Revising non-monotonic theories with sufficient and necessary conditions: the case of Defeasible Logic

In the setting of Defeasible Logic, we deal with the problem of revising and contracting a non-monotonic theory while minimizing the number of rules to be removed from the theory itself. The process is based on the notions of a set of rules being necessary and sufficient in order to prove a claim. The substantial difference among classical and non-monotonic reasoning processes makes this issue significant in order to achieve the correct revision processes. We show that the process is however computationally hard, and can be solved in polynomial time on non-deterministic machines.