Common knowledge: Relating anti-founded situation semantics to modal logic neighbourhood semantics [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Logic, Language and Information 3 (4):285-302 (1994)
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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References found in this work BETA
David Lewis (1969). Convention: A Philosophical Study. Harvard University Press.
Brian F. Chellas (1980). Modal Logic: An Introduction. Cambridge University Press.
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.
Jon Barwise (1987). The Liar: An Essay on Truth and Circularity. Oxford University Press.
Citations of this work BETA
Cedric Paternotte (2011). Being Realistic About Common Knowledge: A Lewisian Approach. Synthese 183 (2):249-276.
Luca Alberucci & Gerhard Jäger (2005). About Cut Elimination for Logics of Common Knowledge. Annals of Pure and Applied Logic 133 (1):73-99.
Aviad Heifetz (1999). Iterative and Fixed Point Common Belief. Journal of Philosophical Logic 28 (1):61-79.
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