AbaPrefModule

The preferences between the assumptions of ABA+ (module abaPref, a graphExtension, of the profile aba_plus; Čyras and Toni 2016): sup(Stronger, Weaker), closed transitively. An attack on an assumption by an argument resting on an assumption weaker than it is reversed: it is removed, and the argument for the stronger assumption attacks every argument whose support (its assumptions, see the module abaLanguage) contains the whole support of the attacker. The reversal hits the arguments resting on the same assumptions as the attacker, not only the attacker: as ABA+ reverses attacks between sets of assumptions, and the arguments do not share a sub-argument for those sets. That holds on the theories satisfying Weak Contraposition (Čyras and Toni 2016, Axiom 4), and those failing it are refused: their semantics are those of sets of assumptions, which the arguments do not capture.