Foundations of Semantic Web Technologies

RDF Formal Semantics 83

• If x ∈ IC ,

then hx, rdfs:Resource

I

i ∈ I

EXT

(rdfs:subClassOf

I

).

Every class x is a subclass of the class of all resources, i.e. the

pair constructed from x and rdfs:Resource is in the extension of

rdfs:subClassOf.

• If hx, yi ∈ I

EXT

(rdfs:subClassOf

I

),

then x, y ∈ IC and I

CEXT

(x) ⊆ I

CEXT

(y).

If x and y are in the rdfs:subClassOf relation, then both x and y

are classes and the (class) extension of x is a subset of the (class)

extension of y.

• I

EXT

(rdfs:subClassOf

I

) is reflexive and transitive on IC .

The rdfs:subClassOf property connects each class with itself.

Moreover if the rdfs:subClassOf property connects a class x with

a class y and y with some class z, it also connects x with z directly.

• If x ∈ I

CEXT

(rdfs:ContainerMembershipProperty ...