Double Rectified Linear Unit-based Modular Semantics for Quantitative Bipolar Argumentation Framework

Abstract: Quantitative Bipolar Argumentation Frameworks (QBAFs) provide an alternative approach to computing argument acceptability in Bipolar Argumentation Frameworks (BAFs). Each argument is assigned an initial strength, which is then updated to a final strength by considering the influence of both its attackers and supporters. Over the years, several semantics have been proposed to compute argument acceptability in QBAFs, yet they often yield divergent or counterintuitive results, even for simple acyclic cases. We introduce novel gradual semantics for QBAFs that address these limitations, producing results that align more closely with intuitive expectations, while satisfying established rationality postulates from the literature. Furthermore, we study its convergence behavior, proving that it converges not only for acyclic QBAFs but also for broader classes of cyclic frameworks.