Under-Approximating Semantics in Clustered Assumption-Based Argumentation

Computational argumentation studies fundamental methods for reasoning within Artificial Intelligence (AI). Such methods are divided into two main approaches, namely the abstract and the structured one. Abstract argumentation focuses on the interactions between arguments, ignoring their internal structure, while structured approaches utilize a given knowledge base to construct the arguments. Thus, the latter approach incorporates the internal structure of arguments into the reasoning process. In this work we introduce a form of abstraction on the well established structured approach of Assumption-Based Argumentation (ABA). Our goal is to provide methods to simplify complicated scenarios, by applying clustering over defeasible parts. Abstraction, particularly clustering, has been explored in recent research on abstract argumentation and in the adjacent field of logic programming. In fact, while clustering has also been applied to ABA, our approach takes a different, or rather dual, direction. In contrast to prior work on over-approximation on ABA, we propose the dual approach of under-approximation. We provide semantics for reasoning over clustered frameworks in a sound manner relative to original semantics, ensuring that any set deemed acceptable in the clustered scenario corresponds to an acceptable set. We show fundamental properties of the under-approximating semantics and illustrate our approach using a conceptual example based on medical recommendations.