On the evaluation of argumentation formalisms

Argumentation theory has become an important topic in the field of AI. The ba-sic idea is to construct arguments in favor and against a statement, to select the“acceptable” ones and, finally, to determine whether the original statement can beaccepted or not. Several argumentation systems have been proposed in the literature. Some ofthem, the so-called rule-based systems, use a particular logical language with strictand defeasible rules. While these systems are useful in different domains (e.g. legalreasoning), they unfortunately lead to very unintuitive results, as is discussed inthis paper. In order to avoid such anomalies, in this paper we are interested in definingprinciples, called rationality postulates, that can be used to judge the quality of arule-based argumentation system. In particular, we define two important rationalitypostulates that should be satisfied: the consistency and the closure of the resultsreturned by that system. We then provide a relatively easy way in which these rationality postulates canbe warranted for a particular rule-based argumentation system developed within aEuropean project on argumentation.