  In this paper we introduce a novel family of semantics called weakly complete
semantics. Differently from Dung's complete semantics, weakly complete
semantics employs a mechanism called undecidedness blocking by which the label
undecided of an attacking argument is not always propagated to an otherwise
accepted attacked argument. The new semantics are conflict-free, non-admissible
but employing a weaker notion of admissibility; they allow reinstatement and
they retain the majority of properties of complete semantics. We show how both
weakly complete and Dung's complete semantics can be generated by applying
different undecidedness blocking strategies, making undecidedness blocking a
unifying mechanism underlying argumentation semantics. The semantics are also
an example of ambiguity blocking Dunganian semantics and the first semantics to
tackle the problem of self-defeating attacking arguments. In the last part of
the paper we compare weakly complete semantics with the recent work of Baumann
et al. on weakly admissible semantics. Since the two families of semantics do
not coincide, a principle-based analysis of the two approaches is provided. The
analysis shows how our semantics satisfy a number of principles satisfied by
Dung's complete semantics but not by Baumann et al. semantics, including
directionality, abstention, SCC-decomposability and cardinality of extensions,
making them a more faithful non-admissible version of Dung' semantics.
