Mathematics of Public Announcements

  • Minghui Ma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6953)


We study some mathematical aspects of public announcement logic (PAL) and its several variants. By a model-theoretic approach, we explore van Benthem’s result that uses recursion axioms to characterize the submodel operation, and show some model-theoretic results on the respecting phenomena. The second approach to understand public announcements is algebraic. Based on a joint work with A. Palmigiano and M. Sadrzadeh, we treat public announcements as devices for getting a new quotient algebra updated by an element in the original one. Then we show the algebraic soundness and completeness result for PAL and generalize this approach to PAL extension of epistemic intuitionistic modal logic. Finally, we give some observations on the PAL extensions of first-order logic as well as epistemic predicate modal logic.


Modal Logic Boolean Algebra Epistemic Logic Inductive Rule Public Announcement 
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  1. 1.
    Ågotnes, T., Balbiani, P., van Ditmarsch, H., Seban, P.: Group announcement logic. Journal of Applied Logic 8, 62–81 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    van Benthem, J.: Exploring Logical Dynamics. CSLI Publications, Stanford (1996)Google Scholar
  3. 3.
    van Benthem, J.: The information in intuitionistic logic. Synthese 167, 251–270 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    van Benthem, J.: Logical Dynamics and Information Flow (2010) (manuscript)Google Scholar
  5. 5.
    van Benthem, J.: Modal Logic for Open Minds. CSLI Publications, Stanford (2010)Google Scholar
  6. 6.
    Bezhanishvili, G.: Varieties of monadic heyting algebras part i. Studia Logica 61, 367–402 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Univeristy Press, Cambridge (2001)CrossRefzbMATHGoogle Scholar
  8. 8.
    Braüner, T., Ghilardi, S.: First-order Modal Logic. In: Handbook of Modal Logic, pp. 208–219. Elsevier, Amsterdam (2007)Google Scholar
  9. 9.
    Celani, S.: Remarks on intuitionistic modal logics. Divulgaciones Matemáticas 9, 137–147 (2001)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Chagrov, A., Zakharyaschev, M.: Modal Logic. Clarendon Press, Oxford (1997)Google Scholar
  11. 11.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer, Heidelberg (2007)CrossRefzbMATHGoogle Scholar
  12. 12.
    Fischer-Servi, G.: Axiomatizations for some intuitionistic modal logics. Rend. Sem. Mat. Polit. de Torino 42, 179–194 (1984)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Fitting, M., Mendelsohn, R.: First-order Modal Logic. Kluwer Academic Publishers, Dordrecht (1998)CrossRefzbMATHGoogle Scholar
  14. 14.
    Ma, M., Palmigiano, A., Sadrzadeh, M.: Algebraic semantics and model completeness for intuitionistic public announcement logic. In: van Ditmarsch, H., Lang, J., Ju, S. (eds.) LORI 2011. LNCS(LNAI), vol. 6953, pp. 394–395. Springer, Heidelberg (2011)Google Scholar
  15. 15.
    Plaza, J.: Logics of public communications. In: Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems, pp. 201–216 (1989)Google Scholar
  16. 16.
    de Rijke, M.: Modal model theory. Report CS-R9517, Computer Science/Department of Software Technology, University of Amsterdam (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Minghui Ma
    • 1
  1. 1.Institute of Logic and IntelligenceSouthwest UniversityBeibeiChina

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