Expressing preferences in default logic

We address the problem of reasoning about preferences among properties (outcomes, desiderata, etc.) in Reiter’s default logic. Preferences are expressed using an ordered default theory, consisting of default rules, world knowledge, and an ordering, reflecting preference, on the default rules. In contrast with previous work in the area, we do not rely on prioritised versions of default logic, but rather we transform an ordered default theory into a second, standard default theory wherein the preferences are respected, in that defaults are applied in the prescribed order. This translation is accomplished via the naming of defaults, so that reference may be made to a default rule from within a theory. In an elaboration of the approach, we allow an ordered default theory where preference information is specified within a default theory. Here one may specify preferences that hold by default, in a particular context, or give preferences among preferences. In the approach, one essentially axiomatises how different orderings interact within a theory and need not rely on metatheoretic characterisations. As well, we can immediately use existing default logic theorem provers for an implementation. From a theoretical point of view, this shows that the explicit representation of priorities among defaults adds nothing to the overall expressibility of default logic.