Both informational attitudes share a common formal structure differing only in the reflexivity vs. seriality condition

So far we have looked at relational models of hard information. A small modification of these models allows us to model a softer informational attitude. Indeed, by simply replacing the assumption of reflexivity of the relation \(\sim_i\) with seriality (for each state \(w\) there is a state \(v\) such that \(w\sim_i v\)), but keeping the other aspects of the model the same, we can capture what epistemic logicians have called “beliefs”. Formally, a doxastic model is a tuple \(\langle W, \{R_i\}_{