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repairing-based approach to the case of AFNs.
The ideas developed in this work remain valid in
the context of Dung style argumentation frameworks
where no assumption is made on the structure of ar-
guments. However, an entire body of work on argu-
mentation is based on structured arguments and a va-
riety of attack relations. This body includes abstract
argumentation systems (Vreeswijk, 1997), defeasible
logic programming (Simari and Loui, 1992) (Gar-
cia and Simari, 2004), defeasible logic (G. Governa-
tori and Billington, 2004), logical-based argumenta-
tion (Besnard and Hunter, 2008), logic-programming
based argumentation system (Prakken and Sartor,
1997) and recently the ASPIC system (Caminada and
Amgoud, 2007), (Prakken, 2010), (Prakken, 2011).
In all these approaches arguments are structured and
represent deductive or defeasible inferences. Thus
the notion of support is already present in such ap-
proaches as an internal mechanism in the argument it-
self. It would be interesting to study the possible links
between these kinds of supports and our necessity re-
lation. We want in particular to check if our necessity
relation can be seen as an abstraction of these kinds
of supports and if it is the case, to define methods al-
lowing to see the argumentation approaches based on
structured arguments as instantiations of AFNs. Also,
working on arguments with structures may lead to re-
vise some of the basic hypotheses of the present work.
For example, it may limit the cases where the in-
teraction between preferences and attacks is handled
simply by inversing the directions of critical attacks.
Consequently, in presence of necessities, even if we
keep the idea that the effective preference of an argu-
ment depends on the preferences of all their required
arguments, the handling of the resulting attacks be-
tween clusters of arguments would require a revision
that takes into account the structures of arguments.
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