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RE: layering (5.3,5.10): a same-syntax model theory

From: Jeremy Carroll <jjc@hplb.hpl.hp.com>
Date: Thu, 30 May 2002 16:04:11 +0100
To: "Dan Connolly" <connolly@w3.org>, <www-webont-wg@w3.org>
Message-ID: <JAEBJCLMIFLKLOJGMELDOEBECEAA.jjc@hplb.hpl.hp.com>



> -----Original Message-----
> From: www-webont-wg-request@w3.org
> [mailto:www-webont-wg-request@w3.org]On Behalf Of Dan Connolly
> Sent: 30 May 2002 05:58
> To: www-webont-wg@w3.org
> Subject: layering (5.3,5.10): a same-syntax model theory
>
>
>
>
> [apologies if this is a duplicate; I'm using
> a different mailer from the one I usually use.]

> Jeremy, wanna look this over and maybe fill in the next few terms?

Hi Dan,

I did the first part.

My only comment is to do with the treatment of lists.

First there is a small typo:



>
> The following closure rules apply:
>
>  ?l ont:first ?x.       ==> ?l ont:item ?x.
>
>  ?l ont:rest ?r.
>  ?r ont:first ?x.	==> ?l ont:item ?x.

That last line should be

>  ?r ont:item ?x.	==> ?l ont:item ?x.


and then I would add that that approach creates unnecessary trouble.
The problem is the implicit closed world assumption on ont:item used to
make a set that is known not to have any other members. (The six
continents example).

A different way of articulating these closed sets without ont:item is as
follows:

An OWL interpretation built on an RDF interpretation has
- a function I that maps nodes to things in the domain of discourse,
- a fucntion IEXT that maps some things in the domain of discourse to
properties
- a function LEXT that maps some things in the domain of discourse to
sets.
  LEXT(I(ont:nil)) = {}

if ?l is in ICEXT(ont:List) if and only if ?l is in the domain of LEXT.

if ?l is in ICEXT(ont:List) and ?l != I(ont:nil) then
  there must be some ?x and some ?r such that
    < ?l, ?x > is in IEXT(I(ont:first))
  and
    < ?l, ?r > is in IEXT(I(ont:rest))

and moveover for all such ?x and ?r,
  ?r is in the domain of LEXT and
  LEXT(?l) = { ?x } union LEXT(?r)

I don't think this can express the pairwise disjointness in
disjointUnion I don't think.
We may need to do that without the list syntax.

(Basically the LEXT stuff allows us to realise the lists in the domain
of discourse the same way that IEXT allows us to realise the properties
within the domain of discourse).
Received on Thursday, 30 May 2002 11:05:25 GMT

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