# A Matrix Approach for Weighted Argumentation Frameworks: a Preliminary Report

## TL;DR

This paper introduces a matrix-based method for analyzing weighted argumentation frameworks, enabling the computation of various extensions and reduction of the framework size for more efficient reasoning.

## Contribution

It presents a novel matrix representation for weighted argumentation frameworks and algorithms for extension computation and framework reduction.

## Key findings

- Matrix representation characterizes basic extensions.
- Reduction method simplifies framework analysis.
- Algorithms incrementally build w-grounded and w-preferred extensions.

## Abstract

The assignment of weights to attacks in a classical Argumentation Framework allows to compute semantics by taking into account the different importance of each argument. We represent a Weighted Argumentation Framework by a non-binary matrix, and we characterize the basic extensions (such as w-admissible, w- stable, w-complete) by analysing sub-blocks of this matrix. Also, we show how to reduce the matrix into another one of smaller size, that is equivalent to the original one for the determination of extensions. Furthermore, we provide two algorithms that allow to build incrementally w-grounded and w-preferred extensions starting from a w-admissible extension.