Pat,
in computational solid geometry, the primitives are solids, and one of
the basic operations is point classification. We found it useful to classify
points as {inn, onn, outt} rather than just {in, out}. This did away with the
need for "regularized set operators" - a modification of the standard set
operators to avoid hanging surfaces, e.g. where an open set is subtracted from
a closed set. It turns out that the logic of these set operator "is the same
as" that of the Logic of Partial Functions, which was convenient, since we were
experimenting with VDM at the time. (01)
A more complex version of this arose from noting that the floating
point numbers are not a metric space, and the calculation of in/on/out
consequently tends to get a little fuzzy. Since carrying round fuzzy logic
variables adds more complexity than was desirable, this fuzzy boundary could be
quantized back to three values, but with an explicit formulation of how wide
the "onn" was - with the choices being between the widest and the narrowest
boundary. This allowed me to be able to compute whether the intersection points
of three lines were topologically valid (although the points might be incorrect
due to numerical error), and so prove the validity of topological algorithms. (02)
Sean Barker
Bristol, UK (03)
This mail is publicly posted to a distribution list as part of a process of
public discussion, any automatically generated statements to the contrary
non-withstanding. It is the opinion of the author, and does not represent an
official company view. (04)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
> Sent: 20 September 2007 15:44
> To: Peter F Brown
> Cc: [ontolog-forum]
> Subject: Re: [ontolog-forum] entity: nothing
>
>
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> >Content-Type: multipart/alternative;
> > boundary="----_=_NextPart_001_01C7FAFF.A42BF83F"
> >
> >A hole is not the same as a ³nothing² there are two
> separate threads
> >in this discussion: are we not talking about two different
> ³things² (I
> >use the word advisedly and very cautiously)?
> >
>
> Quite. Im really not sure what the 'nothing' term is supposed
> to indicate. Early set theorists wrestled with this concept
> for a while before they came up with the empty set. Perhaps
> 'nothing' is the empty set?
>
> Regarding boundaries, I made a stab at
> ontologizing these (at least the spatial/physical
> kind) a while ago. Things get quite complicated quite
> quickly. For example, if the surface of a solid object is a
> boundary of it, then where exactly is the liquid when that
> surface is wet?
> It seemed necessary to introduce the notion of a 'layer' on
> each side of the boundary.
> Goegraphical boundaries are even more difficult:
> one has to distinguish physical from notional boundaries, for
> example (when the coastline erodes, does the country or the county get
> smaller?)
>
> Pat
>
> >Peter B
> >From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> >[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx]
> >On Behalf Of Deborah MacPherson
> >Sent: 18 September 2007 20:01
> >To: [ontolog-forum]
> >Subject: Re: [ontolog-forum] entity: nothing
> >
> >Hi Paola -
> >
> >The Cage analogy came around to silence being able to be bounded by
> >sound. Carved sculptures take away unwanted material until only the
> >essential parts remain. In museum design certain content is
> not ready
> >to be named but it can be classified, subject areas yet to
> be defined
> >are left as blank, un-labeled placeholders allocating space, hoping
> >future requirements will fit without rearranging everything again.
> >
> >More to your point surely is John's statement "more like a boundary
> >than pure nothingness". So with the stretched metaphors
> above.....What
> >do you think needs to be bounded? What are opposite each
> other inside
> >and outside the boundaries?
> >What could possibly be consistent across a range of ontologies? What
> >existing communication system like OWL, or ___, or ___, or
> ___ is best
> >suited to indicating a boundary? How do you know when you
> encounter a
> >boundary? Simply won't process? How do you "see" the holes
> and can you
> >measure how big or small they are?
> >
> >Deborah
> >On 9/18/07,
> ><mailto:paola.dimaio@xxxxxxxxx>paola.dimaio@xxxxxxxxx
> ><<mailto:paola.dimaio@xxxxxxxxx>paola.dimaio@xxxxxxxxx >
> >wrote:
> >I am not entirely sure that we have not yet answered this, I
> may have
> >missed somethin
> >
> >Following the discussion on holes, the one questrion that I am left
> >with is whether holes are entities as such, or non entities and
> >
> >if so
> >whether they would belong to a ' class of nothing' being
> >proposed/discussed somewhere earlier on this forum
> >
> >It looks to me that they are non entity cause they dont have a mass
> >that can be measured I mean an entity is determined by its
> attributes
> >and properties while the only property of a hole that we can say is
> >'absence of energy'
> >
> >This is an attempt to bring the hole discussion into the focus of
> >current ontological question
> >
> >apologies if this is trivial
> >
> >
> >--
> >Paola Di Maio
> >School of IT
> ><http://www.mfu.ac.th>www.mfu.ac.th
> >*********************************************
> >
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