ASPIC-style structured argumentation frameworks provide a formal basis for reasoning in artificial intelligence by combining internal argument structure with abstract argumentation semantics. A key challenge in these frameworks is ensuring compliance with five critical rationality postulates: closure, direct consistency, indirect consistency, non-interference, and crash-resistance. Recent approaches, including ASPIC⊖ and Deductive ASPIC−, have made significant progress but fall short of meeting all postulates simultaneously under a credulous semantics (e.g. preferred) in the presence of undercuts. This paper introduces Deductive ASPIC⊖, a novel framework that integrates gen-rebuttals from ASPIC⊖ with the Joint Support Bipolar Argumentation Frameworks (JSBAFs) of Deductive ASPIC−, incorporating preferences. We show that Deductive ASPIC⊖ satisfies all five rationality postulates under a version of preferred semantics. This work opens new avenues for further research on robust and logically sound structured argumentation systems.
This paper studies the expressive power of ASPIC+ argumentation frameworks with uncertain preference profiles by comparing them with several abstract formalisms with uncertain defeats. Most of our results are negative (and some of them are theoretically unexpected). We also conjecture a positive, non-trivial threshold for the expressivity of uncertain preferences, and prove some essential preliminary steps toward the confirmation of this conjecture.
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.
Gianvincenzo Alfano, Sergio Greco, Lucio La Cava +2
This work proposes novel splitting techniques for argumentation formalisms that incorporate supports between defeasible elements. We base our studies on bipolar set-based argumentation frameworks (BSAFs) which generalize argumentation frameworks with collective attacks (SETAFs), as well as bipolar argumentation frameworks (BAFs), by incorporating both collective attacks and supports. Notably, BSAFs establish a crucial link to structured argumentation as they naturally capture general (potentially non-flat) assumption-based argumentation. The increase in expressiveness calls for diverse forms of splitting. We consider splits over collective attacks (thereby generalizing the recently proposed splitting techniques for SETAFs), splits over collective supports, as well as splits over both collective attacks and supports. We establish suitable splitting schemata and prove their correctness for the most common argumentation semantics.
Matti Berthold, Lydia Blümel, Giovanni Buraglio +1