 Possibility measures assign real numbers in the interval [0,1] to propositions in order to measure their possibility, where 0 corresponds to impossible states and 1 to necessary states  (Dubois and Prade 1990).  Ordinal ranking functions rank propositions via natural numbers closed with ∞  (Goldszmidt and Pearl 1992,  Spohn 1988). One may think of  \(\kappa([\phi])\) as the level of surprise we would face were \(\phi\) to hold, where ∞ represents maximal surprise. Finally, plausibility measures  (Friedman and Halpern 1996,  Rott 2013) associate propositions with  elements in a partially ordered domain with bottom element \(\bot\) and top element \(\top\) in order to compare their plausibilities. Given some simple constraints on \(\mathrm{Pl}\) (such as: If \(\mathrm{Pl}(X) = \mathrm{Pl}(Y) = \bot\) then \(\mathrm{Pl}(X \cup Y) = \bot\)) we speak of qualitative plausibility structures. The following statements are all equivalent which emphasizes the centrality of the core properties in the study of NMLs: 