Different agents may have different points of view. Following a popular approach in the artificial intelligence literature, this can be modelled by means of different abstract argumentation frameworks, each consisting of a set of arguments the agent is contemplating 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 regarding the moral or social values the arguments under scrutiny relate to. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. In doing so, we distinguish different constraints on admissible rationalisations, e.g., concerning the types of preferences used or the number of distinct values involved. We also distinguish two different semantics for rationalisability, which differ in the assumptions made on how agents treat attacks between arguments they do not report. This research agenda, bringing together ideas from abstract argumentation and social choice, is useful for understanding what types of profiles can reasonably be expected to occur in a multiagent system.

Argumentation is a process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such semantics have been pro- posed independently, often associated with some desirable properties. However, there is no comparative study which takes a broader perspective. This is what we propose in this work. We provide a general comparison of all these semantics with respect to the proposed proper- ties. That allows to underline the differences of behavior between the existing semantics.