标题：The matrix approach for abstract argumentation frameworks
作者：Xu, Yuming ;Cayrol, Claudette
作者机构：[Xu, Yuming ] School of Mathematics, Shandong University, Jinan, China;[Cayrol, Claudette ] IRIT, University of Toulouse, Toulouse, France
会议名称：3rd International Workshop on Theory and Applications of Formal Argumentation, TAFA 2015
会议日期：25 July 2015 through 26 July 2015
来源：Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
关键词：Argumentation; Dynamics; Extension; Matrix; Reduction
摘要：Matrices and the operation of dual interchange are introduced into the study of Dung’s argumentation frameworks. It is showed that every argumentation framework can be represented by a matrix, and the basic extensions (such as admissible, stable, complete) can be determined by sub-blocks of its matrix. In particular, an efficient approach for determining the basic extensions has been developed using two types of standard matrix. Furthermore, we develop the topic of matrix reduction along two different lines. The first one enables to reduce the matrix into a less order matrix playing the same role for the determination of extensions. The second one enables to decompose an extension into several extensions of different sub-argumentation frameworks. It makes us not only solve the problem of determining grounded and preferred extensions, but also obtain results about dynamics of argumentation frameworks. © Springer International Publishing Switzerland 2015.