Advertisement

A Runs-and-Systems Semantics for Logics of Announcements

  • Riccardo Pucella
  • Mehrnoosh Sadrzadeh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6006)

Abstract

Logics of announcements are logics of knowledge to reason about agents that communicate by broadcasting interpreted messages. These logics are typically given a semantics in terms of updatable Kripke structures, which tend to be abstract. We revisit the semantics of logics of announcements and develop a concrete semantics using runs and systems. The advantage is that we can devise models that capture scenarios without having to express properties of those scenarios within the logic itself. In this concrete setting, we study honesty as well as belief in the presence of announcements that are not broadcast to all agents in a system.

Keywords

Common Knowledge Global State Previous Time Step Dynamic Logic Kripke Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baltag, A., Coecke, B., Sadrzadeh, M.: Epistemic a Actions as Resources. J. Log. Comput. 17(3), 555–585 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Baltag, A., Moss, L.S.: Logics for Epistemic Programs. Synthese 139, 165–224 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    van Benthem, J.: One is a Lonely Number. In: Chatzidakis, Z., Koepke, P., Pohlers, W. (eds.) LC 2002. Lecture Notes in Logic, vol. 27, pp. 96–129. AK Peters, Wellesley (2006)Google Scholar
  4. 4.
    van Benthem, J., Gerbrandy, J., Pacuit, E.: Merging Frameworks for Interaction: DEL and ETL. In: Samet, D. (ed.) TARK 2007, pp. 72–81. ACM Press, New York (2007)CrossRefGoogle Scholar
  5. 5.
    Burrows, M., Abadi, M., Needham, R.: A Logic of Authentication. ACM Trans. Comput. Syst. 8(1), 18–36 (1990)CrossRefGoogle Scholar
  6. 6.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library, vol. 337. Springer, Heidelberg (2007)Google Scholar
  7. 7.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  8. 8.
    Gerbrandy, J.: Dynamic Epistemic Logic. In: Moss, L.S., Ginzburg, J., de Rijke, M. (eds.) Logic, Language, and Information, vol. 2, pp. 67–84. CSLI Publication, Stanford (1999)Google Scholar
  9. 9.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  10. 10.
    Hintikka, J.: Knowledge and Belief. Cornell University Press (1962)Google Scholar
  11. 11.
    van der Hoek, W., Wooldridge, M.: Time, knowledge, and cooperation: Alternating-time temporal epistemic logic and its applications. In: Arbab, F., Talcott, C. (eds.) COORDINATION 2002. LNCS, vol. 2315, p. 4. Springer, Heidelberg (2002)Google Scholar
  12. 12.
    Kripke, S.: A Semantical Analysis of Modal Logic I: Normal Modal Propositional Calculi. Z. Math. Log. Grundl. Math. 9, 67–96 (1963)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Lichtenstein, O., Pnueli, A., Zuck, L.: The Glory of the Past. In: Parikh, R. (ed.) Logic of Programs 1985. LNCS, vol. 193, pp. 196–218. Springer, Heidelberg (1985)Google Scholar
  14. 14.
    van der Meyden, R., Wong, K.: Complete Axiomatizations for Reasoning about Knowledge and Branching Time. Stud. Log. 75(1), 93–123 (2003)zbMATHCrossRefGoogle Scholar
  15. 15.
    Moore, G.E.: A Reply to my Critics. In: Schilpp, P.A. (ed.) The Philosophy of G. E. Moore. The Library of Living Philosophers, vol. 4, pp. 535–677. Northwestern University (1942)Google Scholar
  16. 16.
    Panangaden, P., Taylor, K.: Concurrent Common Knowledge. Distributed Comp. 6, 73–93 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Parikh, R., Ramanujan, R.: A Knowledge Based Semantics of Messages. J. Log. Lang. Inf. 12(4), 453–467 (2003)zbMATHCrossRefGoogle Scholar
  18. 18.
    Sack, J.: Temporal Languages for Epistemic Programs. J. Log. Lang. Inf. 17(2), 183–216 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Yap, A.: Product Update and Looking Backwards. ILLC Publications PP-2006-39, Universiteit van Amsterdam (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Riccardo Pucella
    • 1
  • Mehrnoosh Sadrzadeh
    • 2
  1. 1.College of Computer and Information ScienceNortheastern UniversityBostonUnited States of America
  2. 2.Computing LaboratoryUniversity of OxfordOxfordUnited Kingdom

Personalised recommendations