Re: relations : Equivalent classes axioms, subClassOf axioms

On Jan 25, 2015, at 6:29, "Leila Bayoudhi" <bayoudhileila@yahoo.fr<mailto:bayoudhileila@yahoo.fr>> wrote:

Hi,
Please, explain me these ambiguous points:


  1.  If we already have C1 subClassOf  C2 , Why cannot we add C2 subClassOf C1? (It is mentioned in some works but for which reasons?)

You absolutely can. I don't know who says you cannot.

  1.      - Is it possible to axiom to add this axiom , delete the two subClass axioms and transform them to equivalentClasses axiom(C1, C2)

Yes? I mean, why not?

  1.  Is equivalent class axiom (C1 , C2) entails that   C1 subClassOf  C2 and C2 subClassOf C2. (please I want to know also this case where C1 and C2  can be arbitray class expressions? ex C1 subClassOf (allValuesFrom (R, C4))

Yes.

  1.  For protégé, when I tried these cases, given C1 subClassOf C2  and  adding C2 subClassOf C1  => It entails that equiavlenttClassesAxiom(C1, C2) , we have no C1 subClassOf C2 and keeps C2 subClassOf C1

I don't know what you mean. All those will be entailed afterwards. Not every display in protege may display all three.
Please help me in finding explanations for these thoughts.