On sceptical vs credulous acceptance for abstract argument systems

At a high level of abstraction, many systems of argumentation can be represented by a set of abstract arguments, and a binary relation between these abstract arguments describing how they contradict each other. Acceptable sets of arguments, called extensions, can be defined as sets of arguments that do not contradict one another, and attack all their attackers. We are interested in this paper in answering the question: is a given argument in all extensions of an argumentation system? In fact, what is likely to be useful in AI systems is not a simple yes/no answer, but some kind of well-argued answer, called a proof: if an argument is in every extension, why is it so? We describe a close connection between this problem and proofs that some meta-argument is in at least one extension of a meta-argumentation system, describing relationships between sets of arguments of the initial system.