Hi Michael,

Hmmm. When an owl user talks about individual, he/she probably means
those x in his/her ontology
such that x type owl:Thing holds. Here IR is about the interpreted
domain and we call elements of IR individuals.
Isn't it a bit confusing?


Under the OWL 2 RDF-Based Semantics, just as for the original version,
the term "individual" refers to the elements of the domain of an 
OWL 2 Full interpretation. In this way the term is used several times
in the Introduction section, as well as in Section 4. There is no other 
meaning of the term "individual" as far as the OWL 2 RDF-Based Semantics 
is concerned.
 
Concerning "owl:Thing" and "IR": owl:Thing actually represents IR aka 
the whole domain:

  ICEXT(I(owl:Thing)) = IR .

This probably is not a big deal either way. To draw an analogy, I cut & paste the following from Direct semantics. If the word "element" is replaced with "individual", it reads a bit strange.

⋅ ^I is the individual interpretation function that assigns to each individual a ∈ V_I an element (a)^I ∈ Δ_I.

I don't quite understand it. The same kind of argument applies to the
pair of owl:complementOf and owl:disjointWith, right?
    


No. Table 3 does /not/ specify the /exact/ property extension
for these two properties, but only sais that their property extensions
are /subsets/ of IC x IC. This is much less specific than in the case
of owl:topObjectProperty, which sais "= IR x IR". The subset relationship
can actually be expressed by two axiomatic triples with rdfs:domain and 
rdfs:range, the "=" relationship cannot.

I see it now ;) Thanks,

Zhe