 A consequence of expressing defeasible inferences via material implication in assumption-based approaches is that defeasible inferences are contrapositable. Clearly, if \(\phi \wedge \pi \supset \psi\) then \(\neg \psi \wedge \pi \supset \neg \phi\). As a consequence, formalisms such as default logic have a more greedy style of applying default rules. We demonstrate this with conditional entailment. Consider a theory consisting of the defaults \(p_1 \rightarrow p_2\), \(p_2 \rightarrow p_3\), \(p_3 \rightarrow p_4\) and the factual information \(\Lambda = \{p_1, \neg p_4\}\) (where \(p_i\) are logical atoms). In assumption-based approaches such as conditional entailment the defeasible rules will be encoded as \(p_1 \wedge \pi_1 \supset p_2\), \(p_2 \wedge \pi_2 \supset p_3\), and \(p_3 \wedge \pi_3 \supset p_4\). It can easily be seen that &lt; = ∅ is an admissible ordering which means that for instance a model \(M\) with \(Ab(M) = \{\pi_1\}\) is \(\lessdot\)-minimal. In such a model we have \(M \models \neg p_3\) and \(M \models \neg p_2\) by reasoning backwards via contraposition from \(\neg p_4 \wedge \pi_3\) to \(\neg p_3\) and from \(\neg p_3 \wedge \pi_2\) to \(\neg p_2\). This means that neither \(p_2\) nor \(p_3\) is conditionally entailed. 