Inference Relationship Ontology

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

ONTOLOGY:
  id: kireth:InferenceRelationshipOntology
  domain: Logical Relationships
  purpose: Model evidence-supported links between premises, rules and conclusions.

TYPES:
  Entity := identified concept or object
  Proposition := (id, statement, context, truth_status)
  Premise := Proposition
  Conclusion := Proposition
  InferenceRule := (id, antecedent_pattern, consequent_pattern, logic_system)
  Inference := (id, premises:Set[Premise], rule:InferenceRule, conclusion:Conclusion, context, provenance)
  Evidence := (id, source, supports, reliability)
  Confidence := Real[0,1]

RELATIONSHIPS:
  hasPremise(Inference, Premise)
  appliesRule(Inference, InferenceRule)
  derives(Inference, Conclusion)
  supports(Evidence, Proposition)
  dependsOn(Conclusion, Premise)
  contradicts(Proposition, Proposition)
  equivalentUnder(Proposition, Proposition, Context)

OPERATORS:
  INFER(P, R, C) := valid_application(R, P, C)
  ENTAILS(P, C, L) := every_model(L, P) satisfies C
  DERIVABLE(P, C, R) := finite_proof(P, C, R)
  CHAIN(I1, I2) := conclusion(I1) unifies with premise(I2)
  EXPLAIN(I) := ordered proof steps + evidence + provenance

RULES:
  R1 ModusPonens: P, (P -> Q) => Q
  R2 ModusTollens: (P -> Q), not Q => not P
  R3 ConjunctionIntroduction: P, Q => P and Q
  R4 ConjunctionElimination: P and Q => P; P and Q => Q
  R5 TransitiveImplication: (P -> Q), (Q -> R) => (P -> R)
  R6 UniversalInstantiation: forall x P(x), Entity(a) => P(a)
  R7 NoCausalLeap: correlation(P,Q) does not imply causes(P,Q)
  R8 NoIdentityLeap: similar(P,Q) does not imply identical(P,Q)

CONSTRAINTS:
  C1: Every inference has >= 1 premise, exactly 1 rule and >= 1 conclusion.
  C2: Premises and conclusions must be well-typed for the applied rule.
  C3: An inference must record the logic system and contextual assumptions.
  C4: Derivability is not equivalent to semantic entailment without soundness assumptions.
  C5: Contradictions are flagged; explosive reasoning is not assumed across all logic systems.
  C6: Cyclic proofs require explicit fixed-point or coinductive semantics.
  C7: Missing evidence must not be represented as verified support.

SEMANTIC_EQUIVALENCE:
  scope: context_and_logic_system
  rule: equivalentUnder(P,Q,K) only when their meanings agree in K
  safeguard: similarity and lexical overlap alone are insufficient

CONFIDENCE:
  range: [0,1]
  inputs: [premise_reliability, rule_validity, evidence_quality, contextual_fit]
  policy: Confidence is a calibrated assessment, not logical truth.
  propagation: Use an explicitly declared model; do not assume independence.

VALIDATION:
  - check_identifiers_unique
  - check_premise_rule_conclusion_types
  - check_proof_step_reproducibility
  - check_assumptions_and_context
  - check_evidence_and_provenance
  - detect_cycles_and_contradictions
  - distinguish_soundness_from_confidence

FLOW_HASH:
  algorithm: SHA-256
  input: canonical_serialisation(ontology_id, version, types, relationships, rules, constraints)
  note: Compute hash at deployment; no hash is fabricated here.

UPDATE_MODEL:
  strategy: versioned_incremental_updates
  triggers: [new_evidence, revised_rule, changed_context, invalidated_premise]
  actions: [revalidate_dependents, recompute_conclusions, update_confidence, preserve_audit_trail]

AI_CONSUMPTION:
  format: typed_machine_readable_flow
  operations: [parse, validate, infer, explain, audit, revise]
  safeguards: [provenance_required, context_aware, uncertainty_explicit, no_unsupported_inference]

END FLOW ALGEBRA