Derived confidence

Flag: --derived (or --compute).

Derived confidence answers “how strongly does the evidence back this claim?” — computed by propagating belief through the evidence graph, independent of any confidence you authored.

The model

Every evidence edge — supports, opposes, undercuts — pointing at a target contributes to its strength. For a target with incoming edges:

sum     = Σ  polarity · weight · believedness(source)
derived = logistic(2 · sum)

where:

• polarity is +1 for supports, −1 for opposes / undercuts.
• weight is the link’s weight, or 0.5 if none is given.
• believedness(source) is how much the source itself is believed: its own derived confidence if it has one (so belief propagates transitively), else its authored confidence, else 1.0 (an unqualified assertion counts as given).
• logistic(x) = 1 / (1 + e⁻ˣ), squashing the sum into 0..1.

The gain constant 2 is chosen so that a single strong support (weight 0.85, fully-believed source) lands the target at ≈0.85. A target with no net evidence sits at logistic(0) = 0.5 — the neutral point.

Propagation order

Belief flows in topological order (Kahn’s algorithm) over the evidence graph, so a conclusion is computed after its premises — it sees their derived strength, not just their authored confidence. Any nodes left on an evidence cycle are resolved once, in declaration order, as a documented best-effort.

The computation is pure and deterministic: same inputs, same output, every time.

Authored belief

The “believedness” of an authored node is the mean midpoint of the non-superseded stances that target it and carry a confidence (a range counts at its midpoint). A belief that’s been revised no longer counts as live evidence.

Undercutting an inference

undercuts has a power opposes doesn’t. When an undercuts edge targets a link (an inference rather than a claim), it doesn’t push the node down — instead it weakens that connection. Each undercut leaves the inference at a fraction of its strength: an undercut with weight 0.85 leaves 1 − 0.85 = 0.15 of it. Multiple undercuts multiply. With no inference-undercut present, every weight is untouched and the output is identical to the simple model above.

Where it appears

derived_confidence is set on every focus and link that is the target of evidence, rounded to three decimals, e.g.:

{ "type": "focus", "id": "displacement-hypothesis",
  "derived_confidence": 0.94 }

In the playground, it shows in the detail panel beside your authored confidence — two bars, never merged. On the bundled hiring-panel.thml, the displacement hypothesis lands ≈0.94 while the optimist’s rebuttal comes out ≈0.22, several hops deep.