Common knowledge: Relating anti-founded situation semantics to modal logic neighbourhood semantics [Book Review]

Two approaches for defining common knowledge coexist in the literature: the infinite iteration definition and the circular or fixed point one. In particular, an original modelization of the fixed point definition was proposed by Barwise (1989) in the context of a non-well-founded set theory and the infinite iteration approach has been technically analyzed within multi-modal epistemic logic using neighbourhood semantics by Lismont (1993). This paper exhibits a relation between these two ways of modelling common knowledge which seem at first quite different.
Keywords Common knowledge  multi-modal logic  neighbourhood semantics  non-well-founded sets  Scott models
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DOI 10.1007/BF01160019
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References found in this work BETA
Jaakko Hintikka (1962). Knowledge and Belief. Ithaca, N.Y.,Cornell University Press.
Jon Barwise (1989). The Situation in Logic. Center for the Study of Language and Inf.

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Citations of this work BETA
Aviad Heifetz (1999). Iterative and Fixed Point Common Belief. Journal of Philosophical Logic 28 (1):61-79.

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