Advertisement

Abstract

We start investigating set algebras from a knowledge theoretical point of view. To this end, we suit hybrid logic to the context of knowledge. The common modal approach is extended in this way, which gives us the necessary expressive power. The main issues of the paper are a completeness and a decidability result for the arising logic of knowledge on algebras.

Keywords

reasoning about knowledge modal and hybrid logic topological reasoning knowledge and algebras decidability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  2. 2.
    Huth, M., Ryan, M.: Logic in Computer Science: Modelling and Reasoning about Systems. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  3. 3.
    Dabrowski, A., Moss, L.S., Parikh, R.: Topological reasoning and the logic of knowledge. Annals of Pure and Applied Logic 78, 73–110 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Georgatos, K.: Knowledge theoretic properties of topological spaces. In: Masuch, M., Pólos, L. (eds.) Logic at Work 1992. LNCS, vol. 808, pp. 147–159. Springer, Heidelberg (1994)Google Scholar
  5. 5.
    Georgatos, K.: Knowledge on treelike spaces. Studia Logica 59, 271–301 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Weiss, M.A., Parikh, R.: Completeness of certain bimodal logics for subset spaces. Studia Logica 71, 1–30 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Heinemann, B.: A hybrid logic of knowledge supporting topological reasoning. In: Rattray, C., Maharaj, S., Shankland, C. (eds.) AMAST 2004. LNCS, vol. 3116, pp. 181–195. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Bauer, H.: Measure and Integration Theory. de Gruyter Studies in Mathematics, vol. 26. Walter de Gruyter, New York (2001)zbMATHGoogle Scholar
  9. 9.
    Wu, Y., Weihrauch, K.: A computable version of the Daniell-Stone Theorem on integration and linear functionals. In: Brattka, V., Staiger, L., Weihrauch, K. (eds.) CCA 2004, Informatik Berichte, Hagen, Germany, vol. 320, pp. 195–207 (2004)Google Scholar
  10. 10.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. In: Cambridge Tracts in Theoretical Computer Science, vol. 53, Cambridge University Press, Cambridge (2001)Google Scholar
  11. 11.
    Blackburn, P.: Representation, reasoning, and relational structures: a hybrid logic manifesto. Logic Journal of the IGPL 8, 339–365 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    McKinsey, J.C.C.: A solution to the decision problem for the Lewis systems S2 and S4, with an application to topology. Journal of Symbolic Logic 6, 117–141 (1941)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Aiello, M., van Benthem, J., Bezhanishvili, G.: Reasoning about space: The modal way. Journal of Logic and Computation 13, 889–920 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Gabelaia, D.: Modal definability in topology. Master’s thesis, ILLC, Universiteit van Amsterdam (2001)Google Scholar
  15. 15.
    Heinemann, B.: Axiomatizing modal theories of subset spaces (an example of the power of hybrid logic). In: HyLo@LICS, Proceedings, Copenhagen, Denmark, 69–83 (2002)Google Scholar
  16. 16.
    Weihrauch, K.: Computable Analysis. Springer, Berlin (2000)zbMATHGoogle Scholar
  17. 17.
    Heinemann, B.: Extended canonicity of certain topological properties of set spaces. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 135–149. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Bernhard Heinemann
    • 1
  1. 1.Fachbereich InformatikFernUniversität in HagenHagenGermany

Personalised recommendations