Are Ranking Semantics Sensitive to the Notion of Core?

In this paper, we study the impact of two notions of core on the output of ranking semantics in logical argumentation frameworks. We consider the existential rules fragment, a language widely used in Semantic Web and Ontology Based Data Access applications. Using burden semantics as example we show how some ranking semantics yield different outputs on the argumentation graph and its cores. We extend existing results in the literature regarding core equivalences on logical argumentation frameworks and propose the first formal characterisation of core-induced modification for a class of ranking semantics satisfying given postulates.