  The semantics as to which set of arguments in a given argumentation graph may
be acceptable (acceptability semantics) can be characterised in a few different
ways. Among them, labelling-based approach allows for concise and flexible
determination of acceptability statuses of arguments through assignment of a
label indicating acceptance, rejection, or undecided to each argument. In this
work, we contemplate a way of broadening it by accommodating may- and must-
conditions for an argument to be accepted or rejected, as determined by the
number(s) of rejected and accepted attacking arguments. We show that the
broadened label-based semantics can be used to express more mild indeterminacy
than inconsistency for acceptability judgement when, for example, it may be the
case that an argument is accepted and when it may also be the case that it is
rejected. We identify that finding which conditions a labelling satisfies for
every argument can be an undecidable problem, which has an unfavourable
implication to existence of a semantics. We propose to address this problem by
enforcing a labelling to maximally respect the conditions, while keeping the
rest that would necessarily cause non-termination labelled undecided. Several
semantics will be presented and the relation among them will be noted. Towards
the end, we will touch upon possible research directions that can be pursued
further.
