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Acceptance semantics

An acceptance semantics is a rule for deciding which subsets of arguments in a framework can coherently "stand together." Dung's original paper defined four main ones; we'll walk through them with examples.

The building blocks​

  • Conflict-free set — no argument in the set attacks another in the set.
  • Admissible set — conflict-free AND defends itself: every attacker of a member is itself attacked by some member.
  • Complete extension — an admissible set that contains every argument it defends. (The minimum complete extension is the grounded extension; maximum complete extensions are preferred.)
  • Stable extension — a conflict-free set that attacks every argument outside it.

Credulous vs skeptical​

  • Credulously accepted — the argument is in at least one preferred extension.
  • Skeptically accepted — the argument is in every preferred extension.

Skeptical is strictly stronger than credulous. Our library exposes both via EncounterArgumentationState::is_credulously_accepted and is_skeptically_accepted.

When they diverge​

Most of the time, all four semantics (grounded / preferred / stable / complete) agree on which arguments are accepted. The Nixon diamond is the canonical case where they diverge:

Nixon diamond
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  • Grounded: {} (no argument is "unconditionally acceptable").
  • Preferred: {A} and {B} (two maximal admissible sets).
  • Stable: {A} and {B} (both are stable).
  • Complete: {}, {A}, {B}.

Credulous acceptance holds for both A and B (each is in some preferred extension). Skeptical acceptance holds for neither (neither is in every preferred extension).

Why we care in scene AI​

Credulous acceptance is a natural fit for "is this claim live right now?" A beat can proceed as long as the proposer's argument is credulously accepted at the current β. Skeptical acceptance is too strict — it would stall scenes the moment any counter-argument exists.

Our bridge's StateActionScorer boosts affordances whose argument is credulously accepted; StateAcceptanceEval rejects only when the responder has put forward a credulously-accepted counter.

Further reading​