 The situation is different in default logic where both \(p_2\) and \(p_3\) are derivable. The reasoning follows a greedy policy in applying default rules: whenever a rule is applicable (i.e., its antecedent holds by the currently held beliefs \(\Xi\) and its consequent doesn’t contradict with \(\Xi\)) it is applied. There is disagreement among scholars whether and when contraposition is a desirable property for defeasible inferences (e.g.,  Caminada 2008,  Prakken 2012). 