In this paper we consider the dynamics of abstract argumentation in Baroni and Giacomin’s framework for the evaluation of extension based argumentation semantics. Following Baroni and Giacomin, we do not consider individual approaches, but we define general properties or postulates that individual approaches may satisfy. In particular, we define refinement properties for the attack relation in the framework. We illustrate the properties on the grounded extension. In this paper we consider only properties for the single extension case, and leave the multiple extension case to further research.