On Gradual Semantics for Assumption-Based Argumentation

In computational argumentation, gradual semantics are fine-grained alternatives to extension-based and labelling-based semantics. They ascribe a dialectical strength to (components of) arguments sanctioning their degree of acceptability. Several gradual semantics have been studied for abstract, bipolar and quantitative bipolar argumentation frameworks (QBAFs), as well as, to a lesser extent, for some forms of structured argumentation. However, this has not been the case for assumption-based argumentation (ABA), despite it being a popular form of structured argumentation with several applications where gradual semantics could be useful. In this paper, we fill this gap and propose a family of novel gradual semantics for equipping assumptions, which are the core components in ABA frameworks, with dialectical strengths. To do so, we use bipolar set-based argumentation frameworks as an abstraction of (potentially non-flat) ABA frameworks and generalise state-of-the-art modular gradual semantics for QBAFs. We show that our gradual ABA semantics satisfy suitable adaptations of desirable properties of gradual QBAF semantics, such as balance and monotonicity. We also explore an argument-based approach that leverages established QBAF modular semantics directly, and use it as baseline. Finally, we conduct experiments with synthetic ABA frameworks to compare our gradual ABA semantics with its argument-based counterpart and assess convergence.