How to avoid knowing it

Beliefs have been formally modelled in the last decades using doxastic logics. The possible worlds model and its associated Kripke semantics provide an intuitive semantics for these logics, but they seem to commit us to model agents that are logically omniscient (they believe every classical tautology) and perfect reasoners (their beliefs are closed under classical deductive closure). Thus, this model would not be appropriate to model non-ideal agents, that have resource limitations that prevent them from attaining such levels of doxastic competence. This report contains a statement of these problems and a brief survey of some of the most interesting approaches that have been suggested to overcome them.