Recursive Execution Relationship Ontology

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

flow "RecursiveExecutionRelationshipOntology" v1.0 {
  ontology:
    id: "recursive-execution-relationship-ontology"
    parent: "recursive-relationships"
    purpose: "Represent, trace and validate recursive execution calls, dependencies, termination and results."

  types:
    Procedure: {id: string, version: string, input_schema: string, output_schema: string}
    Execution: {id: string, procedure_id: string, parent_execution_id: string?, depth: integer, status: enum[pending, running, completed, failed, cancelled], started_at: datetime?, ended_at: datetime?}
    Call: {id: string, caller_execution_id: string, callee_execution_id: string, arguments_hash: string, order: integer}
    BaseCase: {id: string, procedure_id: string, predicate: string, result: string}
    TerminationMeasure: {name: string, value: number, ordering: string}
    Result: {id: string, execution_id: string, value_ref: string?, provenance: string}
    Evidence: {id: string, source: string, timestamp: datetime?, reliability: number?}
    Relationship: {id: string, subject: string, predicate: string, object: string, context: string?, confidence: number, evidence: string[]}

  predicates:
    invokes(caller: Execution, callee: Execution)
    executes(execution: Execution, procedure: Procedure)
    depends_on(execution: Execution, prerequisite: Execution)
    reaches_base_case(execution: Execution, base_case: BaseCase)
    returns(execution: Execution, result: Result)
    precedes(a: Execution, b: Execution)
    terminates(execution: Execution)
    repeats_state(a: Execution, b: Execution)

  constraints:
    - "All relationship endpoints must resolve to typed entities."
    - "Confidence must be within [0,1]."
    - "Each invocation must preserve caller, callee, arguments and execution context."
    - "A completed recursive execution must have a valid base case or an independently justified termination proof."
    - "Where a well-founded termination measure is declared, every recursive call must strictly decrease it."
    - "Cycles and repeated states require explicit handling; recursion does not itself guarantee termination."
    - "Do not infer successful execution from call reachability alone."
    - "Preserve failure, cancellation, resource limits and execution ordering."

  inference:
    rule recursive_call_depth:
      if invokes(a,b) and depth(a) == n
      then depth(b) == n + 1
      confidence: "structural, subject to trace integrity"
    rule execution_dependency:
      if invokes(a,b) and requires_result(a,b)
      then depends_on(a,b)
      confidence: "retain call and dependency evidence"
    rule termination_evidence:
      if reaches_base_case(e,b) and valid(b) and completed(e)
      then terminates(e)
      confidence: "supported by execution trace"
    rule transitive_dependency:
      if depends_on(a,b) and depends_on(b,c)
      then indirectly_depends_on(a,c)
      confidence: "propagate provenance; avoid unsupported certainty"

  SEMANTIC_EQUIVALENCE:
    - "Normalise procedure and execution identifiers using versioned namespaces."
    - "Distinguish identical procedures from distinct execution instances."
    - "Treat equivalent call signatures as comparable, not automatically identical executions."
    - "Preserve input context, procedure version and result provenance."

  CONFIDENCE:
    range: [0,1]
    factors: [trace_completeness, execution_integrity, source_reliability, termination_evidence, reproducibility]
    policy: "Do not increase confidence merely through recursive chaining."

  VALIDATION:
    - "Check typed endpoints, call linkage, unique execution identifiers and status transitions."
    - "Verify base cases, termination measures and bounded resource consumption."
    - "Detect cycles, non-decreasing recursion measures, orphan calls and conflicting results."
    - "Distinguish observed execution outcomes from predicted outcomes."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, typed assertions, execution traces, 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, detect_cycles, evaluate_termination, reconcile, recompute_inferences, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed recursive execution graph with evidence-backed call edges"
    outputs: [execution_traces, recursive_call_edges, termination_annotations, dependency_paths, confidence_scores, provenance_records]
    safeguards: [no_assumed_termination, no_unsupported_success_claims, preserve_execution_context, bound_recursive_evaluation]
}

END FLOW ALGEBRA