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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.

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The burdens of proof as part of the graph (module bp, a graphExtension): for an argument for bp(Statement) and an argument for Statement, the burdened one, an argument for -burdmet(Conclusion) (top rule artificial) is attacked as the burden of proof is, and rebuts or is rebutted by the burdened argument, depending on whether the grounded labelling labels it IN.

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The arguments attacking through a conflict argument (module conflictArguments), with metaConflicts: conflicts are then conclusions of the theory, and an argument attacks through the conflicts its conclusion has with others only while their arguments stand.

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The preferences between rules as conclusions of the theory, taken together (module defeasibleAllPref, a graphExtension): as defeasiblePref, but the attack argument is attacked by an argument for all the preferences invalidating it, preference(Preferences), supported by the arguments for each of them.

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The preferences between rules as conclusions of the theory (module defeasiblePref, a graphExtension): an argument for sup(Rule, Other) makes the attacks that preference invalidates fail, as long as it stands.

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The restricted rebut (module rebutRestriction, a graphExtension): a rebut only succeeds on an argument whose top rule is defeasible.

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The preferences between the rules of the theory, applied to the attacks (module standardPref, a graphExtension): an attack fails when the attacked argument is superior to the attacker (see the module superiority).

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When an argument is superior to another one (module superiority), by the preferences between their rules (sup(Rule, Other) in the context). Two arguments are compared on their defeasible rules and premises (their info, see the module argument): the last defeasible rules or all of them (orderingPrinciple last or weakest), compared as sets by orderingComparator (elitist, democrat or normal).