We introduce a new approach to dealing with the well-known logical omn
iscience problem in epistemic logic. Instead of taking possible worlds
where each world is a model of classical propositional logic, we take
possible worlds which are models of a nonstandard propositional logic
we call NPL, which is somewhat related to relevance logic. This appro
ach gives new insights into the logic of implicit and explicit belief
considered by Levesque and Lakemeyer. In particular, we show that in a
precise sense agents in the structures considered by Levesque and Lak
emeyer are perfect reasoners in NPL.