Re: REQDOC: ontologies as resources

>From: Dan Brickley <danbri@w3.org>
>Subject: Re: REQDOC: ontologies as resources
>Date: Thu, 14 Feb 2002 15:58:54 -0500 (EST)
>
>[...]
>
>>  On Thu, 14 Feb 2002, Peter F. Patel-Schneider wrote:
>>
>>  > In a message expressing my concerns with the requirements document, I
>>  > argued that it is premature to require that ontologies be resources, at
>>  > least if by resource, we mean an RDF resource, i.e., elements of 
>>the domain
>>  > of discourse that can be used just like any other element of the domain of
>>  > discourse.
>>
>>  I think this is the crux of the WebOnt/RDFS layering dispute. While folk
>>  have often focussed on the "RDF schema says that class is a class" aspect,
>>  this spin on the issue gets us closer.
>
>[...]
>
>>  But RDF
>>  (not just RDFS) does establish the convention that
>>  'http://example.com/myvocab#livesWith' is in the domain of discourse, and
>>  as such open to further description by arbitrary parties using arbitrary
>>  vocabularies.
>
>[...]
>
>>  Having properties and classes in the domain
>>  of discourse meant that the RDFS 1.0 WG didn't have to take upon
>>  themselves the task of enumerating all the useful kinds of things one
>>  might say about classes and properties. Having watched various schema
>>  efforts come and go, I strongly suspect this WG will find this an
>>  attractive feature.
>
>[...]
>
>This is all fine and good, except that RDF and RDFS together place a rather
>severe limit in the sorts of things that can be said about classes and
>properties.

Nonsense; they are much less limited than most other languages (than 
DAML, for example.)

>RDF requires that classes and properties (in particular
>rdf:type) live in the domain of discourse,

True, though this might not mean quite what you think. It does not 
require that their property and class extensions are in the domain of 
discourse.

>and thus that the theory of
>classes and properties can be referred to by any theory of classes and
>properties.

No, that does not follow at all. RDFS talks about things called 
rdfs:Class and rdfs:Property. If some other theory wants to talk 
about things called othertheory:Class and othertheory:Property, then 
there is no global presumption that these are the same. (You know 
this, Peter: people talk about ZF sets and NF sets, for example. )

>  RDFS requires that this theory incorporate self-reference.

No, it does not. I don't know where that idea comes from. The only 
unusual thing about RDFS is that it doesn't require well-foundedness 
of class membership or property application, and that is provably 
harmless (see Peter Aczel, Non-well-founded sets, CSLI lecture notes 
#14, 1988) It allows self-application, for example (the triple
aaa aaa aaa .
is legal) but that is not self-REFERENCE. In fact RDF provides no 
explicit way to refer at all, other than by name use.

>(Actually what RDFS requires is rather more complex than this, but
>self-reference is sufficient to get to the problems below.)
>
>It doesn't take much more to allow semantic paradoxes.  In essence all that
>is missing is some notion of pervasive classes (provided by DAML+OIL
>Restrictions) and some notion of complement (provided by a number of
>DAML+OIL constructs).

Aczel gives a relative consistency proof to ZF set theory, which is 
about the best foundational guarantee of consistency that can be 
provided by any piece of mathematics. Giving up the axiom of 
foundation does not produce any semantic paradoxes. Its got nothing 
to do with semantic paradoxes.

>You then have versions of Russel's paradox.
>(The easiest version to construct is the restriction whose instances are
>not related to the restriction by rdf:type.)
>
>So in the interests of generality RDF and RDFS have essentially disallowed
>most logical constructs.

Peter, this is nonsense. RDFS has no self-reference or liar-type 
constructions in it. You are mixing up reference with membership.

>peter
>
>PS:  What does this have to do with ontologies being resources?  Well,
>      nothing directly, but Dan Brickley's comments had to do with classes
>      and properties being resources.

Right, I agree this has nothing to do with the thread.

Pat

--

Received on Friday, 15 February 2002 01:39:15 UTC