Probabilistic Argumentation

Origin. Li, Oren, Norman (2011), Hunter (2013), various. Extends Dung's abstract argumentation frameworks (see Abstract Argumentation) with probability. Uncertainty in arguments. Probabilistic semantics. Bayesian argumentation.

Models. Arguments with probabilities. Uncertain attacks. Graded acceptance. Probabilistic extensions.

Formalism.

Probabilistic AF: ⟨A, R, P⟩ where: A: arguments. R ⊆ A × A: attacks. P: probability distribution.

Argument probability: P(a): probability argument a holds. Uncertain premises. Graded.

Attack probability: P(a → b): probability attack succeeds. Uncertain defeat. Conditional.

Constellation approach: Distribution over subframeworks. Each subframework: subset of A. Semantics applied to each. Expected acceptance.

Grounded probability: P_gr(a) = Σ_F P(F) · 1_{a ∈ gr(F)}. Sum over subframeworks. Weighted by probability. a in grounded extension.

Epistemic approach: Probability = degree of belief. Bayesian updates. Evidence changes P.

Likelihood-based: L(a | E) ∝ P(E | a) · P(a). Evidence E. Posterior from likelihood.

Social choice: Multiple agents. Aggregate probabilistic views. Judgment aggregation meets argumentation.

Li et al. semantics: P(a is IN) based on attackers. P(a is IN) = Π_{b attacks a} P(b is OUT). Product formula. Independence assumption.

Symbols.

Symbol	Unicode	Meaning
P(a)	—	probability of a
P_gr(a)	—	grounded acceptance probability
A, R	—	arguments, attacks
PAF	—	probabilistic AF

Metatheory. Probabilistic semantics. Constellations. Bayesian. Graded acceptance.

Applies to. Uncertain reasoning. Risk assessment. AI. Decision making.

Limitations. Independence assumptions. Probability source. Computational cost. Multiple approaches.