Acyclic Argumentation: Attack = Conflict + Preference

In this paper we study the fragment of Dung's argumentation theory in which the strict attack relation is acyclic. We show that every attack relation satisfying a particular property can be represented by a symmetric conflict relation and a transitive preference relation in the following way. We define an instance of Dung's abstract argumentation theory, in which 'argument A attacks argument B' is defined as 'argument A conflicts with argument B' and 'argument A is at least as preferred as argument B', where the conflict relation is symmetric and the preference relation is transitive. We show that this new preference-based argumentation theory characterizes the acyclic strict attack relation, in the sense that every attack relation defined as such a combination satisfies the property, and for every attack relation satisfying the property we can find a symmetric conflict relation and a transitive preference relation satisfying the equation.