 A cumulative model \(M\) for a universe \(W\) is a triple \(\langle S, l, &lt; \rangle\) where \(S\) is a set of states, \(l: S \rightarrow \cP(W)\) is a labeling function assigning to each state a non-empty set of worlds from the universe \(W\), and \(&lt;\) is a binary relation on \(S\) satisfying the smoothness condition: for all \(A\in L_0\) and all \(s\) such that \(s\mathrel|\mathrel{\mkern-3mu}\equiv A\) either \(s\) is minimal in \(\hat{A} = \{s \in S: s\mathrel|\mathrel{\mkern-3mu}\equiv A\}\) or there is an \(s' &lt; s\) that is minimal in \(\hat{A}\). Here \(s\mathrel|\mathrel{\mkern-3mu}\equiv A\) (read: \(s\) satisfies \(A\)) means that for every world \(w\) in \(l(s)\), \(w \Vdash A\).