On Polymorphic Attacks in the ASPIC+ and ASPICR Formalisms

The recently proposed ASPICR, standing for ASPIC+ revisited is an evolution of the prominent ASPIC+ formalism for structured argumentation, which overcomes some limitations of ASPIC+ by resorting in particular to an alternative notion of attack referring to sets of arguments. While this notion of attack is a key element for achieving the technical advantages offered by ASPICR, it also gives rise to some peculiar situations, where some attacks are, in a sense, polymorphic since there are multiple reasons by which a given set of arguments can attack an argument. After pointing out that polymorphic attacks are also possible in ASPIC+, we provide some examples of polymorphic attacks in ASPIC+ and ASPICR, discuss the underlying technical and conceptual issues and provide a preliminary discussion about how to revise the formalisms in order to encompass alternative options for their management.