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