A Tableau-Based Characterisation for Default Logic

This paper has two objectives: We first give a necessary and sufficient criterion for the existence of extension of default theories in the general case. Second, we present a new, efficient and clear method for computing extensions and deriving formulae of default theory in the general case. It is based on the semantic tableaux method [Smullyan 1968] and works for default theories with a finite set of defaults that are formulated over a decidable subset of first-order logic. We prove that all extensions (if any) of a default theory can be produced by constructing the semantic tableau of one formula built from the general laws and the default consequences.