The matrices of argumentation frameworks

TL;DR

This paper introduces a matrix representation for Dung's argumentation frameworks, enabling more computable analysis of argument extensions compared to traditional graph methods.

Contribution

It presents a novel matrix-based approach to represent and analyze argumentation frameworks, linking matrix blocks to extension semantics.

Findings

Matrix representation of argumentation frameworks is feasible.

Matrix approach enhances computability over traditional graph methods.

Potential for applying matrix theory to argumentation research.

Abstract

We introduce matrix and its block to the Dung's theory of argumentation frameworks. It is showed that each argumentation framework has a matrix representation, and the common extension-based semantics of argumentation framework can be characterized by blocks of matrix and their relations. In contrast with traditional method of directed graph, the matrix way has the advantage of computability. Therefore, it has an extensive perspective to bring the theory of matrix into the research of argumentation frameworks and related areas.