  We contemplate a higher-level bipolar abstract argumentation for
non-elementary arguments such as: X argues against Ys sincerity with the fact
that Y has presented his argument to draw a conclusion C, by omitting other
facts which would not have validated C. Argumentation involving such arguments
requires us to potentially consider an argument as a coherent block of
argumentation, i.e. an argument may itself be an argumentation. In this work,
we formulate block argumentation as a specific instance of Dung-style bipolar
abstract argumentation with the dual nature of arguments. We consider internal
consistency of an argument(ation) under a set of constraints, of graphical
(syntactic) and of semantic nature, and formulate acceptability semantics in
relation to them. We discover that classical acceptability semantics do not in
general hold good with the constraints. In particular, acceptability of
unattacked arguments is not always warranted. Further, there may not be a
unique minimal member in complete semantics, thus sceptic (grounded) semantics
may not be its subset. To retain set-theoretically minimal semantics as a
subset of complete semantics, we define semi-grounded semantics. Through
comparisons, we show how the concept of block argumentation may further
generalise structured argumentation.
