Recursive Knowledge Relationship Ontology

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

flow "RecursiveKnowledgeRelationshipOntology" v1.0 {
  ontology:
    id: "recursive-knowledge-relationship-ontology"
    parent: "recursive-relationships"
    purpose: "Represent, evaluate and audit recursive knowledge dependencies and evidence-backed inference across knowledge graphs."

  types:
    KnowledgeEntity: {id: string, kind: string, label: string, ontology: string?}
    KnowledgeClaim: {id: string, proposition: string, context: string?, status: enum[asserted, inferred, disputed, retracted], provenance: string[]}
    KnowledgeRelation: {id: string, source: string, predicate: string, target: string, context: string?, confidence: number, evidence: string[]}
    InferenceRule: {id: string, premises: string[], conclusion: string, monotonic: boolean, provenance: string}
    RecursionContext: {id: string, graph_id: string, max_depth: integer, iteration_limit: integer, evaluation_mode: enum[least_fixed_point, bounded_traversal]}
    Derivation: {id: string, claim_id: string, rule_id: string, premises: string[], iteration: integer, provenance: string[]}

  predicates:
    depends_on(claim: KnowledgeClaim, prerequisite: KnowledgeClaim)
    derives_from(claim: KnowledgeClaim, source: KnowledgeClaim)
    references(entity: KnowledgeEntity, target: KnowledgeEntity)
    supports(evidence: KnowledgeClaim, claim: KnowledgeClaim)
    contradicts(a: KnowledgeClaim, b: KnowledgeClaim)
    recursively_reachable(a: KnowledgeEntity, b: KnowledgeEntity)
    inferred_by(claim: KnowledgeClaim, rule: InferenceRule)

  constraints:
    - "All references and relationship endpoints must resolve to typed entities or claims."
    - "Confidence values must be in [0, 1] and include their evidential basis."
    - "Recursion depth and iteration limits must be non-negative and finite for bounded execution."
    - "Cycles must be detected; cycles are not automatically contradictions or errors."
    - "Self-reference does not establish truth, identity or independent corroboration."
    - "Non-monotonic rules require explicit revision semantics and must not be treated as monotonic fixed-point rules."
    - "Provenance must distinguish asserted, inferred and retracted claims."

  inference:
    rule recursive_reachability_base:
      if references(a,b)
      then recursively_reachable(a,b)
      confidence: "retain source context and evidence"
    rule recursive_reachability_step:
      if recursively_reachable(a,b) and references(b,c)
      then recursively_reachable(a,c)
      confidence: "do not assume independent evidence or increase confidence through repetition"
    rule knowledge_derivation:
      if all_premises_supported(rule) and rule.monotonic and rule_applicable(rule)
      then infer(rule.conclusion)
      confidence: "calibrate against premises, rule reliability and dependency overlap"
    rule contradiction_flag:
      if contradicts(a,b) and compatible_context(a,b)
      then flag_for_review(a,b)
      confidence: "preserve both evidence trails pending adjudication"

  RECURSIVE_EVALUATION:
    strategy: "worklist-based least-fixed-point evaluation for monotonic rules"
    termination: "stop at fixed point, configured bound or explicit failure"
    deduplication: "canonical claim identity plus context and provenance"
    cycle_policy: "record strongly connected components; do not repeatedly count cyclic support"
    audit: [derivation_steps, iteration_counts, visited_nodes, unresolved_cycles, stopping_reason]

  SEMANTIC_EQUIVALENCE:
    - "Normalise ontology identifiers and aliases using versioned mappings."
    - "Distinguish semantic similarity, logical equivalence and entity identity."
    - "Preserve context, temporal scope and provenance across recursive mappings."

  CONFIDENCE:
    range: [0,1]
    factors: [source_reliability, rule_validity, premise_support, provenance_independence, context_match, recursion_depth]
    policy: "Avoid confidence inflation from cyclic derivations or repeated evidence."

  VALIDATION:
    - "Validate types, references, rule signatures and contextual compatibility."
    - "Check for unsupported conclusions, inconsistent premises and unbounded recursion."
    - "Verify deterministic convergence for finite monotonic evaluation."
    - "Record unresolved uncertainty and contradictory evidence without silently discarding either."

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

  UPDATE_MODEL:
    strategy: "versioned, provenance-preserving incremental recomputation"
    steps: [ingest, normalise, validate, detect_changes, invalidate_affected_derivations, recompute_fixed_point, audit, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed recursive knowledge graph with evidence-backed derivation records"
    outputs: [knowledge_triples, dependency_paths, inferred_claims, confidence_annotations, provenance_records, cycle_reports]
    safeguards: [bounded_execution, no_circular_evidence_inflation, preserve_disagreement, no_unsupported_identity_merges, traceable_inferences]
}

END FLOW ALGEBRA