Abstract argumentation

Claude Opus 5.5, 4 Nov. 2026

NLP and argumentation

Abstract argumentation, introduced by Phan Minh Dung in 1995, models a debate as a directed graph. Each node is an argument, and an arrow from $𝐴$ to $𝐵$ means “$𝐴$ attacks $𝐵$”. The model deliberately ignores what the arguments say. It asks only which arguments can stand together, given who attacks whom.

Acceptance

An argument is acceptable if every argument attacking it is itself defeated by an accepted argument. A set of arguments that can all be accepted together is called an extension. There are several ways to choose one. The most cautious is the grounded extension, which accepts only what is beyond dispute:

1. Accept every argument that nothing attacks.
2. Reject every argument attacked by an accepted one.
3. Repeat, until nothing changes.

Arguments left neither accepted nor rejected, as in a cycle of mutual attacks, stay undecided.

flowchart RL
  C["C: player undercuts the counter"]:::acc --> B["B: character's counter"]:::rej
  B --> A["A: player's rebuttal"]:::acc
  A --> N["character's thesis"]:::rej
  classDef acc fill:#dcfce7,stroke:#166534,color:#111
  classDef rej fill:#fee2e2,stroke:#991b1b,color:#111

In this example, nothing attacks C, so C is accepted (green). C defeats B, so B is rejected (red). A’s only attacker has been defeated, so A is accepted, and the thesis A attacks is rejected.

In Quell

Under this model, a player could win a debate by getting the character’s thesis rejected: attacked by an argument the character cannot answer. The computation is a simple loop, so its cost is negligible at the scale of a conversation.

See also

• Value-based argumentation — an extension in which attacks depend on what the audience values.
• Debate — the mechanic this would serve.

References

• Dung, P. M. (1995). On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77(2), 321–357.

External links

• Argumentation framework — an overview of Dung’s model and its semantics.
• Dung-O-Matic — ARG-tech’s Java implementation.

What links here: Debate, CAPNA, Value-based argumentation, Glossary