An axiomatic analysis of structured argumentation with priorities

Several systems of semantics have been proposed for structured argumentation with priorities. As the proposed semantics often sanction contradictory conclusions (even for skeptical reasoners), there is a fundamental need for guidelines for understanding and evaluating them, especially their conceptual foundation and relationship.In this paper, we present an axiomatic analysis of the semantics of structured defeasible argumentation both with and without preferences by introducing a class of ordinary attack relations satisfying a set of simple and intuitive properties. We show that there exists a "normal form" for ordinary attack relations in the sense that stable extensions wrt any ordinary attack relation are stable extensions wrt the normal attack relations.We relate the ordinary semantics to other approaches, especially to the ASPIC+ framework and the prioritized approaches in logic programming.