Data Point Ontology

FLOW ALGEBRA
DATA POINT ONTOLOGY
Kireth Semantic Library | Mathematical Entities > Statistical Entities
Source: https://kirethresearch.org/booksai-core/entity-graph/mathematical-entities/statistical-entities/data-point-ontology.html
Version: 1.0 | Date: 2026-10-13 | Locale: en-GB
Authors: Mark Higgins — Sky (Recursive AI)

1. PURPOSE
Represent an individual data point as a typed, contextualised observation or recorded value within a statistical dataset. Distinguish data points from variables, observations, records and population members. Preserve measurement provenance, units, missingness and uncertainty.

2. ENTITY DECLARATIONS
entity DataPoint { id: Identifier; dataset: DatasetRef; observational_unit: UnitRef?; variable: VariableRef; value: Value?; unit: MeasurementUnit?; observed_at: Timestamp?; source: SourceRef?; quality: QualityMetadata?; status: ValueStatus; uncertainty: Uncertainty? }
entity Dataset { id: Identifier; schema: Schema; points: Set<DataPoint> }
entity Variable { id: Identifier; domain: ValueDomain; measurement_scale: ScaleType; unit: MeasurementUnit? }
entity Observation { id: Identifier; unit: UnitRef; values: Set<DataPoint> }
entity DataRecord { id: Identifier; fields: Map<VariableRef, DataPoint> }
entity Measurement { method: MethodRef?; instrument: InstrumentRef?; calibration: CalibrationRef? }
enum ValueStatus = { observed, missing, censored, imputed, invalid, derived }
enum ScaleType = { nominal, ordinal, interval, ratio }

3. TYPE CONSTRAINTS
DP-01: DataPoint.id MUST be unique within its dataset.
DP-02: DataPoint.variable MUST resolve to a declared Variable.
DP-03: A non-missing value MUST belong to the variable's declared domain or carry a recorded validation error.
DP-04: Numerical values with physical units MUST use compatible dimensions.
DP-05: Missing is a status, not the numerical value zero.
DP-06: Imputed and derived values MUST preserve their generation method and source lineage.
DP-07: Observation timestamps and dataset ingestion timestamps MUST remain distinguishable.
DP-08: A data point is not necessarily an independent sample or a distinct observational unit.

4. RELATIONSHIP ALGEBRA
DataPoint --belongs_to--> Dataset
DataPoint --measures_variable--> Variable
DataPoint --describes_unit--> ObservationalUnit
DataPoint --is_component_of--> Observation
DataPoint --occupies_field_in--> DataRecord
DataPoint --obtained_by--> Measurement
DataPoint --derived_from--> DataPoint | Dataset
DataPoint --has_quality--> QualityMetadata
DataPoint --has_uncertainty--> Uncertainty
DataPoint --has_timestamp--> TemporalMetadata

5. VALUE AND STATISTICAL ALGEBRA
For numerical observed data x_1,...,x_n with valid inclusion weights:
mean(x) = (1/n) * SUM(i=1..n, x_i)
sample_variance(x) = SUM(i=1..n, (x_i - mean(x))^2) / (n-1), n > 1
weighted_mean(x,w) = SUM(w_i*x_i) / SUM(w_i), with SUM(w_i) > 0
standardised_value(x_i) = (x_i - mean(x)) / s, where s > 0
These statistics require an explicitly selected analysis set; missing, invalid, censored or imputed values MUST follow a declared treatment policy. Formulas do not imply unbiasedness or independence.

6. TRANSFORMATION FLOWS
flow IngestDataPoint(input, schema) -> DataPoint:
  parse input; resolve variable and unit; preserve raw input
  validate domain, type and measurement units
  attach dataset, observational unit and provenance
  classify status and quality; emit result with validation trace

flow NormaliseUnit(point, target_unit) -> DataPoint:
  require numeric value and dimensionally compatible units
  convert using a declared conversion rule
  preserve source value, conversion rule and lineage

flow DerivePoint(inputs, expression) -> DataPoint:
  verify expression typing, input availability and units
  compute derived value when conditions hold
  attach source references, expression and uncertainty policy

flow AggregatePoints(points, operation, policy) -> Statistic:
  apply explicit eligibility and missingness policy
  validate weights, units and grouping keys
  compute operation; report sample count and provenance

7. INFERENCE RULES
R-01: valid(point) AND observed(point) -> eligible_for_analysis(point), subject to analysis policy.
R-02: missing(point) -> NOT assert(value(point) = 0).
R-03: same_unit(p,q) AND same_variable(p,q) -> comparable(p,q), subject to contextual comparability.
R-04: derived_from(p,q) -> depends_on(p,q).
R-05: unit_incompatible(p,variable) -> validation_failure(p).
R-06: imputed(p) -> disclose_imputation(p).
R-07: outlier_flag(p) -> review_candidate(p); NOT automatically invalid(p).
R-08: observed_at(p,t) -> temporal_context(p,t); NOT necessarily ingestion_time(p,t).

8. SEMANTIC DISTINCTIONS
DataPoint != Dataset: a point is an individual datum; a dataset is a collection.
DataPoint != Variable: a point is an instance of a variable's value in context.
DataPoint != Observation: an observation can contain several data points.
DataPoint != Sample: a sample is a selected collection of observational units or observations.
DataPoint != Population: a population is the target set under study.
DataPoint != ProbabilityOutcome: a realised data value can be modelled as an outcome but the concepts are not identical.
Zero != Missing; Invalid != Missing; Imputed != DirectlyObserved.

9. VALIDATION
validate identifiers, referential integrity, schema, value domain, units, provenance, timestamps, status, transformation history and permitted aggregation.
Return {valid: Boolean, errors: List<ValidationError>, warnings: List<ValidationWarning>, confidence: ConfidenceRecord}.
Confidence is evidence- and process-dependent; never infer high confidence solely from schema validity.

10. SEMANTIC_EQUIVALENCE
Equivalent data points require a declared equivalence scope: same observational unit, variable, value, unit normalisation, time context and provenance policy. Numeric equality alone does not establish semantic identity.

11. FLOW_HASH
FLOW_HASH := SHA256(canonical_utf8(ontology_id, version, declarations, constraints, relationships, inference_rules, transformation_flows, validation_rules)).
Canonicalisation MUST define stable field order, Unicode normalisation and whitespace policy. Hashes are recomputed when semantically material content changes. No hash value is asserted without computation.

12. UPDATE_MODEL
On revision: increment version; record changed entities and rules; retain backward mappings where valid; invalidate dependent cached inferences; recompute FLOW_HASH; preserve provenance and audit history.

13. AI_CONSUMPTION
Provide typed entity extraction, schema-grounded retrieval, data lineage, quality flags, unit-aware comparisons, missingness handling and explainable statistical operations. Output evidence references and uncertainty; avoid fabricating values, population representativeness or causal conclusions.

14. EXAMPLE INSTANCE
Dataset: temperature_readings
Variable: ambient_temperature [degree Celsius, ratio-like physical quantity represented on an interval scale in Celsius]
Observational unit: sensor_A at time 2026-10-13T12:00:00Z
DataPoint: dp_001 {value: 18.4, unit: degC, status: observed, source: sensor_A}
Interpretation: one recorded temperature value, not a distribution or population statistic.

END FLOW ALGEBRA