OWL: How to get inheritance of property relations between two classes from those of superclasses?

Question

Let's say we have two classes named People and Disease. These classes are related by the Object Property has.

:People :has :Disease

People has subclass (or individual) John, and Disease has subclass (or individual) Cancer.

:John a :People
:Cancer a :Disease

How can we get the relationship between these subclasses by inference?

:John :has :Cancer

Answer 1

Before you can get to an answer, there are a number of misconceptions you'll need to resolve.

First, subclass and individual are very different concepts. Individuals (instances) are members of classes. Subclass denotes a class is a subset of another class, meaning that an implication (via inference) is that all members of a subclass are members of the (super)class. (Just for reference: there is no concept of inheritance in OWL.)

Second class-level properties, such as :People :has :Disease have no meaning for class individuals. The way to define a property's relationships to classes is to set the domain and range of the property. (Just using :has as a property name indicates a wide set of misconceptions, possibly from other types of languages.) So I'd suggest the name :hasDisease and the assertions:

:hasDisease rdfs:domain :People .
:hasDisease rdfs:range :Disease .

Third, you can assert that :John :hasDisease :Cancer and infer that John has a disease, given that :Cancer is a subclass of :Disease. This requires a standard RDFS reasoner. Also, given the domain and range definitions above, and an assertion :Joy :hasDisease :Gout, an RDFS reasoner will infer that :Joy a :Person and :Gout a :Disease.

There are a few OWL primers out there that you can find via Google. I'd suggest going over some of these to get a basic understanding of how OWL and reasoning profiles work.