On the Complexity of the Discussion-based Semantics in Abstract Argumentation
Artificial Intelligence
2026-04-21 v2
Abstract
We show that deciding whether an argument a is stronger than an argument b with respect to the discussion-based semantics of Amgoud and Ben-Naim is decidable in polynomial time. At its core, this problem is about deciding whether, for two vertices in a graph, the number of walks of each length ending in those vertices is the same. We employ results from automata theory and reduce this problem to the equivalence problem for semiring automata. This offers a new perspective on the computational complexity of ranking semantics, an area in which the complexity of many semantics remains open.
Cite
@article{arxiv.2604.11480,
title = {On the Complexity of the Discussion-based Semantics in Abstract Argumentation},
author = {Lydia Blümel and Kai Sauerwald and Kenneth Skiba and Matthias Thimm},
journal= {arXiv preprint arXiv:2604.11480},
year = {2026}
}