 For this to work, &lt; has to include specificity relations among assumptions. Such orders &lt; are called admissible relative to the background knowledge \(\Gamma'\) if they satisfy the following property: for every set of assumptions \(\Pi \subseteq \{\pi_i \mid i \in I\}\), if \(\Pi\) violates some default \(\phi_j \rightarrow \pi_j\) in view of the given background knowledge \(\Gamma'\) (in signs, \(\Pi, \phi_j, \Gamma' \models \neg \pi_j\)) then there is a \(\pi_k \in \Pi\) for which \(\pi_k &lt; \pi_j\). 