Can we inference the relationship of two classes from their restrictions?

Question

I'm not sure if we can inference relationship of two classes from their restrictions... if we have 2 classes:

owl:class1 rdfs:subClassOf [restriction1...], [restriction2...], [restriction3].

owl:class2 rdfs:subClassOf [restriction1...], [restriction2...].

What inference can we draw from this knowledge? It looks like owl:class2 is broader than owl:class1. Can we inference owl:class1 rdfs:subClassOf owl:class2.?

Answer 1

owl:class1 rdfs:subClassOf [restriction1...], [restriction2...], [restriction3].

owl:class2 rdfs:subClassOf [restriction1...], [restriction2...].

What inference can we draw from this knowledge? It looks like owl:class2 is broader than owl:class1. Can we inference owl:class1 rdfs:subClassOf owl:class2.?

That wouldn't be a legal inference at all. Remember, subclass relationships are just sub-set relationships on sets of individuals. Restriction expressions are just class expressions, which means that they denote sets of individuals. When you're looking at some axioms, you don't know everything, you just know some things that people have stated. E.g., I can tell you that

    A ⊆ {1,2,3,4,5}
    A ⊆ {1,2,3,4}
    A ⊆ {2,3,4,5}

and

    B ⊆ {1,2,3,4,5}
    B ⊆ {1,2,3,4}

Now, we have more subset axioms about A than about B, and all the ones about B also apply to A. It doesn't have to be the case that A ⊆ B, though. E.g., it could be the case that:

    A = {2,3,4}
    B = {2,3}