Preservation of Semantic Properties in Collective Argumentation: The Case of Aggregating Abstract Argumentation Frameworks

An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the second. When modelling a group of agents engaged in such a debate, we may wish to aggregate their individual argumentation frameworks to obtain a single such framework that reflects the consensus of the group. While agents typically will not agree on every single attack, there may well be high-level agreement on semantic properties, such as whether a given argument should be accepted or whether there are any acceptable arguments at all. Using techniques from social choice theory, we analyse the circumstances under which such semantic properties agreed upon by the individual agents will be preserved under aggregation. Our results cover semantic properties formulated in terms of six of the most widely used extension-based semantics for abstract argumentation and range from positive results that show that certain aggregation rules can provide the desired preservation guarantees to impossibility theorems that show that certain combinations of requirements cannot be met by any reasonable aggregation rule.