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 \(\langle W, \{R_i\}_{i\in\Agt},V\rangle\) where \(W\) is a nonempty set of states, \(R_i\) is a transitive, Euclidean and serial relation on \(W\) and \(V\) is a valuation function (cf. Definition 2.1). This notion of belief is very close to the above hard informational attitude and, in fact, shares all the properties of \(K_i\) listed above except Veracity (this is replaced with a weaker assumption that agents are “consistent” and so cannot believe contradictions). This points to a logical analysis of both informational attitudes with various “bridge principles” relating knowledge and belief (such as knowing something implies believing it or if an agent believes \(\phi\) then the agent knows that he believes it). However, we do not discuss this line of research here since these models are not our preferred ways of representing the agents’ soft information (see, for example, Halpern 1991 and Stalnaker 2006).