  In this paper we propose a general approach to define a many-valued
preferential interpretation of gradual argumentation semantics. The approach
allows for conditional reasoning over arguments and boolean combination of
arguments, with respect to a class of gradual semantics, through the
verification of graded (strict or defeasible) implications over a preferential
interpretation. As a proof of concept, in the finitely-valued case, an Answer
set Programming approach is proposed for conditional reasoning in a many-valued
argumentation semantics of weighted argumentation graphs. The paper also
develops and discusses a probabilistic semantics for gradual argumentation,
which builds on the many-valued conditional semantics.
