Relating Carneades with abstract argumentation via the ASPIC+ framework for structured argumentation

Carneades is a recently proposed formalism for structured argumentation with varying proof standards, inspired by legal reasoning but more generally applicable. Its distinctive feature is that each statement can be given its own proof standard, which is claimed to allow a more natural account of reasoning under burden of proof than existing formalisms for structured argumentation, in which proof standards are defined globally. In this article the two formalisms are formally related by translating Carneades into the ASPIC+ framework for structured argumentation. Since ASPIC+ is defined to generate Dung-style abstract argumentation frameworks, this in effect translates Carneades graphs into abstract argumentation frameworks. For this translation, we prove a formal correspondence and show that certain rationality postulates hold. It is furthermore proven that Carneades always induces a unique Dung extension, which is the same in all of Dung’s semantics, allowing us to generalise Carneades to cycle-containing structures.