Flow Relationship Ontology

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

flow "FlowRelationshipOntology" v1.0 {
  ontology:
    id: "flow-relationship-ontology"
    parent: "ai-semantic-library-relationships"
    purpose: "Model typed, directed and evidence-backed relationships between semantic flows, their inputs, outputs, dependencies and transformations."

  types:
    Flow: {id: string, version: string, purpose: string, status: enum[draft, validated, active, deprecated]}
    FlowPort: {id: string, flow_id: string, direction: enum[input, output], data_type: string}
    Artefact: {id: string, kind: string, schema: string?, version: string?}
    Transformation: {id: string, operator: string, deterministic: boolean?, preconditions: string[], postconditions: string[]}
    Evidence: {id: string, source: string, timestamp: datetime?, reliability: number?}
    FlowRelationship: {id: string, source_id: string, predicate: string, target_id: string, context: string?, confidence: number, evidence_ids: string[]}

  predicates:
    depends_on(flow: Flow, prerequisite: Flow)
    consumes(flow: Flow, artefact: Artefact)
    produces(flow: Flow, artefact: Artefact)
    transforms(flow: Flow, operation: Transformation)
    connects(output: FlowPort, input: FlowPort)
    derived_from(output: Artefact, input: Artefact)
    precedes(upstream: Flow, downstream: Flow)
    semantically_maps_to(source: Flow, target: Flow)
    supersedes(new_flow: Flow, old_flow: Flow)

  constraints:
    - "All relationship endpoints must resolve to typed, versioned entities."
    - "Confidence must be in [0, 1], with evidence and context retained."
    - "Port connections must run output to input and satisfy declared schema compatibility."
    - "Dependencies and temporal precedence must not automatically imply causation."
    - "Semantic mapping must not imply identity or interchangeable execution."
    - "Cyclic dependencies require explicit iteration semantics, termination guards or fixed-point policy."
    - "Supersession must preserve historical versions and provenance."
    - "Sensitive or restricted artefacts must retain access controls across derived outputs."

  inference:
    rule dependency_chain:
      if depends_on(a,b) and depends_on(b,c) and acyclic_path(a,b,c)
      then indirectly_depends_on(a,c)
      confidence: "evidence-preserving; no automatic confidence inflation"
    rule flow_lineage:
      if produces(a,x) and consumes(b,x) and verified_identity(x)
      then potential_upstream_of(a,b)
      confidence: "requires verified artefact identity and execution context"
    rule version_lineage:
      if supersedes(a,b) and supersedes(b,c)
      then has_version_ancestor(a,c)
      confidence: "retain original version links"

  SEMANTIC_EQUIVALENCE:
    - "Normalise identifiers using versioned ontology mappings."
    - "Distinguish equivalent intent from equivalent inputs, outputs and runtime behaviour."
    - "Retain domain, execution context, schema versions and transformation semantics."

  CONFIDENCE:
    range: [0,1]
    factors: [source_reliability, schema_compatibility, validation_coverage, execution_evidence, version_consistency]
    policy: "Derived confidence must reflect the weakest relevant evidence and dependence assumptions."

  VALIDATION:
    - "Verify identifiers, endpoint types, version references and provenance."
    - "Check port directions, data types, preconditions and postconditions."
    - "Detect unsupported mappings, dangling references and unguarded cycles."
    - "Check lineage consistency and preserve conflicting claims for review."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, entity and relationship 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 semantic flow graph with provenance-backed edges"
    outputs: [flow_links, dependency_paths, artefact_lineage, semantic_mappings, uncertainty_annotations, provenance_records]
    safeguards: [no_unverified_identity_merges, no_unsupported_causal_claims, preserve_version_context, enforce_access_controls]
}

END FLOW ALGEBRA