Handling support cycles and collective interactions in the logical encoding of higher-order bipolar argumentation frameworks

In our paper [], we have proposed a logical encoding of argumentation frameworks with higher-order interactions (i.e. attacks or supports whose targets are arguments or other attacks or supports) with an evidential interpretation for supports, such frameworks are called REBAF. With this encoding, we are able to characterize the semantics of REBAF under the form of specific logical models. Nevertheless, this encoding has two important drawbacks: first, the handling of support cycles has some weaknesses, and second, the collective interactions (i.e. attacks or supports whose source is a set of arguments and not only one argument) are not taken into account. The present paper proposes an improvement of this encoding for solving these drawbacks. Moreover, we also extend this proposal to another kind of Higher-Order Bipolar Argumentation Framework, the RAFN, in which supports are interpreted as necessity.