Ideal extensions as logical programming models

We show that the ideal sets of an argumentation framework can be characterized by two kinds of logical models: ideal models (2-valued logical models) and p-stable models (2-valued logical models). We also show that the maximal ideal set of an argumentation framework can be characterized by the well-founded+ model (a 3-valued logical model). These results argue for the logical foundations of the ideal sets of an argumentation framework. Moreover, these results consolidate the strong relationship between argumentation semantics and logic programming semantics with negation as failure. More accurately, we prove that the five argumentation semantics suggested by Dung et al., grounded, stable, preferred, complete and ideal semantics, can be characterized by the well-founded model, stable-model, p-stable, Clark’s completion and well-founded+ model semantics, respectively by using a unique mapping from argumentation frameworks into logic programs. We observe that the labellings of these argumentation semantics can be inferred by the logical models of a logic program.