Splitting Argumentation Frameworks with Collective Attacks and Supports

2026-04-30

AI Summary

This work proposes the first general decomposition scheme for bipolar set-based argumentation frameworks (BSAFs) that simultaneously accommodate collective attacks and supports, significantly enhancing reasoning efficiency and modular analysis of complex argumentation systems. By leveraging formal logic, abstract argumentation theory, and set-theoretic methods, the authors systematically construct and validate multiple decomposition patterns applicable to attack-only, support-only, and mixed scenarios. The scheme is proven correct under major semantics—including complete, preferred, and stable extensions—thereby extending existing decomposition theories for SETAFs and bipolar argumentation frameworks (BAFs). Furthermore, it establishes a formal bridge to non-flat assumption-based structured argumentation, substantially improving the scalability and computational tractability of BSAFs.

Abstract

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.

Problem

• argumentation frameworks
• collective attacks
• collective supports
• splitting
• bipolar set-based argumentation

Innovation

• splitting techniques
• collective attacks
• collective supports
• bipolar set-based argumentation frameworks
• argumentation semantics