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.S(Questions and Answers)
.BEGIN NOFILL
(1) Contribution to knowledge? Using the historical paradigm of
heuristic search to automate some of the activities involved in
developing new math theories: directing attention to plausible
concepts to investigate, finding the desired empirical data, inducing
new concepts to study based on the results of previous
investigations.
(2) What exactly are the primitives of AM's behaviors? AM can define
new concepts by joining or modifying defns of existing concepts. AM
can use the heuristic rules it possesses to fill in new entries for
concepts. AM can itself suggest new tasks for its own agenda. AM
can modify facets (e.g., Worth ratings), print messages, prune away
losers, etc. This is such a universal set of behaviors that,
unconstrained, it has little to do with math research. The
plausibility constraints (heurs) give it its character.
(3) What is another use for the heuristic rule which says...
Look at f↑-↑1(b):
groups with very few subgroups;
maximally-divisibles;
f=divisors-of, b=tripletons: result is a kind of squares;
Generalize f if very few examples:
Congruence→Similarity;
Reverse-all-levels→Reverse-top-level
Perfects→Multiply-perfects
(4) Explain the intu's, their failure, etc. These were opaque
(uninspectable by AM) functions which were simulations of real-world
scenarios: seesaws, elevators, archery, etc. AM was supposed to be
able to analogize between various concepts and certain intu's (e.g.,
set(ops) and Venn diagrams). Unfortunately, this contained too much
pre-programmed help (e.g., all the Venn relationships are true, and
they are too easy to get that way; OR: See-saws are anti-symmetric,
and that relation is too easy to get from Seesaws). It wasn't fair:
no relations/connepts were disccvered which the user hadn't forseen
at the time the intutions were coded. So they were all excised, and
not used to make any of the discovereis mentioned herein.
(5) 4 ways to get Multiplications:
Repeated +
Analogue to cross-product: Count(AxB)= [Count(A) ? Count(B)]
Power sets of union: Count(2↑[A∪B]) = [Count(2↑A) ? Count(2↑B)]
Subst A for each element of B, then apply Union to the result.
(6) What does "A. M." stand for? SAM slide: Jim Guard and Eastman.
(7) Uses for AM:
The heuristics themselves:
Everything that AM does can be viewed as testing the underlying body
of heuristics. If AM ever succeeds in a big way, then it might be worthwhile
teaching these heuristics explicitly to math students, just as it might
be a good idea for medical students to learn MYCIN-like rules.
AM itself: get people interested in math, give them a feel for research
Existence of AM: feasibility of automating this kind of process using Heur search
Actually constructing a computer model of this activity has provided
an experimental vehicle for studying the dynamics of plausible
empirical inference.
.END
Suggestions from EAF:
Don't try to defend AM as the right way to automate math research;
rather, defend it as a continuation of a historical line of
application programs, using heuristic search to automate various
aspects of research in assorted sciences. There are some new wrinkles
(agenda, large body of heuristic plausible move generators, allowing
the system to define new concepts and explore them, to give up
whenever it wanted to,etc). Defend on the basis of merely ↓_A_↓
contribution to knowledge, not THE answer to everything.
Emphasize that heuristic search will cause AM to explore a few narrow
ribbons of chanins of discoveries. Vast amounts of valuable concepts
will be missed in this way, but it is ONE way to beat the combin.
explosion. Even so, we saw a minor explosion of red heuristic
arrows! Alternate schemes (e.g., mutate and select) might work, but
they are different:neither better nor worse.