Lexicographic priorities in default

Resolving connicts between default rules is a major subtask in performing default reasoning. A declarative way of controlling the resolution of connicts is to assign priorities to default rules, and to prevent connict resolution in ways that violate the priorities. This work extends Reiter's default logic with a priority mechanism that is based on lexicographic comparison. Given a default theory and a partial ordering on the defaults, the preferred extensions are the lexicographically best extensions. We discuss alternative ways of using lexicographic comparison, and investigate their properties and relations between them. The applicability of the priority mechanism to inheritance reasoning is investigated by presenting two translations from inheritance networks to prioritized default theories, and relating them to inheritance theories presented earlier by Gelfond and Przymusinska and by Brewka.