Closed world assumption in OWL

OWL

By default, OWL operates on an open world assumption, i.e. if you specify the following constraint:

Declaration(Class(Container))
SubClassOf(Container ObjectMinCardinality(2 contains Node))

This will by default never throw an exception, because in an open world there may always be more elements which would satisfy the constraint.

The solution, as mentioned by the Pellet FAQ, is to force the world closed. This can be achieved by making owl:Thing equivalent only to the individuals defined in your world:

SubClassOf(owl:Thing ObjectOneOf(Node1 Node2 Node3 SampleContainer))

This can be achieved in Protege as on the bottom, or by selecting “Superclasses” and typing in the following. In Protege 4.0, no help or auto-complete pops up.

{Node1, Node2, Node3, SampleContainer}

This might still not work, because in your model, you may only be making positive assertions about the world, so unstated assertions may still be true. As a result, you might also have to set negative assertions for what is definitely not true:

Declaration(Individual(SampleContainer))
ClassAssertion(SampleContainer Container)
DifferentIndividuals(Node1 Node2 Node3 SampleContainer)
ObjectPropertyAssertion(contains SampleContainer Node3)
NegativeObjectPropertyAssertion(contains SampleContainer Node1)
NegativeObjectPropertyAssertion(contains SampleContainer Node2)
NegativeObjectPropertyAssertion(contains SampleContainer SampleContainer)