  We examine four approaches for dealing with the logical omniscience problem
and their potential applicability: the syntactic approach, awareness,
algorithmic knowledge, and impossible possible worlds. Although in some
settings these approaches are equi-expressive and can capture all epistemic
states, in other settings of interest (especially with probability in the
picture), we show that they are not equi-expressive. We then consider the
pragmatics of dealing with logical omniscience-- how to choose an approach and
construct an appropriate model.
