Before Relationship Ontology

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

flow "BeforeRelationshipOntology" v1.0 {
  ontology:
    id: "before-relationship-ontology"
    parent: "temporal-relationships"
    purpose: "Represent evidence-backed strict temporal precedence between instants, events and intervals."

  types:
    TimeInstant: {id: string, value: datetime, time_scale: string?, uncertainty: number?, provenance: string}
    TimeInterval: {id: string, start: datetime, end: datetime, endpoint_policy: string?, provenance: string}
    Event: {id: string, interval_id: string?, instant_id: string?, provenance: string}
    TemporalAssertion: {id: string, earlier: string, later: string, interpretation: enum[strict_end_before_start, instant_precedence], confidence: number, evidence: string[], context: string?}

  predicates:
    before_instant(a: TimeInstant, b: TimeInstant)
    before_interval(a: TimeInterval, b: TimeInterval)
    before_event(a: Event, b: Event)
    meets(a: TimeInterval, b: TimeInterval)
    overlaps(a: TimeInterval, b: TimeInterval)

  semantics:
    - "before_instant(a,b) iff time(a) < time(b) on a compatible time scale."
    - "before_interval(a,b) iff end(a) < start(b) for strict separated intervals."
    - "Meeting intervals are not strictly before under the selected strict endpoint convention."
    - "Event precedence requires explicit temporal extent or instant interpretation."

  constraints:
    - "All temporal endpoints must resolve to typed, provenance-backed entities."
    - "Interval start must not exceed interval end."
    - "Confidence must be within [0,1]."
    - "Normalise time zones, time scales and precision before comparing."
    - "Strict before is irreflexive and asymmetric."
    - "Uncertain or overlapping bounds must not yield categorical precedence."
    - "Temporal precedence alone does not establish causation."

  inference:
    rule transitive_precedence:
      if before_instant(a,b) and before_instant(b,c) and comparable(a,b,c)
      then before_instant(a,c)
      confidence: "propagate source uncertainty; never manufacture certainty"
    rule interval_transitivity:
      if before_interval(a,b) and before_interval(b,c) and comparable(a,b,c)
      then before_interval(a,c)
      confidence: "retain endpoint precision and evidence"
    rule inverse_after:
      if before_instant(a,b)
      then after_instant(b,a)
      confidence: "retain original evidence"
    rule contradiction:
      if before_instant(a,b) and before_instant(b,a)
      then flag_temporal_inconsistency(a,b)
      confidence: "review source observations and normalisation"

  SEMANTIC_EQUIVALENCE:
    - "Map 'earlier than' and 'precedes' to strict before only when endpoint semantics agree."
    - "Keep 'before', 'meets', 'overlaps' and 'causes' distinct."
    - "Preserve granularity, time scale, calendar, and observation context."

  CONFIDENCE:
    range: [0,1]
    factors: [timestamp_precision, clock_synchronisation, source_reliability, interval_uncertainty, independent_evidence]
    policy: "Do not raise confidence solely by inference chaining."

  VALIDATION:
    - "Check temporal types, endpoint order, timezone/time-scale compatibility and provenance."
    - "Detect precedence cycles and contradictory assertions."
    - "Mark ambiguous order as unresolved rather than forcing an ordering."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, typed temporal assertions, 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, compare, reconcile, recompute_inferences, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed temporal knowledge graph with evidence-backed precedence edges"
    outputs: [temporal_triples, ordering_constraints, uncertainty_annotations, inferred_edges, provenance_records]
    safeguards: [no_unsupported_causal_claims, no_forced_order_for_uncertain_events, preserve_temporal_precision]
}

END FLOW ALGEBRA