 In this section, we will once again take propositions over the set \(W\) to be the objects of belief. As before, the reader is invited to think of \(W\) as a set of coarse-grained, mutually exclusive, possible ways the actual world might be. We write \(\Bel\) to denote the set of  propositions that the agent believes and use \(\Bel(A)\) as shorthand for \(A\in \Bel\). We will also require some notation for qualitative propositional belief change. For all \(E\subseteq W\), write \(\Bel_E\) for the set of propositions the agent would believe upon learning \(E\) and no stronger proposition. We will also write \(\Bel(A|E)\) as shorthand for \(A\in \Bel_E.\) By convention, \(\Bel= \Bel_W.\) If \({\bf F}\) is a set of propositions, we let \(\Bel_{\bf F}\) be the set \(\{ \Bel_E : E \in {\bf F} \}.\) The set \(\Bel_{\bf F}\) represents an agent’s  dispositions  to update her qualitative beliefs given information from \({\bf F}\). 