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

From: Smith, Michael K <michael.smith@eds.com>
Date: Mon, 18 Mar 2002 08:47:57 -0600
Message-ID: <B8E84F4D9F65D411803500508BE322140C7ECE1F@USPLM207>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, "Smith, Michael K" <michael.smith@eds.com>
Cc: jjc@hplb.hpl.hp.com, www-webont-wg@w3.org
Peter,

When you say

> However, this is not what happens, because of RDF

I think what you mean to say is we are in agreement!  If our choice of
layering forces us to  let RDF impose this sort of interpretation we are in
trouble.

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

I was reacting to the example, which seemed to be saying that these were all
entailed by one another.  If owl:oneOf denotes an ordered list, as your
translation into RDF indicates, then obviously the three cases are not meant
to have the same meaning.  They are three different lists.  In which case
there would be no entailment issue.

I have been taking seriously the notion that DAML+OIL is our point of
departure.  And the daml:oneOf description in
http://www.daml.org/2001/03/reference.html reads:

   This enables us to define a class by exhaustively enumerating its 
   elements. The class defined by the oneOf element contains exactly 
   the enumerated elements, no more, no less. 

From which I assumed it was defining a set.  I don't know what it would mean
for
a class to include foo as an element twice.

And yes, I was compacting the syntax to agree with Jeremy's.  Given that its
OWL, its not clear what the syntax should have been.  Daml would say (?)

<daml:oneOf parseType="daml:collection">
  <daml:Thing rdf:about="#foo"/>
  <daml:Thing rdf:about="#foo"/>
  <daml:Thing rdf:about="#foo"/>
</oneOf>

- Mike

Michael K. Smith
EDS Austin Innovation Centre
98 San Jacinto, #500
Austin, TX 78701
512 404-6683



-----Original Message-----
From: Peter F. Patel-Schneider [mailto:pfps@research.bell-labs.com]
Sent: Monday, March 18, 2002 4:37 AM
To: michael.smith@eds.com
Cc: jjc@hplb.hpl.hp.com; www-webont-wg@w3.org
Subject: RE: SEM Solipsistic answers to Peter's entailments and Paradox


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 09:50:19 GMT

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