The Topology of Full and Weak Belief
نویسندگان
چکیده
We introduce a new topological semantics for belief logics in which the belief modality is interpreted as the interior of the closure of the interior operator. We show that the system wKD45, a weakened version of KD45, is sound and complete w.r.t. the class of all topological spaces. Moreover, we point out a problem regarding updates on extremally disconnected spaces that appears in the setting of [1] and show that our proposal for topological belief semantics on all topological spaces constitutes a solution for it. While generalizing the topological belief semantics proposed in [1] to all spaces, we model conditional beliefs and updates and give complete axiomatizations of the corresponding logics.
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