On Computing Stable Extensions of Abstract Argumentation Frameworks

TL;DR

This paper provides a formal validation of a backtracking algorithm designed to list all stable extensions in abstract argumentation frameworks, contributing to the understanding of computational methods in argumentation theory.

Contribution

It offers a thorough, formal validation of a known backtracking algorithm for computing all stable extensions in abstract argumentation frameworks.

Findings

The algorithm correctly lists all stable extensions.

Formal proof of the algorithm's correctness is provided.

The validation enhances reliability of computational methods in argumentation.

Abstract

An \textit{abstract argumentation framework} ({\sc af} for short) is a directed graph $(A,R)$ where $A$ is a set of \textit{abstract arguments} and $R\subseteq A \times A$ is the \textit{attack} relation. Let $H=(A,R)$ be an {\sc af}, $S \subseteq A$ be a set of arguments and $S^+ = \{y \mid \exists x\in S \text{ with }(x,y)\in R\}$. Then, $S$ is a \textit{stable extension} in $H$ if and only if $S^+ = A\setminus S$. In this paper, we present a thorough, formal validation of a known backtracking algorithm for listing all stable extensions in a given {\sc af}.