- From: Dan Connolly <connolly@w3.org>
- Date: Wed, 07 Nov 2001 09:10:35 -0600
- To: Graham Klyne <GK@ninebynine.org>
- CC: www-rdf-comments@w3.org
Graham Klyne wrote:
>
> At 04:02 AM 11/6/01 -0600, Dan Connolly wrote:
> >But I would like to be able to say that
> >X and Y are sets, which allows you to conclude,
> >from the fact that their extensions/membership
> >are the same that they are identical.
>
> So far, OK.
>
> >So I propose
> > rdfs:Set rdfs:subClassOf rdfs:Class.
>
> I'm deeply suspicious of this. It feels like a "layer violation" -- a
[...]
> So we have the denotation of a node with type rdfs:Set is some value x
> such that ICEXT(x) are the members of the set.
oops; yes, I meant
rdfs:Set rdf:type rdfs:Class.
> >where
> > this log:forAll :x, :y.
> > { :x a rdfs:Set.
> > :y a rdfs:Set.
> > :x rdfs:subClassOf :y.
> > :y rdfs:subClassOf :x.
> > } log:implies {
> > :x ont:equivalentTo :y
> > }.
>
> Rather than trying to define this broad notion of equivalence,
it's actually identity.
[...]
> My intuition about a set as opposed to a class is that the set simply is
> the denotation of a node, not "indirected" via ICEXT like a class.
Yes, that's more intuitive, but what I'm proposing is equivalent,
and it uses the existing model theory without mucking with it.
> And a parting shot: the construction of classes allows a class value to be
> a member of its own extension. Indeed, we have:
>
> I(rdfs:Class) in ICEXT(I(rdfs:Class))
>
> Your proposal for rdfs:Set retains this structure, and nothing has been
> said to prevent a set value being a member of its own class extension.
Quite... I'd have to give the other axioms of sets, in addition
to extensionality (sets with equal members are equals); from memory:
-- the axiomatic existence of the empty set
-- singletons (I mostly get these for free with rdf:type)
-- pairs
-- union
-- power set
-- well-formedness
--
Dan Connolly, W3C http://www.w3.org/People/Connolly/
Received on Wednesday, 7 November 2001 10:10:20 UTC