# Facets in Argumentation: A Formal Approach to Argument Significance

arXiv: https://arxiv.org/abs/2505.10982 · HTML: https://mlsanity.com/paper/2505.10982/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 41 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 5 of 5)

- [Counting Complexity for Reasoning in Abstract Argumentation](https://mlsanity.com/paper/1811.11501/) (2018)
- [Fudge: A light-weight solver for abstract argumentation based on SAT reductions](https://mlsanity.com/paper/2109.03106/) (2021)
- [The pyglaf argumentation reasoner (ICCMA2021)](https://mlsanity.com/paper/2109.03162/) (2021)
- [Default Logic and Bounded Treewidth](https://mlsanity.com/paper/1706.09393/) (2017)
- [Counting and Reasoning with Plans](https://mlsanity.com/paper/2502.00145/) (2025)

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

- [Complexity of Faceted Explanations in Propositional Abduction](https://mlsanity.com/paper/2507.14962/) (2025)
- [Diversity of Extensions in Abstract Argumentation](https://mlsanity.com/paper/2605.13332/) (2026)
- [Representative Sets in Propositional Abduction](https://mlsanity.com/paper/2607.21183/) (2026)

## Abstract (arXiv)

Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the relationship between them, such as stable or admissible. Today's solvers implement tasks such as finding extensions, deciding credulous or skeptical acceptance, counting, or enumerating extensions. While these tasks are well charted, the area between decision, counting/enumeration and fine-grained reasoning requires expensive reasoning so far. We introduce a novel concept (facets) for reasoning between decision and enumeration. Facets are arguments that belong to some extensions (credulous) but not to all extensions (skeptical). They are most natural when a user aims to navigate, filter, or comprehend the significance of specific arguments, according to their needs. We study the complexity and show that tasks involving facets are much easier than counting extensions. Finally, we provide an implementation, and conduct experiments to demonstrate feasibility.