Prioritized Norms and Defaults in Formal Argumentation

Deontic logic sentences define what an agent ought to do when faced with a set of norms. These norms may come into conflict such that a priority ordering over them is necessary to resolve these conflicts. Dung's seminal paper raised the - so far open - challenge of how to use formal argumentation to represent non monotonic logics, highlighting argumentation's value in exchanging, communicating and resolving possibly conflicting viewpoints in distributed scenarios. In this paper, we propose a formal framework to study various properties of prioritized non monotonic reasoning in formal argumentation, in line with this idea. More precisely, we show how a version of prioritized default logic and Brewka-Eiter's construction in answer set programming can be obtained in argumentation via the weakest and last link principles. We also show how to represent Hansen's recent construction for prioritized normative reasoning by adding arguments using weak contraposition via permissive norms, and their relationship to Caminada's "hang yourself" arguments.