Valid attacks in argumentation frameworks with recursive attacks

The purpose of this work is to study a generalisation of Dung's abstract argumentation frameworks that allows representing recursive attacks, that is, a class of attacks whose targets are other attacks. We do this by developing a theory of argumentation where the classic role of attacks in defeating arguments is replaced by a subset of them, which is "extension-dependent" and which, intuitively, represents a set of "valid attacks" with respect to the extension. The studied theory displays a conservative generalisation of Dung's semantics (complete, preferred, stable and grounded) and also of its principles (conflict-freeness, acceptability and admissibility). Furthermore, despite its conceptual differences, we are also able to show that our theory agrees with the AFRA interpretation of recursive attacks for the complete, preferred, stable and grounded semantics and with a recent flattening method.