Steps Towards a First-Order Logic of Explicit and Implicit Belief

Modelling the beliefs of an agent who lacks logical omniscience has been a major concern recently. While most of the work has concentrated on propositional logics of belief, this paper primarily addresses issues raised by adding quantifiers to such logics. In particular, we are focusing on quantifying in and the distinction between "knowing what" and "knowing that". After arguing why a model of limited reasoning should preserve this distinction, we show how this can be accomplished by a semantics based on a restricted form of tautological entailment.