Dear Barry, (01)
See below. (02)
Regards (03)
Matthew West
Reference Data Architecture and Standards Manager
Shell International Petroleum Company Limited
Shell Centre, London SE1 7NA, United Kingdom (04)
Tel: +44 20 7934 4490 Mobile: +44 7796 336538
Email: matthew.west@xxxxxxxxx
http://www.shell.com
http://www.matthew-west.org.uk/ (05)
> Assumption: set is a subtype of type,
>
> Hence: every instance of set is an instance of type,
>
> Hence, in particular {the moon, Matthew West, my left big
> toe} is a type
>
> This is an absurd conclusion. (06)
MW: If we accept your interpretation of type (nothing in Pat's axioms
prevents Cory's interpretation).
>
> Hence the assumption is wrong.
>
> Even the set {all hats} is not a type; rather it is the extension of
> a type (modulo the question of time, which is tricky, here}
>
> And the set {all hats in Cory's closet} is a subset of the
> extension of a type. (07)
MW: Only for 3 Dimensionalists. (08)
> BS
>
> At 07:16 AM 2/4/2006, you wrote:
> >MW,
> >In semantic core I actually came to a "provisional"
> conclusion that set is a
> >subtype of type and that the range of set operations was
> type. I can then
> >talk about all the hats in my closet and many of the typical
> type operations
> >are covered by the set operations. I also have an
> enumerated set whereby
> >the membership is asserted. This is one of those conclusions
> that came based
> >on "this is how all the pieces fit" rather than deep theory
> - and it rather
> >surprised me. I will be interested to see how it works out here.
> >I have NOT assumed all sets (or types) have static
> membership as that would
> >be an orthogonal restriction in the model I have.
> >
> >-Cory
> > > -----Original Message-----
> > > From: ontac-dev-bounces@xxxxxxxxxxxxxx [mailto:ontac-dev-
> > > bounces@xxxxxxxxxxxxxx] On Behalf Of West, Matthew R SIPC-DFD/321
> > > Sent: Saturday, February 04, 2006 6:07 AM
> > > To: ONTAC Taxonomy-Ontology Development Discussion
> > > Subject: RE: [ontac-dev] Representation of attributes
> > >
> > > Dear Chuck,
> > >
> > > > >
> > > > > MW: The key distinction I would tend to make is that a set
> > > > > has extensionality as the basis for identity. That is, if two
> > > > > sets have the same members, then they are the same set.
> > > > >
> > > > > MW: Types on the other hand, are not necessarily expected
> > > > > to be the same if they have the same members.
> > > >
> > > > Yes - all good aspects that I intend to borrow for my
> own evolving
> > > > definitions. Thank you.
> > > >
> > > > I might also interject that what I call Types and what I
> > > > call Classes, are
> > > > in themselves Sets. Every Type is a Set, yet not every Set
> > > > is a Type -
> > > > which agrees with what Barry stated about Types being an
> > > > Extension of Sets.
> > >
> > > MW: The problem saying that every type IS a set (Barry
> actually says
> > > every type HAS a set - at a point in time) is that as a
> type some may
> > > have changing membership, yet sets essentially have
> unchanging membership.
> > >
> > >
> > > Regards
> > >
> > > Matthew West
> > > Reference Data Architecture and Standards Manager
> > > Shell International Petroleum Company Limited
> > > Shell Centre, London SE1 7NA, United Kingdom
> > >
> > > Tel: +44 20 7934 4490 Mobile: +44 7796 336538
> > > Email: matthew.west@xxxxxxxxx
> > > http://www.shell.com
> > > http://www.matthew-west.org.uk/
> > >
> > >
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