Statistical Relationship Ontology

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

flow "StatisticalRelationshipOntology" v1.0

ENTITY_TYPES:
  Variable: {id: str, name: str, scale: [nominal, ordinal, interval, ratio], unit: str?}
  Dataset: {id: str, observations: int, provenance: str?, collected_at: datetime?}
  Observation: {dataset_id: str, variable_id: str, value: any, subject_id: str?}
  StatisticalRelationship: {id: str, lhs: Variable, rhs: Variable, kind: str, context: str?}
  Estimate: {relationship_id: str, statistic: str, value: float, standard_error: float?, confidence_interval: tuple?, sample_size: int}
  Evidence: {method: str, assumptions: list[str], p_value: float?, provenance: str?}

RELATIONSHIP_TYPES:
  ASSOCIATED_WITH: symmetric; not necessarily transitive
  CORRELATED_WITH: symmetric; strength in [-1, 1] for Pearson r
  DEPENDS_STATISTICALLY_ON: directional; not automatically causal
  PREDICTS: directional; model and validation context required
  CONDITIONALLY_INDEPENDENT_OF: symmetric given conditioning set
  CONFOUNDED_BY: directional link to candidate confounder
  CAUSES: requires independent causal identification evidence

OPERATIONS:
  describe(x): compute valid summary statistics for measurement scale
  covariance(x,y): E[(x-E[x])*(y-E[y])]
  pearson_r(x,y): covariance(x,y)/(sd(x)*sd(y)) when sd(x)>0 and sd(y)>0
  spearman_rho(x,y): Pearson correlation of ranked values
  regression(y ~ x + covariates): estimate conditional association under model assumptions
  test(H0,H1,data): return statistic, p_value and assumptions
  confidence_interval(estimator,level): compute interval with declared method
  conditional_independence(x,y|z): assess using stated model/test

INFERENCE_RULES:
  R1: CORRELATED_WITH(x,y,r) -> ASSOCIATED_WITH(x,y)
  R2: CORRELATED_WITH(x,y,r) -> CORRELATED_WITH(y,x,r)
  R3: CONDITIONAL_INDEPENDENCE(x,y|z) -> CONDITIONAL_INDEPENDENCE(y,x|z)
  R4: SIGNIFICANT_ASSOCIATION(x,y) -/-> CAUSES(x,y)
  R5: ASSOCIATED_WITH(x,y) and ASSOCIATED_WITH(y,z) -/-> ASSOCIATED_WITH(x,z)
  R6: OBSERVATIONAL_EVIDENCE alone -/-> CAUSAL_IDENTIFICATION
  R7: PREDICTS(x,y,model) -> require out_of_sample_validation(model)

SEMANTIC_EQUIVALENCE:
  aliases: {"statistical association": "ASSOCIATED_WITH", "linear correlation": "CORRELATED_WITH"}
  distinguish: [association_vs_causation, statistical_vs_practical_significance, independence_vs_zero_correlation]
  equivalence_requires: [same_variable_definitions, compatible_population, matching_conditioning_context, same_statistical_estimand]

CONFIDENCE:
  fields: [estimate, uncertainty, sample_size, assumptions, missingness, sampling_bias, model_validation]
  rule: confidence_is_not_p_value
  rule: do_not_conflate_confidence_interval_with_probability_of_fixed_parameter

VALIDATION:
  - verify_data_types_and_measurement_scales
  - check_sample_size_missingness_and_duplicates
  - verify_estimator_assumptions_and_uncertainty_method
  - check_multiple_testing_when_applicable
  - report_effect_size_and_uncertainty
  - prohibit_unsupported_causal_claims
  - record_population_and_temporal_context

PROVENANCE:
  required: [source_dataset, method, timestamp, analyst_or_system, version]

FLOW_HASH:
  algorithm: SHA-256
  input: canonical_serialisation(flow_definition, entity_schema, rules, version)
  note: compute at publication; no precomputed hash asserted

UPDATE_MODEL:
  strategy: versioned_append_with_provenance
  triggers: [new_evidence, revised_dataset, changed_method, changed_assumptions]
  preserve: [previous_versions, audit_trail, inference_lineage]
  invalidate: [dependent_estimates, cached_inferences] when source changes

AI_CONSUMPTION:
  format: typed_semantic_graph
  expose: [entities, relationship_types, estimates, uncertainty, evidence, context, provenance]
  constraints: [no_causation_from_correlation, disclose_assumptions, maintain_uncertainty, preserve_provenance]
  intended_uses: [knowledge_graphs, scientific_retrieval, statistical_reasoning, explainable_ai]

END FLOW ALGEBRA