Towards Algorithms for Argumentation Frameworks with Higher-order Attacks

Abstract

Computation and decision problems related to argumentation frameworks with higher-order attacks have not received a lot of attention so far. This paper is a step towards these issues. First, it provides a labelling counterpart for the structure semantics of Recursive Argumentation Frameworks (RAF). Second, it investigates the complexity of decision problems associated with RAF. This investigation shows that, for the higher expressiveness offered by these enriched systems, the complexity is the same as for classical argumentation frameworks. As a side contribution, a new semantics for RAF, the semi-stable semantics, and a new process for translating RAF into Argumentation Frameworks without higher-order attacks (AF), are introduced. Finally, new notions which are the counterparts of equivalent notions already existing for AF (among them, the Strongly Connected Components — SCC) are defined and investigated in order to involve them in the future development of algorithms for computing RAF labelling semantics.