Complexity Results and Algorithms for Preferential Argumentative Reasoning in ASPIC+

We provide complexity results and algorithms for reasoning in the central structured argumentation formalism of ASPIC+. Considering ASPIC+ accommodated with preferences under the last-link principle, the results are made possible by rephrasing several argumentation semantics---admissible, complete, stable, preferred and grounded---in terms of defeasible elements of an ASPIC+ theory for both democratic and elitist last-link lifting. Via the rephrasing, we establish that acceptance is polynomial-time computable under grounded semantics, and complete for either NP, coNP, or Pi_P^2, depending on the reasoning mode and semantics. We also detail answer set programming encodings for deciding acceptance for the NP/coNP-complete reasoning tasks, and empirically show that it scales significantly better than first translating ASPIC+ reasoning tasks to abstract argumentation. Finally, we show that, in contrast to the last-link principle, it is NP-hard to compute the grounded extension under the weakest-link principle.