Topological Approaches to Epistemic Logic

Sophia Knight (Uppsala University) and Aybüke Özgün (University of Amsterdam)

Topological semantics for epistemic logic provides an elegant and natural way to model not only knowledge and belief, but also the evidence or justification upon which knowledge is based. This is an important difference with the more common Kripke semantics which have no way to account for evidence, leading to certain well known problems such as the problem of logical omniscience. This course will cover several variants of topological approaches to epistemic logic including the McKinsey/Tarski interpretation, neighbourhood semantics, evidence models, the effort modality, justification, multi-agent topological subset space semantics, dynamic logics with topological semantics, learning theory, and justification logic.