Bipolar Argumentation

Origin. Cayrol, Lagasquie-Schiex (2005). Support and attack. Two relations. Evidence for. Extends Dung frameworks.

Models. Arguments with support and attack. Positive and negative relations. Defended vs supported. Dual dynamics.

Formalism.

Bipolar AF: ⟨A, R⁻, R⁺⟩ where: A: arguments. R⁻ ⊆ A × A: attack. R⁺ ⊆ A × A: support.

Attack (R⁻): (a, b) ∈ R⁻: a attacks b. Negative evidence. Dung-style.

Support (R⁺): (a, b) ∈ R⁺: a supports b. Positive evidence. Strengthens b.

Supported attack: a supported-attacks b if: Path a R⁺* c R⁻ b. Support chain then attack.

Secondary attack: a secondary-attacks b if: c supports b (c R⁺ b). a attacks c (a R⁻ c). Undercut support.

Defense types: Direct defense: attack attacker. Supported defense: via support chains. Multiple modes.

Semantics approaches: Reduce to Dung AF. Direct bipolar semantics. Deductive vs necessary support. Various proposals.

Deductive support: If a accepted and a R⁺ b, then b acceptable. Support transfers acceptance. But controversial.

Necessary support: a supports b: b needs a. a rejected implies b rejected. Support as prerequisite.

Symbols.

Symbol	Unicode	Meaning
R⁻	—	attack relation
R⁺	—	support relation
BAF	—	bipolar argumentation framework
→	U+2192	support or attack

Metatheory. Dual relations. Support semantics. Reduction. Defense modes.

Applies to. Evidence weighing. Pro/con reasoning. Scientific argumentation. Debates.

Limitations. Multiple semantics. Support interpretation disputed. Complexity. No consensus.