Some Non-Classical Methods in (Epistemic) Modal Logic and Games: A Proposal

In this proposal, we discuss several non-classical frameworks, and their applications in epistemic modal logic. We largely consider topological semantics, as opposed to widely used Kripke semantics, paraconsistent systems, as opposed to consistent systems, and non-well-founded sets, as opposed to ZF(C) set theory. We discuss topological public announcement logics, introduce homotopies to modal logic, reason about topological semantics for paraconsistent logics, and introduce non-well-founded type spaces for games. Finally, we discuss several popular game theoretical issues: the Brandenburger Keisler paradox, and strategy logic whose primitives are strategies. Then, we conclude with future research directions.