Re: semantics document moved

Review comments semantics document draft (version of 4 november).

This is not yet a complete review.  I did not yet go through the details
of the proofs in the appendix and of the (new version of the)
mapping from abstract syntax to RDF in Section 4.

- Frank's summary of the Bristol consensus on semantics
asks for a characterization of the situation that fast and large 
entailment coincide [1]. This is not given in the document,
and is, as yet, unknown.  I believe that anything that becomes
known in this direction is very valuable.  What can become known 
before the end of the WG could be worked out in a new, informative 
appendix.

- The document gives three definitions of OWL entailment (abstract,
DL en Full) but does not yet give a normative definition of OWL 
entailment.
The consensus summary says that in case of disagreement between 
fast and large entailment, fast entailment is normative [1].
The quickest implementation of this would be to add a short section
5.5: OWL entailment (Normative), with more or less the following
content: if K,C
are triples KBs such that K+C is the translation of some 
abstract syntax OWL KB with separated vocabulary, then K (normative)
OWL entails C if K OWL DL entails C. If not, then K (normative) 
OWL entails C if K OWL Full entails C.

However, this definition involves abstract syntax, whereas [1] asks about
"triple-based characterizations". Characterizations of the following
are unknown:
  What is an OWL Full KB in triple form (i.e., what is an "OWL Full graph" 
as a
special kind of RDF graph)?
  What is an OWL DL KB in triple form (i.e., what is an "OWL DL graph")?
  What is OWL entailment (any form) in terms of triples?
Again, anything that becomes known on these questions would be
valuable and could be worked out in a new, informative appendix.

As to the last question, note that the RDF model theory document contains 
a 
complete syntactic characterization of what is rdfs entailment.
Pat stated in Bristol (in response to a question I asked after Frank's
presentation) that something like this is much too complicated to do now 
for OWL.  If a characterization is too much to ask, then I believe that
a sequence of simple sufficient conditions for entailment (i.e., simple
inference rules, formally stated, with proofs of validity) could 
form a useful informative addition to the document in order to 
familiarize people with the various kinds of OWL entailment.


The approach in Chapter 5 is claimed to be an extension of 
the RDF model theory. The next three remarks intend to make this claim 
more completely true.

- 4: Speak here and elsewhere of a mapping to RDF graphs, which are sets
of triples (RDF graphs abstract from any ordering/XML serialization 
aspects).
N triples are only a notation for the triples.

- 5.3.1: The document speaks of interpretations of vocabularies as well as
of interpretations of triples. The RDF MT speaks of interpretations of
vocabularies and of interpretations that satisfy triples/KBs.
This language use should also be done here consistently. 
(Note that the proofs in Appendix A do this already often.)
In fact, the definition of satisfaction and entailment can then 
simply be inherited from the general definition patterns described
in the RDF MT document.
Or: An OWL DL interpretation satisfies K if it is an interpretation of 
a vocabulary V' that is a superset of the vocabulary of K and
if it satisfies K as an rdfs interpretation.
(Note that implicitly, Section 5.2, OWL interpretations, defines
a form of weak OWL entailment.)

- imports: The RDF MT document does not speak of imports, but defines
the merge of RDF graphs (this definition might compactly be recalled
as the "blank-node-disjoint" union of RDF graphs). 
The RDF MT also defines entailment from a set (i.e. a merge) of RDF graphs 
to an
RDF graph. This can, for example, be applied to the import closure
of the RDF file defining an RDF graph.  I am in favor of doing a similar
thing in this semantics document. Aspects of syntactic import can then be 
described
elsewhere, in terms of entailment defined more abstractly in the semantics 
document.
Then, it should be mentioned somewhere that OWL graphs can be merged
to form an OWL graph. On the level of the abstract syntax merging could 
also
be done in a natural way (by concatenating sequences of axioms and facts).

- The abstract does not mention the fast and large versions of entailment.
I believe that this should be done. The introduction speaks of "two
formal semantics", where I guess three should be mentioned.

- Section 2.1: A small simplification is possible: use the two rules for
<annotation> also in <directive>, instead of their content.

- 3.1: last sentence: D(d,l) falls out of the air here, should be 
introduced
before the numbered list. (Note that it is introduced much later, at the 
end of 5.1.)

- 3.3: line 7 in the table, right column: the set D is not defined,
I guess that LV should be used here (twice).
line 10 in the same table, left column: SubPropertyOf (p1 p2)
instead of (p1 p1).
line 11 and 12 in the same table, right column: for 1 <= j < k <= n
instead of 1 <= i < j <= n (currently i appears in two ways).

- 5.2: fifth table (RDFS subclasses, subproperties, ....,
as appropriate): second line, right column:
EXTI(x) subsetof EXTI(y) instead of CEXTI(y)

- 2.3.1.3: The definition of functional should be improved, in my view,
if it is included (note that inverse functional, transitive etc. are
not defined).
It now seems that there can be at most one relationship for a pair 
consisting 
of individual and data value. How about: given an individual, there can
be at most one relationship to a data value.

- 5.3.1: second sentence: Recall explicitly what it means that K is a set 
of
triples with vocabulary V (i.e., V is the set of URI references appearing
in K)

- 5.3.2: second paragraph: A separated OWL vocabulary is a set of
URI references <insert: V> with a disjoint partition ...
(This makes it more clear, in my view.)

- 5.3.2: next to last sentence: contains 'whenever' (which means if) where
iff is meant. Replace by: if and only if. (People who have come this far
in the document should be able to digest this.)

- 5.2: some tables further on: instead of card({v:<u,v>...)
I prefer to make it completely explicit with the set from which 
v can be taken:  card({v elementOf ...:<u,v>...)

- Didn't the WG agree on OWL DL and OWL Full without hyphens?

- 5.1.1: third sentence: instead of ,..., I prefer to include the
entire vocabulary list.

- 2: typo: facilities > facilitates

- 2.3.1.2: one extra letter: all values of the property for object<s> 
in the class

- 2.3.2.3: The last sentence does not end with a dot.

- 3.4: last word: allowed instead of llowed.

- 5.3: Make it An OWL/DL ... instead of A OWL/DL ... (this happens more 
often,
use search)


- 3 & 3.4: replace abstract ontologies by abstract syntax ontologies
or ontologies described with the abstract syntax.

- (Why did I make the previous remark? In my view, abstract syntax 
ontologies are 
not completely abstract ontologies. They carry irrelevant ordering 
information.
Section 2.1 rightly states that "an OWL ontology in the abstract syntax
is a sequence of axioms and facts..".
Just as RDF graphs capture the content of sequential RDF files in an 
abstract, set-theoretic way, it could be investigated to capture abstract 
OWL 
ontologies as real sets consisting of axioms and facts which are described 
in 
some combinatorial way.
This remark between brackets is not intended as a proposal to change this
document now before it is going to be published.)


Herman ter Horst
Philips Research


[1] http://lists.w3.org/Archives/Public/www-archive/2002Oct/0022.html