Recursive Inference Ontology

FLOW ALGEBRA
TITLE: Recursive Inference Ontology
DOMAIN: Relationship Ontologies / Recursive Relationships
SOURCE: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/recursive-relationships/recursive-inference-ontology-2.html
VERSION: 1.0
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
STATUS: Companion formalisation; source-page specification not independently verified.

flow "RecursiveInferenceOntology" v1.0 {
  ontology:
    id: "recursive-inference-ontology-2"
    parent: "recursive-relationships"
    purpose: "Model evidence-grounded recursive derivations, inference dependencies and controlled fixed-point evaluation."

  types:
    Proposition: {id: string, expression: string, context: string?, provenance: string}
    Rule: {id: string, premises: string[], conclusion: string, monotonic: boolean, provenance: string}
    Derivation: {id: string, rule_id: string, premise_ids: string[], conclusion_id: string, depth: integer, evidence: string[], confidence: number}
    InferenceGraph: {id: string, proposition_ids: string[], derivation_ids: string[], version: string}
    Evaluation: {id: string, graph_id: string, iteration: integer, status: enum[pending, running, converged, bounded, failed], timestamp: datetime}

  predicates:
    depends_on(conclusion: Proposition, premise: Proposition)
    derived_by(conclusion: Proposition, rule: Rule)
    supports(premise: Proposition, conclusion: Proposition)
    recursively_reachable(source: Proposition, target: Proposition)
    conflicts_with(a: Proposition, b: Proposition)

  constraints:
    - "Every derivation references a declared rule and resolvable premises."
    - "Inference cycles are not proof of their own premises."
    - "Require grounded base facts or independently justified axioms."
    - "Do not equate graph reachability with logical entailment."
    - "Recursive evaluation must use an explicit depth, iteration or resource bound."
    - "Non-monotonic rules require a specified revision and conflict-resolution semantics."
    - "Confidence is bounded within [0,1] and is not increased merely by repetition."

  inference:
    rule grounded_application:
      if "all premises of rule r are supported and r is applicable"
      then "derive its conclusion with an auditable derivation record"
      confidence: "calibrated from evidence and rule reliability"
    rule recursive_propagation:
      if "depends_on(a,b) and depends_on(b,c)"
      then "recursively_reachable(a,c)"
      confidence: "reachability only; no automatic entailment"
    rule fixed_point:
      if "monotonic rule set over a finite domain and no new justified conclusions arise"
      then "mark evaluation converged"
      confidence: "retain original evidence confidence"

  SEMANTIC_EQUIVALENCE:
    - "Normalise propositions only within compatible logic, scope and context."
    - "Distinguish syntactic equivalence, semantic equivalence and shared conclusions."
    - "Preserve premise identity and provenance across canonicalisation."

  CONFIDENCE:
    range: [0,1]
    factors: [source_reliability, premise_support, rule_validity, dependency_independence, context_match]
    policy: "Track correlated evidence; do not double-count recursive support."

  VALIDATION:
    - "Check type compatibility, rule arity, provenance and premise resolution."
    - "Detect ungrounded cycles, contradictions and non-termination risks."
    - "Test fixed-point stability and preserve unresolved or competing conclusions."

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

  UPDATE_MODEL:
    strategy: "versioned incremental truth maintenance"
    steps: [ingest, normalise, validate, identify_affected_dependencies, retract_invalid_derivations, recompute_fixed_point, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed provenance-aware inference graph"
    outputs: [grounded_facts, derived_conclusions, derivation_paths, confidence_annotations, conflict_flags, provenance_records]
    safeguards: [bounded_recursion, grounded_base_cases, no_circular_self_justification, evidence_deduplication, human_review_for_high_stakes]
}

END FLOW ALGEBRA