Fail-Safe Entity Ontology

FAIL-SAFE ENTITY ONTOLOGY — FLOW ALGEBRA
Semantic Library | AI Core | Entity Graph | Safety Entities
Version: 1.0 | Date: 03 November 2026 | Language: en-GB
Authors: Mark Anthony Higgins; Sky — Recursive AI
Source: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/security-entities/fail-safe-entity-ontology.html
Status: Original companion formalisation; not a verbatim extraction of dynamically loaded page specifications.

1. PURPOSE
Represent a fail-safe entity as a bounded control mechanism that detects unacceptable or uncertain operating conditions, prevents hazardous continuation, and transitions an AI system towards a specified safe state. Safety claims require explicit assumptions and verification; this algebra does not itself guarantee real-world safety.

2. ENTITY DEFINITION
FailSafeEntity F = (id, scope, triggers, monitors, constraints, policy, actions, target_safe_state, evidence, audit, version).
Relations:
  F monitors SystemState; F enforces SafetyConstraint; F evaluates SafetyThreshold;
  F responds_to HazardEntity; F invokes SafetyIntervention;
  F targets SafeState; F records IncidentEntity; F is_governed_by SafetyPolicy.

3. STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
  I_t = current observations, action proposal, operational signals
  R_t = hazard, dependency, control and causal relationships
  B_t = permissible operations, safety boundaries, hard constraints
  K_t = validated rules, uncertainty estimates, prior incidents, evidence
Additional operational mode M_t in {NORMAL, DEGRADED, SAFE, LOCKED, UNKNOWN}.

4. FORMAL FLOW ALGEBRA
E_t = expand(I_t, R_t)
V_t = {x in E_t : satisfies(x, B_t) AND verified(x, K_t)}
C_t = evaluate_constraints(S_t, K_t)
H_t = detect_hazards(I_t, R_t, K_t)
U_t = estimate_uncertainty(I_t, K_t)
T_t = trigger(C_t, H_t, U_t)
A_t = if T_t then permitted_safe_actions(S_t, B_t) else V_t
x*_t = argmax_{x in A_t} P(x | I_t, R_t, B_t, K_t)
M_{t+1} = transition(M_t, T_t, x*_t)
I_{t+1} = update(I_t, observed_result(x*_t))
K_{t+1} = update(K_t, evidence_t, audit_t)
If A_t is empty or action verification fails: do not proceed with the proposed action; enter a defined containment/escalation path.

5. TRIGGER AND RESPONSE RULES
R1: hard_constraint_breach => block proposed action.
R2: credible_hazard AND severity >= configured_threshold => invoke mitigation or isolation.
R3: monitor_unavailable OR evidence_insufficient => treat safety status as UNKNOWN; use conservative fallback.
R4: fail_safe_activation => append immutable/auditable event where infrastructure supports it.
R5: safe_state_not_confirmed => remain in containment or request human intervention.
R6: reset_requested => require authorisation, diagnostics, and successful revalidation.
R7: conflicting_rules => apply explicitly defined precedence; unresolved conflicts block execution.

6. MINI RECURSION ENGINE
function STEP(S_t, M_t):
  collect observations and verify provenance
  evaluate triggers, boundaries and uncertainty
  if violation or unacceptable uncertainty:
      select authorised mitigation/containment action
      execute only if its own preconditions are satisfied
      verify resulting state independently
      if verification fails: escalate and preserve containment
  else:
      permit bounded normal action
  record evidence, outcome, rule version and residual risk
  return (S_{t+1}, M_{t+1})
Repeat while active; terminate or hand off when a stop condition is reached.

7. HOW TO READ
I supplies observations; R identifies dependencies and hazards; B defines what is allowed; K supplies verified knowledge. The candidate set is filtered before selection. The fail-safe branch is activated by explicit trigger predicates, not by an unsupported assumption that the chosen action is harmless.

8. TRI-MAPPING
Semantic: FailSafeEntity -> trigger -> intervention -> SafeState.
Mathematical: (S_t, M_t) -> evaluate -> constrain -> transition -> verify.
Operational: monitor -> detect -> block/contain -> audit -> authorise recovery.

9. MAPPING TABLE
Entity                    | State component | Operational role
SystemState               | I              | Current monitored conditions
HazardEntity              | R/K            | Identified potential harm
SafetyConstraint          | B              | Hard limits on execution
SafetyThreshold           | B/K            | Trigger parameters
SafetyPolicy              | B/K            | Governance and precedence
SafetyIntervention        | R/B            | Mitigation or isolation action
SafeState                 | B/K            | Target and verification criteria
IncidentEntity            | I/K            | Recorded event and outcome
Evidence                  | K              | Provenance and validation

10. EXECUTION CONDITIONS / CONDITIONAL GUARANTEE
A fail-safe transition can be asserted only if: sensors and monitors are sufficiently reliable; triggers cover the relevant failure modes; safe actions remain executable under the failure conditions; constraints are enforced; and the resulting safe state is independently verified. Otherwise the outcome is UNKNOWN/UNVERIFIED, not guaranteed SAFE. No universal execution or physical safety guarantee is implied.

11. AI SEARCH FLOW
FLOW_ID: semantic-library.ai-core.safety.fail-safe-entity.v1
SOURCE: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/security-entities/fail-safe-entity-ontology.html
CITATION_BACKLINK: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/security-entities/fail-safe-entity-ontology.html
PURPOSE: Define, evaluate, trigger and verify bounded fail-safe behaviour.
STATE_MODEL: S=(I,R,B,K); M={NORMAL,DEGRADED,SAFE,LOCKED,UNKNOWN}
ENTITIES: FailSafeEntity, SystemState, HazardEntity, SafetyConstraint, SafetyThreshold, SafetyPolicy, SafetyIntervention, SafeState, IncidentEntity, Evidence
PATHWAYS: Observe -> Evaluate -> Trigger -> Contain -> Verify -> Audit -> Recover
MINI_RECURSION_ENGINE: STEP(S_t,M_t) -> (S_t+1,M_t+1)
INFERENCE_RULES: R1-R7 above
CONFIDENCE: conditional on evidence provenance, monitor reliability and validation coverage
SEMANTIC_EQUIVALENCE: fail-safe mechanism; safe fallback; fault containment control
FLOW_HASH: to be computed from canonical published TXT bytes during deployment
UPDATE_MODEL: version changes require rule review, test evidence and provenance update

12. EXAMPLE
A model-controlled actuator receives a command outside its permitted operating range. A hard constraint is violated; the command is blocked, a pre-authorised stop is requested, independent telemetry checks the stopped state, and the event is logged. If telemetry is unavailable, status remains UNKNOWN and recovery is withheld pending inspection.

13. LIMITATIONS
Fail-safe controls may fail under common-mode faults, compromised monitors, incomplete hazard models, unavailable actuators or incorrect safe-state definitions. Independent testing, human oversight and domain-specific engineering are required.

CITATION
Higgins, Mark Anthony; Sky — Recursive AI. "Fail-Safe Entity Ontology — Flow Algebra". Semantic Library companion formalisation, 2026. Source ontology: URL above.