W3C home > Mailing lists > Public > public-owl-wg@w3.org > June 2008

Re: RDF mapping of datarange complements brings problem for DL/Full relationship

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Thu, 05 Jun 2008 06:23:15 -0400 (EDT)
Message-Id: <20080605.062315.109267447.pfps@research.bell-labs.com>
To: schneid@fzi.de
Cc: public-owl-wg@w3.org, jjc@hpl.hp.com

From: "Michael Schneider" <schneid@fzi.de>
Subject: RE: RDF mapping of datarange complements brings problem for DL/Full relationship
Date: Thu, 5 Jun 2008 10:32:01 +0200

> Peter F. Patel-Schneider wrote:
> 
> >From: "Michael Schneider" <schneid@fzi.de>
> >Subject: RE: RDF mapping of datarange complements brings problem for
> >DL/Full relationship
> >Date: Wed, 4 Jun 2008 09:58:12 +0200
> >
> >> Hi Peter!
> >>
> >> >> (Just to be clear: I did not suggest to extend the complements
> >> >> of dataranges to the "whole" domain in OWL DL. This would
> >> >> make no sense. I only stated that in *OWL Full* the complement
> >> >> actually *is* relative to the whole domain, and that this
> >> >> difference between DL and Full may lead to problems.
> >> >> I write this mail here to show such a problem.)
> >> >
> >> >I don't see that the situation in OWL Full is forced.  The complement
> >> >operator for dataranges could, I think, be relative to rdfs:Literal
> >in
> >> >OWL Full.
> >> >
> >> >peter
> >>
> >> AFAICS, this would lead to rdfs:Literal being equivalent to owl:Thing.
> >>
> >> Cheers,
> >> Michael
> >
> >How so?
> >
> >peter
> 
> Let's regard the complement C of rdfs:Literal:
> 
>   (1) C owl:complementOf rdfs:Literal
> 
> The already existing OWL 1 Full semantics of 'owl:complementOf' are
> specified for /every/ class. In particular, rdfs:Literal is a subclass of
> owl:Thing:
> 
>   (2) CEXT_I(S_I(rdfs:Literal)) subset CEXT_I(S_I(owl:Thing)) 
> 
> From the old OWL 1 spec, we thus receive:
> 
>   (3) CEXT_I(S_I(C)) = IOT - CEXT_I(S_I(rdfs:Literal))
> 
> where the set IOT is defined to be:
> 
>   (4) IOT = CEXT_I(S_I(owl:Thing))
> 
> Now, suppose we add a semantic condition, which defines the complements of
> datatypes relative to rdfs:Literal. In OWL Full, datatypes are characterized
> as being instances of the set IDC, defined by:
> 
>   (5) IDC = CEXT_I(S_I(rdfs:Datatype)) 
> 
> In particular, the first table in sec. 5.2 of the OWL Full spec states that
> 
>   (6) S_I(rdfs:Literal) in IDC
> 
> Hence, our new semantic condition would "capture" rdfs:Literal, leading to 
> 
>   (7) CEXT_I(S_I(C)) = CEXT_I(S_I(rdfs:Literal)) - CEXT_I(S_I(rdfs:Literal))
>                      = {}
> 
> So from (3), (4) and (7) we get:
> 
>   (8) CEXT_I(S_I(owl:Thing)) - CEXT_I(S_I(rdfs:Literal)) = {}
> 
> This allows us to conclude:
> 
>   (9) CEXT_I(S_I(owl:Thing)) subset CEXT_I(S_I(rdfs:Literal))
> 
> And from (2) and (9) we get:
> 
>   (10) CEXT_I(S_I(rdfs:Literal)) = CEXT_I(S_I(owl:Thing))
> 
> Finally, the IFF semantics of owl:equivalentClass lead from (10) to:
> 
>   (11) rdfs:Literal owl:equivalentClaas owl:Thing
> 
> Cheers,
> Michael

OK, if you keep the same meaning for owl:complementOf for datatypes and
you keep the same RDF mapping for datatype complements, then you do get
this result.  

The solution is then to change one of the premises, and I'm perfectly
happy modifying the RDF mapping.

peter
Received on Thursday, 5 June 2008 10:25:26 GMT

This archive was generated by hypermail 2.2.0+W3C-0.50 : Thursday, 5 June 2008 10:25:27 GMT