Validation of Labelling Algorithms for Abstract Argumentation Frameworks: The Case of Listing Stable Extensions

An abstract argumentation framework (AF for short) is a pair (A, R) where A is a set of abstract arguments and R subset of A x A is the attack relation. Let H = (A, R) be an af, S subset of A be a set of arguments and S+ = {y | there exists x is an element of S with (x, y) is an element of R}. Then, S is a stable extension in H if and only if S (+) = A\S. In this paper, we present a thorough, formal validation of a known labelling algorithm for listing all stable extensions in a given AF.