Induction

[Gerry Wolff]

Freddy Offenga wrote:
> 
> Compressing the Frame Problem
> 
> An information compression approach to the frame problem
> 
> Freddy Offenga
> Student Cognitive Science
> Katholieke Universiteit Nijmegen
> The Netherlands
> March 1999
> 
> Introduction
> One of the major discussions in cognitive science concerns the so-called
> frame problem. Although there is much disagreement about the exact
> definition of the problem (e.g. Pylyshyn, 1987), the following definition
> from Haselager is sufficient:
> 
>         The frame problem, as originally understood, refers to the wearisome point
> that it seemed necesarry to explicitly specify everything that would not
> change after an event, in order to deal adequatly with a changing world
> (Haselager, 1997).
> 
....

Thanks for writing this interesting piece about the frame problem and
compression.

When I first came across the frame problem I found it puzzling because
it was not obvious to me that there was a problem at all.

I think the problem arises when people try to use 'logic' as a language
for describing real life situations. If, for example, you start with a
red block on top of a green block and then take the red block off and
put it on the table you may need a 'proposition' to say that the red
block is on the table but you may also need another 'proposition' to say
that the top of the green block is clear.

It seems to me there is a much more 'natural' way to deal with this kind
of thing which is similar to the kind of system that military commanders
used to use and may still do. If you want to keep track of what is
happening in a battle, a simple and straightforward way to do it is with
a table which represents the area where the battle is being fought
(marked out with coastlines, buildings etc) and with pieces that
represent tanks, ships etc.

If a ship moves from one place to another, then the wooden or cardboard
piece which represents the ship is moved in the same way on the table.
There is no need for a 'proposition' to say that the old position of the
ship is now empty because that is obvious from the new arrangement of
the table.

What has this got to do with information compression? Imagine that
successive states of the table and pieces are recorded in a sequence of
photographs like frames in a cinema film. From one frame to the next
there is much redundancy because most of the table is the same from one
frame to the next and each piece is the same from one frame to the next.

The information in this sequence of photographs can be compressed most
effectively by keeping a single record for each piece and a single
record for the table (with coastlines, buildings etc) and, for any one
state, keeping a record of the positions (X/Y coordinates) of each piece
on the table.

This is exactly what was proposed by the designers of Simula (the first
obect-oriented programming language): make a software model of a
military scenario with one software 'object' for each real-world object.

In short, an object-oriented kind of representation is also one which
compresses information very effectively.

It seems to me that it is no accident that what is psychologically
'natural' also yields good compression of information: there is a lot of
evidence that brains and nervous systems are very much geared to the
compression of information.

On another subject: you mention "ordered AND objects", "unordered AND
objects" and "OR objects" in the SP scheme. It is true that I proposed
those kinds of things originally but came to the conclusion gradually
that one could make do simply with sequences or 'patterns' without the
need for the previous three kinds of things. The term 'pattern' is
intended to embrace two-dimensional arrays as well as one-dimensional
sequences although I have not attempted to do anything yet with 2D
arrays.

Well, that's all for now.

Thanks again, Freddy, for your interesting essay.

Best wishes,

Gerry