# On Gradual Semantics for Assumption-Based Argumentation

arXiv: https://arxiv.org/abs/2507.10076 · HTML: https://mlsanity.com/paper/2507.10076/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 69 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 8 of 8)

- [Modular Semantics and Characteristics for Bipolar Weighted Argumentation Graphs](https://mlsanity.com/paper/1807.06685/) (2018)
- [SpArX: Sparse Argumentative Explanations for Neural Networks [Technical Report]](https://mlsanity.com/paper/2301.09559/) (2023)
- [ABA+: Assumption-Based Argumentation with Preferences](https://mlsanity.com/paper/1610.03024/) (2016)
- [Instantiations and Computational Aspects of Non-Flat Assumption-based Argumentation](https://mlsanity.com/paper/2404.11431/) (2024)
- [Non-flat ABA is an Instance of Bipolar Argumentation](https://mlsanity.com/paper/2305.12453/) (2023)
- [Harnessing Incremental Answer Set Solving for Reasoning in Assumption-Based Argumentation](https://mlsanity.com/paper/2108.04192/) (2021)
- [A Methodology for Incompleteness-Tolerant and Modular Gradual Semantics for Argumentative Statement Graphs](https://mlsanity.com/paper/2410.22209/) (2024)
- [Intrinsic Argument Strength in Structured Argumentation: a Principled Approach](https://mlsanity.com/paper/2109.00318/) (2021)

## Built on by (most cited first, 3 of 3)

- [From User Preferences to Base Score Extraction Functions in Gradual Argumentation (with Appendix)](https://mlsanity.com/paper/2602.14674/) (2026)
- [Double Rectified Linear Unit-based Modular Semantics for Quantitative Bipolar Argumentation Framework](https://mlsanity.com/paper/2605.02551/) (2026)
- [GRASP: Deterministic argument ranking in interaction graphs](https://mlsanity.com/paper/2605.19141/) (2026)

## Abstract (arXiv)

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.