Re: representing patterns and structures (Fritz Lehmann)
Date: Tue, 22 Nov 94 20:05:27 CST
From: (Fritz Lehmann)
Message-id: <>
Subject: Re: representing patterns and structures
Cc:, anquetil@IRO.UMontreal.CA,,,, billrich@VNET.IBM.COM,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Precedence: bulk
     Daniel Bobrow, Patrick Hayes and Peter Clark responded to my warning
about individual identity in nested descriptions with exceptions.
Hayes' original description was:
    Here's an interesting issue ....
    CAD systems allowed notions of "grouping", so you could
    specify eg. a pattern of holes all of a certain diameter*
    a certain spacing* apart in a hexagonal* grid filling a certain
    area* on a sheet of metal, just by specifying the starred
    parameters. Then it was possible to say that they should be
    all moved a leeeetle bit closer together, and have the system
    draw the result for you on the screen.  Very pretty, until you
    wanted to fill in just one of these holes.  This was impossible
    if the thing was specified this way, since in a real sense
    that particular hole-token didn't actually exist in the
    internal representation.

     I warned about assuming individual identity of the holes,
saying it raised a deep issue of individual identity.  Pat said:
>I dont think we need get
>involved with Criteria Of Identity in order to make useful progress on
>figuring out how to describe exceptional cases to general patterns, and
>treat the result as a pattern. 

     We differ.  Note that _change_ of the description occurred in
the example: move "a leetle bit closer".   My example was of a circle
of eleven holes; the change was "make it a circle of ten holes."
Suppose the order of description and exceptions is: 1. Make a circle
of eleven round holes. 2. Make the top six holes into square holes.
3. Change the number of holes in the circle from eleven to ten.  Question:
How many square holes are there?  Command 2 is an exception to description
1, and command 3 is a further exception.  This is a case of composition of
nested descriptions, described (approvingly) by Daniel Bobrow and Peter
Clark.  To answer the question sensibly, we do indeed have to "get
involved with Criteria of Identity".  If we start with some red dots in a
square, then say "Make the corner ones blue" and then say "Put the dots
in a triangle pattern", the number of resulting blue dots depends on
how the program decides to handle individual identity as operations are
composed (it can "map" dots in the square to dots in the triangle in
various ways, or it can just generate the triangle independently).

     Pat said:
>>     This issue is a very deep one, ..........
>Nah, its not this full of philosphical gold-dust.

     What it's full of is practical peril for the user, unless the
effects of composed exceptions are well-understood. (Those who
follow defeasible inheritance theory will recall the progression from
the Nautilus to Tweety the Penguin to Clyde the Elephant to Nixon
the Pacifist to the Military Chaplain, each example discrediting the
prior analysis.)  I agree with Bobrow, Hayes and Clark on the need for
nested descriptions and exceptions.  But, watch out.

                          Yours truly,   Fritz Lehmann
GRANDAI Software, 4282 Sandburg Way, Irvine, CA 92715, U.S.A.
Tel:(714)-733-0566  Fax:(714)-733-0506

P.S. The difficulties of "mapping" individuals under changes
of description occurs in the non-formal commonsense world.
The co-princes of Andorra were the Bishop of Urgel and the
Count of Foix.  The county of Foix devolved eventually upon
the King of France, so he became Co-prince of Andorra.  The
kingdom of France passed to the House of Bourbon.  So who is
now the Co-prince of Andorra?  The head of the house of Bourbon
(the Count of Paris)?  No; it is the President of France,
Jaques Mitterand, who is Co-prince of Andorra now with the
Bishop of Urgel.  It is non-trivial to say how the original
description "Count of Foix" maps to the appropraiate modern individual.