  We extend the $ASPIC^+$ framework for structured argumentation so as to allow
applications of the reasoning by cases inference scheme for defeasible
arguments. Given an argument with conclusion `$A$ or $B$', an argument based on
$A$ with conclusion $C$, and an argument based on $B$ with conclusion $C$, we
allow the construction of an argument with conclusion $C$. We show how our
framework leads to different results than other approaches in non-monotonic
logic for dealing with disjunctive information, such as disjunctive default
theory or approaches based on the OR-rule (which allows to derive a defeasible
rule `If ($A$ or $B$) then $C$', given two defeasible rules `If $A$ then $C$'
and `If $B$ then $C$'). We raise new questions regarding the subtleties of
reasoning defeasibly with disjunctive information, and show that its
formalization is more intricate than one would presume.
