Data Label Ontology

FLOW ALGEBRA — DATA LABEL ONTOLOGY
Version: 1.0 | Encoding: UTF-8 | Language: en-GB
Source: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/data-label-ontology.html
Status: Companion formalisation; exact page specification not verified.

1. PURPOSE
Formalise data labels as typed, provenance-bearing annotations associated with samples, tasks and label schemas, supporting reliable supervised learning and evaluation.

2. STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
I_t: input samples, annotations and metadata.
R_t: relations among samples, labels, annotators, schemas and datasets.
B_t: constraints on admissible labels, provenance, quality and leakage.
K_t: validated knowledge and label semantics.
E_t = expand(I_t, R_t)
V_t = {x in E_t | satisfies(x, B_t)}
x*_t = argmax_{x in V_t} P(x | I_t, R_t, B_t, K_t)
I_(t+1) = update(I_t, x*_t, feedback_t)

3. ENTITIES
DataLabel: (label_id, value, label_type, schema_id, version).
DataSample: (sample_id, modality, payload_ref, split_id).
Annotation: (annotation_id, sample_id, label_id, annotator_id, timestamp, confidence).
LabelSchema: (schema_id, classes, hierarchy, cardinality, constraints).
Annotator: human, automated system or adjudication process.
GroundTruth: reference annotation with declared provenance and uncertainty.
Dataset: collection of samples and associated annotation records.
QualityRecord: disagreement, review status, audit trail and validation result.

4. RELATIONSHIPS
DataSample --has_annotation--> Annotation
Annotation --assigns--> DataLabel
DataLabel --conforms_to--> LabelSchema
Annotation --created_by--> Annotator
Annotation --validated_by--> QualityRecord
Dataset --contains--> DataSample
GroundTruth --derived_from--> reviewed Annotation(s)

5. LABEL TYPES
Categorical: y in {c_1,...,c_C}.
Multilabel: y in {0,1}^C.
Continuous: y in R^d, with units where applicable.
Ordinal: ordered categories with explicit ordering.
Structured: sequence, span, bounding box, segmentation mask or graph.
Missing or unknown labels must remain distinct from negative labels.

6. FORMAL OPERATIONS
assign(sample, label, schema) -> annotation
validate(annotation, schema) -> {valid, invalid, needs_review}
review(annotation_set) -> adjudicated_label or unresolved
version(label_schema, annotations) -> immutable revision reference
partition(dataset, grouping_keys) -> leakage-controlled splits

For categorical prediction p_theta(c | x):
L_CE = -sum_(c=1)^C y_c log(max(p_theta(c|x), epsilon))
For multilabel prediction:
L_BCE = -sum_c [y_c log(p_c) + (1-y_c) log(1-p_c)]
For continuous labels:
L_MSE = (1/N) sum_i ||f_theta(x_i)-y_i||^2
These are task-dependent example losses, not universal label requirements.

7. QUALITY AND UNCERTAINTY
Observed agreement = count(matching annotations)/count(comparable annotations).
Cohen kappa = (p_o - p_e)/(1 - p_e), provided p_e != 1.
Disagreement is evidence requiring review, not automatic proof of error.
Store label confidence separately from model prediction confidence.
Measure label distributions and subgroup coverage; investigate imbalance.

8. INFERENCE RULES
IF label not in permitted schema THEN reject or quarantine annotation.
IF sample identity overlaps train and test THEN flag possible leakage.
IF annotation lacks provenance THEN mark provenance incomplete.
IF annotators disagree THEN request adjudication or retain uncertainty.
IF schema changes THEN validate migration and preserve previous version.
IF label is unknown THEN do not silently encode it as a negative class.

9. MINI RECURSION ENGINE
step_0: ingest sample and candidate label.
step_1: resolve schema and annotation provenance.
step_2: check type, range, cardinality and consistency.
step_3: compare with other annotations and quality rules.
step_4: accept, quarantine or escalate for review.
step_5: record outcome, confidence and immutable lineage.
step_6: feed quality findings into the next curation iteration.
Stop when no unresolved rule violation remains or review budget is exhausted.

10. TRI-MAPPING
Entity mapping: sample -> annotation -> label -> schema.
Process mapping: capture -> assign -> validate -> adjudicate -> version.
Evidence mapping: provenance -> quality checks -> uncertainty -> audit record.

11. EXECUTION CONSTRAINTS
Every accepted label must reference a sample and a declared schema.
Never overwrite previous annotation versions without an audit trail.
Do not claim ground truth is infallible; document review methods.
Maintain split integrity and avoid target leakage.
Protect sensitive annotations and apply applicable access controls.
Guarantee is conditional on correct implementation and complete inputs.

12. AI SEARCH FLOW
QUERY: identify the meaning, source, type and reliability of a data label.
RESOLVE: locate label, sample, schema, annotator and version.
EXPAND: follow annotation and provenance relationships.
FILTER: enforce validity, access and quality constraints.
RANK: prioritise verified and task-relevant records.
RETURN: label semantics, evidence, uncertainty and source references.
UPDATE: incorporate audited corrections without losing lineage.

13. SEMANTIC EQUIVALENCE
"class label" ~ categorical target (when task context agrees).
"annotation" != "label" (annotation is an assignment event/record).
"ground truth" != "perfect truth" (reference labels can be uncertain).
"missing" != "negative".

14. CITATION
Source ontology: Kireth Research — Semantic Library, Data Label Ontology.
Companion Flow Algebra formalisation; not a verbatim source extraction.