A neighborhood semantics for the logics of unknown truths and of false beliefs

This article outlines a semantic approach to the logics of unknown truths, and the logic of false beliefs, using neighborhood structures, giving results on soundness, completeness, and expressivity. Relational semantics for the logics of unknown truths are also addressed, specifically the conditions under which sound axiomatizations of these logics might be obtained from their normal counterparts, and the relationship between reflexive insensitive logics (RI-logics) and logics containing the provability operator as the primary modal operator.