A Matrix Approach for Weighted Argumentation Frameworks: a Preliminary Report
Stefano Bistarelli, Alessandra Tappini, Carlo Taticchi

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.
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.
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Taxonomy
TopicsMulti-Agent Systems and Negotiation · Logic, Reasoning, and Knowledge · Service-Oriented Architecture and Web Services
