Abstract The paper develops a formal theory of the degree of justification of arguments, which relies solely on the structure of an argumentation framework, and which can be successfully interfaced with approaches to instantiated argumentation. The theory is developed in three steps. First, the paper introduces a graded generalization of the two key notions underpinning Dung's semantics: self-defense and conflict-freeness. This leads to a natural generalization of Dung's semantics, whereby standard extensions are weakened or strengthened depending on the level of self-defense and conflict-freeness they meet. The paper investigates the fixpoint theory of these semantics, establishing existence results for them. Second, the paper shows how graded semantics readily provide an approach to argument rankings, offering a novel contribution to the recently growing research programme on ranking-based semantics. Third, this novel approach to argument ranking is applied and studied in the context of instantiated argumentation frameworks, and in so doing is shown to account for a simple form of accrual of arguments within the Dung paradigm. Finally, the theory is compared in detail with existing approaches.
@cite_13: Abstract argumentation (Dung 1995) is a theory of dialectic that allows us to formalise and study various notions of argument acceptability. We depart from this standard approach and formalise a measure of argument strength by applying the concept of value of a game, as defined in Game Theory (von Neumann 1928). The measure thus obtained satisfies a number of intuitively appealing properties that can be derived mathematically from the minimax theorem.
Finally, Matt and Toni () @cite_13 provide a highly original paradigm for ranking arguments, defining argument strength in terms of the value of a repeated two-person zero-sum strategic game with imperfect information.