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Changes to make S&AS consistent with RDF Semantics document

From: <herman.ter.horst@philips.com>
Date: Fri, 28 Nov 2003 15:43:28 +0100
To: horrocks@cs.man.ac.uk
Cc: www-webont-wg@w3.org
Message-ID: <OF0C642591.291B217F-ONC1256DEC.004592B4-C1256DEC.0050F066@diamond.philips.com>

As was discussed in the last telecon, here is an
overview of changes in S&AS required in view
of changes in the RDF Semantics document.

I only consider the main text, Sections 1 to 5.
Many of the changes I describe below propagate into the proof


Section 5.2, second paragraph.

The changes needed in this paragraph can be summarized as follows:
-delete parenthetical sentences referring to RDF Core's last call
-a vocabulary also includes literals, even plain literals
-not all plain literals are needed in LV
(the assumption that all plain literals are in LV led to
horrible errors and complications in the RDFS Herbrand construction 
and the proof of the RDFS entailment lemma; analogously this 
generalization will simplify formal considerations with OWL
-instead of a "datatype theory T", the RDF Semantics speaks
of a "datatype map D".  This requires many textual changes in S&AS,
which also solve the confusion in S&AS with the mapping to RDF 
graphs, which is also called T.
-LI maps to RI and not to LVI.  This is needed, for example, for
ill-typed XML literals, and also for other ill-typed literals.
-The current text of S&AS gives RDF Core's last call definition of 
the function CEXTI, which has been made more explicit.

Instead of describing the needed corrections more precisely,
it takes less effort to suggest possible new text for this 
paragraph, keeping the current words as they are as much as

"From the RDF Semantics [RDF MT], for V a set of URI references
and literals containing the RDF and RDFS vocabulary and D a datatype
map, a D-interpretation of V is a tuple I=<RI,PI,EXTI,SI,LI,LVI>.
RI is the domain of discourse or universe, i.e., a nonempty set that 
contains the denotations of URI references and literals in V. 
PI is a subset of RI, the properties of I. 
EXTI is used to give meaning to properties, and is a mapping from 
PI to P(RI x RI).  SI is a mapping that takes each URI reference 
in V to its denotation in RI.  LI is a mapping
that takes each typed literal in V to its denotation in RI.
LV is a subset of IR that contains at least all plain literals in V.
The set of classes CI is defined as 
CI = { x in RI | <x,SI(rdfs:Class)> in EXTI(SI(rdf:type)) }
and the mapping CEXTI from CI to P(RI) is defined by
CEXTI(c) = {x in RI | <x,c> in EXTI(SI(rdf:type))} for c in CI.
D-interpretations must meet several other conditions, as detailed
in the RDF semantics.  For example, EXTI(SI(rdfs:subClassOf))
must be a transitive relation and the class extension of all
datatypes must be subsets of LVI. "

Other changes, in the next definition:
- replace "let T be a datatype theory..." by
  "let D be a datatype map..."
- in the same definition, the 5-tuple should be made a 6-tuple
that also includes LVI
- in the same definition, D-interpretation instead of 

- 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

Several corrections in order to make the details of 
this section parallel/consistent with those in Section 5.
Below I suggest additions in the text with /.../:

-first sentence: "...the vocabulary must include all the URI
references /and literals/  in that ontology ... but can
include other URI references /and literals/ as well."

-Definition: "An OWL vocabulary V consists of /a set of
literals L/ and seven sets of URI references: ..."
(It seems that the letter L is still free.)

-again: replace datatype theory T with datatype map D
(the definition given here matches exactly with the
RDF Semantics document).

-Definition: Let D be a datatype map.  An abstract
OWL interpreation w.r.t. T with vocabulary L, VC, etc.

-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 that only plain literals in 
V (and L) are contained in LV.

-"L:TL->LV, where TL is the set of typed literals /in L/"
(As a side-effect advantage of this correction, the set
TL doesn't fall out of the air anymore.)

-"S is extended to plain literals /in L/ by (essentially)
 mapping them onto themselves..."

-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, 

Other remark about Section 3.1:
There are now two definitions of the function S, one with
domain VI and the other with domain VC union etc.
It is confusing that these domains are not explicitly 
assumed to be disjoint, although I can see what the 
intention behind this recently made correction is.
It seems better to handle this intention as follows:
Define S just once, with domain VI union VC union ...
and add the assumption S(VI) subsetof O.


Section 3.4

-datatype map D instead of datatype theory T.
-add L


Section 2.2, abstract syntax:
-The text uses the correct word "plain literal", but the
productions speak (just twice) of "untypedLiteral", which should 
be replaced by "plainLiteral"

-Section 2.1 speaks of "other built-in RDF Schema datatypes which
are problematic for OWL", which should be XML Schema datatypes.

-Section 2.1 speaks of Section 3.4 of RDF Semantics, which 
does not exist.  It should be Section 5.1.


Section 4:
-there are two references to "RDF/XML graphs", which should be
"RDF graphs".
(The references to RDF/XML documents are correct, of course.)


Section 2.3 "as has been made evident in several discussions
in the WG".
Shouldn't this very context-dependent reference, to WebOnt, 
be removed from the document?


-typo: individiual-valued

-Section 2.1: sentence "The class with ... individuals" does not
end with a period.


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


When I compiled this list, I noted the need for a small correction
to the RDF Semantics document, which I sent to rdf-comments [1].

Herman ter Horst

[1] http://lists.w3.org/Archives/Public/www-rdf-comments/2003OctDec/0212.html
Received on Friday, 28 November 2003 09:44:09 GMT

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