Semantic Analytics and Ontologies - Data Governance: Creating Value from Information Assets - page 105

TABLE 5.1
Class and Property Axioms of OWL Lite

Class axioms of OWL Lite as
RDF triples

Short explanation in the first order logic

Class (A partial S1,…,Sn) The extension of A is included in each extension of

Si (i = 1,…,n); here the extension of A denotes
the set of instances of A.

Class (A complete S1,…,Sn) The extension of A is the same as the intersection

of all extensions of S1, …, Sn.

EquivalentClasses(A1,…,An) A1, …, An-1 and An share the same extension.

Property axioms of OWL Lite
as RDF triples
DatatypeProperty (T Short explanation in the first order logic

super(T1)…super(Tn) The extension of T is included in every extension of

Ti (i = 1,…,n).

[Functional] For each x, y, and z, if T(x, y) and T(x,z), then y = z,

where T(x,y) denotes that the extension of T
contains (x,y).

domain(d1)…domain(dm) For each i = 1,…,m and for each x and y, if T(x, y),

then di(x), where di(x) denotes that the extension
of di' contains x.

range(d'1)…range(d'l)) For each i = 1,…,l and for each x and y, if T(x, y),

then d'i(y).

ObjectProperty (R
super(R1)…super(Rn)

The extension of R is included in every extension of
Ri (i = 1,…,n).

[InverseOf R0] For each x and y, R(x, y) if and only if R0(y, x).

[Symmetric] For each x and y, if R(x, y), then R(y, x).

[Functional] For each x, y, and z, if R(x, y) and R(x,z), then y = z.

[InverseFunctional] For each x, y, and z, if R(x, z) and R(y,z), then x = y.

domain(A1)…domain(Am) For each i = 1,…,m and for each x and y, if R(x, y),

then Ai(x).

range(A'1)…range(A'l)) For each i = 1,…,l and for each x and y, if R(x, y),

then A'i(y).

EquivalentProperties(X1,…,Xn) X1, …, Xn-1 and Xn share the same extension.

Subproperty(X1, X2) The extension of X1 is included in that of X2.