Labellings and Games for Extended Argumentation Frameworks

Dung’s abstract theory of argumentation has become established as a general framework for various species of non-monotonic reasoning, and reasoning in the presence of conflict. A Dung framework consists of arguments related by attacks, and the extensions of a framework, and so the status of arguments, are defined under different semantics. Developments of Dung’s work have also defined argument labellings as an alternative way of characterising extensions, and dialectical argument game proof theories for establishing the status of individual arguments. Recently, Extended Argumentation Frameworks extend Dung’s theory so that arguments not only attack arguments, but attacks themselves. In this way, the extended theory provides an abstract framework for principled integration of meta-level argumentation about defeasible preferences applied to resolve conflicts between object level arguments. In this paper we formalise labellings and argument games for a selection of Dung’s semantics defined for the extended frameworks.