Newsgroups: bit.listserv.csg-l
Date:         Tue, 17 Nov 1992 22:31:12 CST
From:         John Gabriel <gabriel@EID.ANL.GOV>
Subject:      Thought about Protocols

[gabriel 921171.21:31CST]

This is my version of Martin Taylor's protocols. I had not articulated
them as protocols until Martin's post, so the original idea is his.

My baseline concept is a Kanerva database of truth values for a set of
N Aristotelian propositions that together discriminate within an area
of discourse.  The truth values are bit strings N long, and can be
thought of as being in a space of N dimensions, containing 2**N points
each representing a possible object in the area of discourse. Typical
values of N are in the range of 100-200, and the space is very sparsely
populated.

The literature ref to Kanerva is "Sparse Distributed Memory;
P. Kanerva, MIT Press 1988" The book is not really hard, but it isn't easy
either, and I still find some of the algorithms fading in and out of
my understanding as I look at them.

Level zero is establishing agreement about the propositions that
discriminate in the area of discourse. Most of them are already known
to both parties and taken as given, and most of the the time they are
all shared. It seems to me that one trouble we have in communicating
about PCT is that our propositions defining or discriminating within
the PCT area of discourse are not all shared by non PCT'ers.  In fact I
think we don't all have the same proposition set, and we certainly
don't seem to place them all in the same order of importance.  This is
an issue about weights and clusters of points in the space, and is
reserved for future discussion at this point.

New propositions can be introduced by refining old ones. For example,
if we both understand "green", we can qualify "green" into subcategories
of the taxonomy by

green.1   Green like grass.
green.2   Green like waterweed.

and if we want to subclaasify green.1

Green.1.1       Green like Kentucky Bluegrass.
Green.1.2       Green like fescue grass.

And I understand there are agricultural tribes who have 100 different
subcategories of green. It's only worth subclassifying green, instead of
saying "Green like grass" if you want to say "Green like grass" a lot.

What green like grass means is that subset of the cluster of instances
of green whose Hamming distance is closest to the cluster of grasses.
But to talk about Hamming distances here one needs perhaps the methods
of spectroscopy and the triangular coordinate syatem to describe hues.

Otherwise one just says "green like grass" or "green like waterweed"
and leaves it at that.

People in the same specialty profession for example have a whole universe
of discourse not accessible to those outside. There's a whole lot of
issues about using weights to discriminate between categories which I
have not thought thru properly yet. But an example is a recent discussion
between Bruce Nevins and Bill Cunningham where Bruce had two meanings
of agreement - one essentially an agreement about something in the past,
and the other a committment to make something happen in the future. I
am inclined when being nitpickish to call the second kind a contract.

Level one introduces a new instance in the universe of discourse,
essentially by giving its' Hamming distance from other instances, e.g.

"there's this kind of hallucination like an elephant but pink"

i.e. it has the elephantine Aristotelian attributes except for color pink,
and being a perception that may not have been experienced directly by
the recipient of the message. But the recipient can either say "I know
what you mean" conveying at least a possibility of no directly shared
experience, but probably haveing heard others talk about pink elephants,
or he/she can say "Yes I saw one of those early on Jan 1st. 1992"
conveying having drunk not wisely but too well the night before.

Level two is the confirmation by the recipient that a match has been
found in recipient's Kanerva database.

I think higher levels exist and have to do with weights or values,
and clusters that are preceived as similar by some community.

For example, when I fight with my boss, I am using a value system where
scientific merit is highest in the list of weights, so I can perceive
small differences in scientific merit. He poor soul is wrestling with
the fact that if expenditure exceeds income by more than epsilon, then
our whole operation will close down. So he, quite reasonably is more
concerned about whether there is a market than about whether the idea
is new and earthshaking. No wonder we disagree. The fact that I perceive
his dilemma does not make me any happier about using the last few years
when I can still think reasonably clearly to clean dull Augean stables.

All this is not well thought through. I think there are some interesting
distinctions though. Some Aristotelian attributes are selectors for
a universe of discourse, others are discriminators within the universe.

If one has a set of axioms relating Aristotelian attributes, neither
set of attributes is clearly unique, unless one has no reduandancy or
non orthogonality. I think the formal statement of this is that if one
falsifies an attribute, this should not lead to inconsistency in the
model (in the sense of first order logic). But all kinds of snakes
spring from this - did Boole REALLY find the "Laws of Thought", and
what about the non standard logics. Avery - Aren't there some people
in the Dept. of Philosophy at Canberra who worry about non standard
logics?

Well, I'm rambling. I could perhaps have made this neater, but it would
not have touched on as many of the questions I find interesting had I
done so.

        John Gabriel   (gabriel@eid.anl.gov)
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