Rationalisation of Profiles of Abstract Argumentation Frameworks

Different agents may have different points of view. This can be modelled using different abstract argumentation frameworks, each consisting of a set of arguments and a binary attack-relation between them. A question arising in this context is whether the diversity of views observed in such a profile of argumentation frameworks is consistent with the assumption that every individual argumentation framework is induced by a combination of, first, some basic factual attack-relation between the arguments and, second, the personal preferences of the agent concerned. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. This is useful for understanding what types of profiles can reasonably be expected to come up in a multiagent system.