Redefining ABA+ Semantics via Abstract Set-to-Set Attacks

Assumption-based argumentation (ABA) is a powerful defeasible reasoning formalism which is based on the interplay of assumptions, their contraries, and inference rules. ABA with preferences (ABA + ) generalizes the basic model by allowing a qualitative comparison of assumptions. The integration of preferences however comes with a cost. In ABA + , the evaluation under two central and well-established semanticsgrounded and complete semantics-is not guaranteed to yield an outcome. Moreover, while ABA frameworks without preferences allow for a graph-based representation in Dung-style frameworks, an according instantiation for general ABA + frameworks has not been established so far. In this work, we tackle both issues: First, we develop a novel abstract argumentation formalism based on set-to-set attacks. We show that our so-called Hyper Argumentation Frameworks (HY-PAFs) capture ABA + . Second, we propose relaxed variants of complete and grounded semantics for HYPAFs that yield an extension for all frameworks by design, while still faithfully generalizing the established semantics of Dung-style Argumentation Frameworks. We exploit the newly established correspondence between ABA + and HYPAFs to obtain variants for grounded and complete ABA + semantics that are guaranteed to yield an outcome. Finally, we discuss basic properties and provide a complexity analysis. Along the way, we settle the computational complexity of several ABA + semantics.

Formal argumentation is a major research area in knowledge representation and reasoning, with applications in various fields in the realm of Artificial Intelligence (Bench-Capon, Prakken, and Sartor 2009;Baroni et al. 2018). The close interplay between rule-based systems and graph-based methods is thereby key to exploit the full potential of argumentative methods. Rule-based formalisms are crucial to understand and evaluate complex dependencies between defeasible elements of a knowledge base. Assumption-Based Argumentation (ABA) (Cyras et al. 2018) is one of the leading rule-based argumentation formalisms. Key elements are assumptions, their contraries, and inference rules; they form the building blocks to construct arguments and to identify conflicts in the given knowledge base. Acceptability of the