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arXiv · 2011.01489

On Computing Stable Extensions of Abstract Argumentation Frameworks

Samer Nofal·Amani Abu Jabal·Abdullah Alfarrarjeh·Ismail Hababeh
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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}.

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Samer Nofal, Amani Abu Jabal, Abdullah Alfarrarjeh, Ismail Hababeh. 2020-11-03. On Computing Stable Extensions of Abstract Argumentation Frameworks. https://arxiv.org/abs/2011.01489

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