 Reiter’s default logic  (Reiter 1980)  uses the notion of an extension to make precise the idea that the consistency condition has to be met both before and after the rule is applied. Given a set \(\Delta\) of defaults, an extension for \(\Delta\) represents a set of inferences that can be drawn reasonably and consistently using defaults from \(\Delta\). Such inferences are those that are warranted on the basis of a maximal set of defaults whose consistency condition is met both before and after their being triggered. 