 In view of these difficulties it is remarkable that there is a probabilistic account according to which \(\phi \nc \psi\) is interpreted as \(P(\psi \mid \phi)\) &gt; ½ and that nevertheless characterizes preferential consequence relations  (Benferhat et al. 1999).  The idea is to restrict the focus to structures \(S= (\Omega, P, \prec)\) that come with specific probability distributions known as atomic bound systems or big-stepped probabilities. First, a linear order \(\prec\) is imposed on the set of classical models in \(\Omega\) over which the probability measure \(P\) is defined. Second, \(P\) is required to respect this order by “taking big steps”, i.e., in such a way that for any \(M \in \Omega\), \(P(\{M\}) &gt; \sum\{P(\{M'\}) \mid M' \prec M\}\). This warrants that \(\phi \nc \psi\) holds if and only if the unique \(\prec\)-maximal model in \([\phi]\) validates \(\psi\) (in signs, \(\max[\phi] \models  \psi\)).[6]  Here is how this helps us with the problematic example above: \(\alpha \nc \beta\) means that \(\max[\alpha] \models \beta\) and hence that \(\max[\alpha] = \max[\alpha \wedge \beta]\). \(\alpha \wedge \beta \nc \gamma\) means that \(\max[\alpha \wedge \beta] \models \gamma\) and hence \(\max[\alpha] \models \gamma\) which implies \(\alpha \nc \gamma\). 