Interpreting Knowledge into Belief in the Presence of Negative Introspection

This paper studies a particular interpretation of propositional modal logic into propositional modal logic. Under an epistemic reading of the modality this interpretation can be understood as taking knowledge to be true belief. All normal modal logics of belief that under this definition of knowledge give rise to S5 as the logic of knowledge are determined. And all the normal modal logics of belief that give rise to S4w5 as the logic of knowledge are determined. Among the latter KD45 shows up as a maximal such logic.