Compiling Reasoning with and about Preferences into Default Logic

We address the problem of introducing preferences into default logic. Two approaches are given, one a generalisation of the other. In the first approach, an ordered default theory consists of a set of default rules, a set of world knowledge, and a set of fixed preferences on the default rules. This theory is transformed into a second, standard default theory, where, via the naming of defaults, the given preference ordering on defaults is respected. In the second approach, we begin with a default theory where preference information is specified as part of an overall default theory. Here one may specify preferences that hold by default, or give preferences among preferences. Again, such a theory is translated into a standard default theory. The approach differs from previous work in that we obtain standard default theories, and do not rely on prioritised versions, as do other approaches. In practical terms this means 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 adds nothing to the overall expressibility of default logic.