Beliefs and evidence

What the numbers mean

Every number on a belief page has one defined meaning, and none of them is a probability unless the page says so. The epistemic score is the deterministic output of the arithmetic below over the recorded evidence: a ranking of how well supported a proposition is given what this mind has seen and how it weighs it. It is comparable between beliefs of one mind; it is not an 83 per cent chance of being true. The calibrated estimate is the observed hit rate of the mind's resolved predictions whose stated confidence fell in the same range, shown only once at least twenty predictions in that range have been decided; predictions are the one place a score meets reality, so they are the only empirical basis offered, and until it exists the page says why not. The primary uncertainty is the deterministic reason the score should be doubted most: a single source family, second-hand evidence only, conflicting evidence, little evidence, or an unclear reading of what was said.

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). Evidence is then grouped by family, the independent source a row ultimately rests on: a person, an integration, an operator, a prediction. Within a family the strongest primary item counts in full, each further primary item adds a quarter, and the total is capped at one and a half times the strongest; derived items (a consolidated memory, an inference, a reflection, a dream, a recalled memory) count only when the family has no primary item at all, because they re-express information rather than corroborate it. The confidence is

confidence = sigmoid( logit(prior) + 1.5 × (for × diversity − against) )

where for and against are the sums of family contributions and diversity rises from 0.6 for a single family to 1.0 for three or more. The result is bounded to [0.02, 0.98]: a mind is never certain and never certain of the negation. The number is an uncalibrated epistemic score, not a probability of truth; the belief page also shows a calibrated estimate drawn from the mind's resolved predictions when at least twenty were decided in the same range, and names the primary uncertainty (a single source family, second-hand only, conflicting evidence, little evidence, an unclear reading). Every evidence row carries its derivation, family and root ids; the breakdown, family by family, is stored with every version and shown on the belief page. Rows written before provenance was recorded are marked as legacy and grouped by their source string; no ancestry is invented for them.

Statuses

unknown (recorded, but no live evidence for or against), hypothesis (a proposal awaiting evidence), tentative, likely, accepted, contested (real evidence on both sides), rejected (evidence or an operator pushed the score low) and superseded (replaced by a corrected proposition or a later state). Status follows the score and the shape of the evidence automatically; an operator can pin rejected. Absence of evidence never collapses towards false: a belief whose evidence has all been retracted becomes unknown, its score is not quoted, and an introspective question is answered with "I do not know".

Time

Every belief is classified deterministically as persistent (a name, a relationship, a fact about the past), transient (a status, a level, a location, a mood) or of unknown scope, and carries the time it was observed. When a newer transient belief conflicts with an older one observed at least a minute earlier, the older one is closed with a validity interval and marked superseded rather than contested; the mind holds the current state and can list the earlier ones. Persistent beliefs that conflict are contradictions in the ordinary sense.

Source reliability

Credibility starts from the channel's trust level. It is then adjusted per source and subject: a source whose supported beliefs were borne out by predictions or upheld by operators becomes more credible on that subject, one whose beliefs were refuted or retracted becomes less so, and nothing carries across subjects. Reliability is applied only once three outcomes exist and is never global, so a monitoring integration that is excellent on disk usage and noisy on latency is treated as exactly that.

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.

A belief is a proposition the mind holds with an explicit, evidence-derived confidence and a status. Beliefs are never edited in place: every change appends a belief_versions row (append-only trigger) and an event.

Structure

What the numbers mean

Every numeric epistemic value in Noema has one defined meaning. None of them is a calibrated probability unless the page says so.

Confidence arithmetic

Confidence is never typed in by a person or produced by a model. It is:

value(e)      = weight × credibility                       for each live evidence row e
family(e)     = the independent source e ultimately rests on (an actor, an integration, an operator, a prediction)
contribution(family) = strongest primary item + ¼ × each further primary item, capped at 1.5 × the strongest
                       (if the family has no primary item: its strongest derived item alone)
for           = Σ contribution over supporting families
against       = Σ contribution over opposing families
diversity     = 0.6 + 0.4 × min(1, (supporting families − 1) / 2)
confidence    = sigmoid( logit(prior) + 1.5 × (for × diversity − against) )   clamped to [0.02, 0.98]

• The prior depends on the epistemic kind: hypothesis 0.25, assumption/opinion 0.4, claim 0.5, observation/memory 0.6, fact 0.8.
• Families are the unit of independence. Five messages from one person, the episodes they became, the semantic memory consolidated from them and an inference drawn from that memory are all one family: they carry one person's information however many times it has been re-expressed.
• Derivations say how a row relates to its roots. Primary derivations bring information in from outside the belief system: direct, assertion, operator, external, prediction. Derived ones re-express it: consolidation, inference, reflection, dream, retrieval. Derived rows never add weight to a family that already has a primary row, which is what stops recursive cognition inflating confidence.
• Repetition within a family is worth a quarter per extra item and never more than half again in total, so a single feed cannot manufacture certainty (threat T4), while three genuinely independent families can.
• Diversity counts families, not rows.
• Absolute certainty is unreachable; the bounds are deliberate (spec §10).

Every evidence row records its derivation, family, root_ids (the originating events or memories) and a provenance_status. Rows written before provenance existed are marked legacy_unknown with family = source; no ancestry is invented for them. The breakdown (prior, per-family contributions, for, against, families, diversity, log-odds, formula, notes) is stored with every version and shown on the belief page under "Independent sources".

Assertions as evidence

Statements people make reach beliefs only through assertions (docs/conversation.md). An assertion evidence row carries the attributed actor as its family, the source message as its root, and a weight that already reflects hedging, reporting and interpretation confidence. Nothing is silently upgraded: a claim stays a claim until evidence from another family arrives.

Status

Statuses: unknown (recorded, but no live evidence for or against), hypothesis (a proposal awaiting evidence), tentative, likely, accepted, contested (real evidence on both sides), rejected (evidence or an operator pushed it low) and superseded (replaced by a corrected proposition).

Absence of evidence

Lack of evidence never collapses towards "false". A belief whose evidence has all been retracted, or that was recorded without any, becomes unknown and its score is not quoted; introspection answers "I do not know whether X". A belief is rejected only when evidence against it, or an operator, drove its score below 0.15. Hypotheses are the one exception: they carry the hypothesis status until evidence arrives because they are proposals by construction.

Derived from the breakdown unless an operator pinned it:

• contested when both sides carry real weight (against ≥ half of the discounted support) and confidence is mid-range;
• rejected below 0.15; hypothesis for hypotheses without support or below 0.5; tentative below 0.7; likely below 0.85; accepted above;
• superseded when replaced by a newer proposition.

Source reliability by domain

A source's track record is kept per (family, domain), where the domain is the belief's subject. It is updated only by outcomes: a prediction derived from a belief resolving (confirmed counts as right, refuted or expired as wrong, for every primary supporting family of that belief) and an operator marking a belief wrong. With at least three outcomes in a domain the record adjusts the credibility of that source's new evidence in that domain: neutral leaves it alone, a perfect record raises it by half, a hopeless one halves it; the adjustment is written into the evidence note. A person wrong three times about database internals keeps their full credibility about their own diary. The trust-level credibility (operator, user, system, tool, source, low) is never rewritten.

Temporal scope

Every belief has a temporal_scope: persistent (a fact without an interval: "atlas is the primary host", "Andy prefers Go"), transient (a state that can change: "the door is open", "server A is down") or unknown when the deterministic classifier (ClassifyScope) cannot tell. Transient beliefs record observed_at and valid_from.

When a newer belief conflicts with an older transient one and was observed at least a minute later, the older belief is not contested and not weakened: its valid_until is set to the newer observation, its status becomes superseded with a version and a belief_updated event saying "state changed", and a supersedes link joins them. "The door was open at 10:00" stays true of 10:00 when the door is closed at 10:05. Conflicting reports of the same moment, and conflicts between persistent propositions, are contradictions as described below. Introspection lists superseded states as "Earlier: ... (true from ... until ...)".

Contradictions

On creation and on gaining support, a belief is compared with the mind's live beliefs. The deterministic pass detects the same content with flipped polarity (negation words plus token Jaccard ≥ 0.6). A hit emits contradiction_detected, links both beliefs, and makes each counter-evidence for the other weighted by the other's confidence, so both move towards contested until more evidence arrives. Paraphrase-level judgement is added by an LLM-assisted process once providers exist; it can only propose, and the same arithmetic applies.

Hypothesis generation

The associate process proposes causal hypotheses when two notable observations occur within a window ("deployment ... may have caused: latency alert"). Each observation is weak evidence (weight 0.15) so the belief starts as a hypothesis around 0.3 to 0.4; independent support is needed to move it. Alternatives ("coincidence", "a third factor") are recorded automatically.

Corrections

• This belief is wrong pins the status to rejected, adds operator counter-evidence, records a belief_wrong correction and a belief_retracted event. History is kept.
• Do not infer this again stores a do_not_infer correction; future creations of a matching proposition (token Jaccard ≥ 0.7) are refused and logged as metacognition.
• This memory is inaccurate retracts the memory and marks belief evidence citing it as retracted; affected beliefs are re-evaluated with a belief_updated event.