 In the case of beliefs, there are more alternatives. A straightforward idea says that the agent believes \(\varphi\) if and only if she has evidence supporting \(\varphi\) (a syntactic definition of the form \(B\varphi := \oBox\varphi)\). However, this would allow the agent to have contradictory beliefs, as two pieces of evidence might contradict themselves (there may be \(X, Y \in E\) such that \(X \cap Y = \emptyset\), and thus \(Bp \land B{\lnot p}\) could be satisfiable). More importantly, this would be a ‘lazy’ approach, as the agent would be able to collect evidence (thus defining E), but nevertheless she would not be doing any ‘reasoning’ with it.