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Re: Problems with dark triples approach

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Wed, 17 Apr 2002 12:13:48 -0400
To: jjc@hplb.hpl.hp.com
Cc: www-webont-wg@w3.org
Message-Id: <20020417121348Z.pfps@research.bell-labs.com>
From: "Jeremy Carroll" <jjc@hplb.hpl.hp.com>
Subject: Problems with dark triples approach
Date: Wed, 17 Apr 2002 14:14:16 +0100

> 
> As my idea of the problem that we are trying to solve is clarifying
> (hopefully not too incorrectly) I am beginning to see problems with the dark
> triples solution to that problem.
> 
> These are:
> 
> 1: OWL syntax cannot be extended using RDF/RDFS/OWL mechanisms.

Well, neither can RDF syntax be extended using RDF/RDFS/OWL mechanisms, nor
is it really possible to restrict RDF syntax using RDF/RDFS/OWL mechanisms.
If it was possible for OWL to be a syntax extension of RDF, then the
problem being addressed by dark triples could go away.

> 2: We still need a theory of classes.

Well, OWL definitely needs a theory of something that goes beyond the
RDF(S) model theory.  Whether you call these things classes or not is up to
you.

Why am I going on about whether these are classes?  Well RDFS has its own
treatment of what a class is, and part of that treatment is that classes
are elements of the domain.  If you make the OWL equivalent of DAML+OIL
restrictions not be and not act like RDFS classes, then there are many more
options available.


> In order:
> 
> Extensibility
> =============
> 
> The first ontology I wrote using DAML started by taking a subclass
> daml:Class, and subproperties of daml:Property etc, and a subclass of
> daml:Ontology.
> 
> The motive was that the ontology I was creating was to represent the
> conceptualization of e-mail in Microsoft's Outlook product and I wished to
> extend the DAML+OIL mechanisms to include OLE mappings for the properties.
> 
> From the point of view of computer science this seems a logical and natural
> thing to do; and a functionality that I hope that OWL can support.
> 
> From the point of view of the semantic web I see extensibility in all
> possible directions as being a fundamental design obligation.
> 
> This relied on *semantic* mechanisms such as subPropertyOf and subClassOf.
> 
> If the semantics of OWL is defined directly on top of the graph syntax then
> this does not work. Rather, to have this work, we would need the conditions
> on an OWL interpretation to be essentially semantic constraints, like the
> additional constraints on RDFS interpretations in Pat's RDF Model Theory.

Yes, sure.  This is about the only way to go, absent a powerful base
representation system (at least the power of first-order logic).

> Building on top of dark triples seems to be a commitment to not permitting
> this extensibility. If this is correct then I am unhappy with the proposal
> to use dark triples to address the semantic layering problems.

This does not follow.  Dark triples can (and must) be given meaning by the
extensions to RDF(S).  OWL will give certain dark triples some meaning.
OWL may also give certain non-dark triples extra meaning.  I hope that OWL
will not give all dark triples an OWL meaning, leaving some with no
inherent meaning so that they can given their base meaning by extensions to
OWL.

It might be easier to think of this in a syntactic fashion (which I much
prefer anyway).  Suppose we could make OWL's *syntax* an extension of the
RDF syntax.  OWL would then give the base meaning to that portion of its
syntax that was not RDF syntax, would retain all the RDF meaning for RDF
syntax, and might give some RDF syntax extra meaning.  


> Theory of Classes
> =================
> 
> (Summary dark triples ain't no magic wand).

Agreed, care has to be take to make sure that OWL doesn't have other
problems.

> As we are all aware, a naive set theory is problematic.
> As Peter has shown, the theory of classes in DAML+OIL can be thought of as
> problematic if one presupposes that the ability to write a description of a
> class is sufficient to ensure its existence.
> It is at least plausible, that even without qualified cardinality
> constraints, a new version of Peter's paradox can be found.
> 
> In axiomatic set theory, the class of syntactic expressions that actually
> correspond to sets that exist is restricted in some way. As a footnote I
> include a version from von Neumann-Bernays-Gödel set theory [1]. In a
> semantic web based theory such restrictions are very hard to state because
> they need to be robust against the open world assumption. As an example, in
> DAML+OIL we can have an innocuous looking qualified cardinality constraint:
> 
> 
>    foo:r, rdf:type, owl:Restriction .
>     foo:r, daml:onProperty, foo:bar .
>     foo:r, daml:maxCardinalityQ, "0" .
>     foo:r, daml:hasClassQ, :_3 .
>       :_3, daml:oneOf, :_4 .
>         :_4, daml:first, foo:singleton .
> 	:_4, daml:rest, daml:nil .
> 
> 
> when combined with another innocuous document
> 
> rdf:type daml:samePropertyAs foo:bar .
> foo:singleton daml:sameInstanceAs foo:r .
> 
> we have the Patel-Schneider paradox.
> 
> I don't see this as a problem relating to RDF, but relating to the radical
> open world assumption that, for me, characterises the semantic web.
> 
> At this stage my assumption is that an adequate theory of classes for the
> semantic web will be a major research undertaking, on a par with creating an
> adequate set theory. I believe that the latter took about 30 years. Given
> that we have the prior work to guide us, we may be able to look for a factor
> of 10 speed up.

I disagree completely here.  As soon as OWL is free from the RDFS view of
rdfs:Class and rdf:type as the *only* way to go, it can choose from any one
of a number of already-existing treatments of such notions.  Two of these
are 
1/ descriptions from description logic
2/ lambda-defined one-place predicates from (roughly first-order) logic

> There appeared to be agreement at the f2f, that a first order theory (aka my
> solipsistic stuff [2]):
> - does clarify OWL semantics without contradicting our set theoretic
> intuitions
> - is the theory used by DAML+OIL
> - does not contain an adequate theory of classes capturing our set theoretic
> intuitions
> 
> Personally I would feel happier with that solution than paying either of the
> prices that my analsysis suggests for a dark triple based theory of classes:
> viz:
> either:
> - a significant delay to the WG product in order for the SEM focus area to
> undertake a research project
> or:
> - the inability to meaningful take a subPropertyOf the properties used in
> constructing an owl ontology.
> 
> 
> Jeremy
> 
> [1] Elliot Mendelson, Introduction to Mathematical Logic, 2nd edition, 1979,
> p 178.
> 
> [Within a first-order theory NBG ... proposed by von Neumann and ... R.
> Robinson, Bernays and Gödel]
> 
> PROPOSITION 4.4 Let phi(X1,....Xn,Y1,...Ym) be a well-formed formula the
> variables of which occur among X1,...Xn,Y1,....Ym and in which only set
> variables are quantified (i.e. phi can be abbreviated in such a way that
> only set variables are quantified). We call such a well-formed formula
> *predicative*. Then,
> 
> turnstile (EZ)(x1)...(xn)(<x1,...,xn> memberOf Z iff
> phi(x1,...,xn,Y1,...,Ym))
> 
> 
> Jeremy: I am trying to draw attention to the syntactic constraint to do with
> quantified variables in the wff; I see this constraint as alien in nature to
> how I perceive the open world of the semantic web.
> 
> [2]
> 
> http://lists.w3.org/Archives/Public/www-webont-wg/2002Mar/0179.html

peter
Received on Wednesday, 17 April 2002 12:14:27 GMT

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