Re: SUO: RE: Axiom and Intentionality vs Extentionality
Dear David, dear Ian,
Pardon my confusion, maybe I'm too unfamiliar with the SUMO, but I find
puzzling your interpretations of this axiom.
To be consistent with the claim that "collections have position in time"
(assuming I'm not mistaken in understanding that it means that at
different time, members may not be the same) shouldn't an axiom stating
the necessary non emptiness of a collection be alike the following:
(=>
(and
(instance ?COLL Collection)
(instance ?TIME TimePosition))
(exists
(?OBJ)
(holdsDuring ?TIME (member ?OBJ ?COLL))))?
That is, at any time a collection has at least one member?
But, one way or another, I confess that it seems odd to me to require of
a collection that it be non empty. If a collection really preserves its
identity under alteration of membership, i.e., "members can be added and
subtracted without thereby changing the identity of the &%Collection".
Does that mean that collections are intermittent beings?
For instance, let t1, t2, and t3 be successive discrete time intervals
such that, for n and p non null, at t1, a collection C has n members, at
t2 it has zero members and at t3 it has p members. Is that your view
that the SUMO ought not be able to describe the emptiness of C during
t2. I.e., C doesn't exist during t2 and C merely exists by
intermittance. However it doesn't seem that any principle reason should
prevent us to continue referring to C during t2 (as the 'same'
collection as it is during t1 or t2), if only to specify that a given
object is _not_ an instance of C.
Am I misconstruing something here? Does that make any sense?
yours,
Pierre
David Whitten wrote:
> > > I was looking at the SUMO browser at:
> > >
> > > http://128.136.11.33:8080/rsigma/SKB.jsp?req=SA&skb=Merge&id=260
> > >
> > > where the axiom:
> > > Formula
> > > (=>
> > > (instance ?COLL Collection)
> > >
> > > (exists
> > > (?OBJ)
> > > (member ?OBJ ?COLL) ) )
> > >
> > >
> > >
> > > Now, as I read this, if a collection exists, it MUST have a member.
...
> > > Now, it seems to me that this axiom requires a collection to have an
> > > instance.
Ian Niles replied:
> > That's right, and this is as it should be, I think, since collections are
> > supposed to be situated in space/time and this wouldn't be possible for a
> > collection that had no members.
> >
--
Pierre Grenon, Cycorp, Inc.
Tel: 512 514 2982 - Fax: 512 342 4040
mailto:pierre@cyc.com http://www.cyc.com