Handling Exceptions in Logic Programming without Negation as Failure

Default rules, i.e. statements of the form normally a’s are b’s, are usually handled in Answer Set Programming by means of negation as failure which provides a way to capture exceptions to normal situations. In this paper we propose another approach which offers an operational counterpart to negation as failure, and which may be thought as a corresponding dual attitude. The approach amounts to an explicit rewriting of exceptions in default rules, together with the addition of completion rules that are consistent with current knowledge. It is shown that the approach can be applied to restore the consistency of inconsistent programs that implicitly involve specificity ordering between the rules. The approach is compared to previous works aiming at providing support to the rewriting of default rules. It is also shown how the proposed approach agrees with the results obtained in the classical way.