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␈↓ ↓H␈↓␈↓ βx␈↓∧␈↓&AUTOMATED   MATHEMATICIAN␈↓)αβ␈↓

␈↓ ↓H␈↓␈↓ ¬∞␈↓∧␈↓&ADVANCED  TALK␈↓)αβ␈↓


␈↓ ↓H␈↓␈↓ β:for the Stanford ␈↓↓Heuristic Programming Project␈↓ Workshop

␈↓ ↓H␈↓␈↓ ¬Q␈↓βJanuary 5-8, 1976␈↓


␈↓ ↓H␈↓␈↓ ¬WDouglas B. Lenat




␈↓ ↓H␈↓REVIEW OF AM

␈↓ ↓H␈↓Let␈α
me␈αopen␈α
with␈αa␈α
10-minute␈αreview␈α
of␈α
the␈αAM␈α
project.␈αAfter␈α
that,␈αI'll␈α
talk␈αa␈α
little␈α
about␈αsome
␈↓ ↓H␈↓issues␈αin␈αmy␈αresearch␈αthat␈αbear␈αon␈αtheory␈αformation␈αor␈αheuristic␈αprogramming␈αin␈αgeneral,␈αand␈αwe
␈↓ ↓H␈↓can all discuss them.

␈↓ ↓H␈↓The␈α
objective␈α
of␈α∞this␈α
project␈α
is␈α∞to␈α
emulate␈α
a␈α
mathematician␈α∞doing␈α
simple␈α
research.␈α∞The␈α
reasons
␈↓ ↓H␈↓are to study the theory formation process in empiricial science.

␈↓ ↓H␈↓As␈αI␈αmentioned␈αMonday,␈α␈↓∧Math␈α
was␈αchosen␈↓␈αas␈αthe␈αscience␈α
to␈αwork␈αin␈αpartly␈αbecause␈αI␈α
wouln't
␈↓ ↓H␈↓have␈αto␈αdeal␈αwith␈αnonprogramming␈αexperts␈αin␈αa␈αdomain␈αalien␈αto␈αme;␈αI␈αcould␈αcollect␈αmy␈αheuristics
␈↓ ↓H␈↓by␈αintrospection.␈αBut␈αthat's␈αnot␈αthe␈αmain␈αsuitability␈α
for␈αmath␈αresearch␈αas␈αa␈αtask␈αdomain␈αfor␈αan␈α
AI
␈↓ ↓H␈↓theory␈αformation␈αprogram.␈α
It␈αis␈αthat␈α
of␈αall␈αscientists,␈α
the␈αmathematician␈αis␈α
the␈αleast␈αencumbered␈α
by
␈↓ ↓H␈↓reality,␈αby␈αthe␈αneed␈αto␈αsolve␈αa␈αspeci≡c␈αproblem.␈αInstead␈αof␈αbeing␈αdriven␈αby␈αpractical␈αproblems,␈αthe
␈↓ ↓H␈↓mathematician␈αis␈α␈↓&driven␈α
by␈αhis␈αintuition␈↓)αβ,␈α
his␈αaeshtetic␈αsense,␈αhis␈α
appreciation␈αof␈αthe␈α
unusual.␈αHe
␈↓ ↓H␈↓looks␈α⊂at␈α⊂something␈α⊃because␈α⊂he␈α⊂thinks␈α⊃it␈α⊂might␈α⊂prove␈α⊃interesting,␈α⊂and␈α⊂he␈α⊃publishes␈α⊂something
␈↓ ↓H␈↓because he thinks it did prove interesting.

␈↓ ↓H␈↓I␈αbelieve␈αthat␈α␈↓&math␈αis␈αan␈αempirical␈αscience␈↓)αβ,␈αand␈αthat␈αit␈αis␈αpossible␈αto␈αwrite␈αdown␈αprecise␈αheuristics
␈↓ ↓H␈↓about␈αthe␈αnotion␈αof␈αaesthetic␈αinterestingness,␈αabout␈αwhat␈αis␈αa␈αpromising␈αnew␈αconcept␈αto␈αde≡ne␈α
and
␈↓ ↓H␈↓study,␈α
what␈αnew␈α
aspect␈αto␈α
consider,␈αabout␈α
when␈αto␈α
quit␈α
and␈αmove␈α
on.␈α A␈α
typical␈αone␈α
of␈αthese␈α
hints
␈↓ ↓H␈↓is␈αto␈αlook␈αfor␈αsituations␈αwhere␈αyou␈αmight␈αcomplete␈αa␈αsquare␈αof␈αfunctions.␈α␈↓∧<square␈αslide>␈↓␈αThis
␈↓ ↓H␈↓particular␈α∞case␈α∞occurs␈α∞when␈α∞you␈α∞know␈α∞about␈α∞ bags,␈α∞cross-product,␈α∞and␈α∞counting␈α∞the␈α∞length␈α∂of␈α∞a
␈↓ ↓H␈↓bag.␈α∞ The␈α∂missing␈α∞operation␈α∂here␈α∞can␈α∂be␈α∞calculated,␈α∂and␈α∞in␈α∂fact␈α∞de≡ned,␈α∂using␈α∞just␈α∂these␈α∞three
␈↓ ↓H␈↓known operations to de≡ne it. It turns out to be what you and I call multiplication.

␈↓ ↓H␈↓One␈αreason␈αfor␈αAM␈αto␈αexist␈αas␈αa␈αprogram␈αis␈αto␈αsee␈αif␈αthese␈αheursitics␈αare␈αreally␈αpowerful␈αenough
␈↓ ↓H␈↓to␈α⊃push␈α⊃the␈α⊃system␈α⊃along␈α⊃fruitful␈α⊃lines␈α⊃of␈α⊃development.␈α⊃ ␈↓∧<tree␈α⊃of␈α⊃concepts␈α⊃slide>␈↓␈α⊃The
␈↓ ↓H␈↓heuristic␈αof␈αcompleting␈αthe␈αsquare␈αcan␈αtake␈αyou␈αfrom␈αhere␈αto␈αhere,␈αfor␈αexample.␈αTHe␈αheuristic␈αof
␈↓ ↓H␈↓investigating␈α
the␈α
inverse␈α
of␈α
each␈αnew,␈α
interesting␈α
relation,␈α
will␈α
take␈αyou␈α
from␈α
here␈α
to␈α
here␈αand␈α
also
␈↓ ↓H␈↓along␈α∂this␈α∞path,␈α∂to␈α∞the␈α∂discovery␈α∞of␈α∂divisors.␈α∞The␈α∂heuristic␈α∞of␈α∂looking␈α∞for␈α∂elements␈α∂which␈α∞give
␈↓ ↓H␈↓extreme␈α⊂results␈α⊂will␈α⊃lead␈α⊂you␈α⊂from␈α⊃divisors␈α⊂to␈α⊂considering␈α⊃numbers␈α⊂with␈α⊂unusual␈α⊃numbers␈α⊂of
␈↓ ↓H␈↓␈↓εDouglas B. Lenat␈↓␈↓ ¬!␈↓β␈↓&Automated Mathematician␈↓)αβ␈↓␈↓ 	ε␈↓εADVANCED Seminar      page   2␈↓


␈↓ ↓H␈↓divisors.␈αTwo␈αextremes␈αare␈αwhat␈αwe␈αcall␈αprimes,␈αand␈αa␈αclass␈αof␈αnumbers␈αwhich␈αhas␈αno␈αname␈αas␈α
of
␈↓ ↓H␈↓yet.␈α Primes␈αare␈αcharacterized␈αby␈αsaying␈α
that␈αa␈αnumber␈αis␈αin␈αhere␈α
if␈αits␈αonly␈αdivisors␈αare␈αitself␈α
and
␈↓ ↓H␈↓1.␈α
 Numbers␈α
in␈α
␈↓βthis␈↓␈α
class␈α
have␈α
many␈α
divisors,␈α
and␈α
can␈α
be␈α
characterized␈α
by␈α
saying␈α
that␈α
a␈αnumber␈α
is
␈↓ ↓H␈↓in␈α
here␈α
if␈αit␈α
has␈α
more␈α
divisors␈αthan␈α
every␈α
smaller␈α
natural␈αnumber.␈α
Another␈α
way␈α
to␈αlook␈α
at␈α
it␈αis,␈α
we
␈↓ ↓H␈↓put␈αin␈αhere␈αthe␈αsmallest␈αnatural␈αnumber␈αwith␈α2␈αdivisors,␈αthe␈αsmallest␈αnumber␈αwith␈α3␈αdivisors,␈αthe
␈↓ ↓H␈↓smallest number which has 8 million divisors, etc.

␈↓ ↓H␈↓But␈α
why␈α
has␈α
␈↓↓␈↓&everybody␈α
heard␈α
of␈α
these␈↓)αβ␈↓,␈α
and␈α
nobody␈α
heard␈α
of␈α
these?␈α
 Well,␈α
the␈α
reason␈α
is␈αthat␈α
there
␈↓ ↓H␈↓are␈α∂many␈α∂theorems␈α∂about␈α⊂primes,␈α∂many␈α∂proofs␈α∂in␈α∂number␈α⊂theory␈α∂that␈α∂use␈α∂primes,␈α⊂a␈α∂canonical
␈↓ ↓H␈↓reeresentation␈α∂of␈α∂numbers␈α∂decomposed␈α∞into␈α∂prime␈α∂factors,␈α∂and␈α∂so␈α∞on.␈α∂Why␈α∂is␈α∂␈↓βthis␈↓␈α∂unheard␈α∞of?
␈↓ ↓H␈↓Because␈α∂until␈α∂last␈α∂weekend,␈α∂there␈α∂were␈α∂no␈α⊂theorems␈α∂about␈α∂this␈α∂set␈α∂of␈α∂numbers,␈α∂no␈α⊂proofs␈α∂that
␈↓ ↓H␈↓would␈α
go␈α
easier␈α
if␈α
you␈α
used␈α
them␈α
somehow,␈αno␈α
ties␈α
to␈α
any␈α
other␈α
known␈α
concepts,␈α
except␈α
in␈αthe␈α
way
␈↓ ↓H␈↓they␈α⊂were␈α⊂de≡ned.␈α⊃Last␈α⊂weekend,␈α⊂based␈α⊃on␈α⊂suggestions␈α⊂from␈α⊂AM,␈α⊃Randy␈α⊂and␈α⊂I␈α⊃established␈α⊂a
␈↓ ↓H␈↓meaningful␈α∞conjecture␈α∞about␈α∂this␈α∞concept.␈α∞I␈α∂think␈α∞we␈α∞have␈α∞a␈α∂method␈α∞for␈α∞generating␈α∂an␈α∞in≡nite
␈↓ ↓H␈↓sequence␈αof␈αnumbers␈αof␈αthis␈αtype.␈αIn␈αparticular,␈αthey␈αall␈αhave␈αthe␈αfollowing␈αform␈α␈↓∧<Max␈αslide>␈↓.
␈↓ ↓H␈↓I won't force you through this again today.

␈↓ ↓H␈↓At␈α∞each␈α∞moment,␈α∞a␈α∞mathematician,␈α∞just␈α∞like␈α∞ AM,␈α∞has␈α∞a␈α∞list␈α∞of␈α∞hundreds␈α∞of␈α∞concepts␈α∞which␈α
he
␈↓ ↓H␈↓knows␈α∂something␈α∂about.␈α∂His␈α∂basic␈α∞activity␈α∂is␈α∂to␈α∂≡nd␈α∂out␈α∞more␈α∂about␈α∂those␈α∂concepts,␈α∂and␈α∂in␈α∞so
␈↓ ↓H␈↓doing he occasionally decides that some new concept is worth naming and investigating.

␈↓ ↓H␈↓In␈α∂the␈α∞AM␈α∂program,␈α∞each␈α∂concept␈α∞can␈α∂have␈α∞many␈α∂di≥erent␈α∞kinds␈α∂of␈α∞knowledge␈α∂tacked␈α∂onto␈α∞it
␈↓ ↓H␈↓␈↓∧<facets␈αslide>.␈↓␈αSome␈αof␈αthis␈αis␈αactually␈αa␈αcollection␈αof␈αheuristics,␈αwritten␈αas␈αproductions,␈αwhich
␈↓ ↓H␈↓contain␈αhints␈αfor␈αdealing␈αwith␈α
the␈αconcept:␈αwhy␈αit␈αis␈αuseful,␈α
how␈αone␈αof␈αthese␈αmight␈αbe␈α
interesting,
␈↓ ↓H␈↓how␈α∞to␈α
≡ll␈α∞in␈α
more␈α∞knowledge␈α
about␈α∞of␈α
one␈α∞of␈α
these,␈α∞suggestions␈α
for␈α∞new␈α
activities␈α∞to␈α∞try␈α
(some
␈↓ ↓H␈↓relating␈αto␈αthis␈αconcept,␈αsome␈αto␈αothers),␈αand␈α
warnings␈αof␈αtraps␈αnot␈αto␈αfall␈αinto␈αwhen␈αhandling␈α
this
␈↓ ↓H␈↓concept.␈↓↓<slide␈α
for␈α
COMPOSE␈α
concept>␈↓␈α
Here␈α
is␈α
a␈α
typical␈α
concept.␈α
 Note␈α
that␈α
I've␈α
indicated␈α
that␈α
the
␈↓ ↓H␈↓system maintains multiple representations for the same knowledge. We may talk about that later.

␈↓ ↓H␈↓WHAT␈α∩does␈α∩the␈α∩system␈α∪actually␈α∩do,␈α∩then?␈α∩It␈α∩expands␈α∪its␈α∩knowledge,␈α∩both␈α∩by␈α∪creating␈α∩new
␈↓ ↓H␈↓concepts␈αand␈αby␈α≡nding␈αout␈αmore␈αabout␈αthe␈αalready-known␈αones.␈α That␈αmeans␈αit␈αcreates␈αnew␈αdata
␈↓ ↓H␈↓structures like these, and it ≡lls out the facets of existing ones.

␈↓ ↓H␈↓The␈α⊃basic␈α⊃control␈α⊃structure␈α⊃can␈α⊃be␈α⊃characterized␈α⊃as␈α⊃␈↓∧<planning␈α⊃slide>␈↓␈α⊃a␈α⊃select,␈α∩plan,␈α⊃and
␈↓ ↓H␈↓execute␈α
loop.␈α The␈α
selection␈α
is␈αmade␈α
from␈α
a␈αglobal␈α
list␈α
of␈αthings␈α
AM␈α
thinks␈αare␈α
worth␈αdoing.␈α
Each
␈↓ ↓H␈↓of␈α∂these␈α∂has␈α∂tacked␈α⊂onto␈α∂it␈α∂a␈α∂predicate␈α∂indicating␈α⊂why␈α∂it␈α∂was␈α∂suggested,␈α∂how␈α⊂to␈α∂quantitatively
␈↓ ↓H␈↓estimate␈αits␈αworth,␈αand␈αso␈αon.␈α So␈αselecting␈αis␈αdone␈αby␈αasking␈αeach␈αof␈αthese␈αhow␈αpromising␈αit␈αis␈αat
␈↓ ↓H␈↓the moment.

␈↓ ↓H␈↓The␈αstatement␈αof␈αthe␈αactivity␈αto␈α
be␈αperformed␈αis␈αitself␈αa␈αsimple␈α
kind␈αof␈αplan.␈αThat␈αis,␈αthese␈αare␈α
all
␈↓ ↓H␈↓really␈α⊃plans␈α∩for␈α⊃things␈α⊃that␈α∩AM␈α⊃might␈α⊃do.␈α∩ It␈α⊃isn't␈α⊃of␈α∩the␈α⊃form␈α⊃"Compose␈α∩Set-intersect␈α⊃with
␈↓ ↓H␈↓Complement", but rather just "Do ␈↓βsome␈↓ composition".

␈↓ ↓H␈↓At␈α⊂this␈α∂stage,␈α⊂a␈α∂plan␈α⊂of␈α∂attack␈α⊂is␈α∂assembled␈α⊂by␈α∂throwing␈α⊂together␈α∂all␈α⊂the␈α∂heuristics␈α⊂who␈α∂have
␈↓ ↓H␈↓anything␈α∂to␈α∞say␈α∂about␈α∂ either␈α∞this␈α∂activity␈α∞or␈α∂one␈α∂of␈α∞these␈α∂operands.␈α∞ Recall␈α∂that␈α∂heuristics␈α∞are
␈↓ ↓H␈↓represented as productions.  By running the resultant production system, this task should get done.

␈↓ ↓H␈↓During␈α∩this␈α∩execution,␈α∩several␈α∩things␈α∩may␈α∩happen.␈α∩Depending␈α∩on␈α∩the␈α∩outcome,␈α∩some␈α∪of␈α∩the
␈↓ ↓H␈↓␈↓εDouglas B. Lenat␈↓␈↓ ¬!␈↓β␈↓&Automated Mathematician␈↓)αβ␈↓␈↓ 	ε␈↓εADVANCED Seminar      page   3␈↓


␈↓ ↓H␈↓relevant␈α
heuristics␈αmight␈α
make␈α␈↓&new␈α
suggestions␈↓)αβ␈αon␈α
what␈αwould␈α
be␈αinteresting␈α
to␈αdo.␈α
 Here,␈α
if␈αno
␈↓ ↓H␈↓examples␈α∂were␈α∞found,␈α∂one␈α∞heuristic␈α∂might␈α∂suggest␈α∞that␈α∂AM␈α∞sometime␈α∂consider␈α∂generalizing␈α∞the
␈↓ ↓H␈↓concept␈αof␈αCompose.␈α Sometimes,␈α
some␈α␈↓&new␈αconcepts␈αwill␈α
be␈αcreated␈↓)αβ.␈αAny␈αinteresting␈α
examples␈αof
␈↓ ↓H␈↓Compose␈α∂which␈α∂are␈α∂found␈α∂will␈α∂be␈α∂operations␈α∂themselves,␈α∂hence␈α∂can␈α∂be␈α∂considered␈α∂as␈α∂potential
␈↓ ↓H␈↓concepts.

␈↓ ↓H␈↓For␈α⊃those␈α⊃facets␈α⊃which␈α⊃are␈α⊃stored␈α⊃as␈α⊃procedures,␈α⊃≡lling␈α⊃them␈α⊃in␈α⊃will␈α⊃mean␈α⊃writing␈α∩new␈α⊃little
␈↓ ↓H␈↓programs.␈α
Well,␈α
we␈α
know␈α
enough␈α
about␈α
automatic␈α∞programming␈α
to␈α
do␈α
that.␈α
This␈α
is␈α
the␈α∞kind␈α
of
␈↓ ↓H␈↓task␈α
that␈α
I␈α
worked␈α
on␈αwith␈α
Cordell␈α
for␈α
2␈α
years.␈α
 The␈αknowledge␈α
tacked␈α
onto␈α
 the␈α
Fillin␈α
facet␈αof␈α
the
␈↓ ↓H␈↓Algorithms␈α
concept,␈αfor␈α
example,␈αwill␈α
be␈αautomatic␈α
programming␈αtechniques,␈α
which␈αcan␈α
use,␈αsay,
␈↓ ↓H␈↓the␈αde≡nition␈α
of␈αany␈αconcept␈α
to␈αproduce␈α
an␈αexecutable␈αalgorithm␈α
for␈αit.␈α
 In␈αfact,␈αthe␈α
representation
␈↓ ↓H␈↓used␈α∂for␈α⊂concpets␈α∂is␈α⊂not␈α∂simply␈α⊂the␈α∂property␈α∂list␈α⊂one,␈α∂but␈α⊂rather␈α∂the␈α⊂BEINGs␈α∂one,␈α⊂which␈α∂was
␈↓ ↓H␈↓developed␈αfor␈αautomatic␈α
programming.␈α I␈αintentionally␈α
want␈αto␈αignore␈αthat␈α
aspect␈αof␈αAM,␈α
since␈αI
␈↓ ↓H␈↓don't␈αthink␈αit␈αhas␈αany␈αrelevance␈αto␈αtheory␈αformation␈αin␈αgeneral.␈α Instead,␈αlet's␈αdiscuss␈αsome␈αof␈αthe
␈↓ ↓H␈↓more general questions that AM raises.  PROBLEMS WE FACE

␈↓ ↓H␈↓Updating Knowledge Base:

␈↓ ↓H␈↓One␈α⊂ problem␈α⊃we␈α⊂all␈α⊃face␈α⊂is␈α⊃how␈α⊂to␈α⊂cope␈α⊃with␈α⊂changes␈α⊃in␈α⊂the␈α⊃system's␈α⊂knowledge␈α⊃base.␈α⊂The
␈↓ ↓H␈↓standard␈αsolution␈αis␈αto␈αtrack␈αdown␈αall␈αthe␈αe≥ects␈αof␈αeach␈αchange,␈αand␈αupdate␈αthe␈αwhole␈αdata␈αbase.
␈↓ ↓H␈↓The␈α
solution␈αAM␈α
uses,␈αand␈α
perhaps␈αpeople␈α
too,␈α
is␈αto␈α
just␈αrecord␈α
the␈αchanged␈α
information,␈αand␈α
␈↓βnot␈↓
␈↓ ↓H␈↓to␈αupdate␈αeverything.␈α When␈αa␈αcontradiction␈α
of␈αsome␈αkind␈αoccurs,␈αthen␈αthe␈α
con∨icting␈αknowledge
␈↓ ↓H␈↓is␈α
checked,␈αthe␈α
knowledge␈α␈↓βit␈↓␈α
was␈αbased␈α
on␈αis␈α
checked,␈αand␈α
so␈αon,␈α
until␈αwe␈α
encounter␈αsome␈α
changed
␈↓ ↓H␈↓opinion␈α∃which␈α∃explains␈α∃the␈α∃disagreement.␈α∃ So␈α∃the␈α∃system␈α∃is␈α∃allowed␈α∃to␈α∃hold␈α∀contradictory
␈↓ ↓H␈↓viewpoints,␈α
so␈α
long␈α
as␈α∞it␈α
could␈α
resolve␈α
any␈α∞dispute␈α
if␈α
it␈α
had␈α
to.␈α∞ This␈α
is␈α
one␈α
solution␈α∞you␈α
might
␈↓ ↓H␈↓keep in mind for your knowledge-based systems.

␈↓ ↓H␈↓How to measure performance

␈↓ ↓H␈↓There␈α
is␈αno␈α
speci≡c␈α"goal"␈α
that␈αAM␈α
is␈αsupposed␈α
to␈αachieve;␈α
in␈αfact,␈α
the␈αspeci≡cation␈α
of␈α
any␈αsuch
␈↓ ↓H␈↓preconceived␈α∞goal␈α∞would␈α∞probably␈α∞interfere␈α∞with␈α
creating␈α∞a␈α∞system␈α∞general␈α∞enough␈α∞to␈α∞explore␈α
a
␈↓ ↓H␈↓large␈α
space␈α
of␈α
concepts.␈α
 We␈α
could␈α
set␈α
some␈α
milestones␈α
out,␈α
like␈α
De≡ne␈α
some␈α
brand␈α
new␈α
concept;
␈↓ ↓H␈↓making␈α∩a␈α∩new␈α∩conjecture;␈α∩≡nding␈α∩some␈α∪new␈α∩result␈α∩which␈α∩is␈α∩not␈α∩only␈α∩interesting␈α∪but␈α∩useful.
␈↓ ↓H␈↓Developing␈α∞an␈α∞entirely␈α∞new␈α∂theory.␈α∞ A␈α∞crude␈α∞approximation␈α∞ to␈α∂this␈α∞might␈α∞be␈α∞where␈α∂its␈α∞results
␈↓ ↓H␈↓were␈αpublishable.␈αIn␈αjournals␈αin␈αAI?␈αin␈αthe␈αchosen␈αscienti≡c␈α≡eld?␈α in␈αScienti≡c␈αAmerican?␈α Or␈αwe
␈↓ ↓H␈↓could␈α⊂construct␈α⊂some␈α⊂more␈α⊂relative␈α⊂criteria␈α⊂to␈α⊂judge␈α⊂its␈α⊂performance␈α⊂by␈α⊂Comparing␈α⊂the␈α⊂given
␈↓ ↓H␈↓initial␈α∞knowledge␈α∞to␈α∞the␈α∞derived␈α∞knowledge.␈α∞ Examining␈α
the␈α∞route␈α∞AM␈α∞took␈α∞to␈α∞do␈α∞anything,␈α
its
␈↓ ↓H␈↓chains␈α
of␈αreasoning␈α
and␈αguessing.␈α
 You␈αcould␈α
rate␈αa␈α
theory␈αformation␈α
system␈αas␈α
a␈α
user␈αprogram:
␈↓ ↓H␈↓can␈αresearchers␈αin␈α
its␈α≡eld␈αactually␈αuse␈α
it␈αe≥ectively.␈αDoes␈αit␈α
do␈αwhat␈α␈↓βthey␈↓␈αwould␈α
like␈αit␈αto?␈α
Is␈αthe
␈↓ ↓H␈↓program␈α⊃a␈α∩good␈α⊃enough␈α⊃theorist␈α∩that␈α⊃it␈α∩becomes␈α⊃worthwhile␈α⊃to␈α∩perform␈α⊃experiments␈α∩with␈α⊃it
␈↓ ↓H␈↓(removing, adding, modifying the heuristics and the starting concepts, and seeing the results).

␈↓ ↓H␈↓Role␈α∂of␈α∂the␈α∂user␈α∞Continuum␈α∂from␈α∂passive␈α∂observor,␈α∞to␈α∂active␈α∂co-researcher,␈α∂to␈α∂absolute␈α∞mentor
␈↓ ↓H␈↓(latter␈αex:␈αthe␈αFOL␈αProof-checker).␈α What␈αis␈αthe␈αoptimum␈αrole?␈αAssume␈αit␈αchanges␈αdynamically.␈αIs
␈↓ ↓H␈↓there␈αany␈αgeneral␈αcriteria␈αwe␈αcan␈αcite␈αfor␈αwhen␈αyou␈αdo/don't␈αwant␈αthe␈αuser␈αto␈αsay␈αsomething?␈αThe
␈↓ ↓H␈↓more he must do, the better informed he must be about what the system is doing, why, and how.

␈↓ ↓H␈↓What␈αconsiderations␈αcome␈αinto␈α
play␈αwhen␈αchoosing␈αa␈α
name␈αfor␈αthe␈αsystem,␈α
There␈αis␈αthe␈αdanger␈α
of
␈↓ ↓H␈↓being␈α∞pretentious:␈α∂HACKER,␈α∞PLANNER,␈α∞CONNIVER,␈α∂A.M.,LOGIC␈α∞THEORIST,␈α∂GPS.␈α∞ Or
␈↓ ↓H␈↓the strange other extreme, of intentional meaninglessness: GOOOOO37.
␈↓ ↓H␈↓␈↓εDouglas B. Lenat␈↓␈↓ ¬!␈↓β␈↓&Automated Mathematician␈↓)αβ␈↓␈↓ 	ε␈↓εADVANCED Seminar      page   4␈↓


␈↓ ↓H␈↓A≥ect␈αof␈αdata␈α
structure␈αreprs.␈αand␈αother␈α
hidden␈αassumptions␈αin␈αa␈α
theory␈αformation␈αpgm␈αthat␈α
limit
␈↓ ↓H␈↓its␈αpotential.␈α
EG:␈αmeta-dendral:␈αlimited␈α
to␈αinferring␈α
a␈αgrammar␈αwhose␈α
rules␈αhave␈α
a␈αcertain␈αkind␈α
of
␈↓ ↓H␈↓format.␈α
The␈α∞way␈α
AM␈α∞is␈α
set␈α∞up,␈α
t␈α∞is␈α
more␈α∞natural␈α
for␈α∞it␈α
to␈α∞derive␈α
our␈α∞concepts␈α
of␈α∞number␈α
than
␈↓ ↓H␈↓Knuth's surreal ones.

␈↓ ↓H␈↓Intuition:␈α
its␈α
role␈α
in␈α
math␈αresearch␈α
(guide,␈α
check),␈α
AM␈α
(abstract␈αmanip.␈α
reprs).␈α
 Is␈α
it␈α
the␈α
same␈αas
␈↓ ↓H␈↓that of abstraction spaces? Hence, same as planning?

␈↓ ↓H␈↓Acquiring␈αnew␈αHeurisitcs␈α
is␈αconsiderably␈αharder␈α
than␈αthe␈αprevious␈α
paradigm␈αof␈αtheory␈α
formation.
␈↓ ↓H␈↓It␈αrequires␈αa␈αquantum␈αleap␈αof␈αinsight␈αand␈αdaring,␈αand␈αmuch␈αlonger␈αperiods␈αof␈αtime␈αto␈αtest␈αit␈αout.
␈↓ ↓H␈↓The␈α∀heuristics␈α∪for␈α∀acquiring␈α∀new␈α∪heuristics␈α∀are␈α∀almost␈α∪unthinkable.␈α∀Newell's␈α∀suggestion:␈α∪go
␈↓ ↓H␈↓through␈αthe␈αdevelopment␈α
of␈αmath␈α(or␈α
any␈αsim.␈αsci),␈αand␈α
factor␈αout␈αall␈α
the␈αhack␈αdiscoveries␈α
--␈αthe
␈↓ ↓H␈↓kind␈αthat␈αAM␈αmight␈αbe␈αable␈αto␈αmake.␈αWhat␈αyou␈αhave␈αleft␈αwould␈αbasically␈αbe␈αa␈αsequence␈αof␈αthese
␈↓ ↓H␈↓huge␈α
leaps,␈α∞where␈α
either␈α
luck␈α∞or␈α
some␈α
piece␈α∞of␈α
this␈α
heuristic-generating␈α∞knowlege␈α
created␈α∞a␈α
new
␈↓ ↓H␈↓heuristic␈α
which␈α∞led␈α
to␈α
a␈α∞new␈α
kind␈α
of␈α∞discovery.␈α
An␈α
example␈α∞is␈α
Einsten's␈α
doubting␈α∞the␈α
common-
␈↓ ↓H␈↓sense␈αnotions␈α
of␈αsimultaneity,␈αor␈α
Riemann␈αdenying␈α
Euclid's␈αparallel␈αpostulate.␈α
 After␈αthe␈α≡rst␈α
move
␈↓ ↓H␈↓of␈αthis␈αkind,␈αthe␈α≡rst␈αtime␈αsomeone␈αconsidered␈αdenying␈αwhat␈αwas␈αhitherto␈αunquestioned,␈αwhat␈α
was
␈↓ ↓H␈↓so␈α∞intuitively␈α
true␈α∞that␈α
it␈α∞had␈α
never␈α∞occurred␈α
to␈α∞anyone␈α
that␈α∞denying␈α
it␈α∞could␈α
lead␈α∞to␈α
consistent
␈↓ ↓H␈↓results.␈α∪ It␈α∪became␈α∩a␈α∪standard␈α∪heuristic␈α∩which␈α∪physicists␈α∪and␈α∩mathematicians␈α∪now␈α∪use␈α∩quite
␈↓ ↓H␈↓frequently.

␈↓ ↓H␈↓What␈α
it␈αwould␈α
take␈α
to␈αbe␈α
able␈αto␈α
do␈α
research␈αin␈α
various␈αareas␈α
of␈α
mathematics,␈αin␈α
other␈αsciences,␈α
in
␈↓ ↓H␈↓softer␈α∞≡elds␈α
like␈α∞sociology␈α
(the␈α∞concept␈α∞of␈α
CLAN,␈α∞POWER).␈α
 The␈α∞possibility␈α
that␈α∞you␈α∞might␈α
be
␈↓ ↓H␈↓able␈α∩to␈α⊃represent␈α∩concepts,␈α∩albeit␈α⊃crudely,␈α∩but␈α∩good␈α⊃enuf␈α∩to␈α∩get␈α⊃some␈α∩interesting␈α∩results␈α⊃(e.g.,
␈↓ ↓H␈↓prediction␈αof␈αnew␈αpsychological␈αe≥ects,␈αor␈αat␈αleast␈αinteresting␈αexperiments␈αto␈αtry,␈αeven␈α though␈αthe
␈↓ ↓H␈↓facets of the concept labbelled HUMANS will not be complete).

␈↓ ↓H␈↓Justi≡cation␈α_for␈α_starting␈α_knowledge␈α_and␈α↔heuristics␈α_Minimal,␈α_complete,␈α_analogous␈α_to␈α↔some
␈↓ ↓H␈↓human/group of humans (children:Piaget).

␈↓ ↓H␈↓Overestimation␈α∞of␈α∞our␈α∞own␈α
understanding␈α∞of␈α∞phenomena␈α∞Because␈α
when␈α∞you␈α∞talk␈α∞to␈α∞yourself␈α
or
␈↓ ↓H␈↓another human, you needn't be as precise as when talking to a PDP10.

␈↓ ↓H␈↓What␈α⊃characteristics␈α⊃make␈α∩a␈α⊃task␈α⊃ripe␈α∩for␈α⊃attack␈α⊃by␈α∩AI␈α⊃methods,␈α⊃say␈α∩heuristic␈α⊃programming
␈↓ ↓H␈↓methods.␈α The␈α
experts␈αin␈α
the␈α≡eld␈αare␈α
much␈αbetter␈α
than␈αthe␈αaverage␈α
intelligent␈αman.␈α
 E.g.:␈αchess,
␈↓ ↓H␈↓math,␈α
Mycin's␈α
Task,␈α∞...␈α
 OR:␈α
The␈α
combinatorial␈α∞nature␈α
of␈α
the␈α
problem␈α∞is␈α
between␈α
one␈α∞and␈α
four
␈↓ ↓H␈↓orders␈α⊂of␈α⊂magnitude␈α⊂above␈α⊂human␈α⊂abilities.␈α⊂EG:␈α⊂CONGEN.␈α⊂ OR:␈α⊂The␈α⊂task␈α⊂is␈α⊂thought␈α⊂to␈α⊂be
␈↓ ↓H␈↓intellectual␈αby␈αthe␈αscienti≡c␈αcommunity,␈αwhether␈αit␈αis␈αor␈αnot␈α(preparing␈αdetailed␈αastrological␈αcharts
␈↓ ↓H␈↓may␈αbe␈α
very␈αcomplex,␈αbut␈α
no␈αone␈αhere␈α
would␈αrespect␈αa␈α
program␈αvery␈αmuch␈α
that␈αdid␈α
that.␈αMany
␈↓ ↓H␈↓management␈α∪sciences␈α∩algorithms␈α∪are␈α∪kept␈α∩from␈α∪being␈α∩considered␈α∪part␈α∪of␈α∩AI␈α∪because␈α∪of␈α∩the
␈↓ ↓H␈↓nonscienti≡c motivations and uses they're put to).
␈↓ ↓H␈↓␈↓εDouglas B. Lenat␈↓␈↓ ¬!␈↓β␈↓&Automated Mathematician␈↓)αβ␈↓␈↓ 	ε␈↓εADVANCED Seminar      page   5␈↓



␈↓ ↓H␈↓Plans for the future
␈↓ ↓H␈↓intuitions
␈↓ ↓H␈↓expanded breadth -- new domains of math, of science (chem. concepts: an O=C-C-¬C)
␈↓ ↓H␈↓expanded depth -- deeper no. thy. results, new rsults
␈↓ ↓H␈↓better user interface
␈↓ ↓H␈↓experiments
␈↓ ↓H␈↓documentation, public relations, papers, talks
␈↓ ↓H␈↓theoretical analysis, extracting the new key ideas and cleaning them o≥.
␈↓ ↓H␈↓AM next year at SStanford? anywhere? more diss. topics?