Skip to Main content Skip to Navigation
Conference papers

The Matrix Approach for Abstract Argumentation Framework

Abstract : 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.
Complete list of metadata

Cited literature [23 references]  Display  Hide  Download
Contributor : Open Archive Toulouse Archive Ouverte (oatao) <>
Submitted on : Wednesday, May 31, 2017 - 4:39:30 PM
Last modification on : Thursday, March 18, 2021 - 2:25:22 PM
Long-term archiving on: : Wednesday, September 6, 2017 - 5:15:09 PM


Files produced by the author(s)


  • HAL Id : hal-01530404, version 1
  • OATAO : 16985


Yuming Xu, Claudette Cayrol. The Matrix Approach for Abstract Argumentation Framework. 3rd International Workshop on Theory and Applications of Formal Argumentation (TAFA 2015), an IJCAI-15 workshop, Jul 2015, Buenos Aires, Argentina. pp. 243-259. ⟨hal-01530404⟩



Record views


Files downloads