Concurrence for well-formed CAFs: Naive Semantics

TL;DR

This paper proves that determining concurrence for naive semantics in well-formed claim-augmented frameworks is computationally hard (coNP-hard), resolving an open problem in abstract argumentation theory.

Contribution

It establishes the coNP-hardness of the concurrence problem for naive semantics in well-formed CAFs, advancing understanding of computational complexity in argumentation frameworks.

Findings

Concurrence problem is coNP-hard for well-formed CAFs.

Resolves an open problem from Dvorák et al. (2021).

Provides complexity results for naive semantics in claim-based reasoning.

Abstract

In the area of claim-based reasoning in abstract argumentation, a claim-based semantics is said to be concurrent in a given framework if all its variants yield the same extensions. In this note, we show that the concurrence problem with respect to naive semantics is coNP-hard for well-formed CAFs. This solves a problem that has been left open in Dvor\'ak et al. (2021).