RE: Annotations in 1.0-DL and 1.1-DL

Peter F. Patel-Schneider wrote:

>> >EC turns Individual constructs into sets, possibly empty.  
>Individual
>> >constructs with a name are singleton sets if the denotation 
>of the name
>> >satisfies the conditions, empty otherwise.
>> 
>> Ok. Thanks!
>> 
>> >Individual constructs without names can have larger cardinality.
>> 
>> Hm, this is not clear to me. How can there be larger cardinalities?
>> Shouldn't individual constructs, either named or not, only 
>denote singletons
>> at max?
>
>Whether they should or not is not the issue.  In the OWL 1 DL semantics
>they just do, as shown by
>
>EC(Individual(annotation(p1 o1) ... annotation(pk ok)
>              type(c1) ... type(cm) pv1 ... pvn)) =
>	EC(annotation(p1 o1)) intersect .... intersect 
>EC(annotation(pk ok))
> 	intersect EC(c1) interset ... intersect EC(cm) 
>	intersect EC(pv1) intersect ... intersect EC(pvn)

Ok, I think I finally get it:

  EC(Individual(C1 ... Cn)) = EC(C1) ^ ... ^ EC(Cn)

And if the individual is named by "i", then there is a singleton set "{S(i)}" as part of the whole intersection.

>> Further, shouldn't the "Conditions on interpretations" table 
>entry above
>> provide additional assertions of the form:
>> 
>>   S(i) in EC(annotation(p1 o1)) ... S(i) in EC(annotation(pk ok))
>
>If there is no name for the individual, then this doesn't make sense.
>If there is a name, then this condition is carried by the 
>	{S(i)} intersect
>bit for named individuals.

Ok.

>> in the same way as these assertions exist for classes:
>> 
>> >    Conditions on interpretations:
>> >    ------------------------------
>> >  --> S(c) in EC(annotation(p1 o1)) ... S(c) in 
>EC(annotation(pk ok))
>> >      EC(c) subset EC(descr1) ^ ... ^ EC(descrn)
>
>> At least under the condition that EC(Individual(i ...)) is non-empty?
>
>Note that {S(i)} is a superset of EC(Individual(i ...), 
>Aso if 
>EC(Individual(i ...)) is non-empty then S(i) is an element of
>EC(Individual(i ...)).

Yes. 

Thanks,
Michael

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
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