Logical Relationship Ontology

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

ONTOLOGY:
  id: kireth:logical-relationship-ontology
  domain: Relationship Ontologies / Logical Relationships
  purpose: Represent and validate logical relationships among propositions, assertions, rules and conclusions.

TYPES:
  Proposition: {id: IRI, expression: String, truth_status: TruthStatus}
  Assertion: {proposition: Proposition, context: Context, provenance: Evidence}
  Rule: {premises: Set[Proposition], conclusion: Proposition, logic_profile: LogicProfile}
  Context: {id: IRI, assumptions: Set[Proposition], scope: String}
  Evidence: {source: IRI?, method: String?, timestamp: DateTime?}
  LogicalRelationship: {source: Proposition, target: Proposition, kind: RelationKind, context: Context, confidence: Decimal[0..1], provenance: Evidence?}
  TruthStatus: TRUE | FALSE | UNKNOWN | INCONSISTENT
  RelationKind: IMPLIES | EQUIVALENT | CONTRADICTS | ENTAILS | CONSISTENT_WITH | INDEPENDENT_OF | CONJUNCT_WITH | DISJUNCT_WITH
  LogicProfile: CLASSICAL | INTUITIONISTIC | PARACONSISTENT | MODAL | FUZZY

RELATIONSHIPS:
  IMPLIES(P,Q): P -> Q, material implication in classical logic.
  ENTAILS(Gamma,Q): every model satisfying Gamma also satisfies Q.
  EQUIVALENT(P,Q): P and Q have the same truth value in every admissible model.
  CONTRADICTS(P,Q): no admissible model satisfies both P and Q.
  CONSISTENT_WITH(P,Q): at least one admissible model satisfies both.
  INDEPENDENT_OF(P,Q): neither P entails Q nor Q entails P, relative to a specified theory.
  CONJUNCT_WITH(P,Q): composite proposition P AND Q.
  DISJUNCT_WITH(P,Q): composite proposition P OR Q.

RULES:
  R1_MODUS_PONENS: TRUE(P) AND TRUE(P -> Q) => TRUE(Q).
  R2_EQUIVALENCE_ELIMINATION: EQUIVALENT(P,Q) => ENTAILS({P},Q) AND ENTAILS({Q},P).
  R3_ENTAILMENT_TRANSITIVITY: ENTAILS({P},Q) AND ENTAILS({Q},R) => ENTAILS({P},R).
  R4_CONTRADICTION_SYMMETRY: CONTRADICTS(P,Q) => CONTRADICTS(Q,P).
  R5_EQUIVALENCE_SYMMETRY: EQUIVALENT(P,Q) => EQUIVALENT(Q,P).
  R6_EQUIVALENCE_TRANSITIVITY: EQUIVALENT(P,Q) AND EQUIVALENT(Q,R) => EQUIVALENT(P,R).
  R7_SCOPE_GUARD: infer only when logic_profile, context and assumptions are compatible.
  R8_NO_UNJUSTIFIED_CONTRAPOSITION: contraposition requires a logic profile supporting it.
  R9_NO_EXPLOSION_BY_DEFAULT: inconsistent premises do not authorise arbitrary conclusions in paraconsistent logic.

SEMANTIC_EQUIVALENCE:
  policy: distinguish logical equivalence from linguistic similarity and entity identity.
  condition: equivalence holds only under explicit interpretation and model class.
  non_equivalence: lexical synonymy alone does not prove logical equivalence.

CONFIDENCE:
  range: [0,1]
  policy: confidence measures support for a recorded relationship, not logical truth itself.
  derivation: deductive conclusions are valid only when premises and rules are accepted under the chosen logic profile.
  propagation: preserve provenance; do not manufacture numerical certainty.

VALIDATION:
  - All proposition and context identifiers must resolve.
  - Relation kind must belong to RelationKind.
  - Confidence must be between 0 and 1 inclusive.
  - Premises, conclusion and interpretation must be recorded for inferred relationships.
  - Detect contradictory assertions without silently deleting either.
  - Separate material implication from semantic entailment.
  - Check symmetry and transitivity only for relation kinds where defined.
  - Reject circular derivations lacking independent justification.

FLOW_HASH:
  algorithm: SHA-256
  input: canonical_serialisation(ontology_id, version, entities, relationships, rules, context, provenance)
  output: lowercase_hex_digest
  note: calculate hash at runtime; no fixed digest is asserted here.

UPDATE_MODEL:
  triggers: [new_evidence, changed_context, revised_rule, corrected_assertion, ontology_version_change]
  steps: [validate_input, retain_prior_version, apply_change, recompute_inferences, check_consistency, recalculate_flow_hash, publish_revision]
  policy: preserve audit trail and mark superseded assertions.

AI_CONSUMPTION:
  formats: [plain_text, typed_graph, JSON-LD_mapping]
  retrieval_keys: [proposition_id, relation_kind, context_id, logic_profile]
  safeguards: [source_attribution, context_awareness, uncertainty_preservation, no_unsupported_inference]
  output_contract: {claims: typed, provenance: retained, confidence: explicit, validation: required}

END FLOW ALGEBRA