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Beliefs are the mind's propositions about the world, each with a confidence that is derived from evidence rather than asserted. This page gives the arithmetic, the lifecycle and the operator controls.
Confidence
A belief starts from a prior set by its epistemic kind (a hypothesis at 0.25, a claim at 0.50, a fact at 0.80; the full table is under concepts). Each piece of evidence contributes its weight multiplied by the credibility of its source, for or against. Confidence is
confidence = sigmoid( logit(prior) + 1.5 × (for × diversity − against) )
where diversity rises from 0.6 for a single source to 1.0 for three or more independent sources, so repetition from one place is discounted. The result is bounded to [0.02, 0.98]: a mind is never certain and never certain of the negation. The breakdown (prior, each evidence row, the diversity factor, the formula) is stored with every version and shown on the belief page.
Statuses
hypothesis (below 0.35), tentative, likely, accepted (above 0.85), contested (significant evidence on both sides), rejected (retracted by evidence or an operator) and superseded (replaced by a corrected proposition). Status follows confidence and evidence shape automatically; an operator can pin rejected.
Contradictions
A deterministic detector compares new propositions with existing ones on the same subject using negation patterns and lexical overlap. A detected contradiction creates a contradiction_detected event, links the two beliefs, marks both contested when the evidence is comparable, and gives curiosity something to ask about. Contradictions are never resolved by picking the newer statement; they are resolved by evidence, or by an operator.
Alternatives and links
A belief may carry alternative propositions (hypothesis generation always includes "these are unrelated"). Beliefs link to each other with supports, contradicts and depends_on, which the interface renders and which re-evaluation follows.
Evidence kinds
Evidence points at memories, events, operator statements, tool results, predictions and other beliefs, with a direction, a weight, a note and the source's credibility. Retracting a memory retracts the evidence rows that cite it and re-evaluates the affected beliefs. Prediction outcomes add evidence automatically: a refuted prediction weakens the beliefs it was derived from.
Operator corrections
From the belief page or noemactl belief wrong, an operator can mark a belief wrong (operator counter-evidence at high credibility), retract it outright, or attach a "do not infer" correction that prevents the same proposition being re-derived by consolidation or association. Every correction is an event, an audit entry and, for the mind, an autobiographical memory.
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