Re: The Mel99 semantics for RDF

Graham Klyne wrote:
[...]
> (BTW, I may appear to be picking at your posting, but I do regard it as
> very constructive and useful to have something like this to chew on.)

That's what it's there for. I'm not sure I understand it
myself, and as PatH said, the best way to be sure you know
something is to teach it to somebody else.

> At 09:41 PM 5/17/01 -0500, Dan Connolly wrote:
> >Graham Klyne wrote:
> > >
> > > At 10:15 PM 5/16/01 -0500, Dan Connolly wrote:
> >[...]
> > > >II. Semantics.
> > > >
> > > >An interpretation I is a directed,
> > > >labelled graph; the vertices
> > > >and the edge labels come from the
> > > >same set; let's call it N[I], for nodes.
> > > >Let's call the labelled
> > > >[[[edges - #g]]] S[I]; so S[I] \subset N[I] x N[I] x N[I].
> 
> > > Case 1:  F contains a single atomic formula with no variables; i.e. the
> > > interpretation of all terms in F is a specific member of N.
> > >    A satisfies F iff I assigns the truth value TRUE to the member of
> > > F.  (i.e. irrespective of A)
> >
> >er... I assigning TRUE to F's interpretation, (p', s', o'), is
> >the same as (p', s', o') \elt S[I].
> 
> Is this necessarily the case?

Well, it's the case in this semantics, as I understand it.

> The rules of wffs of RDF allow any statements, regardless of whether or not
> they are held to be TRUE (when interpreted as binary predicates).
> 
> So it seems to me that:
> 
> (a) you are defining truth in terms of inclusion on the corresponding
> graph.  This seems to me to be a rather trivial semantics, since every
> possible RDF statement is true by this definition.

Yes, without more axioms to constrain things, this is the case.
I think.

With more axioms, the set of interpretations that satisfy
an RDF formula shrinks, as we'll see below...

> OR
> 
> (b) RDF singleton statements are assigned the truth value TRUE if the
> corresponding binary predicate p(s,o) is held to be true.  This is what I
> thought was the intended interpretation of RDF.

"held to be true for I" in this semantics is represented as
"in S[I]" (after you trade the terms for their denotations).

[...]
> > > I'm not sure that having a unique resource for each statement is quite what
> > > RDF anticipates.  It seems to me that RDF allows multiple resources (i.e.
> > > interpretations of different URIs) that have a similar relationship to the
> > > original statement.  Maybe Rf would be more usefully defines as a relation?
> >
> >I don't think I follow you. But I'm quite sure that the spec
> >says that if subject(x)=subject(y) and predicate(x)=predicate(y)
> >and object(x)=object(y), then x=y. That's what "triple" means, no?
> 
> Same statement triple, yes.  But there may be more than one resource that
> reifies that statement.

No, not in this semantics, and not in my reading of the spec.

>  Your use of a partial function suggested a
> *unique* resource r (or didn't acknowledge the possibility of other
> resources that reify the same statement;  e.g.
> 
>     (s, p, o)
>     (r1, rdf:type, rdf:Statement)
>     (r1, rdf:subject, s)
>     (r1, rdf:property, p)
>     (r1, rdf:object, o)
>     (r2, rdf:type, rdf:Statement)
>     (r2, rdf:subject, s)
>     (r2, rdf:property, p)
>     (r2, rdf:object, o)
> 
> This is a perfectly legitimate RDF graph, is it not?

Well, provided r1=r2, yes.

If you mean that r1 and r2 are distinct elements of N, then
no, this semantics rules that out, which matches
my understanding of the RDF spec.

At the base semantics layer, no formula is unsatisfyable.
But as soon as you introduce reification or any
other non-trivial notion, like
type/class/subclass/subproperty/domain/range,
or collections, you eliminate some formulas/interpretations.
By "trivial" I mean things like label/comment/seeAlso
whose semantics are captured at the base level.
(Hmm... perhaps we need axioms that label/comment/seeAlso
denote distinct elements of N?)

[...]
> > > Ummm... that might be the edge of a precipice.  It seems to be OK for the
> > > model theory you've outlined, but also seems to fall outside the expected
> > > interpretation of URIs discussed elsewhere.
> >
> >I don't see that.
> 
> I thought that under the intended interpretation, the members of N were
> resources.  Not URIs.  Not entities.  Not other representations of
> resources.  I don't see how a resource can be a string.

easy; for example: data:,abc denotes "abc".

Pretty much anything (except something crazy like the set
of all sets that are not memebers of themselves) can
be a resource in this sense. [We really should stop
using the term 'resource' this way; Roy F has a point;
it's just confusing to extend it beyond the RFC2396
definition. Let's use object or node or something.]

> 
> > > I guess the real problem comes if you then want to introduce (and define
> > > semantics for) some function that operates in the domain of discourse to
> > > map a string to some proposition.
> >
> >Why does that look like a problem?
> 
> Because that seems to invoke the kind of reflexion that Pat asserts is very
> difficult.

I don't understand. Having things like s-expressions in the
domain of discourse in KIF/LISP/ACL2 is straightforward and
powerful. It's done in all the interesting logics I can
think of.

> If N contains only resources then there's no danger of the wffs of RDF, as
> defined, actually appearing in the domain of discourse.

"only resources" doesn't prohibit anything, does it?


-- 
Dan Connolly, W3C http://www.w3.org/People/Connolly/

Received on Friday, 18 May 2001 10:03:04 UTC