- 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