Assumption-Based Argumentation

Origin. Bondarenko, Dung, Kowalski, Toni (1997). Structured argumentation. Arguments from assumptions. Rules derive conclusions. Attacks via contraries. Foundation for logic-based argumentation.

Models. Deductive system with assumptions. Arguments: proofs from assumptions. Attacks: contrary assumptions. Maps to abstract frameworks. Computation via logic programming.

Formalism.

ABA framework: (L, R, A, ‾) L: language R: inference rules (non-assumption → formula) A ⊆ L: assumptions ‾: contrary function A → L

Argument: Tree with root claim, leaves assumptions. Applies rules from R. Assumptions S ⊢_R c: argument for c.

Attack: Argument with claim c̄ attacks argument using assumption a where c̄ = ā.

Contrary: ā: contrary of a ∈ A. If ā derivable, a cannot be assumed.

Contraries vs contradictories: Contrary: ā attacks a. Contradictory: mutual attack.

Flat ABA: Assumptions not derived. Maps directly to Dung framework.

Non-flat: Assumptions can have derivations. More expressive.

Semantics: Inherited from Dung: grounded, preferred, stable. Apply to sets of assumptions.

Example: Rule: flies(X) ← bird(X), ¬ab(X) Assumption: ¬ab(X) with contrary ab(X) Attacked by: penguin(X) → ab(X)

Symbols.

Symbol	Unicode	Name	Meaning
A	—	Assumptions	Assumable formulas
ā	—	Contrary	Contrary of a
R	—	Rules	Inference rules
⊢	U+22A2	Derives	Proof relation

Metatheory. Generalizes logic programming. Maps to Dung. Captures default, autoepistemic. Complexity known.

Applies to. Logic programming semantics. Legal reasoning. Medical reasoning. Dialogue systems.

Limitations. Contrary function design. Flat vs non-flat choice. Computational cost. Rule encoding effort.