Re: The Mel99 semantics for RDF

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?

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.

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.


[...]
> > >An interpretation is a model for a
> > >set of formulas if it satisfies all the formulas.
> >
> > The definition of model that I have is more strict here:
> >
> > defn:  A formula F is true for I iff every assignment A of N to variables
> > satisfies F
>
>Er... that's for universally quantified variables, no?
>No such thing in RDF 1.0.

Oh yes, I missed that.


> > >Does that answer the sorts of questions
> > >that a model-theoretic semantics is supposed
> > >to answer?
> >
> > It seems to tell us that for every valid interpretation of RDF, for each
> > statement there exists a unique resource with certain properties.  It don't
> > think it says anything about how statements about this resource relate to
> > the corresponding statement.
>
>Er... right; would you expect it to?

No... I was just trying to pose some questions to test your meta-question.

> >  Question: If we apply model operators to this
> > resource, do we need something outside the semantics of the model operator
> > to tell us that it applies to the corresponding statement?
>
>I don't know what a model operator is.

Neither do I.  I think I meant "modal".




> > 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.  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?

> > (e.g. Rf( p, s, o, r ) being TRUE if r is a reification of (p,s,o) in S.)
>
>No, that doesn't seem right.

I'm trying to capture the above.

> > >(of course, N may contain some strings and URIs and such,
> > >but that's beside the point, right?)
> >
> > 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.

> > 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.

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

...

(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.)

#g


------------
Graham Klyne
(GK@ACM.ORG)

Received on Friday, 18 May 2001 08:54:40 UTC