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Re: layering (5.3,5.10): a first-order same-syntax model theory

From: Dan Connolly <connolly@w3.org>
Date: 20 Jun 2002 10:55:17 -0500
To: "Peter F. "Patel-Schneider <pfps@research.bell-labs.com>
Cc: www-webont-wg@w3.org
Message-Id: <1024588517.26130.1457.camel@dirk>

On Wed, 2002-06-19 at 17:21, Peter F. Patel-Schneider wrote:
> Good.  A proposal.

thanks for the quick feedback...

> 
> From: Dan Connolly <connolly@w3.org>
> Subject: layering (5.3,5.10): a first-order same-syntax model theory
> Date: 19 Jun 2002 16:26:58 -0500
> 
> [...]
> 
> > Additionally, owl reserves the following vocabulary:
> 
> [...]
> 
> I have no idea what ``reserves the ... vocabulary'' could mean.

basically, it means that these symbols denote something
in every OWL interpretation.

I guess the allusion to [RDFMT] wasn't sufficiently explicit...

"An interpretation assigns meanings to symbols in a particular
vocabulary of urirefs. Some interpretations may assign special meanings
to the symbols in a particular namespace, which we will call a reserved
vocabulary."

  -- http://www.w3.org/TR/2002/WD-rdf-mt-20020429/#urisandlit

> 
> [...]
> 
> > onProperty/hasClass:
> > if <?r, ?p> is in IEXT(I(ont:onProperty))
> > and <?r, ?a> is in IEXT(I(ont:hasClass)),
> > then the set
> >   { ?o: for some ?s in ICEXT(?r), <?s, ?o> is in IEXT(?p)
> >         and ?o is in ICEXT(?a) }
> > has at least one element.
> 
> Completely wrong.

Oops; I must have misread the DAML+OIL model theory...

>  Something like
>    then ICEXT(?r) = { ?o : exists ?x in ICEXT(?a) st <?o,?x> in IEXT(?p) }
> is needed here.  Similarly for other restrictions.

OK...


> > imports:
> > none. imports doesn't constrain interpretations
> > (other than having the subproperty relationship
> > with rdfs:seeAlso).
> 
> Don't think so.  imports means that the OWL KB pointed to should be
> considered to be part of this KB.
> 
> A treatment of imports would be something like
> 
> 	if <?KB1,?KB2> in IEXT(owl:imports)
> 	then the models of ?KB1 are a subset of the models of ?KB2.

Hmm... not sure the domain and rangeof imports are KBs... I think
of them as documents. This issue is on our list; I don't think
I'll try to address it in this proposal.

http://www.w3.org/2001/sw/WebOnt/webont-issues.html#I5.6-daml:imports-as-magic-syntax

> No particularly standard-first-order, however.



> 
> [...]
> 
> 
> > conversely,
> > 
> > if <?a, ?b> is in IEXT(I(ont:intersectionOf1))
> > and <?a, ?c> is in IEXT(I(ont:intersectionOf2))
> > and ?x is in ICEXT(?a).
> > then ?x is in ICEXT(?b) and in ICEXT(?c)
> 
> What if happens if there is another ont:intersectionOf1 link from ?a?

Well, whatever follows follows. It's probably easy
to state inconsistencies. But I don't see this
as a problem.

> [...]
> 
> > oneOf1/oneOf2:
> > 
> > if  <?a, ?b> is in IEXT(I(ont:oneOf1))
> > and <?a, ?c> is in IEXT(I(ont:oneOf2))
> > then ?b is in ICEXT(?a)
> > and ICEXT(?c) is a subset of ICEXT(?a).
> > 
> >  conversely,
> > if  <?a, ?b> is in IEXT(I(ont:oneOf1))
> > and <?a, ?c> is in IEXT(I(ont:oneOf2))
> > and ?x is in ICEXT(?a)
> > then either ?x = ?b or ?x is in ICEXT(?c).
> 
> Hmm. How does a oneOf finish?  
> 
> Suppose we have 
> 	IEXT(I(ont:oneOf1)) = { <x,a> }
> 	IEXT(I(ont:oneOf2)) = { }
> Then what is the class extension of x?

It's not constrained; the if... part
of the semantic constraint above is not satisfied.

> Suppose we have 
> 	IEXT(I(ont:oneOf1)) = { <x,a> }
> 	IEXT(I(ont:oneOf2)) = { <x,x> }
> Then what is the class extension of x?

It contains at least a; it's otherwise
not constrained.

> [...]
> 
> And, of course, there are no comprehension constraints, so
> 
>      x rdf:type _:y .
>      _:y one:intersectionOf1 a .
>      _:y one:intersectionOf2 b .
> 
> does not entail that
> 
>      x rdf:type _:z .
>      _:z one:intersectionOf1 b .
>      _:z one:intersectionOf2 a .

Yes, that's by design. This is my position on...

http://www.w3.org/2001/sw/WebOnt/webont-issues.html#I5.10-DAML-OIL-semantics-is-too-weak

as I said earlier...

# DDTF/layering: weak class theory seems good enough (5.3, 5.10)
Dan Connolly (Tue, May 28 2002)
http://www.w3.org/2001/sw/WebOnt/webont-issues.html#I5.6-daml:imports-as-magic-syntax

> So, in sum, lots of problems.

I see just one, for which thanks for the fix.

I'll see if I can spin another draft presently...

-- 
Dan Connolly, W3C http://www.w3.org/People/Connolly/
Received on Thursday, 20 June 2002 11:55:03 GMT

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