There are several contexts of non-monotonic reasoning where a priority between rules is established with the purpose of solving conflicts. We investigate how to modify such a priority (preference) relation in a non-monotonic logic in order to change the conclusions of the theory itself. We shall argue that the approach we adopt has a natural counterpart in legal reasoning and argumentation, where users cannot typically change the facts or the rules, but can propose their preferences about the relative strength of the rules.

The main result of the present work is the proof that the problem of revising a non-monotonic theory by changing only the superiority order between conflicting rules is, in general, computationally hard.

After such an analysis, we identify three contraction/revision/update operations and study them against the AGM postulates for belief revision, to discover that only a (small) part of these postulates are satisfied in the specific non-monotonic setting.