Ranking semantics for argumentation systems with necessities

Abstract

Bipolar argumentation studies argumentation graphs where attacks are combined with another relation between arguments. Many kind of relations (e.g. deductive support, evidential support, necessities etc.) have been defined and investigated from a Dung semantics perspective. We place ourselves in the context of argumentation systems with necessities and provide the first study to investigate ranking semantics in this setting. To this end, we (1) provide a set of postulates specifically designed for necessities and (2) propose the first ranking-based semantics in the literature to be shown to respect these postulates.