Reasoning over Attack-incomplete AAFs in the Presence of Correlations

Attack-Incomplete Abstract Argumentation Frameworks (att-iAAFs) are a popular extension of AAFs where attacks are marked as uncertain when they are not unanimously perceived by different agents reasoning on the same arguments. We here extend att-iAAFs with the possibility of specifying correlations involving the uncertain attacks. This feature supports a unified and more precise representation of the different scenarios for the argumentation, where, for instance, it can be stated that an attack α has to be considered only if an attack β is considered, or that α and β are alternative, and so on. In order to provide a user-friendly language for specifying the correlations, we allow the argumentation analyst to express them in terms of a set of elementary dependencies, using common logical operators (namely, OR, NAND, CHOICE, ⇒). In this context, we focus on the problem of verifying extensions under the possible perspective, and study the sensitivity of its computational complexity to the forms of correlations expressed and the semantics of the extensions.