Having devoted its attention to prime numbers, AM then discovered
the concept of maximally divisible numbers, 35 which in a sense are the
opposite of prime numbers, and proceeded to propose theorems about
them. One reason why this was interesting is that Lenat did not know
anything about maximally divisible numbers when he wrote the program
and in fact he believed the program to be on a false track when it first
went in that direction!
The methodology of Lenat's program is not dissimilar to the ap-
proached used in more recent work on automating the discovery of sci-
entific knowledge—employing heuristics to search the whole “space” of
ideas and concepts within the realm under investigation. By the late
1990s there were already several programs sufficiently accomplished at
scientific investigation to enable the publication, by their human collabo-
rators, of discoveries that had been made by the programs. One example
is the use of the rule induction system RL, 36 in discovering qualitative
laws that can predict which chemicals are likely to have the long-term
effect of causing cancer in humans exposed to them. John Aronis, Bruce
Buchanan and Yongwon Lee, the program's human collaborators at the
University of Pittsburgh, were taught a set of rules by the program, rules
that themselves state which conditions must be present for a particular
rule to be valid. These rules were found to be substantially more accurate
than existing prediction schemes and became the subject of papers in the
learned journals Mutation Research (in 1995) and Environmental Health
Perspectives (in 1996).
MECHEM, developed by Raul Valdes-Perez, finds explanatory hy-
potheses in chemistry from experimental evidence, the hypotheses
explaining the sequence of steps for a given chemical reaction. The pro-
gram is given information about the starting materials of a chemical re-
action, any observed products of the reaction, and any products that
exist only at intermediate steps in the reaction. The program also has
background knowledge about catalytic chemistry expressed as constraints
(i.e., rules). MECHEM is able to discover all of the simplest hypotheses
that explain how the products are formed, given the known constraints.
The program works by carrying out an examination of all the reaction
pathways , as these processes are known, and starts by looking at the
35 A number is maximally divisible if it has more prime factors than any lower number. For
example 12 is maximally divisible because it has six divisors: 1, 2, 3, 4, 6 and 12, whereas no
number less than 12 has as many divisors.
36 For Rule Learner.