Default logic: Orderings and extensions

An ordering on default rules is defined that formalises intuitive relationships between rules. Unlike Etherington's [Eth88] orderings on literals which were only used to guarantee the existence of a computable extension, ours are defined proof-theoretically and used as an integral part of an algorithm that efficiently calculates all extensions for several useful sub-classes of default logic. The algorithm represents a significant reduction in complexity over other existing methods, especially for large multi-domain examples where indepeneant partial extensions can be calculated for different groups of unrelated rules which can be combined to produce complete extensions. Also, by changing the definition of the orderings without altering the underlying algorithm, extensions can be calculated for variants of default logic that have been proposed since Reiter's original paper.