Cumulative default logic: In defense of nonmonotonic inference rules

摘要

Two problems of Reiter's default logic have recently been discussed in the literature: first, inconsistencies between justifications of nonnormal defaults may lead to unintuitive results, and second, default logic is not cumulative, i.e., the addition of theorems to the set of premises may change the derivable formulas. To solve these two problems we strengthen the applicability condition for defaults and make the reasons for believing something an explicit part of the derived formulas. The resulting new logic turns out to be semi-monotonic. If the additional expressiveness of nonnormal defaults is to be retained only some of the extensions of this logic are to be taken as acceptable sets of beliefs, however: those preserving priorities between defaults.