Reasoning about Preferences in Structured Extended Argumentation Frameworks

This paper combines two recent extensions of Dung's abstract argumentation frameworks in order to define an abstract formalism for reasoning about preferences in structured argumentation frameworks. First, extended argumentation frameworks extend Dung frameworks with attacks on attacks, thus providing an abstract dialectical semantics that accommodates argumentation-based reasoning about preferences over arguments. Second, a recent extension of the ASPIC framework (ASPIC+) instantiates Dung frameworks with accounts of the structure of arguments, the nature of attack and the use of preferences to resolve attacks. In this paper, ASPIC+ is further developed in order to define attacks on attacks, resulting in a dialectical semantics that accommodates argumentation based reasoning about preferences in structured argumentation. Then, some recently proposed rationality postulates for structured extended argumentation are proven to hold.