Re: Annotations in 1.0-DL and 1.1-DL

From: "Michael Schneider" <schneid@fzi.de>
Subject: RE: Annotations in 1.0-DL and 1.1-DL
Date: Tue, 8 Apr 2008 10:32:51 +0200

> Peter F. Patel-Schneider answered to me:

[...]

> >> But here I am confused: The function "EC(.)" isn't defined for individuals
> >> at all. And I also am not sure whether I understand what the intended
> >> semantics is here.
> >
> >From [1, 3.2]
> >
> >	EC is extended to the syntactic constructs of descriptions, data
> >	ranges, individuals, values, and annotations as in the EC
> >	Extension Table.
> >
> >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)

> 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.

> 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 ...), so if 
EC(Individual(i ...)) is non-empty then S(i) is an element of
EC(Individual(i ...)).


> Cheers,
> Michael

peter

Received on Tuesday, 8 April 2008 10:14:11 UTC