Curriculum Domain Ontology

FLOW ALGEBRA
TITLE: Curriculum Domain Ontology
VERSION: 1.0
DOMAIN: Education / Curriculum
SOURCE_URL: https://kirethresearch.org/booksai-core/ontologies/domain-ontologies/education-domains/curriculum-domain-ontology.html
STATUS: Domain-based draft; source webpage content not independently verified.
AUTHORS: Mark Higgins — Sky (Recursive AI)

1. PURPOSE
Represent curriculum design, organisation, delivery, alignment, evaluation and revision as typed, traceable semantic flows. Distinguish prescribed, taught, assessed and attained curricula.

2. TYPED ENTITIES
Curriculum: {id, title, jurisdiction?, institution?, level, version, valid_from?, valid_to?}
Programme: {id, title, award?, duration?, curriculum_id}
Course: {id, title, programme_id?, credits?, level?}
Module: {id, title, course_id?, sequence?}
Unit: {id, title, module_id?, sequence?}
Topic: {id, label, subject_area}
LearningOutcome: {id, statement, cognitive_level?, measurable:bool}
Competency: {id, label, proficiency_scale?}
Standard: {id, issuer, identifier, version, jurisdiction?}
Prerequisite: {id, target_id, requirement_id}
LearningActivity: {id, method, duration?, accessibility_features?}
Resource: {id, type, licence?, accessibility_metadata?}
Assessment: {id, type, rubric_id?, formative:bool}
Rubric: {id, criteria[], levels[]}
LearnerCohort: {id, level, context?, aggregated_attributes?}
Educator: {id, role, qualifications?}
Evidence: {id, kind, provenance, timestamp?}
CurriculumRevision: {id, change_set, rationale, approved_by?, effective_date?}

3. RELATIONSHIP SIGNATURES
CONTAINS(Curriculum|Programme|Course|Module, Programme|Course|Module|Unit|Topic)
SPECIFIES(Curriculum|Course|Module|Unit, LearningOutcome)
TARGETS(LearningOutcome, Competency)
ALIGNS_WITH(LearningOutcome|Assessment|LearningActivity, Standard|LearningOutcome)
REQUIRES(Course|Module|Unit|Topic|Competency, Prerequisite|Competency)
TEACHES(LearningActivity, Topic|LearningOutcome)
USES(LearningActivity, Resource)
MEASURES(Assessment, LearningOutcome|Competency)
EVALUATED_BY(Assessment, Rubric)
DELIVERED_TO(Curriculum|Course|Module, LearnerCohort)
SUPPORTED_BY(Assertion, Evidence)
REVISES(CurriculumRevision, Curriculum)
SUPERSEDES(Curriculum, Curriculum)

4. CONSTRAINTS AND VALIDATION
- Every entity ID must be unique within its namespace.
- CONTAINS hierarchy must be acyclic.
- Every summative assessment must map to at least one learning outcome.
- Every mandatory learning outcome should map to at least one teaching activity and an assessment.
- Prerequisite graphs must be acyclic unless explicitly modelled as iterative competency development.
- Standard alignment must specify standard version and relevant jurisdiction.
- Preserve the distinction between intended, taught, assessed and attained learning; do not infer attainment from curriculum coverage alone.
- Avoid storing directly identifying learner data unless authorised and necessary.

5. INFERENCE RULES
R1: CONTAINS(A,B) AND CONTAINS(B,C) -> INDIRECTLY_CONTAINS(A,C).
R2: MEASURES(Assessment,Outcome) AND SPECIFIES(Unit,Outcome) -> ASSESSES_OUTCOME_OF(Assessment,Unit).
R3: TEACHES(Activity,Outcome) AND SPECIFIES(Unit,Outcome) -> SUPPORTS_DELIVERY_OF(Activity,Unit).
R4: SPECIFIES(Unit,Outcome) AND NOT EXISTS Assessment WHERE MEASURES(Assessment,Outcome) -> FLAG_ASSESSMENT_GAP(Unit,Outcome).
R5: SPECIFIES(Unit,Outcome) AND NOT EXISTS Activity WHERE TEACHES(Activity,Outcome) -> FLAG_DELIVERY_GAP(Unit,Outcome).
R6: REQUIRES(X,Prerequisite) AND UNSATISFIED(Prerequisite,Cohort) -> FLAG_READINESS_RISK(X,Cohort).
R7: SUPERSEDES(New,Old) AND EFFECTIVE(New,t) -> SELECT_VERSION(New,t), subject to jurisdiction and approval checks.
All inferred claims carry rule ID, source references, confidence and temporal scope. Closed-world absence tests R4/R5 require complete datasets; otherwise return UNKNOWN.

6. CONFIDENCE
CONFIDENCE(assertion) = {value:0.0..1.0, method, evidence_ids[], limitations[]}
Direct documented mapping may receive higher confidence than inferred alignment. Confidence is not a probability of student success and must not be treated as such without calibration.

7. SEMANTIC_EQUIVALENCE
SEMANTIC_EQUIVALENCE(A,B) = {relation: exactMatch|closeMatch|broaderThan|narrowerThan|relatedTo, context, confidence, evidence}
Do not merge outcomes solely because their wording is similar; check level, scope, performance verb and assessment criterion.

8. PROVENANCE
PROVENANCE = {source_id, source_url?, author_or_issuer?, publication_date?, retrieved_at?, version?, transformation?, licence?}
Separate official standards, institutional curricula, teacher plans, research findings and AI-generated suggestions.

9. FLOW ALGEBRA PIPELINE
INPUT(CurriculumSources, Standards, Outcomes, Activities, Assessments)
 -> NORMALISE(Identifiers, Terminology, Versions)
 -> TYPE(Entities)
 -> LINK(Relationships)
 -> VALIDATE(Constraints)
 -> ALIGN(Standards, Outcomes, Activities, Assessments)
 -> INFER(Gaps, Dependencies, Coverage)
 -> SCORE(CONFIDENCE)
 -> TRACE(PROVENANCE)
 -> PUBLISH(VersionedKnowledgeGraph, Reports)

10. FLOW_HASH
FLOW_HASH = SHA256(canonical_serialisation({ontology_id, version, typed_entities, relationships, rules, source_versions}))
Canonicalisation: stable key ordering, Unicode NFC, deterministic identifiers, normalised timestamps. Recompute on semantic changes.

11. UPDATE_MODEL
UPDATE_MODEL = {trigger: standard_revision|curriculum_revision|assessment_change|evidence_change, detect, compare, validate, approve, version, publish, retain_history}
Never silently overwrite a previously approved curriculum. Re-run dependent inferences after updates.

12. AI_CONSUMPTION
AI_CONSUMPTION = {format: typed_graph_or_json, schema_version, entity_ids, relation_types, source_attribution, confidence, validity_period, uncertainty_flags, safety_constraints}
AI systems should expose missing mappings and uncertainty, avoid claiming legal or institutional compliance without authoritative verification, and support human curriculum review.

13. EXAMPLE
SPECIFIES(Unit_Algebra_1, Outcome_Solve_Linear_Equations)
TEACHES(Activity_Guided_Practice, Outcome_Solve_Linear_Equations)
MEASURES(Assessment_Quiz_1, Outcome_Solve_Linear_Equations)
ALIGNS_WITH(Outcome_Solve_Linear_Equations, Standard_Maths_Example_v1)
=> Outcome_Solve_Linear_Equations has mapped instruction and assessment, subject to verification of evidence and standard alignment.

END FLOW ALGEBRA