Formalizing dynamics of argumentation has received increasing attention over the last years. While AGM-like representation results for revision of argumentation frameworks (AFs) are now available, similar results for the problem of merging are still missing. In this paper, we close this gap and adapt model-based propositional belief merging to define extension-based merging operators for AFs. We state an axiomatic and a constructive characterization of merging operators through a family of rationality postulates and a representation theorem. Then we exhibit merging operators which satisfy the postulates. In contrast to the case of revision, we observe that obtaining a single framework as result of merging turns out to be a more subtle issue. Finally, we establish links between our new results and previous approaches to merging of AFs, which mainly relied on axioms from Social Choice Theory, but lacked AGM-like representation theorems.

We study the problem of aggregation of Dung's abstract argumentation frameworks. Some operators for this aggregation have been proposed, as well as some rationality properties for this process. In this work we study the existing operators and new ones that we propose in light of the proposed properties, highlighting the fact that existing operators do not satisfy a lot of these properties. The conclusions are that on one hand none of the existing operators seem fully satisfactory, but on the other hand some of the properties proposed so far seem also too demanding.