On the instantiation of argument-incomplete argumentation frameworks

Argument-incomplete argumentation frameworks provide an intuitive way of representing uncertainty in argumentative contexts. It is however possible that, taking structured argumentation as a reference point, the general assumptions of these models present the same risks of hasty generalization attributed to some abstract argumentation models, as they do not have a structured counterpart. Here, we focus on a specific instantiation of argument-incomplete argumentation frameworks: rooting the uncertainty about arguments in the uncertainty about the application of ASPIC+-inference rules. We show (Proposition 1) that the abovementioned risk is concrete. Therefore a more fine-grained representation of uncertainty at the abstract level is needed, which we provide with implicative argument-incomplete argumentation frameworks and prove to work (Theorem 1).