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Re: Possible semantic bugs concerning domain and range

From: Dan Connolly <connolly@w3.org>
Date: 16 Oct 2002 14:00:53 -0500
To: Ian Horrocks <horrocks@cs.man.ac.uk>
Cc: Jos De_Roo <jos.deroo.jd@belgium.agfa.com>, Pat Hayes <phayes@ai.uwf.edu>, www-webont-wg@w3.org
Message-Id: <1034794854.4220.323.camel@dirk>

On Wed, 2002-10-16 at 13:00, Ian Horrocks wrote:
> On October 16, Dan Connolly writes:
> > 
> > On Tue, 2002-10-15 at 16:47, Jos De_Roo wrote:
> > > 
> > > >> >>  Range(P, A) -> (forall x,y P(x,y) -> A(y) )
> > > >> >>
> > > >> >>  You want
> > > >> >>
> > > >> >>  Range(P,A) <-> (forall x,y P(x,y) -> A(y) )
> > > >> >>
> > > >> >>  They are about equally clear and intuitive; but the latter rules out
> > > >> >>  some possibilities which the former permits. I believe that all the
> > > >> >>  'intuitive' entailments that people want in fact hold in both these
> > > >> >>  cases; and that the former is therefore to be preferred.
> > > >> >
> > > >> >I am agnostic about which of these is to be preferred - as a humble
> > > >> >engineer, all I need to know is which one it is so that I have a clear
> > > >> >spec to which I can build my systems.
> > > >
> > > >I'm kinda agnostic too... I was leaning toward the IF, rather
> > > >than the IFF...
> > > 
> > > I'm not agnostic at all...
> > > i.e. I can't see how to write
> > >   (forall x,y P(x,y) -> A(y)) -> Range(P,A)
> > > in Horn-clauses or in Datalog
> > > (although I like nested implications
> > > in propositional proof arguments)
> > 
> > Oohh; that's quite compelling... currently, you can
> > implement a complete RDFS reasoner with a
> > horn/datalog reasoner. If we changed range to IFF,
> > it's not clear that this property would hold.
> > 
> > Likewise for subClassOf.
> 
> If you use a direct encoding such as the one Benjamin and I have been
> suggesting (i.e., classes as unary predicates, properties as binary
> predicates),

I don't see how that's relevant; if a test for C(i) -> D(i)
would work, then so would a test for
	holds(rdf:type, C, i) -> holds(rdf:type, D, i)

> then you can check if subClassOf(C,D) holds simply by
> inventing a new individual i and checking if C(i) -> D(i) holds.

But in any case, how can I encode that as a horn clause?

	subClassOf(C, D) :- ... what to put here? ...


> Similarly for Range(P,A), you can invent two new individuals i1 and i2
> and check if P(i1,i2) -> A(i2) holds.
> 
> Ian

-- 
Dan Connolly, W3C http://www.w3.org/People/Connolly/
Received on Wednesday, 16 October 2002 15:00:20 GMT

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