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RE: SEM Solipsistic answers to Peter's entailments and Paradox

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Mon, 18 Mar 2002 05:37:20 -0500
To: michael.smith@eds.com
Cc: jjc@hplb.hpl.hp.com, www-webont-wg@w3.org
Message-Id: <20020318053720P.pfps@research.bell-labs.com>
I agree that it would be much better to say that 

> > owl:oneOf ( <foo> )
> > owl:oneOf ( <foo> <foo> )
> > owl:oneOf ( <foo> <foo> <foo> ) ...

all have the same meaning.  However, this is not what happens, because of
RDF.  In fact the above are not even legal DAML+OIL syntax.

Instead the first of the above is really

:_1 rdf:type rdfs:Class .
:_1 daml:oneOf :_2 .
:_2 daml:first <foo> .
:_2 daml:rest daml:nil .

The second is

:_3 rdf:type rdfs:Class .
:_3 daml:oneOf :_4 .
:_4 daml:first <foo> .
:_4 daml:rest :_5
:_5 daml:first <foo> .
:_5 daml:rest daml:nil .

and so on.

So what there are are several (potentially different) classes, :_1, :_3,
..., each of which has a oneOf to a (different) list.  The class extension
of each of these classes is, of course the same.

This situation occurs because of the RDF requirement that all syntax is
triples and all triples have meaning in the model-theoretic semantics.

peter



From: "Smith, Michael K" <michael.smith@eds.com>
Subject: RE: SEM Solipsistic answers to Peter's entailments and Paradox
Date: Sun, 17 Mar 2002 11:43:11 -0600

> Help me with this one.  I am definitely missing something.  
> 
> > owl:oneOf ( <foo> )
> > owl:oneOf ( <foo> <foo> )
> > owl:oneOf ( <foo> <foo> <foo> ) ...
> 
> This particular example seems to be confusing surface syntax with semantics.
> A tool, when asked to return an answer, will not be required to list all
> possible equivalent surface syntactic forms.  More to the point, what a tool
> does and what the semantics entitle it to do are two different things.
> 
> I am assuming that by owl:oneOf we are defining a construct like the
> daml:oneOf enumeration.  And that therefore
>  owl:oneOf ( x1 ... xn )
> will be assigned an interpretation in the model theory that is the SET 
> made up of the interpretations of x1 ... xn.  (Assuming a oneOf construct
> that is unordered.) 
> 
> Having used some variant of set theory to formalize parts of the model we
> get all of a set's desirable properties.  The infinite possible expressions
> of this set in our surface syntax are by definition identical in the model.
> And tools that reason about such things will do their best to canonicalize
> expressions so that repetition and ordering don't matter.
> 
> This resonates to one of the interesting properties of the RDF model.
> Normally we would expect collections to be relatively straightforward to
> formalize.  After all, they have been many times. But, RDF is at heart a
> scopeless set of arcs (triples) defining a graph. It seems that a set
> theoretic interpretation of a collection doesn't graft onto that in a
> completely obvious way.  
> 
> - Mike
> 
> Michael K. Smith
> EDS Austin Innovation Centre
> 98 San Jacinto, #500
> Austin, TX 78701
> 512 404-6683
> 
> -----Original Message-----
> From: Jeremy Carroll [mailto:jjc@hplb.hpl.hp.com]
> Sent: Saturday, March 16, 2002 9:14 AM
> To: Jim Hendler
> Cc: www-webont-wg@w3.org
> Subject: RE: SEM Solipsistic answers to Peter's entailments and Paradox
> 
> Jim found a semantically significant typo.
> 
> Jeremy:
> [[[
> 
> Using this API it is very natural to ask give me all the triples that have
> <foo> as subject and <type> as predicate.
> 
> 
> [MISTAKE: delete "not"]
> It will not be:
> - difficult to implement
> - and unhelpful to all users
> 
> if the correct answer is at least
> 
> owl:oneOf ( <foo> )
> owl:oneOf ( <foo> <foo> )
> owl:oneOf ( <foo> <foo> <foo> )
> 
> ....
> 
> solipsism provides better answers and a more usable system, and hence a more
> useable language.
> ]]]
> 
> Jim:
> [[[ (snip)
>  but do you mean it will be or it will not be difficult to implement and
> unhelpful?  that is I think you mean it is bad to have  the infinite series
> of oneOfs as answers, but the above seems to argue you suddenly are in favor
> of it -- is this a typo or a conceptual problem on my part?
> ]]]
> 
> Typo.
> I think the "not" in "It will not be" was a mistake, sorry.
> 
> What I was trying to say is that my understanding of Peter's assumption is
> that all the set theoretic consequences of any owl ontology should be
> present in all models. While I shared that assumption until the last
> telecon, I believe that that presents signification implementation
> difficulties, and if we can avoid it in a sound fashion then it is
> positively desirable and not merely a way out of a hole.
> 
> 
> Jim:
> > p.s. Solipcism would not be my choice for what to call this,
> 
> I am quite happy to change the name ... For the sake of this discussion, I
> did want an extreme label.
Received on Monday, 18 March 2002 05:37:42 GMT

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