Beyond Possible Worlds: Non-standard Approaches to Epistemic Logic

In this thesis, I explore non-standard solutions to limitations of the classical picture of epistemic logic - that is, logics that seek to model attitudes as knowledge, belief, etc. I present different frameworks that leverage the advantages of possible world semantics, while avoiding the limitations discussed: first, how we model the deductive process in the proof theory, second, how we model partial suppositions, and third, how we model agents that are not logically omniscient.