# Re: New RDF model theory (well, damn nearly)

From: <jos.deroo.jd@belgium.agfa.com>
Date: Tue, 21 Aug 2001 12:34:47 +0100

Message-Id: <OFB8D9E63D.49CF1E30-ON41256AAF.00328858@bayer-ag.com>

[...]
> The model theory assigns interpretations directly to the graph, which is
> taken as being the primary RDF syntax, in the sense that two RDF documents,
> in whatever lexical form, are syntactically equivalent if and only if they
> map to the same RDF graph. We will refer to this as the 'graph syntax' to
> avoid ambiguity, since the bare term 'syntax' is often assumed to refer to
> a lexicalization.
>
> A graph which is like an RDF graph except that it violates the last condition,
> ie has two or more nodes with the same label, will be called an untidy graph.

that 'last condition' seems to refer to a part that I can't find
(but it is repeated and so it is clear what is meant here).

[...]
> <comment> ( An earlier version of the model theory included anonymous nodes
> in the vocabulary of a set of triples, but it seems clearer to  omit them
> when considering graphs. ) </comment>

fully agreed with that, after all anonymous nodes are like 'blank' node tokens
(as you write later on)

[...]
> Anonymity lemma 1. Suppose E' is like E except that at least one anonymous
> node in E is labelled with a URI in E'. Then E does not entail E'.  ***

We tested that (with Euler) and (after correcting a NullPointerException)
it seems to be ok
Suppose E is pat1.nt
_:x <b> <c>.
<d> <e> _:y.
and E' pat2.nt
<a> <b> <c>.
<d> <e> _:y.
then we get
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
@@ assert <d> <e> [].
@@ assert [] <b> <c>.
[1]CALL: <a> <b> <c>.
[1]FAIL: <a> <b> <c>.
# Generated with http://www.agfa.com/w3c/euler/#27.051 on Tue Aug 21 12:21:58 CEST 2001
# for query file:/n3/pat2.nt
# given [file:/n3/pat1.nt]

# No proof found for file:/n3/pat2.nt in 1 steps (122 steps/sec)
````````````````````````````````````````````````````````````````
so E does not entail E' (but E' does entail E)

[...]
> <comment> The subsets referred to in subPropertyOf are sets of pairs. </comment>
> <comment> The M&S seems to imply that the proper condition on subClass and
> subProperty is that the extensions are *proper* subsets, ie the identity case
> is disallowed, and hence 'subclass loops' are illegal. If we decide to change
> this to allow  'subclass loops', as assumed by DAML+OIL, then "proper" should
> be deleted from these conditions. </comment>

I would go for "to allow  'subclass loops', as assumed by DAML+OIL"

--
Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/
Received on Tuesday, 21 August 2001 06:35:22 UTC

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