Package-level declarations

The language of assumption-based argumentation (module abaLanguage, a graphLanguage of the profile aba), mapped to the one of arg2p as flat ABA is an instance of ASPIC+ (Prakken 2010): each assumption (assumption(A)) an ordinary premise asm(A), each contrary (contrary(A, C)) the conflict of C with A, one way (an argument for C attacks those resting on A). Rules are the strict rules of arg2p.

The language of Dung frameworks (module abstractLanguage, the graphLanguage of the profile abstract): arguments and attacks alone, which the module abstractGraph reads. It adds no premise nor conflict; it checks the theory has none of the notations of the structured profiles, which an abstract framework would drop.

The language of ASPIC+ (module aspicLanguage, a graphLanguage of the profiles aspic_plus and aspic): the one of arg2p, well formed (Modgil and Prakken 2013). A contrary, a conflict declared one way only (conflict(X, Y) with no conflict(Y, X)), targets defeasible statements alone: neither an axiom nor the conclusion of a strict rule, which no attack could reach. The contradictories (negations, conflicts declared both ways) are those transposition closes the strict rules over.

The conflicts between statements (module conflict). Without metaConflicts they are the built-in ones (a literal and its negation, and those between obligations and permissions) and those the theory declares (conflict/2,3); with metaConflicts they are only those concluded by an argument for conflict(A, B) or conflict(A, B, Guard).

The defeasible part of the language of ASPIC+ (module defeasibleLanguage, a graphLanguage of the profile aspic_defeasible): defeasible rules alone, facts as rules with no premise (r : [] => a.). It adds no premise nor conflict; it checks the theory has no strict rule, axiom nor premise.

The rules of a theory, read by the graph builders (module parser): convertAllRules/1 converts the rules, premises, preferences and burdens of the theory, which classicRule/2,3 and the other predicates read.

The transpositions of the strict rules (module transposition), with autoTransposition: for a strict rule r : a, b -> c, the rules concluding a contradictory of each premise from a contradictory of the conclusion and the other premises (r_i : -c, b -> -a, r_ii : -c, a -> -b). The contradictories of a statement are its negation, and the statements the theory declares in conflict with it both ways, with no guard (conflict([c], [d]) and conflict([d], [c])): the transpositions through those are named transposed(Id, ConclusionContradictory, PremiseContradictory), Id the name of the one through negations.