Algorithms

In this chapter we present several general algorithms (independent of the specific logic) to compute the preferred options for a given knowledge base. We start by showing a naive algorithm that makes no assumptions about the weakening mechanism or the preference relation. We also show that for specific combinations of weakening mechanisms and preference relations, the preferred options coincide with the computation of maximal consistent subsets and therefore can be computed efficiently for certain logics. Finally, we develop two algorithms that exploit properties of monotonicity and anti-monotonicity in the preference relation, respectively, in order to compute the preferred options more efficiently.