 for all worlds \(w\) at which \(A\) is true, while \(\kappa(w\mid A)= \infty\) for all worlds \(w\) where \(A\) is false. In less formal terms, if our agent comes to believe \(A,\) then the ranks of all \(A\)-worlds are lowered by the rank of \(A\). And the rank of all \(\neg A\)-worlds is set to infinity, which means that she definitely disbelieves those worlds. The conditionalization of a belief function \(\beta\) is defined analogously: