 A preferential model is a triple \(\langle W,V,\prec \rangle \) where \(W\) is a set of possible worlds, \(V\) is a valuation function and \(\prec\) is an arbitrary relation on the elements of \(W\). Recall from Section  Section 1.2  that \(V(\alpha)\) is the set of worlds in which \(\alpha\) is true. The relation \(\prec\) is transitive iff \(x\prec z\) whenever \(x\prec y\) and \(y \prec z \). The relation \(\prec \) is irreflexive iff for all \(w\in W\) it is not the case that \(w\prec w\). A transitive, irreflexive relation is called a strict order. We write \(w\preceq v\) iff \(w\prec v\) or \(w=v\). The strict order \(\prec\) is  total iff for \(w,v\in W\) either \(w\prec v\) or \(v\prec w\).