The Matrix Approach for Abstract Argumentation Framework

Yuming Xu (1) , Claudette Cayrol (2)

1 Shandong University
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage

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.

Mots clés: Graphes; ARG; Dynamics; Reduction; Extension; Argumentation; Matrix

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

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⟩