The matrices of argumentation frameworks

by   Xu Yuming, et al.
Shandong University

We introduce matrix and its block to the Dung's theory of argumentation frameworks. It is showed that each argumentation framework has a matrix representation, and the common extension-based semantics of argumentation framework can be characterized by blocks of matrix and their relations. In contrast with traditional method of directed graph, the matrix way has the advantage of computability. Therefore, it has an extensive perspective to bring the theory of matrix into the research of argumentation frameworks and related areas.


Handling controversial arguments by matrix

We introduce matrix and its block to the Dung's theory of argumentation ...

A matrix approach for computing extensions of argumentation frameworks

The matrices and their sub-blocks are introduced into the study of deter...

A Comment on Argumentation

We use the theory of defaults and their meaning of [GS16] to develop (th...

The MatrixX Solver For Argumentation Frameworks

MatrixX is a solver for Abstract Argumentation Frameworks. Offensive and...

Value Based Argumentation Frameworks

This paper introduces the notion of value-based argumentation frameworks...

Complexity Results and Algorithms for Bipolar Argumentation

Bipolar Argumentation Frameworks (BAFs) admit several interpretations of...

Compact Argumentation Frameworks

Abstract argumentation frameworks (AFs) are one of the most studied form...


  • [1] P. Baroni, M. Giacomin, On principle-based evaluation of extension-based argumentation semantics, Artificial Intelligence 171 (2007), 675-700.
  • [2] T. J. M. Bench-Capon, Paul E. Dunne, Argumentation in artificial intelligence, Artificial intelligence 171(2007)619-641
  • [3] M.Caminada, Semi-stable semantics, in: Frontiers in Artificial Intelligence and its Applications, vol. 144, IOS Press, 2006, pp. 121-130.
  • [4] C.Cayrol, M.C.Lagasquie-Schiex, Graduality in argumentation, J. AI Res. 23 (2005)245-297.
  • [5] S.Coste-Marquis, C.Devred, C.Devred, Symmetric argumentation frameworks, in: Lecture Notes in Artificial Intelligence, vol. 3571, Springer-Verlag, 2005, pp. 317-328.
  • [6] S.Coste-Marquis, C.Devred, P. Marquis, Prudent semantics for argumentation frameworks, in: Proc. 17th ICTAI, 2005, pp. 568-572.
  • [7]

    Y.Dimopoulos, A. Torres, Graph theoretical structures in logic programs and default theories, Teoret. Comput. Sci. 170(1996)209-244.

  • [8] P.M. Dung, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and -person games, Artificial Intelligence 77 (1995), 321-357.
  • [9] P.M.Dung, P. Mancarella, F. Toni, A dialectic procedure for sceptical assumption-based argumentation, in: Frontiers in Artificial Intelligence and its Applications, vol. 144, IOS Press, 2006, pp. 145-156.
  • [10] P.E.Dunne, Computational properties of argument systems satisfying graph-theoretic constrains, Artificial Intelligence 171 (2007), 701-729.
  • [11] P.E.Dunne, T. J. M. Bench-Capon, Coherence in finite argument systems, Artificial intelligence 141(2002)187-203.
  • [12] P.E.Dunne, T. J. M. Bench-Capon, Two party immediate response disputes: properties and efficiency, Artificial Intelligence 149 (2003), 221-250.
  • [13] H.Jakobovits, D.Vermeir, Dialectic semantics for argumentation frameworks, in: Proc. 7th ICAIL, 1999, pp. 53-62.
  • [14] E. Oikarinen, S.Woltron, Characterizing strong equivalence for argumentation frameworks, Artificial intelligence(2011), doi:10.1016/j.artint.2011.06.003.
  • [15] G. Vreeswijk, Abstract argumentation system, Artificial intelligence 90(1997)225-279.
  • [16] G. Vreeswijk, H.Pakken, Credulous and sceptical argument games for preferred semantics, in: Proceedings of JELIA’2000, the 7th European Workshop on Logic for Artificial Intelligence, Berlin, 2000, pp. 224-238.