Constrained Assumption-Based Argumentation Frameworks
This work addresses a representational restriction in structured argumentation for AI and logic, though it appears incremental as it builds on existing ABA frameworks.
The paper tackles the limitation of Assumption-based Argumentation (ABA) frameworks to ground arguments by introducing constrained ABA (CABA) with variables over infinite domains, and shows that its non-ground semantics conservatively generalize standard ABA semantics.
Assumption-based Argumentation (ABA) is a well-established form of structured argumentation. ABA frameworks with an underlying atomic language are widely studied, but their applicability is limited by a representational restriction to ground (variable-free) arguments and attacks built from propositional atoms. In this paper, we lift this restriction and propose a novel notion of constrained ABA (CABA), whose components, as well as arguments built from them, may include constrained variables, ranging over possibly infinite domains. We define non-ground semantics for CABA, in terms of various notions of non-ground attacks. We show that the new semantics conservatively generalise standard ABA semantics.