Attacks and supports

An attack is a directed edge from one argument to another, saying: "if A holds, B fails." A support is its dual: "if A holds, B gains strength."

Attacks give you contradiction. Supports give you reinforcement. Together they form a bipolar argumentation framework — the structure that all semantics operate on.

Attacks alone (Dung, 1995)

Dung's original paper cared only about attacks. An argument is acceptable (roughly) if every argument that attacks it is itself attacked by some argument that survives. Recursion and fixed-points make this interesting:

Simple attack chain

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A attacks B; B attacks C. Under the standard (grounded) semantics, A is accepted, C is accepted (because its attacker B is itself attacked), and B is rejected.

Why supports?

Cayrol & Lagasquie-Schiex (2005) argued that attack alone misses something: two arguments can reinforce each other without either being an attack. "Dr. Vance (engineer) says X" and "Dr. Chen (engineer) independently says X" are distinct arguments that support the same conclusion.

Supports form the backbone of coalition detection: strongly-connected components of the support graph are arguments that stand or fall together.

Mutual support (coalition)

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A and B mutually support → they are in a coalition. C attacks A, which by the coalition indirectly weakens B too.

In our library

• argumentation_bipolar::BipolarFramework — attacks + supports.
• argumentation_weighted_bipolar::WeightedBipolarFramework — adds edge weights (see the weighted & β page).
• EncounterArgumentationState::add_weighted_attack / add_weighted_support — the consumer-facing API in the encounter bridge.
• EncounterArgumentationState::coalitions — strongly-connected components over the support graph.

Further reading

• Dung (1995) — attacks only; the seminal paper.
• Cayrol & Lagasquie-Schiex (2005) — bipolar frameworks.
• Amgoud et al. (2008) — "On bipolarity in argumentation frameworks" (survey).