Embedding Default Theories in Propositional Argumentation Systems

In this paper we present a transformation of propositional default theories into so-called propositional argumentation systems. This transformation allows to characterize all notions of Reiter’s default logic in the framework of argumentation systems. This means that computing extension, or determining if a given formula belongs to one extension or all extensions can be answered without leaving the field of monotonic propositional logic. Interestingly, this framework allows to immediately recognize the special cases of default theories having none or exactly one “trivial” extension where no default is applicable. The transformation provided is exact and linear in the number of defaults.