Re: Good and Bad IS-A hierarchies (Pat Hayes)
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Date: Wed, 26 Jul 1995 14:43:08 -0500
To: (Peter Clark)
From: (Pat Hayes)
Subject: Re: Good and Bad IS-A hierarchies
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At 12:39 PM 7/24/95 -0500, Peter Clark wrote:
>> [Pat Hayes wrote]
>> There is no way to organize the concepts, or even the axioms, into neat 
>> little packets so that the various alternatives can be assembled by 
>> choosing some and ignoring others. There just are genuine alternatives, 
>> and one has to make committments in selecting a temporal theory to work with.
>Well, the above paragraph suggests that we simply have N different 
>representations and we pick one. It ignores the idea of being able to 
>compose representations from components (I'm not sure if that was 
>intensional) given a particular ontological commitment.

It doesnt ignore it, it reports a sober conclusion that that is impossible.
Believe me, I love the idea, but it just doesnt work here. (Actually, the
point is more subtle. One can make little 'packets' of axioms, to some
extent, but they cant just be assembled, they need to be adapted to each

Heres an example: there is a way to define "starts" (between intervals) in
terms of "meets" as follows: 
I starts J iff 
exists K, L, M.  K meets I & K meets J & I meets L and L meets M and J meets M. 
The picture is like this:


The idea is to use a common meeting as a way of pinning down the endpoints,
so that (K meets I & K meets J) establishes that J and I start at the same
point. You probably get the idea, and can write definitions for all the
other 13 interval relations in terms of meets. Fine. However, some axioms
allow intervals to be oriented backwards, so we can have a negative
interval. If we do this, then these K and M intervals are no longer
necessary, since we can just say that neg(J) meets I and L meets neg(J).
HOwever, we now need to assert that the interval L is the right way round,
otherwise this could be saying that J starts I. The definition therefore
changes to this:

I starts J iff 
exists L. Positive(L) & neg(J) meets I & L meets neg(J) & I meets L.

Now, and this is my point here, you cannot get from one to the other of
these by 'reassembling' sets of axioms: you have to actually change them.
They share the same ontology, most of the same vocabulary, and express the
same underlying intuition. But they have to be quite different, because of
a little alteration to the other axioms. 

This kind of thing happens a lot.

Pat Hayes

Until September: 
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