 At each possible world, either a proposition or its negation is true. We call a world at which a proposition \(A\) is true an \(A\)-world, and identify the proposition \(A\) with the set of \(A\)-worlds. The rank \(\kappa(A)\) of a proposition \(A\) is the rank of those possible worlds \(w\) whose rank \(\kappa(w)\) is minimal among the \(A\)-worlds. In  Figure 3,  the rank of \(A\) is thus \(0\) and the rank of \(\neg A\) is \(1\). A proposition \(A\) is believed iff \(\kappa(\neg A)&gt;0\).