Two approaches to dialectical argumentation:

admissible sets and argumentation stages

Bart Verheij

University of Limburg, Department of Metajuridica

P.O. Box 616, 6200 MD Maastricht, The Netherlands,


Currently there is a revival of the study of dialectical argumentation in the artificial intelligence community. There are good reasons why: First, the notions of argument and counterargument shed new light on nonmonotonic reasoning. Second, the process character of dialectical argumentation inspires new computational techniques.

In a recent important paper, Dung (1995) has studied the relations of (unstructured) arguments and their counterarguments in terms of admissible sets. He has investigated the relations between several types of extensions of argumentation theories.

In this paper, we propose a model of the stages of argumentation, related to that of Verheij (1995a, 1995b). Each stage is characterized by the arguments that have been taken into account and by the status of these arguments, either undefeated or defeated. This stage approach provides additional understanding of the process of argumentation, and gives naturally rise to two new types of extensions. Their definitions formalize the idea that as many arguments are taken into account as possible.

We show the connections with Dung's work and give a number of examples. It turns out that the argumentation stage approach generalizes the admissible set approach. The main conclusion of the paper is that the argumentation stage approach can give more insight in the procedural nature of dialectical argumentation than the admissible set approach.


1 Introduction
2 Definition of admissible stages and argumentation stages
3 Connections between the two approaches
4 Examples and argumentation diagrams
4.1 Counterattack and reinstatement
4.2 Mutual attack and multiple extensions
4.3 Loop of attacks and non-admissible stage extensions
4.4 Mutual attack skewly breaking a loop of attacks
4.5 No exhausting sequence of compatible stages
5 Conclusions