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Knowledge, belief and time

  • Sarit Kraus
  • Daniel Lehmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 226)

Abstract

In the conclusion of [HM2] Halpern and Moses expressed their interest in a logical system in which one could talk about knowledge and belief (and belief about knowledge, knowledge about belief and so on). We investigate such systems. In the first part of the paper knowledge and belief, without time, are considered. Common knowledge and common belief are defined and compared. A logical system and a family of models are proposed, a completeness result is proved and a decision procedure described. In the second part of the paper, time is considered. Different notions of beliefs are distinguished, obeying different properties of persistence. One interpretation of belief which obeys a very strong persistence axiom is put forward and used in the analysis of "wise men" puzzle.

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References

  1. [FH]
    R. Fagin and J.Y. Halpern, Belief,Awareness, and Limited Reasoning, Nineth International Joint Conference on Artificial Intelligence, (August 1985).Google Scholar
  2. [FV]
    R.Fagin and M. Y. Vardi, An internal semantics for modal logic, Proc. of the 17th Annual ACM, Symposium on Theory of Computing,1985, pp 305–315.Google Scholar
  3. [GPSS]
    Gabbay,D.,Pnueli, A.,Shelah, S. and Stavi,J. On the temporal analysis of fairness,Conf, Record of 7th Annual ACM Symposium on Principles of Programming Languages, Las Vegas, Nevada (Jan, 1980), pp. 174–183.Google Scholar
  4. [H]
    J.Y. Halpern, privet communication, 1985.Google Scholar
  5. [Hi]
    Hintikka, Jaakko, Knowledge and belief, an introduction to the logic of the two notions, Cornell Univ. Press, Ithaca and London (1962).Google Scholar
  6. [HM1]
    J.Y. Halpern and Y. Moses, Knowledge and common knowledge in distributed environment, Proceeding of the 3rd ACM Symposium on Principles of Distributed Computing, 1984,pp. 50–61.Google Scholar
  7. [HM2]
    J.Y. Halpern and Y. Moses, Towards a Theory of knowledge and ignorance: IBM,RJ 4448,1984.Google Scholar
  8. [HM3]
    J.Y. Halpern and Y. Moses, A guide to the modal logic of knowledge and belief.Google Scholar
  9. [Leh]
    D.J. Lehmann, Knowledge, common knowledge, and related puzzles, in Proceeding of the 3rd ACM Symposium on Principles of Distributed Computing, 1984,pp. 62–67.Google Scholar
  10. [Lev]
    H.J.Levesque,A logic of implicit and explicit belief,Proc Nat'l Conf. on Artificial Intelligence(1984),pp.198–202.Google Scholar
  11. [Lew]
    Lewis, David K, Convention, A philosophical study, Harvard University Press, Cambridge, Massachusetts, 1969.Google Scholar
  12. [LS]
    Lehmann, D. and Shelah, S. Reasoning with Time and Chance, Information and Control, Vol.53, pp. 165–198.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Sarit Kraus
    • 1
  • Daniel Lehmann
    • 1
  1. 1.Institute of Mathematics and Computer ScienceHebrew UniversityJerusalemIsrael

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