On the Complexity of the Grounded Semantics for Infinite Argumentation Frameworks

Over the past three decades, formal argumentation has established itself as a prominent research area within Artificial Intelligence, owing to its versatility in addressing various reasoning tasks. These include nonmonotonic reasoning, multi-agent systems, rule-based systems, and the analysis of debates or dialogues. Formal argumentation provides a unifying framework for representing diverse reasoning approaches, ranging from highly skeptical to more permissive forms of inference (for a comprehensive introduction to this area, see the handbook [4]). At the heart of formal argumentation lies Dung's abstract argumentation frameworks (AFs) [15], which are modeled as directed graphs, where nodes correspond to arguments, and directed edges represent the attack relations between them. AFs serve as a common foundational core across various reasoning systems in formal argumentation, with many extensions and refinements, e.g.