A Fully Rational Argumentation System for Preordered Defeasible Rules

Structured argumentation is a family of formal approaches for the handling of defeasible, potentially inconsistent information. Many models for structured argumentation distinguish between strict and defeasible inference rules. Defeasible rules often come with varying degrees of strength which is formally represented by a preorder over the defeasible rules. Various lifting principles have been presented in the literature to determine the relative strength of an argument by considering the strength of the defeasible rules used in its construction. The strength of arguments then comes into play when determining whether an attack (a purely syntactic relationship between arguments) results in a defeat (i.e. a successful attack). In [5, 22], several rationality postulates were proposed that serve as a measure to assess the normative rationality of structured argumentation formalisms. In [14], the first formalism satisfying all rationality postulates for structured argumentation when taking into account totally ordered defeasible rules was proposed. In many settings, assuming a total order greatly limits the realistic modelling capabilities of a formal system, e.g. when agents do not know the actual preferences of each rule or since different agents have different preferences over defeasible rules. Our paper shows that in the more general setting of preorders, violations of several rationality postulates can occur. We show how for a wide class of lifting principles, these violations can be avoided, resulting in the first Dung-based system that satisfies all four rationality postulates for preordered defeasible rule bases.