The apparent clash between philosophical views about knowledge which predict that logical validities ought to be easy to come to know (e.g. in virtue of the fact that they do not require empirical confirmation) and the technical fact that the validity and satisfiability problems for even the weakest familiar systems are intractable is the origin of two developments which traditionally have been of interest to epistemologists: the problem of logical omniscience and the study of theories of minimal or bounded rationality.