Journal of Philosophical Logic

, Volume 28, Issue 1, pp 61–79

Iterative and fixed point common belief

Authors

  • Aviad Heifetz
    • The School of EconomicsTel Aviv University
Article

DOI: 10.1023/A:1004357300525

Cite this article as:
Heifetz, A. Journal of Philosophical Logic (1999) 28: 61. doi:10.1023/A:1004357300525

Abstract

We define infinitary extensions to classical epistemic logic systems, and add also a common belief modality, axiomatized in a finitary, fixed-point manner. In the infinitary K system, common belief turns to be provably equivalent to the conjunction of all the finite levels of mutual belief. In contrast, in the infinitary monotonic system, common belief implies every transfinite level of mutual belief but is never implied by it. We conclude that the fixed- point notion of common belief is more powerful than the iterative notion of common belief.

common knowledge common belief infinitary logic

Copyright information

© Kluwer Academic Publishers 1999