A nonstandard approach to the logical omniscience problem

We introduce a new approach to dealing with the well-known logical omniscience 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 approach 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 Lakemeyer are perfect reasoners in NPL. © 1995.