OWL axiom: Given an individual of a particular class, enforce an existence of an Object Property relation with another individual

Question

In OWL, is there a way to state that an individual of a particular class must be related to another individual via a specific object property?

For example, I would like to state that:

forall(x) Object(x) -> exists(y) Shape(y) ^ hasShape(x, y)

i.e., "For all objects, there exists a shape that is the shape of the object."

so that if there is an individual of the type Object that has no shape associated with it, a reasoner would find it to be inconsistent.

I tried an axiom:

Object SubClassOf hasShape min 1 Shape

but it's not working.

It seems like the issue is because Object Property in OWL has no identity, but is there a workaround for this issue?

(I'm using Protege 5.2.0)

Answer 1

You are correct that the meaning of Object SubClassOf hasShape min 1 Shape is that every individual of Object is associated with an individual of Shape via the hasShape property.

So if you create an individual x of type Object without x being associated with an individual of Shape, why does the reasoner not determine that your ontology is inconsistent? The reason for this is due to the open world assumption. Informally it means that the only inferences that the reasoner can make from an ontology is based on explicit information stated in the ontology or what can derived from explicit stated information.

When you state x is an Object, there is no explicit information in the ontology that states that x is not associated with an individual of Shape via the hasShape property. To make explicit that x is not is such a relation, you have to define x as follows:

Individual: x
  Types: 
    Object,
    hasShape max 0 owl:Thing

Btw, this problem has nothing to do with identity as you stated.