KR Conference 2016 Conference Paper
- Leila Amgoud
- Jonathan Ben-Naim
- Dragan Doder
- Srdjan Vesic
In almost all existing semantics in argumentation, a strong attack has a lethal effect on its target that a set of several weak attacks may not have. This paper investigates the case where several weak attacks may compensate one strong attack. It defines a broad class of ranking semantics, called α−BBS, which satisfy compensation. α−BBS assign a burden number to each argument and order the arguments with respect to those numbers. We study formal properties of α−BBS, implement an algorithm that calculates the ranking, and perform experiments that show that the approach computes the ranking very quickly. Moreover, an approximation of the ranking can be provided at any time. p q r a p s b F2 v t p An argumentation framework consists of an argumentation graph, that is arguments and attacks between them, and a semantics for evaluating the arguments, and thus for specifying which arguments are acceptable. The most dominant semantics in the literature are those that compute extensions of arguments, initially proposed by Dung (1995). Such semantics are based on the assumption that a successful attack completely destroys its target. Consequently, several successful attacks cannot destroy the target at a greater extent. There are applications where this assumption makes perfect sense (Dung 1995). In other applications, like decision making or dialogues, an attack only weakens its target. Think about a committee which recruits young researchers. Once an argument against a candidate is given, even if this argument is attacked, the initial argument is still considered by the members of the committee (but with a lower strength). Consequently, one attack does not necessarily have the same effect as several attacks. Consider argumentation graph F1 from Figure 1. Arguments a and b are both attacked by strong (i. e. non attacked) arguments. However, b is weakened by more attacks, thus a can be seen as more acceptable than b. Note that the number of attackers plays a role in this example. A similar reasoning holds for F2. Indeed, b should be more acceptable than a since a is weakened whereas b is not. In graph F3, the arguments a and b have the same number of attackers. However, the a b F1