Complexity of Recursive Normal Default Logic

Normal default logic, the fragment of default logic obtained by restricting defaults to rules of the form α:Mβ β , is the most important and widely studied part of default logic. In [MNR94], we proved a basis theorem for extensions of recursive propositional logic normal default theories and hence for finite predicate logic normal default theories. That is, we proved that every recursive propositional normal default theory possesses an extension which is r.e. in 0. Here we show that this bound is tight. Specifically, we show that for every r.e. set A and every set B r.e. in A there is a recursive normal default theory 〈D, W 〉 with a unique extension which is Turingequivalent to A ⊕ B. A similar result holds for finite predicate logic normal default theories.