PatH,
OK, I didn’t say or intend that the time
theories could be *reduced* a one theory, just that they can be *described*
by a small set of primitives. What I meant by *described by* is,
as far as I can tell the same as your “expressed in terms of”.
I’m not sure if this changes anything else.
PatC
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx
From: Pat Hayes
[mailto:phayes@xxxxxxx]
Sent: Thursday, January 08, 2009 5:10 PM
To: Patrick Cassidy
Cc: [ontolog-forum]
Subject: Re: [ontolog-forum] Next steps in using ontologies as standards
On Jan 8, 2009, at 4:00 PM, Patrick Cassidy wrote:
(6) [PC] >> At this point we seem to be getting
redundant. I believe that these can all be described by a single set of
primitives, and apparently PH doesn’t think so. It
can’t be resolved here, and needs to be the subject of a proper
experiment.
[PH] > I know they cannot, and the 'experiment' is
already done. Those various temporal theories can all be expressed in terms of three
concepts: time-point, time-interval and duration. Duration cannot be reduced to
the other two (there's a model-thoeretic argument in the paper) and the other
two can be reduced to oine in some, but not all, of the theories. That gets you
down to two or at most three concepts, known to be irreducible to smaller sets.
And still, there are many variations possible in the ontologies.
I am getting confused here. Your first sentence says the
time theories *cannot* be expressed by a small set of primitives, and
the seocnd sentence says they *can* be expressed by a set of three
primitives. I am clearly misundersanding something you are saying –
we must be using words in different senses.
Well, I am not sure what you are meaning. My point was
only that your claim that all these various temporal ontologies can be
'reduced' to a single small set of 'primitive' concepts is pretty much
meaningless, since they only use a small set already, so there isn't any more
'reducing' possible. Yet they are not compatible, and not
reducible to one another. The way I have understood your argument, this is
already a clear counterexample to your claims for the hypothetical single basic
FO. Unless, of course, it simply does not refer to time at all.
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