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Re: Changes to make S&AS consistent with RDF Semantics document

From: <herman.ter.horst@philips.com>
Date: Tue, 2 Dec 2003 12:00:38 +0100
To: horrocks@cs.man.ac.uk
Cc: www-webont-wg@w3.org
Message-ID: <OF964D11A4.19C2E853-ONC1256DEF.005276A8-C1256DF0.003C892A@diamond.philips.com>

Most of the comments I made in [1] are reflected in the
current editors's draft.

Four comments are not yet dealt with:

>- In Section 5.2, it should be said that an OWL interpretation,
>and also an OWL Full interpretation and an OWL DL interpretation,
>are defined with respect to a datatype map D.
>The same is true for OWL Full entailment and OWL DL entailment.
>This is also made explicit in this way for abstract OWL
>interpretations and abstract OWL entailment in Section 3.
>Also, the statement of the correspondence theorem needs to be made
>more explicit in this way.

(Section 3.1: second bulleted condition:)
>-It is now assumed that LV contains each Unicode string
>and each pair of two Unicode strings.
>For the correspondence with Section 5, it would be
>sufficient to assume only that plain literals in
>V (and L) are contained in LV.
On further reflection, it seems that not only the assumption
about plain literals but also the assumption about
typed literals could be weakened.
The condition could be rephrased, for example, as follows:
"LV, the literal values of I, is a subset of R that
contains the values of plain literals in V, and,
for each datatype d in D and well-typed literal
"v"^^d in V, the value L2V(d)(v)."
It seems that this assumption would suffice for
all the normative text in S&AS.
A motivation to make this change is that similar 
unneccesary assumptions in the RDF Semantics led
to many complications and the need for a similar

>-In order to make the definition more strongly parallel
>to the definition of ill-typed literals (and datatype
>clash) in the RDF Semantics document, it seems to be better
>to replace, in the last bulleted condition,
>   R-V(d)
>   R-LV

> ... many of the changes I describe here lead to the need
> for corresponding changes in the proof appendix.

The proof appendix is not yet up to date with the changes


One comment needs to be added to those in [1]:

Both S&AS and RDF Semantics define datatype maps
to be partial maps from URI references to datatypes.
RDF Semantics assumes, in addition, that each datatype
map contains rdf:XMLLiteral.
S&AS assumes, in addition, that each datatype map
contains xsd:string and xsd:integer.

S&AS could be made consistent with RDF Semantics
by correcting the third definition in Section 3.1 
in for example the following way:

"As in RDF, a datatype map D is a partial mapping from
URI references to datatypes that maps rdf:XMLLiteral
to the built-in XML Literal datatype defined in the
RDF Concepts and Abstract Syntax document [RDF Concepts].
In addition, it is assumed that datatype maps
map xsd:string and xsd:integer to the appropriate 
XML Schema datatypes."

A corresponding addition to the first definition in 
Section 5.2 would then be needed.

It should be noted that if XMLLiteral is not added
by default to each datatype map, as in the RDF Semantics,
document, then S&AS seems to be inconsistent.
To see this, consider the following example:

RDF graph G, just two triples
  v p l
  p rdfs:range rdfs:Literal
where l is an ill-typed XML literal.
Since G has no rdfs-interpretations, it has no D-interpretations
for any datatype map D, and also no OWL DL interpretations
for any datatype map D, so G is OWL DL inconsistent.

Abstract syntax ontology O, containing
  Individual(v value(p l))
  DataProperty(p range(rdfs:Literal))
If D is a datatype map that does not contain rdf:XMLLiteral,
then O is consistent.

It is clear that the translation of O with the mapping T of 
S&AS contains the RDF graph G.
This contradicts the corollary to Theorem 1 in Section 5.4
in S&AS, for any datatype map D that does not contain
(I am using here my first comment above, that Theorem 1 etc.
should be read as holding for a certain datatype map.)


[1]  http://lists.w3.org/Archives/Public/www-webont-wg/2003Nov/0132.html
Received on Tuesday, 2 December 2003 06:01:18 UTC

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