David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Journal of Symbolic Logic 59 (1):209-252 (1994)
We do a quantitative analysis of modal logic. For example, for each Kripke structure M, we study the least ordinal μ such that for each state of M, the beliefs of up to level μ characterize the agents' beliefs (that is, there is only one way to extend these beliefs to higher levels). As another example, we show the equivalence of three conditions, that on the face of it look quite different, for what it means to say that the agents' beliefs have a countable description, or putting it another way, have a "countable amount of information". The first condition says that the beliefs of the agents are those at a state of a countable Kripke structure. The second condition says that the beliefs of the agents can be described in an infinitary language, where conjunctions of arbitrary countable sets of formulas are allowed. The third condition says that countably many levels of belief are sufficient to capture all of the uncertainty of the agents (along with a technical condition). The fact that all of these conditions are equivalent shows the robustness of the concept of the agents' beliefs having a "countable description".
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Dominik Klein & Eric Pacuit (2014). Changing Types: Information Dynamics for Qualitative Type Spaces. Studia Logica 102 (2):297-319.
Lawrence S. Moss (1999). Coalgebraic logic. Annals of Pure and Applied Logic 96 (1-3):277-317.
Paolo Galeazzi & Emiliano Lorini (forthcoming). Epistemic Logic Meets Epistemic Game Theory: A Comparison Between Multi-Agent Kripke Models and Type Spaces. Synthese:1-31.
Adam Brandenburger & H. Jerome Keisler (2006). An Impossibility Theorem on Beliefs in Games. Studia Logica 84 (2):211 - 240.
Aviad Heifetz (1999). Iterative and Fixed Point Common Belief. Journal of Philosophical Logic 28 (1):61-79.
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