Re: [OWLAPI-developer] relations : Equivalent classes axioms, subClassOf axioms

Hi,The problem seems to be OWL-semantically fixed.Having subClassOf(A , B) and subClassOf (B, A) ====> we can entail and state explicitly equivalentClasses(A, B) and if we want delete the two other subClasso axioms. (tell if it is correct)But when we add these axioms , they will be irelevant:Example: We have student subClassOf Person ==> that's oklater we add Person subClassOf student ===> not ok ; we have to prohibit such axiom, how? 

     Le Mercredi 28 janvier 2015 15h50, Simon Spero <sesuncedu@gmail.com> a écrit :
   

 The solution is correct. Ask yourself WWQD - What Would Quine Do? 
Think extensionally. Assume we have two OWL "classes" [1], A and B, and that B is an OWL subclass of A. From the OWL Direct Semantics [2], we know that (B)C ⊆ (A)C, where (.)C is a function that returns the extension of the "class". Notice that the relationship is '⊆',  not '⊂' - that is, the relationship is 'subset of *or equal*'. To rule out the possibility of the two extensions being equal, there has to be some member  of (B)C that is not a member of (A)C.  If you don't know or care what that element is, you can use a blank node. Simon[1] 🐰undetached air-quote parts🐇
[2] http://www.w3.org/TR/owl2-direct-semantics/#Class_Expression_AxiomsOn Jan 28, 2015 8:52 AM, "Leila Bayoudhi" <bayoudhileila@yahoo.fr> wrote:

 
Hi, I further focused on the problem. I noticed that works prohibitting having subClassOf(A , B) when having (subClassOf(B , A)) are considering ontologies are graphs in particular DAG Direct Acyclic Graph , other consider it as a circulatory error (Can I consider it as this later (circulatory error).However, others liking to prevent such contradiction(i.e a parent cannot be a child of its child...) . This is what I found in this forum:How to state that a subclass cannot be equal to its parent class in OWL? - ANSWERS s

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| How to state that a subclass cannot be equal to its pare...How to state that a subclass cannot be equal to its parent class in OWL? Dear all, I'm approaching for the first time to ontologies and I'm trying to verify whether.... |
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   However their solution does not seem to be logic and sufficient. they suggest::C  a  owl:Class;
    rdfs:subClassOf  :D .
:D  a  owl:Class .
[]  a  :D, [ owl:complementOf  :C ] .
   What do think? Have any other alternative?specifically where I want to say that such subClassOf (in other sens)axiom must not be stated? Thank you for your interest? 

 


On Jan 25, 2015, at 5:23 AM, Leila Bayoudhi <bayoudhileila@yahoo.fr> wrote:

> Hi,
> Please, explain me these ambiguous points:
> 
>     • 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 can. Of course it is only correct to add this if it is true :-). 

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

Yes, if you like. The assertion

equivalentClasses axiom(C1, C2)

is exactly equivalent to the combination (conjunction) of the two assertions 

> C1 subClassOf  C2 
C2 subClassOf C1


>     • Is equivalent class axiom (C1 , C2) entails that  C1 subClassOf  C2 and C2 subClassOf C2.

Yes, in all cases. And the conjunction of the two subClasses entails the equivalentClass. 

> (please I want to know also this case where C1 and C2  can be arbitray class expressions? ex C1 subClassOf (allValuesFrom (R, C4))
>     • 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 have no idea why protege keeps one of them, but it is not incorrect to keep redundant axioms which are entailed by other axioms. 

Pat Hayes

> Please help me in finding explanations for these thoughts.

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