Title Abstract Contents 1 2 3 4 5 Acknowlegments References Footnotes

5 Conclusions

In this paper, two approaches to dialectical argumentation have been compared: Dung's admissible sets of arguments and Verheij's argumentation stages. The main difference is that the arguments in an admissible set must be defended against all challenging arguments, while the undefeated arguments of an argumentation stage only need to be defended against the challenging arguments taken into account.

Theorem 3 showed that both approaches are strongly related: All argumentation stages of an argumentation theory correspond to the admissible sets of the restrictions of that theory. As a result, they are equivalent as far as the relations of arguments and counterarguments is concerned.

However, for a fixed theory, argumentation stages generalize admissible sets. We have shown that Dung's preferred and stable extensions correspond to preferred stages and complete stage extensions, respectively. In the stage approach, there are two natural new types of extensions: admissible stage extensions and stage extensions. Their definitions are based on the idea that one wants to take as many arguments into account as possible. These types of extensions have no counterpart in the admissible set approach. Figure 1 summarizes the relations between the types of extensions.

We have shown that the argumentation stages give in a natural way rise to argumentation diagrams, in which paths can be interpreted as lines of argumentation. Therefore, the stages approach gives insight in the process character of dialectical argumentation.

This is especially important since recently the importance of the fundamentally procedural nature of argumentation-as-justification has been re-emphasized in the artificial intelligence community (see, e.g., Hage et al., 1994; Gordon, 1995; Lodder, 1996; Loui, 1991, 1995; Vreeswijk, 1995). Argumentation diagrams are useful for the understanding of the process of argumentation. For instance, argumentation strategies and protocols can be regarded as constraints on lines of argumentation, and therefore correspond to partial argumentation diagrams.

Title Abstract Contents 1 2 3 4 5 Acknowlegments References Footnotes