Abstract
In abstract argumentation, arguments jointly attacking single
arguments is a well-understood concept, captured by the
established notion of SETAFs---argumentation frameworks with
collective attacks. In contrast, the idea of sets attacking
other sets of arguments has not received much attention so far.
In this work, we contribute to the development of set-to-set
defeat in formal argumentation. To this end, we introduce so
called hyper argumentation frameworks (HYPAFs), a new formalism
that extends SETAFs by allowing for set-to-set attacks. We
investigate this notion by interpreting these novel attacks in
terms of universal, indeterministic, and collective defeat. We
will see that universal defeat can be naturally captured by the
already existing SETAFs. While this is not the case for
indeterministic defeat, we show a close connection to
attack-incomplete argumentation frameworks. To formalize our
interpretation of collective defeat, we develop novel semantics
yielding a natural generalization of attacks between arguments
to set-to-set attacks. We investigate fundamental properties and
identify several surprising obstacles; for instance, the
well-known fundamental lemma is violated, and the grounded
extension might not exist. Finally, we investigate the
computational complexity of the thereby arising problems.
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