Abstract Argumentation is a reasoning model based on the construction and evaluation of arguments. Dung has proposed an abstract argumentation framework in which arguments are assumed to have the same strength. This assumption is unfortunately not realistic. Consequently, three main extensions of the framework have been proposed in the literature. The basic idea is that if an argument is stronger than its attacker, the attack fails. The aim of the paper is twofold: First, it shows that the three extensions of Dung framework may lead to unintended results. Second, it proposes a new approach that takes into account the strengths of arguments, and that ensures sound results. We start by presenting two minimal requirements that any preference-based argumentation framework should satisfy, namely the conflflict-freeness of arguments extensions and the generalization of Dung’s framework. Inspired from works on handling inconsistency in knowledge bases, the proposed approach defifines a binary relation on the powerset of arguments. The maximal elements of this relation represent the extensions of the new framework