 These modes are called “ranked” because the property of Modularity of the strict partial order &lt; is equivalent to there being a totally ordered set \(\Omega\) (the strict order on \(\Omega\) will be denoted by \(\bangle\)) and a ranking function \(r : S \rightarrow \Omega\) such that \(s &lt; t\) iff \(r(s) \bangle r(t)\). Intuitively, a state of smaller rank is “more normal” than a state of higher rank.