Simultaneous Relationship Ontology

FLOW ALGEBRA
TITLE: Simultaneous Relationship Ontology
DOMAIN: Relationship Ontologies / Temporal Relationships
SOURCE: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/temporal-relationships/simultaneous-relationship-ontology.html
VERSION: 1.0
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
STATUS: Companion formalisation; source-page specification not independently verified.

flow "SimultaneousRelationshipOntology" v1.0 {
  ontology:
    id: "simultaneous-relationship-ontology"
    parent: "temporal-relationships"
    purpose: "Represent, qualify and validate simultaneous events or temporal intervals without confusing simultaneity with causation."

  types:
    TemporalEntity: {id: string, kind: enum[event, process, observation, interval], provenance: string}
    TimeInstant: {value: datetime, timezone: string?, clock: string?, uncertainty_seconds: number?}
    TimeInterval: {start: TimeInstant, end: TimeInstant, boundary_policy: enum[closed, open, left_closed, right_closed]}
    TemporalFrame: {id: string, reference_system: string, synchronisation_method: string?, precision_seconds: number?}
    Relationship: {id: string, subject: string, predicate: string, object: string, frame: string, tolerance_seconds: number?, confidence: number, evidence: string[]}

  predicates:
    simultaneous_with(a: TemporalEntity, b: TemporalEntity, frame: TemporalFrame)
    same_start_time(a: TemporalEntity, b: TemporalEntity, frame: TemporalFrame)
    same_end_time(a: TemporalEntity, b: TemporalEntity, frame: TemporalFrame)
    temporally_overlaps(a: TemporalEntity, b: TemporalEntity, frame: TemporalFrame)
    temporally_equal(a: TemporalEntity, b: TemporalEntity, frame: TemporalFrame)
    observed_at(entity: TemporalEntity, instant: TimeInstant)

  semantics:
    - "For point events, simultaneity means equal event times in the specified frame, subject to stated measurement uncertainty."
    - "For intervals, equal start and end boundaries define temporal equality; partial overlap alone does not establish simultaneity."
    - "Operational near-simultaneity within a tolerance must be distinguished from exact simultaneity."
    - "Simultaneity is frame-dependent when physical reference frames differ."

  constraints:
    - "Relationship endpoints must resolve to typed temporal entities."
    - "Confidence must lie within [0,1]."
    - "Intervals must have start <= end; boundary inclusion must be explicit."
    - "Compare times only after compatible timezone, clock, frame and precision normalisation."
    - "Do not infer causation, shared origin or identity from simultaneity."
    - "Tolerance-based near-simultaneity is not generally transitive."

  inference:
    rule symmetry:
      if simultaneous_with(a,b,f)
      then simultaneous_with(b,a,f)
      confidence: "retain evidence and temporal frame"
    rule exact_transitivity:
      if temporally_equal(a,b,f) and temporally_equal(b,c,f)
      then temporally_equal(a,c,f)
      confidence: "requires compatible exact interval semantics"
    rule interval_equality:
      if same_start_time(a,b,f) and same_end_time(a,b,f) and compatible_boundaries(a,b)
      then temporally_equal(a,b,f)
      confidence: "dependent on boundary precision and provenance"
    rule simultaneous_observations:
      if observed_at(a,t1) and observed_at(b,t2) and same_instant(t1,t2,f)
      then simultaneous_with(a,b,f)
      confidence: "dependent on clock synchronisation and uncertainty"

  SEMANTIC_EQUIVALENCE:
    - "Normalise simultaneous, concurrent and co-temporal labels only where their formal definitions agree."
    - "Distinguish exact simultaneity, approximate simultaneity, overlap and temporal equality."
    - "Preserve reference frames, tolerance and boundary policies."

  CONFIDENCE:
    range: [0,1]
    factors: [timestamp_precision, clock_synchronisation, measurement_uncertainty, source_reliability, frame_compatibility]
    policy: "Propagate uncertainty without manufacturing certainty from inference chains."

  VALIDATION:
    - "Verify endpoint types, interval ordering and compatible temporal frames."
    - "Check timestamp precision, timezone conversions, uncertainty and tolerance."
    - "Flag simultaneous and strict-before claims that conflict under the same frame and interval semantics."
    - "Retain alternative interpretations when time measurements are inconclusive."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, assertions, reference frames, rules and provenance"
    note: "Compute hash at execution; no hash value is claimed here."

  UPDATE_MODEL:
    strategy: "versioned, provenance-preserving incremental update"
    steps: [ingest, normalise, validate, reconcile, recompute_inferences, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed temporal knowledge graph with evidence-backed relationships"
    outputs: [temporal_triples, synchronisation_annotations, uncertainty_annotations, inferred_edges, provenance_records]
    safeguards: [no_unsupported_causal_claims, no_tolerance_transitivity, preserve_reference_frames, preserve_time_precision]
}

END FLOW ALGEBRA