Igor Sedlár (May 7 and May 14)

We will explore topological semantics for modal logic and its applications in epistemic logic. In the first lecture, we will establish the completeness of modal logic S4 under interior semantics with respect to various classes of topological spaces, including all spaces, Alexandroff spaces, and T_0-spaces.

In the second lecture, we will explain how interior semantics can be interpreted epistemically — open sets can be seen as pieces of evidence. We will introduce topological evidence logics based on a coherentist account of epistemic justification and prove completeness for a simple version amounting to an extension of S4 with a universal modality. If time permits, we will show how to extend the topological evidence framework to account for the fact that accessing evidence usually requires resources.