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Re: Some basic questions about OWL-Full

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Mon, 22 Oct 2007 16:27:36 -0400 (EDT)
Message-Id: <20071022.162736.249965663.pfps@research.bell-labs.com>
To: schneid@fzi.de
Cc: public-owl-dev@w3.org

From: "Michael Schneider" <schneid@fzi.de>
Subject: Some basic questions about OWL-Full
Date: Mon, 22 Oct 2007 22:06:40 +0200

> Hi!
> 
> OWL-Full has ever been a complete mystery to me, and I admit that I have
> never really made an approach to explore it. But now that people have
> started to work on a new version of OWL, I think it is a good time for me to
> at least try to learn a few fundamental facts. So dear OWL-Full experts: I
> will put a few questions, all very basic, and all of them can be answered by
> just saying "yes" or "no". But I won't bite you if you also add a small
> explanation to each of your answers. :)
> 
> (1) My first question is about syntactically correct OWL-Full ontologies. I
> always thought that simply "everything" is allowed in OWL-Full. So my
> question: Is every RDF graph an allowed OWL-Full ontology?

Yes.  Some RDF graphs make better OWL-Full ontologies than others, but
they all are acceptable.

> (2) The rest of my questions all deal with semantics. I think I have heard
> somewhere that one can "change the semantics" of OWL-Full itself by stating
> axioms about OWL vocabulary, but I don't know if this is true, and not even
> what this exactly means. Ok, let's test this by creating a concrete example!
> I would have said that the following two statements lead to inconsistency
> even in OWL-Full:
> 
>   :x owl:sameAs :y .
>   :x owl:differentFrom :y .
> 
> But what if I add the following axiom:
> 
>   EquivalentProperties(owl:sameAs owl:differentFrom)
> 
> This should at least be syntactically ok in OWL-Full (see (1)). But have I
> also managed to make this ontology semantically consistent with this trick?
> I don't believe so, but I am also not certain. And whatever answer is
> correct, I do not have an explanation for any of them.

As OWL (even OWL Full) is monotonic, you can't make an inconsistent
ontology consistent by adding more things to it.

Note that 
   :x owl:sameAs :y .
   EquivalentProperties(owl:sameAs owl:differentFrom)
   	[actually a translation of it into an RDF graph, but let's
	   ignore this detail]
is inconsistent, as it says that the denotation of :x is equal to the
denotation of :y (obviously) and *also* that the denotation of :x is not
equal to the denotation of :y.

For homework:  Is EquivalentProperties(owl:sameAs owl:differentFrom)
    	       itself inconsisten?

> (3) A more general question: Is it true that whenever an OWL-DL ontology is
> inconsistent under OWL-DL semantics, then it is also inconsistent under
> OWL-Full semantics? Would sound reasonable to me, but I am not sure.

Yes, but not vice versa.  (See theorem 2 in 
http://www.w3.org/TR/2004/REC-owl-semantics-20040210/rdfs.html.)

> (4) Looking at both questions (2) and (3) brings me to my last question. The
> ontology in question (2) is *not* an allowed OWL-DL ontology, of course, but
> it contains a sub-ontology which is syntactically allowed in OWL-DL: The
> first two statements above. So I ask if the following claim is true: "Given
> [] an OWL-Full ontology [that] contains an OWL-DL sub-ontology [] which is
> inconsistent under OWL-DL semantics, then the complete OWL-Full ontology is
> inconsistent under OWL-Full semantics." Is this true or wrong?

Yes, from just above and monotonicity.

> Ok, I think that this is enough for me for the moment to get a first feeling
> for OWL-Full.
> 
> Cheers,
> Michael

Have fun,

peter
Received on Monday, 22 October 2007 20:35:11 GMT

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