On topology-related properties of abstract argumentation semantics. A correction and extension to "Dynamics of argumentation systems: A division-based method"

This research note provides novel results concerning the incremental computation of the stable and ideal argumentation semantics, by extending the division-based method presented in [1] and correcting a flawed claim given there.
As a basis for these results, the note synthetically reviews and discusses the topology-related properties of directionality and SCC-recursiveness in abstract argumentation semantics and analyzes their relationships with the division-based method.