Sequence Relationship Ontology

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

flow "SequenceRelationshipOntology" v1.0 {
  ontology:
    id: "sequence-relationship-ontology"
    parent: "temporal-relationships"
    purpose: "Represent ordered events, temporal succession, and evidence-backed sequence constraints without conflating order with causation."

  types:
    Event: {id: string, label: string, start: datetime?, end: datetime?, time_frame: string?, provenance: string}
    Sequence: {id: string, members: string[], ordering: enum[total, partial], provenance: string}
    SequencePosition: {sequence_id: string, event_id: string, index: integer?}
    Relationship: {id: string, subject: string, predicate: string, object: string, sequence_id: string?, confidence: number, evidence: string[]}

  predicates:
    precedes(a: Event, b: Event)
    immediately_precedes(a: Event, b: Event, sequence: Sequence)
    follows(a: Event, b: Event)
    member_of(event: Event, sequence: Sequence)
    position_in(event: Event, sequence: Sequence, index: integer)
    overlaps(a: Event, b: Event)
    concurrent_with(a: Event, b: Event)

  constraints:
    - "Relationship endpoints must resolve to typed events."
    - "Confidence must lie within [0, 1]."
    - "Strict precedence is irreflexive and asymmetric."
    - "A valid strict precedence graph must be acyclic."
    - "Sequence indices, when specified, are unique within a total sequence."
    - "Partial orders must not be silently converted into total orders."
    - "Immediate precedence is scoped to a specified sequence and its completeness assumptions."
    - "Temporal order alone does not establish causation."
    - "Timestamps must be normalised to a common temporal frame before comparison."

  inference:
    rule inverse_order:
      if precedes(a,b)
      then follows(b,a)
      confidence: "retain supporting evidence"
    rule transitive_precedence:
      if precedes(a,b) and precedes(b,c) and compatible_temporal_frame(a,b,c)
      then precedes(a,c)
      confidence: "propagate uncertainty; never manufacture certainty"
    rule immediate_implies_precedence:
      if immediately_precedes(a,b,s)
      then precedes(a,b)
      confidence: "inherit evidence and sequence scope"
    rule ordered_positions:
      if position_in(a,s,i) and position_in(b,s,j) and i < j and complete_order(s)
      then precedes(a,b)
      confidence: "sequence reliability dependent"

  SEMANTIC_EQUIVALENCE:
    - "Distinguish sequence membership, precedence, immediate precedence and causal dependency."
    - "Normalise temporal terms and preserve sequence-specific scope."
    - "Do not merge event identities solely because timestamps or labels match."

  CONFIDENCE:
    range: [0,1]
    factors: [timestamp_precision, source_reliability, sequence_completeness, temporal_frame_consistency, independent_confirmation]
    policy: "Do not increase confidence solely through inference chaining."

  VALIDATION:
    - "Check event existence, unique identifiers and temporal-frame compatibility."
    - "Reject strict precedence cycles and self-precedence."
    - "Flag contradictory timestamps, sequence positions and ordering claims."
    - "Preserve unknown ordering for incomparable events."
    - "Retain provenance for asserted and inferred edges."

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

  AI_CONSUMPTION:
    representation: "typed temporal knowledge graph and ordered event sequences"
    outputs: [ordered_events, precedence_edges, sequence_positions, uncertainty_annotations, provenance_records]
    safeguards: [no_unsupported_causal_claims, no_forced_total_order, detect_cycles, preserve_temporal_context]
}

END FLOW ALGEBRA