# Re: RDF Model Theory Working Draft: Comment

```At 08:35 PM 10/7/01 -0400, Arjun Ray wrote:
>That's the point: there is nothing but assertion to establish their
>equivalence, ...

(In what follows, the version of Model Theory (MT) I am referencing is this:
http://www.w3.org/TR/2001/WD-rdf-mt-20010925/.)

The MT is currently based upon the graph, and the representation of the
graph in triple form per section 0.2 of the MT document.  We don't yet have
a formal definition of the correspondence between triples or RDF syntax and
the graph, but that is still in the works.  Meanwhile, I think the general
intent (vis-a-vis triples) is fairly clear from the MT document, section
0.2, modulo the "isolated node" issue.

...

>  and as matters stand, the "graph-based" syntax *in the
>spec* is a bunch of baloney.

This may be your opinion, but it's not a helpful statement for building
understanding.

> > Thus, assuming the quoted statement above to be exactly true, a
> > graph consisting of the single statement:
> >
> >      My:Subject My:property My:Object .
> >
> > would contain three nodes and one arc thus:
> >
> >      [My:Subject] --My:property--> [My:Object]
> >
> >      [My:property]
>
>Actually, no.  The single statement is
>
>   A:Triple : My:Subject My:property My:Object .

I disagree.  Where did the label "A:Triple" come from?

>The graph would have three nodes [My:Subject], [My:property] and
>[My:Object] for the terms of the triple;

I'm not sure what you mean by "for" in "for the terms of the triple".  I
would disagree that the three nodes are part of the triple.

>... the issue is representing
>A:Triple, the relation among them.  The relation is positionally
>ordered in the sense that each slot has a distinct informative - I
>want to say "semantic" - role, which more than coincidentally you have
>adumbrated in your choice of labels - in other contexts this kind of
>conflative illustration might get called "persuasive definition" or
>
>One could draw a supernode around these three and label it [A:Triple]
>but that wouldn't be terribly graph-like.  One could draw an arc
>between the node for the first slot of the triple and the node for the
>third slot of the triple - I am being long-winded deliberately in
>order to avoid implicit conflations - and then draw an arrow from the
>node for the second slot of the triple to that arc; while this
>wouldn't be terribly graph-like either, it would suggest that the
>"slot role" of each node has some bearing on the arc(s) we should be
>drawing for the triple that grouped the slot-correspondent nodes to
>begin with.  Thus, one could have a fourth node for [A:Triple] and
>hook it up with the nodes for the slots with three separate arcs, the
>need to label which would rather naturally induce the use of symbols
>such as "Subject", "Object" and "property":)  Now, this would be
>graph-like; I'm not convinced that it would damage the Model Theoretic
>formulation in the Working Draft; but it would put paid to some of the
>pretty pictures in the RDFMS spec.  A minor embarrasment.

You seem to describe here many things that *could* be done, but as far as I
can tell this is not close to what the model theory document has described.

> > In this case, the [My:property] *node* has no arcs to or from.
> > The model theory assigns truth values to a graph purely in terms
> > of the arcs,
>
>Actually, no.  It assigns truth values according to the IEXT mapping
>(from a subset of resources into a relational extension), and all of
>this is conducted using the lexicon of set theory.  The words "node"
>and "arc" are not used at all in the formal definition of I, the
>interpretation.

Yes, the truth of an asserted triple is, as you say, defined in terms of
the IEXT of the property resource, and the resources corresponding to
subject and object nodes.

The property resource is a member of IP, a subset of IR corresponding to
properties.  These property resources are denoted by a URI in V, which is
mapped by IS to IR (section 1.3).

The triple is a triple of URIs, whose correspondence to a graph is
described in section 0.2, 4th para.

>   What is unclear in the draft, however, is the
>provenance of the 'E' in I(E)

I agree it's not especially clear.  I read E is a syntactic element of the
triple-based representation of a graph;  i.e. a literal, URI, triple or
collection of triples.

>  - the denotation rules canvass literals,
>urirefs *and*, lo and behold, triples analysed in terms of all three
>parts [cf the alternative graph I outlined.] Nowhere is it said (and
>nowhere does it seem necessary to say) that each element in IEXT "is"
>or "maps" to an "arc", let alone a single one.  In fact, I'd say the
>closest picture would be the arrow-labelled quasi-graph I described
>earlier.

That may or may not be a valid picture -- I cannot say.  The model theory
document does create a formal framework for RDF that makes sense to me.  I
have tried to explain my understanding, but maybe my powers of explanation
are not up to the task here.

However, by keeping a clear distinction between:

- the graph syntax of nodes and arcs, labelled with URIrefs and literals,

- the serial syntax of triples of URIrefs and literals, each triple
corresponding to an arc of the graph, and

- the interpretation of a graph as a truth value based on literal values
(interpretations of literals), resources and resource extensions
(interpretations of URIrefs),

I find the model theory to clarify many of the aspects of RDFM&S that were
previously difficult to decide.

> > so the existence of an isolated node has no effect on the graph's
> > meaning;  thus, its presence in the graph may be regarded as moot.
>
>I'm sorry, but this smacks of factitious retrofitting.  Why, for
>instance, didn't the RDFMS spec make this face-saving point, given
>that Walton's comments were posted long before the spec reached Rec
>status?

In a sense, the model theory is unashamedly retrofitting -- trying to make
formal sense of what is unclear in the RDFM&S.  I cannot answer your
question above, and am disinclined to try.

>And what happens when the node ins't "isolated" (for a set of more
>than one triple?  Where did the arc labels come from?)

Do you mean something like this?:

My:Subject   My:property1 My:Object1 .
My:property1 My:property2 My:Object2 .

I think it would contain five nodes and two arcs thus:

[My:Subject]  --My:property1--> [My:Object1]

[My:propery1] --My:property2--> [My:Object2]

[My:property2]

(Also note that the meaning of the graph as a whole is defined as a truth
value that is dependent only on the interpretations of asserted triples
within the graph (section 1.3).)

#g

------------
Graham Klyne
GK@NineByNine.org
```

Received on Monday, 8 October 2001 05:34:13 UTC