A Stochastic Interpretation of Propositional Dynamic Logic: Expressivity

  • Ernst-Erich Doberkat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6521)


We propose a probabilistic interpretation of Propositional Dynamic Logic (PDL). We show that logical and behavioral equivalence are equivalent over general measurable spaces. Bisimilarity is also discussed and shown to be equivalent to logical and behavioral equivalence, provided the base spaces are Polish spaces. We adapt techniques from coalgebraic stochastic logic and point out some connections to Souslin’s operation \(\mathcal{A}\) from descriptive set theory.


Modal Logic Measurable Space Polish Space Equivalent Model Probabilistic Interpretation 
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  1. 1.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001)CrossRefzbMATHGoogle Scholar
  2. 2.
    Blackburn, P., van Benthem, J.: Modal logic: A semantic perspective. In: Blackburn, P., et al. (eds.) Handbook of Modal Logic, pp. 1–84. Elsevier, Amsterdam (2007)Google Scholar
  3. 3.
    Desharnais, J., Edalat, A., Panangaden, P.: Bisimulation of labelled Markov-processes. Information and Computation 179(2), 163–193 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Doberkat, E.-E.: Stochastic Coalgebraic Logic. EATCS Monographs in Theoretical Computer Science. Springer, Heidelberg (2009)CrossRefzbMATHGoogle Scholar
  5. 5.
    Doberkat, E.-E., Schubert, C.: Coalgebraic logic over general measurable spaces - a survey. Math. Struct. Comp. Science (in print, 2011) (Special issue on coalgebraic logic)Google Scholar
  6. 6.
    Doberkat, E.-E., Srivastava, S.M.: Measurable selections, transition probabilities and Kripke models. Technical Report 185, Chair for Software Technology, Technische Universität Dortmund (May 2010)Google Scholar
  7. 7.
    Hennessy, M., Milner, R.: On observing nondeterminism and concurrency. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 395–409. Springer, Heidelberg (1980)Google Scholar
  8. 8.
    Moderer, D., Samet, D.: Approximating common knowledge with common belief. Games and Economic Behavior 1, 170–190 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Pauly, M., Parikh, R.: Game logic — an overview. Studia Logica 75, 165–182 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theor. Comp. Sci. 249(1), 3–80 (2000) (Special issue on modern algebra and its applications)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Schröder, L., Pattinson, D.: Modular algorithms for heterogeneous modal logics. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 459–471. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Srivastava, S.M.: A Course on Borel Sets. Graduate Texts in Mathematics. Springer, Berlin (1998)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ernst-Erich Doberkat
    • 1
  1. 1.Chair for Software TechnologyTechnische Universität DortmundGermany

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