A General Account of Argumentation with Preferences - Erratum

We show that the ASPIC elitist set comparison relation, as defined in [3], is not reasonable inducing and hence cannot guarantee normative rationality for structured argumentation. Rather, one should revert to Prakken’s original strict elitist set comparison, as defined in [4], in order to guarantee that instantiations of Dung’s framework satisfy rationality postulates. We also show that by reverting to [4]’s elitist set comparison, Dung’s counter-example [2] is avoided. 1 The Elitist Set Comparison Relation in [3] is not Reasonable Inducing Recall that the property of reasonable inducing for a given set comparison relation E over the defeasible elements in arguments, is necessary to ensure that preference relations over arguments, defined on the basis of E, are normatively rational In what follows, Pfin(X) denotes the set of all finite subsets of a set X, and the symbol “⊆fin” means “is a finite subset of”, so U ∈ Pfin(X) ⇐⇒ U ⊆fin X. Recall that for a set comparison relation E, Γ / Γ′ ⇐⇒ [Γ E Γ′, Γ′ 6E Γ]. Definition 1.1. (From [3, page 376, Definition 22]) Given 〈P,≤〉 a preset (pre-ordered set), a set comparison E⊆ [Pfin(P )] is reasonable inducing iff 1. E is transitive. 2. For any Γ0, Γ1, · · · , Γn ⊆fin P (for n ≥ 1), if