AS & S review: Direct model-theoretic semantics

AS & S Section 3 Direct model-theoretic semantics
Review comments

The semantics of minCardinality and maxCardinality should 
in fact be interchanged.

First sentences in Section 3.1:
"The semantics here starts with the notion of a vocabulary, 
which can be thought of as the URI references that are of 
interest in an OWL ontology. 
It is, however, not necessary that a vocabulary consist only 
of the URI references in an OWL ontology."
- Here the first sentence is vague and should be more specific.
What does "of interest" mean? Replace by something like: 
   a vocabulary is a set of URI references including those 
   appearing in a given OWL ontology.
- Make the second sentence more specific: what else could it be?

Next sentence: there should be the word   and 
between owl:Thing and owl:Nothing

The second line about Individual(...) in the table of 
Section 3.2 requires a subscript 1 with c in EC(c).

In the same table: the two lines on oneOf could use explanation:
the i's are individual ids, the v's are data values.
Without such explanation, it is unclear why there are two
lines for oneOf.

First sentence in Section 3:
replace "the abstract syntax" by the OWL/DL abstract syntax
(to use the recently introduced improvement to terminology)
and mention that OWL Lite is not dealt with separately.
(Instead of such a sentence only in Section 4, this could
be stated here for both Sections 3 and 4.)

Definition of abstract OWL interpretation:
Jan Wielemaker and Guus mentioned to me that they needed to recall the
2^X notation.  In fact, it is preferable to use the notation P(X) 
for power set: this is more mnemonic, more 
widely used in mathematical theories, and does not need the 
use of ^ to simulate superscripts.
Suggestion: use notation P(X) (with P italics), and mention briefly 
what power set means.

Section 3.2: table
This table is called "Description Interpretation table".
However, the last five entries do not deal with descriptions
but with "fact fragments".

The table in Section 3.2 uses single arrows for implication.
The standard use of arrow is in function notation, also appearing
in this section.  I suggest to move for implication to double
arrows: =>, a more standard notation anyway.

Near the end of the section there is the sentence:
"An Abstract OWL interpretation, I, satisfies an OWL ontology, O, 
iff I satisfies each axiom and fact in the imports closure of O."
Suggestion to add the following sentence to clarify a point that
is left implicit in the entire section:
   This implies that the vocabulary V of the interpretation includes 
   all the URI references included in the imports closure of O.

An abstract OWL ontology should in my view not have a capital
first A in the word abstract (as is done often).