Computing Stable Conclusions under the Weakest-Link Principle in the ASPIC+ Argumentation Formalism

Rephrasing argumentation semantics in terms of subsets of defeasible elements allows for gaining new insights for reasoning about acceptance in established fragments of the central structured argumentation formalism of ASPIC+. We provide a non-trivial generalization of these recent results, capturing preferences in ASPIC+. In particular, considering preferences under the weakest-link principle, we show that the stable semantics can be phrased in terms of subsets of defeasible elements. We employ the rephrasing for establishing both complexity results and practical algorithms for reasoning about acceptance in this variant of ASPIC+. Justified by completeness for the second level of the polynomial hierarchy, we develop an iterative answer set solving based approach to reasoning about acceptance under the so-called elitist lifting in ASPIC+ frameworks. Our implementation of the approach scales well in practice.