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

Abstract
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 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. 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
Convention: A Philosophical Study.David Lewis - 1969 - Harvard University Press.
Knowledge and Belief.Jaakko Hintikka - 1962 - Ithaca: Cornell University Press.
The Situation in Logic.Jon Barwise - 1989 - Center for the Study of Language and Inf.
La Connaissance Commune En Logique Modale.Luc Lismont - 1993 - Mathematical Logic Quarterly 39 (1):115-130.

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Citations of this work BETA
About Cut Elimination for Logics of Common Knowledge.Luca Alberucci & Gerhard Jäger - 2005 - Annals of Pure and Applied Logic 133 (1):73-99.
Iterative and Fixed Point Common Belief.Aviad Heifetz - 1999 - Journal of Philosophical Logic 28 (1):61-79.

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