From DEL to EDL: Exploring the Power of Converse Events

  • Guillaume Aucher
  • Andreas Herzig
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4724)


Dynamic epistemic logic (DEL) as viewed by Baltag et col. and propositional dynamic logic (PDL) offer different semantics of events. On the one hand, DEL adds dynamics to epistemic logic by introducing so-called epistemic action models as syntactic objects into the language. On the other hand, PDL has instead transition relations between possible worlds. This last approach allows to easily introduce converse events. We add epistemics to this, and call the resulting logic epistemic dynamic logic (EDL). We show that DEL can be translated into EDL thanks to this use of the converse operator: this device enables us to translate the structure of the action (or event) model directly within a particular axiomatization of EDL, without having to refer to a particular epistemic action (event) model in the language (as done in DEL). It follows that EDL is more expressive and general than DEL.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alchourrón, C., GÄardenfors, P., Makinson, D.: On the logic of theory change:Partial meet contraction and revision functions. J. of Symbolic Logic 50, 510–530 (1985)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Baltag, A.: A logic of epistemic actions. Technical report, CWI (2000),
  3. 3.
    Baltag, A., Moss, L.S.: Logics for epistemic programs. Synthese 139(2), 165–224 (2004)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. In: Proc. TARK 1998, pp. 43–56. Morgan Kaufmann, San Francisco (1998)Google Scholar
  5. 5.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about knowledge. MIT Press, Cambridge (1995)MATHGoogle Scholar
  6. 6.
    Gerbrandy, J.: Bisimulations on Planet Kripke. PhD thesis, University of Amsterdam (1999)Google Scholar
  7. 7.
    Gerbrandy, J., Groeneveld, W.: Reasoning about information change. J. of Logic, Language and Information 6(2) (1997)Google Scholar
  8. 8.
    Herzig, A., Lang, J., Longin, D., Polacsek, T.: A logic for planning under partial observability. In: Proc. Nat (US) Conf. on Artificial Intelligence (AAAI 2000), Austin, Texas (August 2000)Google Scholar
  9. 9.
    Katsuno, H., Mendelzon, A.O.: On the di Rerence between updating a knowledge base and revising it. In: GÄardenfors, P. (ed.) Belief revision, pp. 387–394. CambridgeUniversity Press, Cambridge (prelimnary version In: Allen, J.A.,Fikes, R., Sandewall, E. (eds.) Principles of Knowledge Representation and Reasoning: Proc. 2nd Int. Conf., pp. 387–394. Morgan Kaufmann Publishers (1992)Google Scholar
  10. 10.
    Plaza, J.A.: Logics of public communications. In: Emrich, M.L., Pfeifer, M.Z., Hadzikadic, M., Ras, Z.W. (eds.) Proc. 4th Int. Symposium on Methodologies or Intelligent Systems, pp. 201–216 (1989)Google Scholar
  11. 11.
    Sahlqvist, H.: Completeness and correspondence in the first and second order semanticsfor modal logics. In: Kanger, S. (ed.) Proc. 3rd Scandinavian Logic Symposium 1973. Studies in Logic, vol. 82. North-Holland, Amsterdam (1975)Google Scholar
  12. 12.
    Segerberg, K.: Belief revision from the point of view of doxastic logic. Bulletin of the IGPL 3, 534–553 (1995)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Segerberg, K.: Two traditions in the logic of belief: bringing them together. In: Ohlbach, H.J., Reyle, U. (eds.) Logic, Language and Reasoning: essays in honour of Dov Gabbay, Trends in Logic, vol. 5, pp. 135–147. Kluwer Academic Publishers, Dordrecht (1999)CrossRefGoogle Scholar
  14. 14.
    van Benthem, J.: One is a lonely number: on the logic of communication. In: Chatzidakis, Z., Koepke, P., Pohlers, W. (eds.) Logic Colloquium 2002, pp. 96–129 (2006) ASL &A.K. Peters,Wellesley MA. Tech Report PP-2002-27, ILLCAmsterdam(2002)Google Scholar
  15. 15.
    van Benthem, J., Pacuit, E.: The tree of knowledge in action: Towards a common perspective. In: Advances in Modal Logic, pp. 87–106 (2006)Google Scholar
  16. 16.
    van Ditmarsch, H.P.: Descriptions of game actions. J. of Logic, Language and Information (JoLLI) 11, 349–365 (2002)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    van Ditmarsch, H.P., van der Hoek, W., Kooi, B.: Dynamic Epis- temic Logic. Kluwer Academic Publishers, Dordrecht (2007)CrossRefGoogle Scholar
  18. 18.
    van Eijck, J.: Reducing dynamic epistemic logic to pdl by program transformation.Technical Report SEN-E0423, CWI (2004)Google Scholar
  19. 19.
    Yap, A.: Product update and looking backward. prepublications PP-2006-39, ILLC (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Guillaume Aucher
    • 1
  • Andreas Herzig
    • 1
  1. 1.University of Otago (NZ) - University Paul Sabatier (F) IRIT, Université Paul SabatierToulouse Cedex (F)France

Personalised recommendations