- From: Graham Klyne <GK@ninebynine.org>
- Date: Wed, 07 Nov 2001 18:48:13 +0000
- To: Dan Connolly <connolly@w3.org>
- Cc: www-rdf-comments@w3.org
At 09:10 AM 11/7/01 -0600, Dan Connolly wrote: >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. Ah, that changes everything, I think... > > >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 > > > }. ... but :x rdfs:subClassOf :y . implies that :x and :y are *classes*, which is not entailed by: rdfs:Set rdf:type rdfs:Class . :x rdf:type rdfs:Set . :y rdf:type rdfs:Set . Looking at this, I think you probably *did* mean: rdfs:Set rdfs:subClassOf rdfs:Class . > > > > Rather than trying to define this broad notion of equivalence, > >it's actually identity. Which is, I think, about as broad a notion of equivalence as you can get. (I think of equivalence as yielding the same truth under certain usage; identity would yield the same truth values under all usages.) >[...] > > 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 OK. I felt had to try the challenge, though even as I wrote it I didn't feel I could make it stick. #g ------------ Graham Klyne GK@NineByNine.org
Received on Wednesday, 7 November 2001 16:12:05 UTC