  This paper formally compares some central notions from two well-known
formalisms for rule-based argumentation, DeLP and ASPIC+. The comparisons
especially focus on intuitive adequacy and inter-translatability, consistency,
and closure properties. As for differences in the definitions of arguments and
attack, it turns out that DeLP's definitions are intuitively appealing but that
they may not fully comply with Caminada and Amgoud's rationality postulates of
strict closure and indirect consistency. For some special cases, the DeLP
definitions are shown to fare better than ASPIC+. Next, it is argued that there
are reasons to consider a variant of DeLP with grounded semantics, since in
some examples its current notion of warrant arguably has counterintuitive
consequences and may lead to sets of warranted arguments that are not
admissible. Finally, under some minimality and consistency assumptions on
ASPIC+ arguments, a one-to-many correspondence between ASPIC+ arguments and
DeLP arguments is identified in such a way that if the DeLP warranting
procedure is changed to grounded semantics, then DeLP notion of warrant and
ASPIC+'s notion of justification are equivalent. This result is proven for
three alternative definitions of attack.
