Independence and D-separation in Abstract Argumentation

We investigate the notion of independence in abstract argumentation, i.e., the question of whether the evaluation of one set of arguments is independent of the evaluation of another set of arguments, given that we already know the status of a third set of arguments. We provide a semantic definition of this notion and develop a method to discover independencies based on transforming an argumentation framework into a DAG on which we then apply the well-known d-separation criterion. We also introduce the SCC Markov property for argumentation semantics, which generalises the Markov property from the classical acyclic case and guarantees the soundness of our approach.