Adding Priorities and Specificity to Default Logic

Reiter's Default Logic (DL) is one of the most popular formalizations of default reasoning. Nevertheless, the logic has a serious deficiency: the specificity principle, i.e. the commonly accepted idea that in case of a conflict more specific defaults should be preferred over more general ones, is lacking. In this paper we show how this principle can be added to Default Logic. We first present a prioritized version of DL for normal defaults, called PDL. Adapting ideas underlying Geffner and Pearl's conditional entailment we then show how the priorities needed to handle specificity can be defined. This treatment of specificity avoids two serious problems in Pearl's system Z and leads to stronger conclusions than conditional entailment in many cases.