 An equivalent definition is in terms of selection functions (Stalnaker 1968; Nute 1980). An sf-frame is a pair \(\langle W, f\rangle\) where \(W\) is a non-empty set of possible worlds and \(f: W \times \cP(W) \to \cP(W)\) is a function taking a world and a proposition (i.e., a set of worlds) and yielding a proposition. \(f\) is called the selection function of the model, and intuitively \(v \in f(w,U)\), where \(U\subseteq W\), means that world \(v\) is a world in \(U\) that is (in some sense) closest or most similar to \(w\), as compared to all the other worlds in \(U\). The correspondence with the previous approach is straightforward, if we let \(f(w,\lvert A\rvert^M)\) coincide with \(R_{\lvert A\rvert^M}(w)\). An sf-model is a triple \(M = \langle W, f, V\rangle\) such that \(\langle W, f\rangle\) is an sf-frame and \(V\) is a valuation function. The truth condition for the variably strict conditional becomes: