SUO: Re: Axiom & Intent/sionality vs Extent/sionality
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Pierre,
Don't be non+ed -- TekTak is a whole nuther language.
It is bound to be confusing to anybody who has ever
taken a math course once in their life. Remember,
"TekTak Standardizes Unto Others" -- it does not
have to care what is already standard to others.
Jon Awbrey
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Pierre Grenon wrote:
>
> 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
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