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Re: DTTF: How unasserted triples help

From: Dan Connolly <connolly@w3.org>
Date: 22 May 2002 14:59:10 -0500
To: Jonathan Borden <jonathan@openhealth.org>
Cc: WebOnt WG <www-webont-wg@w3.org>
Message-Id: <1022097551.14013.77.camel@dirk>
On Wed, 2002-05-22 at 14:38, Jonathan Borden wrote:
> DanC raises the important question of how unasserted triples help OWL's
> problem.
> http://lists.w3.org/Archives/Public/www-webont-wg/2002May/0177.html
> My impression is that since certain triples are unasserted by the RDF MT,
> the OWL MT or axiomatic semantics etc. would be "free" to assert its own
> meaning. For example
> First using "asserted" triples, the following:
> intersectionOf( student, employee ) or in N3
> _:c1 rdf:type owl:Class
> _:c1 owl:intersectionOf _:L1
> _:L1 rdf:type owl:List
> _:L1 owl:first <#student>
> _:L1 owl:rest _:L2
> _:L2 rdf:type owl:List
> _:L2 owl:first <#employee>
> _:L2 owl:rest owl:nil
> which roughly translates to: "There exists a class having the intersectionOf
> property whose object is a List, whose first element is #student and whose
> rest is another List whose first element is #employee and whose rest is nil"
> As "asserted" triples, these statements are said to be _truths_, which is a
> bit strange because this isn't what we really mean.

It's not strange at all; it's exactly what we mean:

"for intersectionOf(X, Y) read: X is the intersection of the classes in
the list Y"
 -- http://www.w3.org/2001/10/daml+oil

> Instead we mean to say:
> "There exists a class which is the intersectionOf #student and #employee."

That's an informal corrollary of the above, but it can't be
stated formally/directly using 2-place predicates.

> So presumably the OWL MT would have a statement or axiom or something to the
> effect that:
> "intersectionOf(a , b) <=> intersectionOf( b, a)"

Sorry, this is too hand-wavy to be convincing.

> In this way, having _unasserted_ triples allows the OWL MT to apply its own
> semantics to the triples (which we are using as syntax). The answer is that
> having unasserted triples:
> 1) prevents paradoxes
> 2) allows the OWL MT to do its job of defining semantics for OWL statements

I can imaging that it might; but I would be entirely more convinced
if there were an existence proof showing *how* unasserted triples
allows the OWL MT to do this.

> other examples would be
> owl:import
> etc. etc.
> the idea being not that these statements would be lacking semantics, rather
> that the truths stated in these OWL statements would be defined by the OWL
> MT i.e.
> "If it is true that John is a member of the intersectionOf(student,
> employee) then it necessarily follows that John is a member of the
> intersectionOf(employee,student)"
> Problem solved, etcetera.

Not to my satisfaction.

> Jonathan
Dan Connolly, W3C http://www.w3.org/People/Connolly/
Received on Wednesday, 22 May 2002 15:59:11 UTC

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