Re: ACTION: task force unasserted triples

On Wed, 2002-04-24 at 16:07, Pat Hayes wrote:
> >What do you mean by 'syntactic constructions' here?
> >By my reckonning, the syntactic constructions of
> >WebOnt are exactly the same as those of RDF:
> >
> >   terms: literals, bnodes, and URIref names
> >   atoms: S P O triples.
> >   formulas: conjunctions of atoms.
> Well, that is obviously wrong,


> even of DAML, since the DAML meanings 
> of the RDF graphs are not *conjunctions* of the RDF meanings of the 
> DAML triples.

Yes, they are; that is: the DAML meanings are
complete w.r.t. the RDF semantics; the DAML+OIL semantics
(the way I see them; ala the axiomatic semantics)
further constrain interpretations. But we've switched from syntax
to semantics somehow here...

> >Please give an example of what you mean by syntactic
> >construct.
> In the case of DAML, I mean the lists in things like intersectionOf. 
> The DAML MT treats them (correctly) as syntactic primitives, not as 
> implicit existential assertions.

intersectionOf is (a name for) a property that relates
one class to a list of classes. It's not a syntactic

It is specified thus:

    for intersectionOf(X, Y) read: X is the intersection of the classes
in the list Y;
    i.e. if something is in all the classes in Y, then it's in X, and
vice versa.
    cf OIL AND


See also:

> >>  as assertions of the existence of a class corresponding
> >>  to the syntactic construct(and in fact of a great deal else as well,
> >>  eg lists). This is because the RDF meaning of the RDF encoding of
> >>  every piece of the WebOnt language amounts to an assertion of the
> >>  existence of that class.
> >
> >Quite. That's by design, and seems quite natural to me.
> Even when the class that RDF says exists is the Russell set in OWL? 
> Why would that be natural?

No, that's not natural. I'm not convinced that RDF (along
with DAML+OIL semantics) says it exists.

> >>  And, as Peter has shown, such a requirement
> >>  is very dangerous,
> >
> >He has shown that it *can* be very dangerous.
> >He has not shown, to my satisfaction, that it
> >is must be dangerous in every case; that
> >there is no design that avoids the problems.
> Right. OK, if you want to get involved with foundations of set theory 
> every time a web language is created, then I guess you are entitled 
> to take your life in that direction. Seems pointless to me. Apart 
> from the waste of time, I would have no confidence that Id be able to 
> do it. Proving consistency of set theories is heavy work.

OK, stalemate there.

> >Look, if it's that well-studied, just spell out (or at
> >least point to) the argument. An appeal to authority
> >only makes me more suspicious of your position;
> >recall our exchange about orthodoxy and Des-Cartes
> >experiences.
> Im thinking of the Russell paradox in set theory, Goedel 
> incompleteness, Turing undecideability,

Those I'm familiar with...

> Tarski's results on 
> meta-descriptions (a consistent language can't be the same expressive 
> power as its own metatheory),

That one I don't know; it seems clearly relevant; I'll
have to study it. Pointers are welcome.

> Montague's paradox (showing that even 
> quite weak languages can't consistently describe their own 
> semantics),

[... other bits skipped for lack of time...]

> >I don't understand how to reconcile your messages.
> I think Ive been fairly consistent on this issue. Maybe Ive been too 
> polite at times, but we all have to try to get along.

OK; I see now. Thanks.

Dan Connolly, W3C

Received on Wednesday, 24 April 2002 18:08:03 UTC