Bridging the Gap between Abstract Argumentation Systems and Logic

Dung's argumentation system takes as input a set of arguments and a binary relation encoding attacks among these arguments, and returns different extensions of arguments. However, no indication is given on how to instantiate this setting, i.e. how to build arguments from a knowledge base and how to choose an appropriate attack relation. This leads in some cases to undesirable results like inconsistent extensions (i.e. the set of formulas forming an extension is inconsistent). This is due to the gap between the abstract setting and the knowledge base from which it is defined. The purpose of this paper is twofold: First it proposes to fill in this gap by extending Dung's system. The idea is to consider all the ingredients involved in an argumentation problem. We start with an abstract monotonic logic which consists of a set of formulas and a consequence operator. We show how to build arguments from a knowledge base using the consequence operator of the logic. Second, we show that the choice of an attack relation is crucial for ensuring consistent results, and should not be arbitrary. In particular, we argue that an attack relation should be at least grounded on the minimal conflicts contained in the knowledge base. Moreover, due to the binary character of this relation, some attack relations may lead to unintended results. Namely, symmetric relations are not suitable when ternary (or more) minimal conflicts are in the knowledge base. We propose then the characteristics of attack relations that ensure sound results.