Towards the proof-theoretic unification of Dung’s argumentation framework: an adaptive logic approach

The article presents a unifying adaptive logic framework for abstract argumentation. It consists of a core system for abstract argumentation and various adaptive logics based on it. These logics represent in an accurate sense all standard extensions defined within Dung’s abstract argumentation system with respect to sceptical and credulous acceptance. The models of our logics correspond exactly to specific extensions of given argument systems. Additionally, the dynamics of adaptive proofs mirror the argumentative reasoning of a rational agent. In particular, the presented logics allow for external dynamics, i.e. they are able to deal with the arrival of new arguments and are therefore apt to model open-ended argumentations by providing provisional conclusions.