Static and dynamic orderings on Dungean argumentation frameworks - An overview

Abstract

The article is devoted to the issue of comparing argumentation frameworks (AFs) which has received increasing attention in recent years. Knowing whether a given framework F possesses less information than an AF G or whether the latter is at least reachable from F in a certain future scenario is an important issue for several applications. The question what we precisely mean by information will depend on the particular context in which they are being used. Our analysis does not express any preferences here. However, if AFs are applied to fields like criminal justice, finance, and healthcare, where it is necessary to exercise caution, skeptical accepted arguments may be the most appropriate form of reasoning. The presented overview considers classical Dung semantics including the stable, admissible, complete, grounded and preferred one. The article is divided into two main axes: the distinction between extension-based and kernel-based orderings and the analysis of their static and dynamic versions. The results show that there are various relationships between these concepts, indicating that some orderings are stronger or weaker than others. The considered orderings are so-called preorders, i.e. they satisfy reflexivity and transitivity. We analyzed them w.r.t. bounds, meets and joins and also considered the induced equivalences. The latter often coincide with well-known equivalences, namely ordinary and strong equivalence.