Assumption-based argumentation for closed and consistent defeasible reasoning

Assumption-based argumentation is a concrete but general-purpose argumentation framework that has been shown, in particular, to generalise several existing mechanisms for non-monotonic reasoning, and is equipped with a computational counterpart and an implemented system. It can thus serve as a computational tool for argumentation-based reasoning, and for automatising the process of finding solutions to problems that can be understood in assumption-based argumentation terms. In this paper we consider the problem of reasoning with defeasible and strict rules, for example as required in a legal setting. We provide a mapping of defeasible reasoning into assumption-based argumentation, and show that the framework obtained has properties of closedness and consistency, that have been advocated elsewhere as important for defeasible reasoning in the presence of strict rules. Whereas other argumentation approaches have been proven closed and consistent under some specific semantics, we prove that assumption-based argumentation is closed and consistent under all argumentation semantics.