On Constrained Default Theories

We introduce a variant of default logic, called constrained default logic. With it, we make default logic commit to its assumptions without extending the first order language. In contrast to [1] wherein “formulas with constraints” were introduced, we introduce constrained extensions. Then, we employ constrained default logic in order to clarify the relationships among the constrained variants of default logic [4, 1, 3]. Finally, the proof–oriented notion of a lemma default rule is introduced that accounts for the practical impact of cumulativity: the capability of handling nonmonotonic lemmata.