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 (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.
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A first version of this paper was written while the author was an assistant at the Universite Catholique de Louvain. It was part of a doctoral thesis presented in June 1992.
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Lismont, L. Common knowledge: Relating anti-founded situation semantics to modal logic neighbourhood semantics. J Logic Lang Inf 3, 285–302 (1994). https://doi.org/10.1007/BF01160019
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DOI: https://doi.org/10.1007/BF01160019