Convergence and Open-Mindedness of Discrete and Continuous Semantics for Bipolar Weighted Argumentation (Technical Report)

Weighted bipolar argumentation frameworks determine the strength of arguments based on an initial weight and the strength of their attackers and supporters. They find applications in decision support and social media analysis. Mossakowski and Neuhaus recently introduced a unification of different models and gave sufficient conditions for convergence and divergence in cyclic graphs. We build up on this work, incorporate additional models and extend results in several directions. In particular, we explain that the convergence guarantees can be seen as special cases of the contraction principle. We use this observation to unify and to generalize results and add runtime guarantees. Unfortunately, we find that guarantees obtained in this way are bought at the expense of open-mindedness, that is, the ability to move strength values away from the initial weights. However, we also demonstrate that divergence problems can be solved without giving up open-mindedness by continuizing the models. Finally, we integrate the Duality property that assures a symmetric impact of attack and support relations into the framework by Mossakowski and Neuhaus.