Evidence in epistemic logic A topological perspective

This dissertation brings together epistemic logic and topology. It studies formal representations of the notion of evidence and its link to justification, justified belief, knowledge, and evidence-based information dynamics, by using tools from topology and (dynamic) epistemic logic.
Part I is concerned with evidence-based interpretations of justified belief and knowledge. Starting with a by-now-standard topological interpretation of knowledge as the interior operator, we develop, in a gradual manner, a topological framework that (1) can talk about evidence not only semantically, but also at the syntactic level, thereby making the notion of evidence more explicit; (2) takes evidence as the most primitive notion, and defines belief and knowledge purely based on it, thereby linking these two crucial notions of epistemology at a deeper, more basic level.
In Part II of this dissertation, we focus on notions of knowledge as well as various types of information dynamics comprising learning new evidence. More precisely, this part is centered around the notions of absolutely certain knowledge and knowability as "potential knowledge", as well as the connections between the abstract notion of epistemic effort encompassin any method of evidence acquisition and the well-studied dynamic attitudes such as public and arbitrary public announcements.
To sum up, this dissertation on one hand re-interprets some existing epistemic and doxastic logics and their dynamic extensions from a topological perspective, providing an evidence-based interpretation. On the other hand, it uses topological tools to refine and extend earlier analysis, leading to novel logics of evidence and information dynamics.