From: kaufman@edu.gmu.aic (Ken Kaufman)
To: David.Page@comlab
Subject: East-West Challenge: Question about Competition 2
Cc: jwnek@edu.gmu, michalsk@edu.gmu

As we explored Competition 2, we encountered the following problem:

The instructions indicate that you want to encourage the discovery and
use of "strong regularities" in the trains of Figures 1 and 2.  We discovered
some simple rules that have stronger regularities than others that have
lower Prolog complexity ("P-complexity") scores according to your program.

For example, one of the rules we found for Competition 1 is:

	Rule 1.  A train is eastbound if
		 Car 3 has a triangular load or
		 Car 1 is rectangular, Car 2 is short, and Car 3 is not double

Rule 1 has a P-complexity score of 20.

Another rule:

        Rule 2.  A train is eastbound if
		 Car 3 has a triangular or hexagonal load or
		 Car 3 has a circular load and is not double

has a P-complexity score of 22.

Rule 2 represents a stronger regularity than Rule 1 because of its ease
of understanding and conceptual simplicity, for all conditions refer to
the same car.  Nonetheless, we feel that it is not worth our while to
submit it to Competition 1, when we can submit rules with lower
P-complexities.

The phenomenon of simpler rules having higher P-complexities is due to
the fact that the expressive power of Prolog is lower than the expressive
power of the knowledge representations we use.  Since cognitive simplicity
has been recognized by many machine learning researchers as a very
important knowledge selection criterion, we feel that we are at a
disadvantage and would like rules such as Rule 2 to be recognized in
the Challenge.

Since you encourage the discovery and submission of strong regularities
for Competition 2, can we submit such rules to serve among the oracles
for the competition?  On what basis would they be evaluated and scored?
It is likely that Rule 2 would be among the lowest-scoring quartile in
Competition 1, were it to be submitted.  In what way can we get credit
for very strong rules that a human can evaluate very easily, even if the
rules have somewhat higher P-complexity scores than other, less simple rules?

Furthermore, how do we submit an entry to Competition 2 (i.e, a
classification of the 100 trains) based on these concepts?  Clearly, we
could train a neural net whose construction was based on one of these
rules and score 100%.  Is that what is desired?

--Ken Kaufman