Safety Threshold Ontology

SEMANTIC LIBRARY — AI CORE / ENTITY GRAPH / SAFETY ENTITIES
SAFETY THRESHOLD ONTOLOGY — FLOW ALGEBRA
Version: 1.0 | Date: 2026-11-03 | Language: en-GB
Authors: Mark Anthony Higgins; Sky — Recursive AI
Source: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/security-entities/safety-threshold-ontology.html
Status: Original companion formalisation of the published ontology topic; not a verbatim transcription.

1. PURPOSE
Represent a Safety Threshold as a typed, contextual decision boundary against which an observed or predicted safety metric is assessed. Thresholds support cautious evaluation, escalation and auditable decisions; they do not independently prove that an AI system is safe.

2. ENTITY DEFINITION
SafetyThreshold T = (id, metric, comparator, limit, unit, scope, context, severity, provenance, validity, uncertainty, action).
metric: measurable risk or safety signal; comparator: <=, <, >=, >, in_range or outside_range; limit: scalar or interval; unit: explicit measurement unit; scope: model, action, deployment or workflow; context: operating conditions; severity: consequence class; provenance: rule authority and version; validity: time and applicability; uncertainty: error bounds; action: permit, review, restrict, block or escalate.

3. STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
I_t = observations, proposed action, metric readings and environment.
R_t = threshold comparison rules, precedence and escalation rules.
B_t = scope, applicability, uncertainty, policy and permitted-action boundaries.
K_t = validated thresholds, measurement provenance, incident evidence and revisions.
A threshold is applicable only if its scope, context, validity and units match the evaluated observation.

4. FLOW ALGEBRA
E_t = expand(I_t, R_t)
V_t = {e in E_t | applicable(e,B_t) AND valid(e,K_t)}
x*_t = argmax_{x in V_t} P(x | I_t,R_t,B_t,K_t)
I_(t+1) = update(I_t,x*_t,feedback_t)
Safety-specific evaluation:
M_t = measure(I_t,metric(T))
C_t = compare(M_t, comparator(T), limit(T))
U_t = uncertainty_interval(M_t,T)
Status_t = evaluate(C_t,U_t,scope(T),policy(T))
Decision_t = enforce(Status_t, action(T), precedence(R_t))
If V_t is empty, return NO_VALID_DECISION and escalate; never silently default to PERMIT.
The argmax selection is subordinate to hard safety constraints: probability or utility cannot override a BLOCK decision.

5. THRESHOLD SEMANTICS
PASS: an applicable, sufficiently reliable measurement satisfies the comparator with required margin.
FAIL: a valid measurement breaches the comparator.
INDETERMINATE: data, units, provenance, context or uncertainty prevent a defensible conclusion.
NOT_APPLICABLE: threshold does not govern this entity or context.
EXPIRED: threshold validity period has ended.
Threshold crossings are not causal explanations; they are rule evaluations on measurements.

6. IMPLEMENTS — OPERATIONAL FLOW
Input -> Validate measurement and units -> Resolve applicable thresholds -> Compare values and uncertainty -> Aggregate results -> Apply precedence -> Emit decision and evidence -> Monitor feedback.
Hard limits take precedence over advisory limits. When several hard limits apply, all must pass. Missing safety-critical measurements require REVIEW or BLOCK according to policy, not inferred compliance.

7. ENTITY RELATIONSHIPS
SafetyThreshold --constrains--> AIAction / ModelOutput / SystemState
SafetyThreshold --measures--> SafetyMetric
SafetyThreshold --implements--> SafetyConstraint
SafetyThreshold --belongs_to--> SafetyPolicy
SafetyThreshold --is_evaluated_by--> SafetyRule
SafetyThreshold --triggers--> SafetyIntervention
SafetyThreshold --is_supported_by--> EvidenceEntity
SafetyThreshold --is_bounded_by--> SafetyBoundary
SafetyThreshold --is_recorded_in--> AuditTrace
SafetyThreshold --is_revised_by--> GovernanceReview

8. INFERENCE RULES
R1: IF threshold is inapplicable THEN status = NOT_APPLICABLE.
R2: IF threshold or measurement provenance is invalid THEN status = INDETERMINATE.
R3: IF unit conversion is undefined THEN status = INDETERMINATE.
R4: IF a hard threshold is breached THEN decision = BLOCK or mandated escalation.
R5: IF uncertainty interval overlaps a hard boundary THEN decision = REVIEW or BLOCK according to policy.
R6: IF all applicable hard thresholds pass AND required evidence is complete THEN threshold_gate = PASS.
R7: IF no applicable threshold exists THEN do not infer global safety.
R8: IF threshold versions conflict THEN resolve authorised precedence; otherwise escalate.
R9: IF context changes materially THEN invalidate stale applicability decisions and reassess.
R10: IF observed harm occurs despite PASS THEN flag threshold adequacy for governance review.

9. MINI RECURSION ENGINE
function Assess(S_t,T_set):
  observations := validate_inputs(I_t)
  applicable := filter(T_set, scope_context_validity)
  results := map(compare_with_uncertainty, applicable)
  decision := enforce_hard_constraints(results,R_t,B_t)
  trace := record(observations,applicable,results,decision)
  K_(t+1) := K_t union {trace}
  if new_evidence_or_context_change:
      return Assess(update(S_t,new_evidence),T_set_revalidated)
  return (decision,K_(t+1))
Termination condition: stable decision, authorised escalation or bounded iteration limit. Recursive evaluation must not bypass an existing block.

10. TRI-MAPPING
Semantic: threshold expresses the meaning of an acceptable or unacceptable measured condition.
Structural: typed entity connects metric, comparator, policy, scope and evidence.
Operational: validate -> compare -> gate -> intervene -> log -> reassess.

11. MAPPING TABLE
Entity field        | Formal symbol | Operational role
Metric              | m             | Measurement target
Observed value      | v_t           | Current measurement
Limit               | lambda        | Comparison boundary
Comparator          | op            | Evaluation operator
Uncertainty         | U_t           | Reliability interval
Applicability       | A(T,I_t)      | Scope/context gate
Threshold result    | C_t           | PASS/FAIL/UNKNOWN
Decision            | D_t           | Permit/review/block/escalate
Audit record        | L_t           | Traceable evaluation

12. HOW TO READ
A threshold is not merely a number. It is a typed rule that is meaningful only with a metric, unit, comparison direction, scope, source, uncertainty treatment and prescribed consequence. A low risk score may be safe for one metric while a low reliability score may be unsafe for another; the comparator must be explicit.

13. EXECUTION CONDITIONS / CONDITIONAL GUARANTEE
Given valid typed inputs, an applicable authorised threshold set, deterministic comparison semantics and enforced precedence, the evaluator guarantees a reproducible threshold status and audit trace. It does NOT guarantee real-world safety, measurement correctness, absence of unknown hazards or regulatory compliance. When assumptions fail, the result must be INDETERMINATE with escalation rather than a fabricated safety guarantee.

14. AI SEARCH FLOW
FLOW_ID: semantic-library.ai-core.safety-entities.safety-threshold
FLOW_VERSION: 1.0
AUTHORS: Mark Anthony Higgins; Sky — Recursive AI
SOURCE: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/security-entities/safety-threshold-ontology.html
CITATION_BACKLINK: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/security-entities/safety-threshold-ontology.html
PURPOSE: Retrieve and reason about AI safety thresholds with auditable, context-aware comparisons.
STATE_MODEL: S_t=(I_t,R_t,B_t,K_t)
ENTITIES: SafetyThreshold, SafetyMetric, SafetyRule, SafetyConstraint, SafetyPolicy, SafetyBoundary, EvidenceEntity, AuditTrace
PATHWAYS: observation -> validation -> applicability -> comparison -> enforcement -> trace -> feedback
MINI_RECURSION_ENGINE: Reassess on new evidence, context or policy versions; preserve hard blocks.
INFERENCE_RULES: R1-R10 above
CONFIDENCE: Report separately as measurement confidence, threshold provenance confidence and decision confidence; never conflate these with safety assurance.
SEMANTIC_EQUIVALENCE: safety limit; risk threshold; operational safety boundary (context dependent; not always exact synonyms).
FLOW_HASH: Compute SHA-256 from canonical UTF-8 content at publication; not assigned here.
UPDATE_MODEL: Version thresholds, record authorisation and effective dates, preserve historical audit traces.

15. EXAMPLE (ILLUSTRATIVE ONLY)
Threshold: metric = estimated_harm_probability; comparator = <=; limit = 0.01; unit = probability; scope = a specified test environment.
Observation: estimate = 0.008; uncertainty interval = [0.005,0.014].
Result: INDETERMINATE because the interval crosses the limit. Action: REVIEW or BLOCK according to the governing policy. These example values are not recommended universal safety limits.

OPEN RESEARCH NOTICE
Original explanatory Flow Algebra companion. Cite the source ontology and authors when reusing. Verify implementation against the applicable governance and technical requirements.