# On the Complexity of the Grounded Semantics for Infinite Argumentation Frameworks

arXiv: https://arxiv.org/abs/2511.22376 · HTML: https://mlsanity.com/paper/2511.22376/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 27 references that are in the map.
- First posted on arXiv 27 Nov 2025.

## Builds on (most cited first, 2 of 2)

- [A General Account of Argumentation with Preferences](https://mlsanity.com/paper/1804.06763/) (2018)
- [Automata for Infinite Argumentation Structures](https://mlsanity.com/paper/1810.04892/) (2018)

## Built on by (most cited first, 1 of 1)

- [Tenability and Weak Semantics: Modeling Non-uniform Defense -- Extended Version](https://mlsanity.com/paper/2605.02024/) (2026)

## Abstract (arXiv)

Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically computability and set theory, to analyze the grounded extension, a widely-used model of maximally skeptical reasoning, defined as the least fixed-point of a natural defense operator. Without additional constraints, finding this fixed-point requires transfinite iterations. We identify the exact ordinal number corresponding to the length of this iterative process and determine the complexity of deciding grounded acceptance, showing it to be maximally complex. This shows a marked distinction from the finite case where the grounded extension is polynomial-time computable, thus simpler than other reasoning problems explored in formal argumentation.