Handling controversial arguments by matrix

TL;DR

This paper introduces a matrix-based approach to Dung's argumentation framework, enabling efficient computation of indirect relations and controversial arguments, and offering a new mathematical perspective for analyzing argumentation semantics.

Contribution

It develops a novel matrix representation for argumentation frameworks, allowing for easier computation of indirect relations and semantics compared to traditional graph methods.

Findings

Matrix representation characterizes indirect attack and defense relations.

Various semantics can be determined by matrix comparison.

Matrix method is computationally efficient and suitable for computer implementation.

Abstract

We introduce matrix and its block to the Dung's theory of argumentation framework. It is showed that each argumentation framework has a matrix representation, and the indirect attack relation and indirect defence relation can be characterized by computing the matrix. This provide a powerful mathematics way to determine the "controversial arguments" in an argumentation framework. Also, we introduce several kinds of blocks based on the matrix, and various prudent semantics of argumentation frameworks can all be determined by computing and comparing the matrices and their blocks which we have defined. In contrast with traditional method of directed graph, the matrix method has an excellent advantage: computability(even can be realized on computer easily). So, there is an intensive perspective to import the theory of matrix to the research of argumentation frameworks and its related areas.