After Relationship Ontology

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

flow "AfterRelationshipOntology" v1.0 {
  ontology:
    id: "after-relationship-ontology"
    parent: "temporal-relationships"
    purpose: "Represent, evaluate and validate strict temporal succession between events and intervals."

  types:
    TemporalEntity: {id: string, kind: enum[event, interval, instant, process], provenance: string}
    Instant: {value: datetime, timescale: string, uncertainty: number?}
    Interval: {start: Instant, end: Instant, start_inclusive: bool, end_inclusive: bool}
    Relationship: {id: string, subject: string, predicate: string, object: string, confidence: number, evidence: string[], context: string?}

  predicates:
    after(a: TemporalEntity, b: TemporalEntity)
    before(a: TemporalEntity, b: TemporalEntity)
    meets(a: TemporalEntity, b: TemporalEntity)
    overlaps(a: TemporalEntity, b: TemporalEntity)
    simultaneous_with(a: TemporalEntity, b: TemporalEntity)

  semantics:
    - "For intervals, after(A,B) iff start(A) > end(B) on a common timescale."
    - "For instants, after(A,B) iff time(A) > time(B)."
    - "For events with duration, evaluate the defined event extent; do not silently replace duration with a timestamp."
    - "Strict after excludes equality and immediate meeting at a shared boundary."
    - "Unknown or uncertain temporal bounds may yield indeterminate rather than false."

  constraints:
    - "All referenced entities must exist and have compatible temporal representations."
    - "Intervals must satisfy start <= end; distinguish zero-duration instants from intervals."
    - "Normalise timezone and timescale before comparisons; retain original precision."
    - "Confidence must lie within [0,1]."
    - "Do not infer causation from temporal succession."
    - "No after(A,A) in a consistent strict temporal ordering."

  inference:
    rule inverse_before:
      if after(a,b)
      then before(b,a)
      confidence: "inherit evidence and context"
    rule transitive_after:
      if after(a,b) and after(b,c) and compatible_timeframes(a,b,c)
      then after(a,c)
      confidence: "propagate uncertainty without automatic increase"
    rule asymmetry:
      if after(a,b)
      then reject(after(b,a))
      confidence: "subject to consistency and temporal-frame validation"
    rule uncertain_comparison:
      if temporal_bounds_overlap_under_uncertainty(a,b)
      then status(after(a,b)) = "indeterminate"
      confidence: "retain measurement uncertainty"

  SEMANTIC_EQUIVALENCE:
    - "Map later_than and succeeds_temporally to strict after only where interval semantics agree."
    - "Distinguish after from meets, starts_after, ends_after and causal_follows."
    - "Preserve time precision, reference timescale and interval boundary conventions."

  CONFIDENCE:
    range: [0,1]
    factors: [timestamp_accuracy, temporal_resolution, source_reliability, clock_synchronisation, independent_evidence]
    policy: "Chained inferences must not manufacture certainty."

  VALIDATION:
    - "Check endpoint existence, temporal type compatibility and interval validity."
    - "Detect cycles in strict after relations and contradictory before/after assertions."
    - "Check timezone conversion, daylight-saving ambiguities and timescale differences."
    - "Preserve evidence for ambiguous or partially ordered events."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, assertions, inference 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, ordered_events, inferred_relations, uncertainty_annotations, provenance_records]
    safeguards: [no_unsupported_causation, no_false_precision, no_unqualified_temporal_order]
}

END FLOW ALGEBRA