Pat - See below (01)
Sean Barker
BAE SYSTEMS - Advanced Technology Centre
Bristol, UK
+44(0) 117 302 8184 (02)
BAE Systems (Operations) Limited
Registered Office: Warwick House, PO Box 87, Farnborough Aerospace
Centre, Farnborough, Hants, GU14 6YU, UK
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________________________________ (04)
From: Pat Hayes [mailto:phayes@xxxxxxx]
Sent: 24 January 2008 17:02
To: [ontolog-forum]
Cc: Barker, Sean (UK)
Subject: Re: [ontolog-forum] Time representation (05)
At 10:23 AM +0000 1/24/08, Barker, Sean (UK) wrote: (06)
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. (07)
The problem with "points" is that one cannot exactly
explicitly
represent most points - or any non-rational number. (08)
Why does one need to explicitly represent (I think you mean
numerically represent) something in order for it to be useful in one's
ontology? One does not. A physics ontology might talk of atoms, even
though they are too small to see and impossible to capture or name
singly. (09)
And in any case, you are presuming that time is the real line.
Maybe it isn't. Intuitive time doesn't seem to be. (010)
Computers make
matters worse, as they only explicitly represent a small
subset of the
rationals. I did start looking at formalization of fuzzy
edged intervals
as part of a PhD in formal definitions of computational
geometry, but
when I realised I'd have to start by rewriting topology,
I got on with
my life. (011)
:-) I almost went to graduate school to study topology.
Fascinating subject. Fuzzy intervals aren't the way to go, IMO tolerance
spaces are much more 'natural' and don't need real numbers. They also
have a natural metric structure. (012)
<SB>
CAD is computationally intensive, and one doesn't want to carry round
error intervals with every point, line etc. The problem is that many
algorithms that make geometric calculations do so on the basis of
topological properties (usually ones which map to the integers - is
topology an ontology of geometry?) - for example, that you cannot go
from the inside of a circle to the outside without crossing the
boundary. (013)
The problem I was looking at was not how to represent points accurately,
but in the presence of (unquantified) inaccuracy, to ensure that
topological validity was preserved. In practice, the geometrical errors
were too small to worry about, but the topological errors were
intractable, at least with the tools we had at the time. (014)
In the resulting system, intervals did not have end-points, though you
could separate two intervals by a point. Alternatively, you could say
that all intervals were open sets, AS WERE THEIR COMPLIMENTS. Or rather,
a point could be classified against an interval as being IN, OUT or ON,
with ON corresponding to the indeterminate value of the Logic of Partial
Functions. (015)
I should add, in the system I was working on, in 2D we did distinguish
between points, lines and circles, but that was a matter of
representation.
</SB> (016)
The discussion reminds me of the story of a man looking
for his keys by
a street lamp. When asked where he had dropped them, he
pointed to a
place a little way off - "but the light is much better
over here". (017)
Old story, but I fail to see the relevance. The, er, point of
points is that they are useful.
<SB>
Its not that points are not useful, the problem is, if we both use the
term "point", how much work do we need to do before the conversation
makes sense.
</SB>
And, by the way, you can't not have them, in a sense. One can construct
the points from the intervals. So in a sense they have to be there,
whether you talk about them or not. (018)
<SB>
Not necessarily in the system I was using.
</SB> (019)
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