Journal of Philosophical Logic 28 (1):61-79 (1999)
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
|Keywords||common knowledge common belief infinitary logic|
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References found in this work BETA
On the Logic of Common Belief and Common Knowledge.Luc Lismont & Philippe Mongin - 1994 - Theory and Decision 37 (1):75-106.
A Quantitative Analysis of Modal Logic.Ronald Fagin - 1994 - Journal of Symbolic Logic 59 (1):209-252.
La Connaissance Commune En Logique Modale.Luc Lismont - 1993 - Mathematical Logic Quarterly 39 (1):115-130.
Common Knowledge: Relating Anti-Founded Situation Semantics to Modal Logic Neighbourhood Semantics. [REVIEW]L. Lismont - 1994 - Journal of Logic, Language and Information 3 (4):285-302.
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