Recursive Semantic Relationship Ontology

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

flow "RecursiveSemanticRelationshipOntology" v1.0 {
  ontology:
    id: "recursive-semantic-relationship-ontology"
    parent: "recursive-relationships"
    purpose: "Represent and validate recursively derived semantic relationships while retaining contextual meaning, evidence, and termination safeguards."

  types:
    Concept: {id: string, label: string, ontology: string, version: string?}
    Context: {id: string, domain: string?, language: string?, temporal_scope: string?}
    SemanticRelation: {id: string, source: string, predicate: string, target: string, context: string, confidence: number, evidence: string[]}
    InferenceStep: {id: string, rule: string, premises: string[], conclusion: string, depth: integer, provenance: string[]}
    RecursivePath: {id: string, steps: string[], visited: string[], status: enum[active, complete, cycle_detected, depth_limited, invalid]}

  predicates:
    semantically_related(a: Concept, b: Concept, context: Context)
    equivalent_in(a: Concept, b: Concept, context: Context)
    broader_than(a: Concept, b: Concept, context: Context)
    narrower_than(a: Concept, b: Concept, context: Context)
    derived_from(relation: SemanticRelation, premise: SemanticRelation)
    participates_in(relation: SemanticRelation, path: RecursivePath)

  constraints:
    - "All relation endpoints and contexts must resolve to typed entities."
    - "Confidence must be within [0, 1]."
    - "Recursive traversal must track visited relation-state pairs and impose finite execution limits."
    - "Generic semantic relatedness is not automatically transitive."
    - "Equivalence transitivity requires compatible meaning, context and declared equivalence semantics."
    - "Broader/narrower propagation requires a declared transitive hierarchy and cycle checks."
    - "Similarity, association and alias must not be silently promoted to identity."
    - "No inferred edge may be published without an inspectable derivation and provenance."

  inference:
    rule contextual_equivalence:
      if equivalent_in(a,b,c) and equivalent_in(b,d,c) and compatible(a,b,d,c)
      then equivalent_in(a,d,c)
      confidence: "derive conservatively from supporting evidence"
    rule hierarchical_chain:
      if broader_than(a,b,c) and broader_than(b,d,c) and hierarchy_is_transitive(c)
      then broader_than(a,d,c)
      confidence: "preserve premise uncertainty"
    rule inverse_hierarchy:
      if broader_than(a,b,c)
      then narrower_than(b,a,c)
      confidence: "inherit source confidence and context"
    rule recursive_closure:
      if new_valid_relation(r) and not_previously_derived(r)
      then enqueue_for_re_evaluation(r)
      confidence: "do not manufacture certainty through repetition"

  RECURSION:
    evaluation: "worklist-based least fixed point over finite validated assertions"
    visited_key: "canonical(source, predicate, target, context, ontology_version)"
    safeguards: [cycle_detection, duplicate_suppression, max_depth, max_iterations, bounded_resources]
    stop_when: [no_new_valid_assertions, resource_limit, contradiction_requires_review]

  SEMANTIC_EQUIVALENCE:
    policy: "Normalise labels and identifiers only within declared contextual and ontology mappings."
    distinguish: [identity, equivalence, similarity, association, alias, subsumption]
    preserve: [language, context, ontology_version, provenance]

  CONFIDENCE:
    range: [0, 1]
    factors: [source_reliability, contextual_match, premise_quality, mapping_uncertainty, independent_support]
    policy: "Repeated or cyclic derivations do not count as independent corroboration."

  VALIDATION:
    - "Verify type compatibility, contexts, graph integrity and rule applicability."
    - "Detect cycles, conflicting semantic claims and invalid hierarchy propagation."
    - "Retain provenance for every asserted and inferred relationship."
    - "Flag unresolved ambiguities rather than merging concepts automatically."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, typed assertions, inference rules and provenance"
    note: "Compute at execution; no hash value is claimed here."

  UPDATE_MODEL:
    strategy: "versioned, provenance-preserving incremental fixed-point update"
    steps: [ingest, normalise, validate, detect_changes, retract_stale_derivations, recompute_closure, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed semantic knowledge graph with recursive derivation traces"
    outputs: [semantic_edges, inferred_relations, derivation_paths, confidence_annotations, provenance_records, validation_flags]
    safeguards: [bounded_recursion, no_unqualified_identity_merges, contextual_consistency, evidence_traceability]
}

END FLOW ALGEBRA