Re: continuing technical issues in the RDF Semantics document

>The current version of the RDF Semantics document, titled RDF Semantics
>Editors Draft August 21, has continuing technical issues that I discovered
>in a quick, incomplete pass this morning.
>
>
>The document does not define ``character string'' or ``language tag''.
>These need precise definitions as the definition of simple interpretations
depends on them.

Section 1.2:
"Throughout this document we use the term 'character string' or 
'string' to refer to a sequence of Unicode characters in Normal Form 
C, c.f. section 6.5 in [RDF-CONCEPTS]. "

Every occurrence of the term  'language tag' is linked to the 
definition in Concepts, which refers to RFC 3066; I have added an 
explicit piece of text to indicate this link in the visible text.

>
>In the examples (in Section 1.4), the pictures do not correspond to the
>text, as they have Thing 1 in the domain whereas the text has 1 in the
>domain.

This has been true for some time. I found that that the use of the 
bald numeral in the diagram caused some confusion. I believe the 
example is sufficiently clear.

>The first picture also has the incorrect claim that ``The universe
>has just two things in it.''

That is true, and I will modify the picture to remove that, which was 
left over from an earlier version. This will take a while.

>
>The set of rdf-interpretations has changed significantly.  An
>rdf-interpretation need not have domain elements corresponding to every
>possible XML literal.  This does not affect RDF, but may be a problem for
>languages built on top of RDF.

Well, it may be, but then the earlier version may also have been a 
problem. Since it would be possible to impose the stronger condition 
as a semantic extension without affecting any RDF or RDFS 
entailments, this version seems less likely to give rise to any 
problems.

>There are conditions imposed on the non-core RDF vocabulary by
>rdf-interpretations, counter to several claims in the document.

The text refers to 'significant' formal constraints. I do not believe 
that this is likely to be misunderstood.

>The redundancy of ``all but one of the RDF axiomatic triples'' cannot be
>derived from ``the RDFS axiomatic triples and the smenatic conditions on
>rdfs:domain and rdfs:range''.  It also requires the semantic condition for
>ICEXT to make these derivations.

The text was written under the assumption that we were referring to 
the RDFS semantic condition in any case, and the fact that ICEXT can 
be regarded as defined was noted earlier; but I have amended the text 
to refer to "the semantic conditions on ICEXT, ..."

>As well, the semantic conditions for
>rdfs:range are not needed.

True; there is a further redundancy there also. Since this is a 
parenthetical remark, however, having a further parenthetical remark 
to it seems out of place.

>The definition of the Herbrand interpretation of a graph has all
>well-formed XML literals in LV

No, it only requires LV to contain all well-formed XML literals *in 
V*, where V is the vocabulary of the interpretation.

>, which is permissable, but incorrectly
>states that these are required to be in LV, and makes Herbrand
>interpretations non-minimal.

I do not think this is correct. The use of the terminology 'minimal' 
is only in the text, and always surrounded by scare quotes. The 
formal proof uses the << relationship, which need not be asymmetric.

>  It is not the case that a
>Herbrand interpretations is a simple interpretation - consider the Herbrand
>interpretation of the empty graph.

Good point. There is no need to require that IP be nonempty in a 
simple interpretation, and I have removed that stipulation. This does 
not affect RDF or RDFS interpretations, of course. I have also add a 
short discussion of the (trivial) entailment properties of the empty 
graph, and added the nonemptyness condition on graphs defining a 
Herbrand interpretation.

>As well, Herbrand interpretations abide
>by part of the RDF meaning of rdf:type, which also makes them non-minimal.

They are in the sense defined, ie that they make the smallest number 
of triples true. Adding items to IP makes no difference to this, and 
is convenient for the RDF entailment lemma.

An alternative would be to re-define the interpretation H' described 
in the proof of the RDF entailment lemma so that it satisfied this 
condition, and then describe a forgetful projection from H' to H 
which ignores items in IP<H'> which do not occur in a property 
position, and observe that their omission from IP does not affect the 
truths of any triples.  I have made this change, since the risk of 
misunderstanding the IP condition is rather high, and it is more 
elegant in any case.

>The Herbrand lemma is false as Herbrand interpretations are non-minimal.

I believe it is true (with or without the IP condition). Can you give 
a counterexample?

>The problems with Herbrand interpretations make the proof othe RDF
>entailment lemma and the RDFS entailment lemma suspect.
>
>The proof of the RDF entailment lemma is suspect in other ways, as the
>rdf-interpretation constructed (H') appears to have both XML values and
>blank nodes in the class extension of rdf:XMLLiteral.

That was not the intention: H' is an rdf-interpretation in which XML 
literals denote XML literal values. The 'corresponding' Herbrand 
interpretation H does have blank nodes which are of type 
rdf:XMLLiteral, but the RDF entailment rules ensure that these blank 
nodes play the same role in H that their corresponding literals do in 
H'.

>The details of XML
>literals are sufficiently arcane that I cannot determine whether this is
>permissable.

Think of the RDF entailment rules as having the pattern (forall 
literal (exists a thing...)) and then skolemize. The resulting skolem 
terms, which could be written as rdf2("well-formed-XML"), are the 
'markers' in the Herbrand interpretation H for the actual XML literal 
values in the RDF interpretation H'.  The rules guarantee that H and 
H' make the same triples true in an closure, so that H' << H. Since H 
is minimal, so is H'.

>On a minor note, the definition of proper instance means that
>	<ex:a> <ex:b> "a" .
>is not a proper instance of
>	<ex:a> <ex:b> _:xx .
>This affects the definition of lean graphs, and reduces the scope of the
>anonymity lemma.

Whoops. I have changed the definition to cover plain literals.

Pat
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Received on Wednesday, 27 August 2003 13:11:55 UTC