Noul

A Noul question asks whether a proposition is true and returns the probability that the answer is yes. Use it for boolean decisions.

When should I use Noul?

• The customer is eligible for a full refund.
• This message contains a payment error.
• The document answers the question.
• The passage supports the claim.

Noul is the right primitive whenever the outcome is a yes/no determination.

Request shape

{
  "type": "noul",
  "instructions": "The customer is eligible for a full refund under the store policy."
}

• instructions states the proposition to evaluate.
• criteria is optional and lets you rename the two labels.

Custom labels:

{
  "type": "noul",
  "instructions": "The request is approved.",
  "criteria": { "yes": "Approved", "no": "Rejected" }
}

Response shape

{
  "type": "noul",
  "noul": 0.87
}

• noul — the probability of the affirmative answer, between 0.0 and 1.0.

Noul does not return probabilities or confidence; the single value is already the calibrated affirmative probability.

How is it scored?

The proposition is rendered with two labels (Yes/No by default, or the custom labels). The model reads those two label logits at the decision position and applies a binary softmax.

---
accTitle: Noul scoring
accDescr: A proposition is rendered with a yes/no label pair; the binary softmax over the two logits yields the affirmative probability.
---
flowchart LR
  proposition["proposition"]:::primary
  labels["labels<br/>Yes · No"]:::accent
  logits["two label logits"]:::neutral
  binary["binary softmax"]:::accent
  result["noul<br/>0.0 to 1.0"]:::success

  proposition --> labels --> logits --> binary --> result

  classDef primary fill:#ede9fe,stroke:#7c3aed,color:#3b0764,stroke-width:1.5px
  classDef accent fill:#dbeafe,stroke:#2563eb,color:#0c4a6e,stroke-width:1.5px
  classDef success fill:#d1fae5,stroke:#059669,color:#064e3b,stroke-width:1.5px
  classDef neutral fill:#f4f4f5,stroke:#a1a1aa,color:#18181b,stroke-width:1.5px

How do I use the value?

noul is a probability, not a hard label. Decide the threshold in your code:

• > 0.5 — affirmative.
• A stricter threshold such as > 0.8 — affirmative only when the model is confident.
• The uncertain band in between — route to a human or a slower path.

---
accTitle: Thresholding a noul value
accDescr: A noul probability is thresholded into a reject band, a review band and an accept band.
---
flowchart LR
  value["noul value"]:::neutral
  reject["reject<br/>&lt; 0.3"]:::danger
  review["human review<br/>0.3 to 0.8"]:::warning
  accept["accept<br/>&gt; 0.8"]:::success

  value --> reject
  value --> review
  value --> accept

  classDef success fill:#d1fae5,stroke:#059669,color:#064e3b,stroke-width:1.5px
  classDef warning fill:#fef3c7,stroke:#d97706,color:#78350f,stroke-width:1.5px
  classDef danger fill:#fee2e2,stroke:#dc2626,color:#7f1d1d,stroke-width:1.5px
  classDef neutral fill:#f4f4f5,stroke:#a1a1aa,color:#18181b,stroke-width:1.5px

Best practices

• State the proposition as a fact, not as a question: “The customer is eligible…” rather than “Is the customer eligible?”.
• Ask one thing. If a proposition hides two conditions, split it into two nouls and combine them in code.
• Anchor the policy in the state or context so the model has the rule it must apply.

Next steps

• Choice and Score — the other primitives.
• Confidence-gated routing — acting on certainty.
• State — giving the model the facts it needs.