During Relationship Ontology

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

flow "DuringRelationshipOntology" v1.0 {
  ontology:
    id: "during-relationship-ontology"
    parent: "temporal-relationships"
    purpose: "Represent and validate strict temporal containment of events and intervals."

  types:
    Instant: {value: datetime, timezone: string?, precision: string?}
    Interval: {id: string, start: Instant, end: Instant, start_closed: bool, end_closed: bool}
    Event: {id: string, interval: Interval?, provenance: string}
    TemporalRelation: {id: string, subject: string, predicate: string, object: string, confidence: number, evidence: string[], context: string?}

  predicates:
    during(inner: Interval, outer: Interval)
    contains(outer: Interval, inner: Interval)
    starts_before(a: Interval, b: Interval)
    ends_before(a: Interval, b: Interval)
    overlaps(a: Interval, b: Interval)
    simultaneous(a: Interval, b: Interval)

  semantics:
    - "Strict Allen during: during(a,b) iff start(b) < start(a) AND end(a) < end(b)."
    - "Intervals sharing either endpoint are not strictly during; use starts, finishes, or equality as appropriate."
    - "The inverse of during is contains, using the same strict definition."
    - "Event-level during requires explicitly identified event intervals."

  constraints:
    - "Each interval must have start <= end, with valid temporal precision."
    - "Compare instants only after normalising compatible time scales and time zones."
    - "Confidence must lie within [0,1]."
    - "Do not equate during with generic overlap or causal dependence."
    - "Uncertain endpoints require qualified, not absolute, temporal claims."

  inference:
    rule inverse_containment:
      if during(a,b)
      then contains(b,a)
      confidence: "retain source evidence and context"
    rule transitive_during:
      if during(a,b) and during(b,c) and compatible_temporal_frames(a,b,c)
      then during(a,c)
      confidence: "propagate uncertainty without manufacturing certainty"
    rule implies_overlap:
      if during(a,b) and nonempty(a)
      then overlaps(a,b)
      confidence: "derived from interval semantics"

  SEMANTIC_EQUIVALENCE:
    - "Normalise during, temporally_inside, and strictly_contained_in only when definitions agree."
    - "Distinguish strict during from inclusive containment, overlap, starts, and finishes."
    - "Preserve time zone, time scale, granularity, and boundary conventions."

  CONFIDENCE:
    range: [0,1]
    factors: [timestamp_accuracy, interval_precision, source_reliability, clock_synchronisation, independent_confirmation]
    policy: "Do not increase confidence solely through inference chaining."

  VALIDATION:
    - "Verify typed endpoints, valid interval bounds and temporal frame compatibility."
    - "Detect contradictions between during, before, after and disjoint assertions."
    - "Retain provenance and unresolved temporal uncertainty."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, typed 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 relations"
    outputs: [interval_entities, temporal_relation_triples, inferred_relations, confidence_annotations, provenance_records]
    safeguards: [preserve_boundary_semantics, preserve_temporal_precision, avoid_unsupported_causation]
}

END FLOW ALGEBRA