Topological Models for Belief and Belief Revision
Aybüke Özgün

Abstract:
We introduce a new topological semantics for belief logics in which the belief modality is interpreted as the closure of the interior operator. We show that our semantics validates the axioms of Stalnaker’s combined system of knowledge and belief, in fact, that it constitutes the most general extensional (and compositional) semantics validating these axioms. We further prove that in this semantics the logic KD45 is sound and complete with respect to the class of extremally disconnected spaces. We have a critical look at the topological interpretation of belief in terms of the derived set operator and compare it with our proposal. We also provide two topological semantics for conditional beliefs of which especially the latter is quite successful in capturing the rationality postulates of AGM theory. We further investigate a topological analogue of dynamic belief change, namely, update. In addition, we provide a completeness result of the system wKD45, a weakened version of KD45.