Re: Converses (Re: Availability of the ANSI standard proposal?) (Pat Hayes)
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Date: Wed, 27 Mar 1996 14:09:45 -0600
To: Peter Clark <>
From: (Pat Hayes)
Subject: Re: Converses  (Re: Availability of the ANSI standard proposal?)
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Peter Clark
>Hmmm....generalization and canonicalization seem like slightly different
>processes to me -- "canonicalizing" doesn't necessarily involve abstraction.

Yes, I agree. Perhaps I threw in a wild card ( metaphor?), if so sorry to
have mussed the discussion up, just ignore it.

>> Pat Hayes writes:
>> This raises another issue, however. Its all very well to say that only one
>> ordering needs to be kept and not the converses, but how is it specified
>> what the canonical ordering IS? If I write between(d,e,f), what order are
>> those points supposed to be in on a line? Where is that information
>> represented?
>Isn't this simply given by an axiom for between(), eg.
>        (d < e) & (e < f) -> between(d,e,f)
>Am I missing something here?

Oh well, if we are allowed to write axioms then where is the problem?  Its
easy to just choose one of the permutations as the 'real' one, and then
define each converse by a single trivial defining axiom:

Parent(x y) =df Child(y,x)

Whether we call this an axiom or regard it as so simple that it can be
incorporated into a user inerface seems relatively unimportant. (Or am I
missing the point?)

>Sometimes two different views, from two independent databases, may
>simply be incompatible. For example: in the oil industry, company A
>considers the probability of finding oil as the combination of 4 separate
>factors, whereas company B considers it the combination of 6 (different)
>factors. These two databases (each containing factors & overall probs)
>can't be canonicalized together -- the two companies have simply used two
>different ontologies to talk about prospective oil sites. So presumably
>in the database world, too, this issue of maintaining multiple and
>possibly incompatible representations comes up and has to be addressed.
But couldnt there be 'bridge laws', ie axioms which make the connections?
They might need to lose some information in one direction egf by replacing
something definite by an existential quantifier, but they might still serve
to make the needed connections.

Actually having said this it occurs to me that there will be a common
problem, which is that one case makes distinctions between cases which are
simply inexpressible in the other language, and so the only way to express
a bridging law would be to extend the weaker language at least by having a
modality (something like 'it might be true that....under some
circumstances', where the particular kind of 'circumstances' cant be even

This might be a rather general mechanism for allowing partial bridges
between apparently incompatible vocabularies. Anybody know of any work in
this direction?

Pat Hayes

PS Mailing to these lists gets me more bounced bad mail than I ever want to
see. Is anyone responsible for maintaining these lists? If so, its time to
do some cleaning.

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