  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.
