RE: Axiomatic triples in OWL-R-Full?

>-----Original Message-----
>From: Ivan Herman [mailto:ivan@w3.org] 
>Sent: Wednesday, April 09, 2008 12:38 PM
>To: Michael Schneider
>Cc: W3C OWL Working Group
>Subject: Re: Axiomatic triples in OWL-R-Full?
>
>
>
>Michael Schneider wrote:
>> Hi, Ivan!
>> 
>> This is a good observation, and I think an issue should be 
>raised for it.
>
>Maybe we should decide on the group this evening whether this 
>should be 
>entered as an Issue

If not, then I would put it in the Full-TF issues list at

  <http://www.w3.org/2007/OWL/wiki/FullIssues#Open_TF_Issues>

simply to avoid that this topic gets lost.

>> The question whether to include axiomatic triples or not 
>depends on whether we want the semantics of OWL R Full to be 
>an upper semantics of RDFS or not.
>> 
>> Just one technical/theoretical remark for the moment: To 
>receive strict RDFS compatibility, it is necessary to include 
>all of the following axiomatic triples, for every natural language n:
>> 
>
>My understanding of Horst's paper is that _for a given graph_ 
>calculating the RDFS closure (ie, by induction, the OWL-R-Full 
>closure, 
>too) is doable because one can add only those rdf:_n related axiomatic 
>triples by limiting 'n' to the highest occurrence of an rdf:_i 
>usage in 
>the original graph. 

I understand terHorst in this way, too. This always leads to a finite entailment closure for the empty RDF graph. IIRC, several of the theorems in the pD* paper are based on this result.

>I may have missed something in fine print in the 
>paper, but my understanding is that this is perfectly doable, proper, 
>and we would then get back to a safe, finite world.

Without having thought more deeply about this, I wouldn't expect any semantical disadvantages in only having these "input driven" finite sets of axiomatic triples. 

The only theoretical problem which immediately comes to my mind would be if there was a comprehension principle for RDF collections in the same way as their is one for lists. Such a comprehension principle would state: 

  "If you have entities x1, ..., xn,
  then there exists some bag 
  which contains x1, ..., xn as its members." 

But there isn't such a comprehension principle in current OWL 1 Full, simply because OWL Full does not use containers, only lists. So no danger from this side.

Such a "on demand" introduction of axiomatic triples would probably put a slight burdon on the implementors to do some preprocessing on the input graph in order to create the necessary axiomatic triples. But this shouldn't be no big deal in practice, I suppose. Perhaps for very large RDF graphs contained in databases, but people will certainly come to clever ideas like "lazy axiomatic triple introduction" or whatever.

Cheers,
Michael

>But I yield to your knowledge of RDFS semantics...
>
>
>Ivan
>
>
>> From RDF semantics:
>> 
>>    rdf:_n rdf:type rdf:Property
>> 
>> From RDFS semantics:
>> 
>>    rdf:_n rdf:type rdfs:ContainerMembershipProperty
>>    rdf:_n rdfs:domain rdfs:Resource
>>    rdf:_n rdfs:range rdfs:Resource
>> 
>> Obviously, these are *infinitely* many axiomatic triples. In 
>practice this would mean that complete OWL R Full conformance 
>would probably not be possible to achieve. So it would be up 
>to the implementors to decide about the intended conformance 
>level of their product.
>> 
>> Cheers,
>> Michael
>> 
>> Ivan Herman wrote:
>> 
>>> (This may have to be raised as a more formal ISSUE. Also: it 
>>> is _not_ my 
>>> intention to get this problem solved before the upcoming 
>>> publication round!)
>>>
>>> The current OWL-R-Full does not include 'axiomatic triples' to 
>>> be added 
>>> to the resulting graph. What I mean is to add triples like
>>>
>>> (owl:FunctionalProperty,rdfs:subClassOf,rdf:Property)
>>> (rdfs:subPropertyOf,rdfs:domain,rdf:Property)
>>>
>>> etc. See for the RDF Semantics for a bunch of those in RDFS, 
>>> and Horst's 
>>> paper on pD* for their OWL equivalents.
>>>
>>> I am not saying we must have those; this is clearly 
>touching upon the 
>>> issue whether the core RDF/RDFS/OWL vocabulary is an object of 
>>> discourse 
>>> or not in OWL-R-Full. We _could_ therefore, explicitly say 
>that those 
>>> axiomatic triples are not defined in OWL-R-Full. That would 
>mean that 
>>> some (valid) RDFS or OWL Full entailements are not meaningful in 
>>> OWL-R-Full, ie, OWL-R is also defined as a syntactic 
>>> restriction v.a.v. 
>>> OWL 2 Full and not only OWL 2 DL.
>>>
>>> Again, I am not saying this is wrong. But the decision 
>should be made 
>>> explicitly and documented in the profile document as well. 
>>> Alternatively, we could add those axiomatic triples for 
>>> OWL-R-Full (but 
>>> then the relationship between OWL-R-Full and OWL-R-DL becomes 
>>> less clear...)
>>>
>>> Ivan
>>>
>>>
>>> -- 
>>>
>>> Ivan Herman, W3C Semantic Web Activity Lead
>>> Home: http://www.w3.org/People/Ivan/
>>> PGP Key: http://www.ivan-herman.net/pgpkey.html
>>> FOAF: http://www.ivan-herman.net/foaf.rdf
>>>
>> 
>> --
>> Dipl.-Inform. Michael Schneider
>> FZI Forschungszentrum Informatik Karlsruhe
>> Abtl. Information Process Engineering (IPE)
>> Tel  : +49-721-9654-726
>> Fax  : +49-721-9654-727
>> Email: Michael.Schneider@fzi.de
>> Web  : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555
>> 
>> FZI Forschungszentrum Informatik an der Universität Karlsruhe
>> Haid-und-Neu-Str. 10-14, D-76131 Karlsruhe
>> Tel.: +49-721-9654-0, Fax: +49-721-9654-959
>> Stiftung des bürgerlichen Rechts
>> Az: 14-0563.1 Regierungspräsidium Karlsruhe
>> Vorstand: Rüdiger Dillmann, Michael Flor, Jivka Ovtcharova, 
>Rudi Studer
>> Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus
>
>-- 
>
>Ivan Herman, W3C Semantic Web Activity Lead
>Home: http://www.w3.org/People/Ivan/
>PGP Key: http://www.ivan-herman.net/pgpkey.html
>FOAF: http://www.ivan-herman.net/foaf.rdf
>
>

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
Tel  : +49-721-9654-726
Fax  : +49-721-9654-727
Email: Michael.Schneider@fzi.de
Web  : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555

FZI Forschungszentrum Informatik an der Universität Karlsruhe
Haid-und-Neu-Str. 10-14, D-76131 Karlsruhe
Tel.: +49-721-9654-0, Fax: +49-721-9654-959
Stiftung des bürgerlichen Rechts
Az: 14-0563.1 Regierungspräsidium Karlsruhe
Vorstand: Rüdiger Dillmann, Michael Flor, Jivka Ovtcharova, Rudi Studer
Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus