Generalizing Consistency and Reinstatement in Abstract Argumentation

We introduce two generic notions related to consistency and reinstatement in an abstract labelling setting, based on a relation of intolerance between the labelled elements and two specific relations, called incompatibility and reinstatement violation, between the labels assigned to them. This way, the approach allows a spectrum of consistency and reinstatement requirements depending on the actual choice of these relations. As a first application to formal argumentation, we show that traditional Dung’s semantics can be expressed as combinations of different consistency and reinstatement requirements in this context.