LNCS, vol. 3157, pp. 65–74. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  21. 21.
    Revesz, P.Z.: On the semantics of arbitration. Journal of Algebra and Computation 7(2), 133–160 (1997)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jean-François Condotta
    • 1
  • Souhila Kaci
    • 1
  • Pierre Marquis
    • 1
  • Nicolas Schwind
    • 1
  1. 1.Université d’Artois CRIL CNRS UMR 8188Lens

Personalised recommendations