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Labelling-based formal argumentation relies on labelling functions thattypically assign one of 3 labels to indicate either acceptance, rejection, orelse undecided-to-be-either, to each argument. While a classicallabelling-based approach applies globally uniform conditions as to how anargument is to be labelled, they can be determined more locally per argument.Abstract dialectical frameworks (ADF) is a well-known argumentation formalismthat belongs to this category, offering a greater labelling flexibility. As thesize of an argumentation increases in the numbers of arguments andargument-to-argument relations, however, it becomes increasingly more costly tocheck whether a labelling function satisfies those local conditions or evenwhether the conditions are as per the intention of those who had specifiedthem. Some compromise is thus required for reasoning about a largerargumentation. In this context, there is a more recently proposed formalism ofmay-must argumentation (MMA) that enforces still local but more abstractlabelling conditions. We identify how they link to each other in this work. Weprove that there is a Galois connection between them, in which ADF is aconcretisation of MMA and MMA is an abstraction of ADF. We explore theconsequence of abstract interpretation at play in formal argumentation,demonstrating a sound reasoning about the judgement ofacceptability/rejectability in ADF from within MMA. As far as we are aware,there is seldom any work that incorporates abstract interpretation into formalargumentation in the literature, and, in the stated context, this work is thefirst to demonstrate its use and relevance.

Abstract Interpretation in Formal Argumentation: with a Galois  Connection for Abstract Dialectical Frameworks and May-Must Argumentation  (First Report)