Relating truth, knowledge and belief in epistemic states

We define and investigate a structure incorporating what is true, what is known and what is believed by a rational agent in models of the S4.2 logic of knowledge. The notion of KB R -structures introduced, provides a fine-grained modal analysis of an agent's epistemic state, actually one that differentiates knowledge from belief and accounts for an agent without full introspective power (concerning her knowledge sets). Many epistemic properties of this structure are proved and it is shown that belief collapses in the form of a Stalnaker stable set (while knowledge does not). Finally, a representation theorem is proved, which exactly matches KB R -structures to S4.2 models of the world. © 2011 Springer-Verlag Berlin Heidelberg