SUO: RE: RE: RE: First piece of 4D ontology
Dear Ian,
> -----Original Message-----
> From: Ian Niles [mailto:iniles@teknowledge.com]
> Sent: 09 March 2001 17:51
> To: Standard-Upper-Ontology (E-mail)
> Subject: SUO: RE: RE: First piece of 4D ontology
>
>
>
> Matthew,
>
> See my comment below. Edits for brevity.
>
> -Ian
>
> > > > ;
> > > > ; #2:
> > > > ;
> > > > ; for all X, if there exists a Y and Y is a member of X,
> > > then X is a
> > > > ; member of collection.
> > > > ;
> > > > ; i.e. any thing that has a member is a collection.
> > > > ;
> > > > (forall ?x
> > > > (=> (exists ?y
> > > > (?x ?y)
> > > > )
> > > > (collection ?x)
> > > > )
> > > > )
> > > > ; Note: This (?x ?y) is not valid SUO-KIF today, but I
> > > understand it
> > > > ; will be in the near future.
> > >
> > >
> > > I'm wondering what you mean by "collection" in your axiom. I
> > > thought we
> > > were using this term to denote things like wolf packs,
> > > football teams, etc.,
> > > which are set-like, in that they have members, but, unlike
> > > sets, they have a
> > > spatio-temporal location. However, if this is what you
> > mean, then you
> > > exclude sets and classes, which have members but are not
> > > collections in the
> > > sense just explained.
> >
> > MW: In this context the string "collection" is a label that
> > means precisely what the axioms say it means, not more and
> > not less. So do sets and classes meet the axioms as stated?
> > I.e. do they have members? If so then they are also collections.
>
> You are right, of course. But it does create some degree of
> confusion, you
> must admit, to axiomatize your formal notion of "collection"
> in such a way
> that it means set or class or collection, as we appear to be
> using these
> three terms on the SUO mailing list.
>
MW: Well I had in mind that collection would be unrestricted (e.g.
collections could be members of themselves) classes would be collections to
which we attach significance, and sets would be those iteratively
constructed things that seem to be necessary for ZF set theory. But that
comes later in the story.
Regards
Matthew
============================================================
Matthew West
Operations & Asset Management - Shell Services International
Shell Visiting Professor, The Keyworth Institute
H3229, Shell Centre, London, SE1 7NA, UK.
Tel: +44 207 934 4490 Fax: 7929 Mobile: +44 7796 336538
http://www.shellservices.com/
http://www.keyworth.leeds.ac.uk/
http://www.matthew-west.org.uk/
============================================================