The adoption of a generic contrariness notion in ASPIC+
substantially enhances its expressiveness with respect to other formalisms for
structured argumentation. In particular, it opens the way to novel
investigation directions, like the use of multivalued logics in the
construction of arguments. This paper points out however that in the current
version of ASPIC+ a serious technical difficulty related with generic
contrariness is present. With the aim of preserving the same level of
generality, the paper provides a solution based on a novel notion of closure of
the contrariness relation at the level of sets of formulas and an abstract
representation of conflicts between sets of arguments. The proposed solution is
shown to satisfy the same rationality postulates as ASPIC+ and represents a
starting point for further technical and conceptual developments in structured
argumentation.