Axioms Reference¶

Axioms are formal semantic constraints that express logical assertions about how L1 classes and relations must behave. They map directly to OWL 2 constructs and can be consumed by reasoners, knowledge graphs, and AI agents.

Axioms vs. Other Constraints

JSON Schema validates file structure (field types, naming patterns)
Governance Rules (G-01~G-08) enforce process and evolution constraints
Axioms express domain-level semantic truths (disjointness, cardinality, transitivity)

These three mechanisms are independent and complementary.

Axiom Types¶

Type	OWL 2 Mapping	Description
`disjoint`	`owl:disjointWith`	Two or more classes cannot share instances
`cardinality_min`	`owl:minCardinality`	Minimum number of values for a property
`cardinality_max`	`owl:maxCardinality`	Maximum number of values for a property
`cardinality_exact`	`owl:cardinality`	Exact number of values for a property
`existential`	`owl:someValuesFrom`	At least one value must exist from a given class
`universal`	`owl:allValuesFrom`	All values must come from a given class
`functional`	`owl:FunctionalProperty`	Property has at most one value per subject
`inverse_functional`	`owl:InverseFunctionalProperty`	Each value maps back to exactly one subject
`symmetric`	`owl:SymmetricProperty`	If A relates to B, then B relates to A
`asymmetric`	`owl:AsymmetricProperty`	If A relates to B, then B cannot relate to A
`transitive`	`owl:TransitiveProperty`	If A-B and B-C, then A-C
`subproperty`	`rdfs:subPropertyOf`	One relation is a specialization of another

Axiom JSON Structure¶

{
  "id": "ax_person_org_disjoint",
  "type": "disjoint",
  "label_zh": "...",
  "label_en": "Person and Organization are disjoint",
  "classes": ["Person", "Organization"],
  "status": "stable",
  "since": "2.0.0",
  "definition": "...",
  "definition_en": "An instance cannot be both a Person and an Organization"
}

All axiom IDs use the ax_ prefix with snake_case naming (e.g., ax_part_of_transitive).

L1 Core Axioms¶

Disjoint Class Axioms¶

ID	Classes	Description
`ax_person_org_disjoint`	Person, Organization	A natural person cannot also be an organization
`ax_entity_governance_disjoint`	Entity, Governance	Entity and Governance domains are mutually exclusive
`ax_entity_operational_disjoint`	Entity, Operational	Entity and Operational domains are mutually exclusive
`ax_entity_measurement_disjoint`	Entity, Measurement	Entity and Measurement domains are mutually exclusive
`ax_governance_operational_disjoint`	Governance, Operational	Governance and Operational domains are mutually exclusive
`ax_governance_measurement_disjoint`	Governance, Measurement	Governance and Measurement domains are mutually exclusive
`ax_operational_measurement_disjoint`	Operational, Measurement	Operational and Measurement domains are mutually exclusive
`ax_policy_rule_disjoint`	Policy, Rule	A policy cannot also be a rule

Property Characteristics¶

ID	Relation	Type	Description
`ax_part_of_transitive`	`part_of`	transitive	If A is part of B and B is part of C, then A is part of C
`ax_part_of_asymmetric`	`part_of`	asymmetric	If A is part of B, then B cannot be part of A

Existential Constraints¶

ID	Subject	Relation	Object	Description
`ax_process_realizes_capability`	Capability	`realized_by`	Process	Every Capability is realized by at least one Process
`ax_risk_mitigated_by_control`	Risk	`mitigated_by`	Control	Every Risk is mitigated by at least one Control
`ax_kpi_measures_operational`	KPI	`measured_by`	Operational	Every KPI measures at least one Operational element
`ax_plays_role_domain_party`	Role	`plays_role`	Party	Every Role is played by at least one Party

Universal Constraints¶

ID	Subject	Relation	Object	Description
`ax_owns_domain_party`	Party	`owns`	Resource	All things owned must be Resources
`ax_governed_by_range_governance`	Operational	`governed_by`	Governance	All governance targets must be Governance subclasses

Cardinality Constraints¶

ID	Subject	Relation	Min	Description
`ax_org_min_one_role`	Organization	`plays_role`	1	Every Organization plays at least one Role

Subproperty Axioms¶

ID	Relation	Parent	Description
`ax_composed_of_sub_part_of`	`composed_of`	`part_of`	Composition is a specialization of part-of

OWL 2 Mapping Examples¶

DisjointTransitiveExistentialCardinality

uod:Person owl:disjointWith uod:Organization .

# For multiple classes:
[] a owl:AllDisjointClasses ;
    owl:members ( uod:Entity uod:Governance uod:Operational uod:Measurement ) .

uod:part_of a owl:TransitiveProperty .

uod:Capability rdfs:subClassOf [
    a owl:Restriction ;
    owl:onProperty uod:realized_by ;
    owl:someValuesFrom uod:Process
] .

uod:Organization rdfs:subClassOf [
    a owl:Restriction ;
    owl:onProperty uod:plays_role ;
    owl:minCardinality "1"^^xsd:nonNegativeInteger
] .

Scope¶

Axioms are L1-only. L2 Industry and Domain Extension and L3 Enterprise layers do not define their own axioms. All semantic constraints are centrally managed in the core ontology to maintain consistency.