Constrained Assumption-Based Argumentation Frameworks
Emanuele De Angelis, Fabio Fioravanti, Maria Chiara Meo, Alberto Pettorossi, Maurizio Proietti, Francesca Toni
TL;DR
This work extends assumption-based argumentation by introducing Constrained ABA (CABA), which incorporates a constraint theory $\mathcal{C\ T}$ and allows non-ground rule schemata over possibly infinite domains. It provides two complementary semantic axes: a grounding-based approach that maps CABA to standard ABA via $Ground(F_c)$, and a native, non-ground approach with constrained arguments and attacks (TCArg/MGCArg, full/partial attacks, NGCF, and Argument Splitting). The paper proves that constrained semantics conservatively generalise ABA semantics and shows conditions under which non-ground semantics align with grounded counterparts, enabling finite non-ground extensions via splitting. These results enable robust, constraint-aware argumentation over infinite domains while preserving ABA’s theoretical foundations, with potential applications in legal reasoning and other constraint-rich settings.
Abstract
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.