A preferential model semantics for default logic

Shoham proposed a uniform approach to systems for nonmonotonic reasoning, which consists in considering standard logics augmented with a preference relation on the interpretations. Circumscription can easily seen to be a special case of this preference logic framework, but capturing default logic turned out to be, more difficult, and is even thought to be impossible by some researchers of nonmonotonic reasoning. In this paper a preferential model semantics for default logic is given, by defining a preference relation on partial models called hypervaluations. Alternatively, Kripke models for K45 could have been used instead of hypervaluations. The given semantics slightly strengthens Shoham's notion of preferential entailment, and reflection on the question why such a strengthening is necessary provides some insight into the relation between default logic and circumscription