In reading the book Semantic Web for the Working Ontologist I have come across an example that I cannot wrap my head around.
owl:equivalenceClass can be defined in terms of these two triples:
owl:equivalentClass rdf:type owl:symmetricProperty.
owl:equivalentClass rdfs:subPropertyOf rdfs:subClassOf.
I could use help understanding this.
The first triple says that if a property P is a owl:symmetricProperty than we can infer the triple P owl:inverseOf P.
The second triple says that if a property P is a subPropertyOf Q then from A P B we can infer A Q B.
If a class C is a subclass of D then from x rdf:type C we can infer x rdf:type D.
Now lets put it all together with owl:equivalentClass:
Because owl:equivalentClass is a rdfs:subPropertyOf rdfs:subClassOf then whenever we have A owl:equivalentClass B we can infer A subClassOf B, and because owl:equivalentClass is a symmetricProperty we can also infer B subClassOf A.