  Recently, Strength-based Argumentation Frameworks (StrAFs) have been proposed
to model situations where some quantitative strength is associated with
arguments. In this setting, the notion of accrual corresponds to sets of
arguments that collectively attack an argument. Some semantics have already
been defined, which are sensitive to the existence of accruals that
collectively defeat their target, while their individual elements cannot.
However, until now, only the surface of this framework and semantics have been
studied. Indeed, the existing literature focuses on the adaptation of the
stable semantics to StrAFs. In this paper, we push forward the study and
investigate the adaptation of admissibility-based semantics. Especially, we
show that the strong admissibility defined in the literature does not satisfy a
desirable property, namely Dung's fundamental lemma. We therefore propose an
alternative definition that induces semantics that behave as expected. We then
study computational issues for these new semantics, in particular we show that
complexity of reasoning is similar to the complexity of the corresponding
decision problems for standard argumentation frameworks in almost all cases. We
then propose a translation in pseudo-Boolean constraints for computing (strong
and weak) extensions. We conclude with an experimental evaluation of our
approach which shows in particular that it scales up well for solving the
problem of providing one extension as well as enumerating them all.
