subclassof

SubClassOf is a fundamental axiom in description logics and the Web Ontology Language (OWL) that expresses a subsumption relationship between two class expressions. If C is a subclass of D, then every instance of C is also an instance of D.

Formal semantics: In an interpretation I, SubClassOf(C, D) means that C interpreted as a set, C^I, is a subset of D interpreted as a set, D^I. In OWL and RDF contexts, this relation is written as C rdfs:subClassOf D. The left-hand side may be a named class or a more complex class expression; the right-hand side is a class expression.

Use and implications: SubClassOf forms the backbone of class hierarchies in ontologies. It enables reasoning tools to infer new class memberships; for example, Cat SubClassOf Mammal and Mammal SubClassOf Animal imply Cat SubClassOf Animal. It is transitive: if A ⊆ B and B ⊆ C, then A ⊆ C. When both A ⊆ B and B ⊆ A hold, A and B are equivalent. The left-hand side can be complex, allowing definitions that combine class expressions with intersections, unions, and existential or universal restrictions.

Practical notes: SubClassOf axioms must be consistent with other axioms in the ontology, such as disjointness or property restrictions. Reasoners use SubClassOf to compute class hierarchies and to check ontology consistency.