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␈↓ α∧␈↓␈↓ u1


␈↓ α∧␈↓␈↓ ∧x␈↓αPROGRAMS WITH COMMON SENSE␈↓

␈↓ α∧␈↓␈↓ εtby

␈↓ α∧␈↓␈↓ ε≥John McCarthy



␈↓ α∧␈↓␈↓ εFSummary

␈↓ α∧␈↓Interesting␈α
work␈αis␈α
being␈α
done␈αin␈α
programming␈α
computers␈αto␈α
solve␈α
problems␈αwhich␈α
require␈αa␈α
high
␈↓ α∧␈↓degree␈α⊃of␈α⊃intelligence␈α∩in␈α⊃humans.␈α⊃ However,␈α⊃certain␈α∩elementary␈α⊃verbal␈α⊃reasoning␈α∩processes␈α⊃so
␈↓ α∧␈↓simple␈α
that␈αthey␈α
can␈αbe␈α
carried␈αout␈α
by␈αany␈α
non-feeble␈αminded␈α
human␈αhave␈α
yet␈αto␈α
be␈αsimulated␈α
by
␈↓ α∧␈↓machine programs.

␈↓ α∧␈↓␈↓ αTThis␈αpaper␈αwill␈αdiscuss␈α
programs␈αto␈αmanipulate␈αin␈αa␈α
suitable␈αformal␈αlanguage␈α(most␈αlikely␈α
a
␈↓ α∧␈↓part␈α∂of␈α∂the␈α∂predicate␈α∂calculus)␈α∂common␈α∂instrumental␈α∂statements.␈α∂ The␈α∂basic␈α∂program␈α⊂will␈α∂draw
␈↓ α∧␈↓immediate␈α∂conclusions␈α∂from␈α∂a␈α⊂list␈α∂of␈α∂premises.␈α∂ These␈α⊂conclusions␈α∂will␈α∂be␈α∂either␈α⊂declarative␈α∂or
␈↓ α∧␈↓imperative␈α≠sentences.␈α≤ When␈α≠an␈α≠imperative␈α≤sentence␈α≠is␈α≠deduced␈α≤the␈α≠program␈α≤takes␈α≠a
␈↓ α∧␈↓corresponding␈α∂action.␈α∂ These␈α∂actions␈α∂may␈α⊂include␈α∂printing␈α∂sentences,␈α∂moving␈α∂sentences␈α⊂on␈α∂lists,
␈↓ α∧␈↓and reinitiating the basic deduction process on these lists.

␈↓ α∧␈↓␈↓ αTFacilities␈α∩will␈α∩be␈α∩provided␈α∩for␈α∩communication␈α∩with␈α∩humans␈α∩in␈α∩the␈α∩system␈α∪via␈α∩manual
␈↓ α∧␈↓intervention and display devices connected to the computer.

␈↓ α∧␈↓␈↓ ε*                  

␈↓ α∧␈↓The␈α
␈↓↓advice␈αtaker␈↓␈α
is␈α
a␈αproposed␈α
program␈α
for␈αsolving␈α
problems␈α
by␈αmanipulating␈α
sentences␈αin␈α
formal
␈↓ α∧␈↓languages.␈α∪ The␈α∪main␈α∪difference␈α∪between␈α∀it␈α∪and␈α∪other␈α∪programs␈α∪or␈α∪proposed␈α∀programs␈α∪for
␈↓ α∧␈↓manipulating␈α
formal␈α∞languages␈α
(the␈α
␈↓↓Logic␈α∞Theory␈α
Machine␈↓␈α∞of␈α
Newell,␈α
Simon␈α∞and␈α
Shaw␈α∞and␈α
the
␈↓ α∧␈↓Geometry␈α⊂Program␈α⊂of␈α⊂Gelernter)␈α⊂is␈α⊂that␈α⊂in␈α⊂the␈α⊂previous␈α⊂programs␈α⊂the␈α⊂formal␈α⊂system␈α⊂was␈α⊂the
␈↓ α∧␈↓subject␈α∪matter␈α∀but␈α∪the␈α∀heuristics␈α∪were␈α∀all␈α∪embodied␈α∪in␈α∀the␈α∪program.␈α∀ In␈α∪this␈α∀program␈α∪the
␈↓ α∧␈↓procedures␈α∂will␈α∂be␈α∂described␈α∂as␈α∂much␈α∂as␈α∂possible␈α∂in␈α∂the␈α∂language␈α∂itself␈α∂and,␈α∂in␈α∂particular,␈α∂the
␈↓ α∧␈↓heuristics are all so described.

␈↓ α∧␈↓␈↓ αTThe␈α⊃main␈α∩advantages␈α⊃we␈α∩expect␈α⊃the␈α⊃␈↓↓advice␈α∩taker␈↓␈α⊃to␈α∩have␈α⊃is␈α⊃that␈α∩its␈α⊃behavior␈α∩will␈α⊃be
␈↓ α∧␈↓improvable␈αmerely␈αby␈αmaking␈αstatements␈αto␈αit,␈αtelling␈αit␈αabout␈αits␈αsymbolic␈αenvironment␈αand␈αwhat
␈↓ α∧␈↓is␈α
wanted␈α
from␈α
it.␈α
 To␈α
make␈α
these␈α
statements␈αwill␈α
require␈α
little␈α
if␈α
any␈α
knowledge␈α
of␈α
the␈αprogram␈α
or
␈↓ α∧␈↓the␈αprevious␈αknowledge␈αof␈αthe␈α␈↓↓advice␈αtaker␈↓.␈α One␈αwill␈αbe␈αable␈αto␈αassume␈αthat␈αthe␈α␈↓↓advice␈αtaker␈↓␈αwill
␈↓ α∧␈↓have␈αavailable␈αto␈αit␈α
a␈αfairly␈αwide␈αclass␈α
of␈αimmediate␈αlogical␈αconsequence␈α
of␈αanything␈αit␈αis␈αtold␈α
and
␈↓ α∧␈↓its␈αprevious␈αknowledge.␈α This␈αproperty␈αis␈αexpected␈αto␈αhave␈αmuch␈αin␈αcommon␈αwith␈αwhat␈αmakes␈αus
␈↓ α∧␈↓describe␈α⊂certain␈α∂humans␈α⊂as␈α∂having␈α⊂␈↓↓common␈α∂sense␈↓.␈α⊂ We␈α∂shall␈α⊂therefore␈α∂say␈α⊂that␈α∂␈↓↓a␈α⊂program␈α∂has
␈↓ α∧␈↓↓common␈α⊗sense␈α↔if␈α⊗it␈α⊗automatically␈α↔deduces␈α⊗for␈α↔itself␈α⊗a␈α⊗sufficiently␈α↔wide␈α⊗class␈α↔of␈α⊗immediate
␈↓ α∧␈↓↓consequences of anything it is told and what it already knows.␈↓

␈↓ α∧␈↓␈↓ αTThe␈αdesign␈αof␈αthis␈αsystem␈αwill␈αbe␈αa␈αjoint␈αproject␈αwith␈αMarvin␈αMinsky,␈αbut␈αMinsky␈αis␈αnot␈α
to
␈↓ α∧␈↓be held responsible for the views expressed here.

␈↓ α∧␈↓␈↓ αTBefore␈α∂describing␈α∂the␈α∂␈↓↓advice␈α∂taker␈↓␈α∞in␈α∂any␈α∂detail,␈α∂I␈α∂would␈α∞like␈α∂to␈α∂describe␈α∂more␈α∂fully␈α∞our
␈↓ α∧␈↓␈↓ u2


␈↓ α∧␈↓motivation␈α⊂for␈α∂proceeding␈α⊂in␈α∂this␈α⊂direction.␈α∂ Our␈α⊂ultimate␈α∂objective␈α⊂is␈α∂to␈α⊂make␈α⊂programs␈α∂that
␈↓ α∧␈↓learn␈α
from␈αtheir␈α
experience␈αas␈α
effectively␈α
as␈αhumans␈α
do.␈α It␈α
may␈α
not␈αbe␈α
realized␈αhow␈α
far␈α
we␈αare
␈↓ α∧␈↓presently␈α∞from␈α∂this␈α∞objective.␈α∂ It␈α∞is␈α∞not␈α∂hard␈α∞to␈α∂make␈α∞machines␈α∞learn␈α∂from␈α∞experience␈α∂to␈α∞make
␈↓ α∧␈↓simple␈αchanges␈αin␈αtheir␈αbehavior␈αof␈αa␈αkind␈αwhich␈αhas␈αbeen␈αanticipated␈αby␈αthe␈αprogrammer.␈α For
␈↓ α∧␈↓example,␈α∂Samuel␈α∂has␈α∂included␈α∂in␈α∂his␈α∂checker␈α∂program␈α∂facilities␈α∂for␈α∂improving␈α∂the␈α∂weights␈α∞the
␈↓ α∧␈↓machine␈α∪assigns␈α∩to␈α∪various␈α∩factors␈α∪in␈α∩evaluating␈α∪positions.␈α∩ He␈α∪has␈α∩also␈α∪included␈α∪a␈α∩scheme
␈↓ α∧␈↓whereby␈α
the␈α
machine␈α∞remembers␈α
games␈α
it␈α∞has␈α
played␈α
previously␈α∞and␈α
deviates␈α
from␈α∞its␈α
previous
␈↓ α∧␈↓play␈α∂when␈α⊂it␈α∂finds␈α⊂a␈α∂position␈α⊂which␈α∂it␈α⊂previously␈α∂lost.␈α⊂ Suppose,␈α∂however,␈α⊂that␈α∂we␈α⊂wanted␈α∂an
␈↓ α∧␈↓improvement␈αin␈αbehavior␈αcorresponding,␈αsay,␈αto␈αthe␈αdiscovery␈αby␈αthe␈αmachine␈αof␈αthe␈αprinciple␈αof
␈↓ α∧␈↓the␈αopposition␈αin␈αcheckers.␈α No␈αpresent␈αor␈αpresently␈αproposed␈αschemes␈αare␈αcapable␈αof␈αdiscovering
␈↓ α∧␈↓phenomena as abstract as this.

␈↓ α∧␈↓␈↓ αTIf␈α
one␈αwants␈α
a␈αmachine␈α
to␈αbe␈α
able␈αto␈α
discover␈αan␈α
abstraction,␈αit␈α
seems␈αmost␈α
likely␈α
that␈αthe
␈↓ α∧␈↓machine must be able to represent this abstraction in some relatively simple way.

␈↓ α∧␈↓␈↓ αTThere␈αis␈αone␈αknown␈αway␈αof␈αmaking␈αa␈αmachine␈αcapable␈αof␈αlearning␈αarbitrary␈αbehavior;␈αthus
␈↓ α∧␈↓to␈α∂anticipate␈α∂every␈α∂kind␈α∂of␈α∞behavior.␈α∂ This␈α∂is␈α∂to␈α∂make␈α∞it␈α∂possible␈α∂for␈α∂the␈α∂machine␈α∂to␈α∞simulate
␈↓ α∧␈↓arbitrary␈αbehaviors␈αand␈αtry␈α
them␈αout.␈α These␈αbehaviors␈αmay␈α
be␈αrepresented␈αeither␈αby␈α
nerve␈αnets
␈↓ α∧␈↓(␈↓↓ref.2␈↓),␈αby␈αTuring␈αmachines␈α(␈↓↓ref.3␈↓),␈αor␈αby␈αcalculator␈αprograms␈α(␈↓↓ref.4␈↓).␈α The␈αdifficulty␈αis␈αtwo-fold.
␈↓ α∧␈↓First,␈α∪in␈α∪any␈α∪of␈α∪these␈α∪representations␈α∩the␈α∪density␈α∪of␈α∪interesting␈α∪behaviors␈α∪is␈α∪incredibly␈α∩low.
␈↓ α∧␈↓Second,␈αand␈αeven␈αmore␈αimportant,␈αsmall␈αinteresting␈α
changes␈αin␈αbehavior␈αexpressed␈αat␈αa␈αhigh␈α
level
␈↓ α∧␈↓of␈α∞abstraction␈α∞do␈α∞not␈α∞have␈α∞simple␈α∞representations.␈α∞ It␈α∞is␈α∞as␈α∞though␈α∞the␈α∞human␈α∂genetic␈α∞structure
␈↓ α∧␈↓were␈α∞represented␈α
by␈α∞a␈α
set␈α∞of␈α
blue-prints.␈α∞ Then␈α
a␈α∞mutation␈α
would␈α∞usually␈α
result␈α∞in␈α
a␈α∞wart␈α∞or␈α
a
␈↓ α∧␈↓failure␈αof␈αparts␈αto␈αmeet,␈αor␈αeven␈αan␈αungrammatical␈αblue-print␈αwhich␈αcould␈αnot␈αbe␈αtranslated␈αinto
␈↓ α∧␈↓an␈αanimal␈α
at␈αall.␈α It␈α
is␈αvery␈αdifficult␈α
to␈αsee␈αhow␈α
the␈αgenetic␈αrepresentation␈α
scheme␈αmanages␈α
to␈αbe
␈↓ α∧␈↓general␈αenough␈α
to␈αrepresent␈αthe␈α
great␈αvariety␈α
of␈αanimals␈αobserved␈α
and␈αyet␈αbe␈α
such␈αthat␈α
so␈αmany
␈↓ α∧␈↓interesting␈α∞changes␈α∞in␈α∂the␈α∞organism␈α∞are␈α∂represented␈α∞by␈α∞small␈α∂genetic␈α∞changes.␈α∞ The␈α∂problem␈α∞of
␈↓ α∧␈↓how␈α∞such␈α∞a␈α∞representation␈α∞controls␈α∞the␈α∞development␈α
of␈α∞a␈α∞fertilized␈α∞egg␈α∞into␈α∞a␈α∞mature␈α∞animal␈α
is
␈↓ α∧␈↓even more difficult.

␈↓ α∧␈↓␈↓ αTIn␈α
our␈α
opinion,␈α
a␈α
system␈αwhich␈α
is␈α
to␈α
evolve␈α
intelligence␈αof␈α
human␈α
order␈α
should␈α
have␈αat␈α
least
␈↓ α∧␈↓the following features:


␈↓ α∧␈↓␈↓ β∧1.␈↓ βDAll␈α∞behaviors␈α∞must␈α∞be␈α∞representable␈α
in␈α∞the␈α∞system.␈α∞ Therefore,␈α∞the␈α∞system␈α
should
␈↓ α∧␈↓␈↓ βDeither␈α∩be␈α∩able␈α∩to␈α∩construct␈α∩arbitrary␈α∩automata␈α∩or␈α∩to␈α∩program␈α∩in␈α∩some␈α∩general
␈↓ α∧␈↓␈↓ βDpurpose programming language.

␈↓ α∧␈↓␈↓ β∧2.␈↓ βDInteresting changes in behavior must be expressible in a simple way.

␈↓ α∧␈↓␈↓ β∧3.␈↓ βDAll␈αaspects␈αof␈αbehavior␈αexcept␈αthe␈αmost␈αroutine␈αmust␈αbe␈αimprovable.␈α In␈αparticular,
␈↓ α∧␈↓␈↓ βDthe improving mechanism should be improvable.

␈↓ α∧␈↓␈↓ β∧4.␈↓ βDThe␈α
machine␈α
must␈α
have␈α
or␈α
evolve␈α
concepts␈α
of␈α
partial␈α
success␈α
because␈α
on␈αdifficult
␈↓ α∧␈↓␈↓ βDproblems decisive successes or failures come too infrequently.

␈↓ α∧␈↓␈↓ β∧5.␈↓ βDThe␈α
system␈αmust␈α
be␈α
able␈αto␈α
create␈αsubroutines␈α
which␈α
can␈αbe␈α
included␈αin␈α
procedures
␈↓ α∧␈↓␈↓ βDas␈αunits.␈α
 The␈αlearning␈αof␈α
subroutines␈αis␈α
complicated␈αby␈αthe␈α
fact␈αthat␈α
the␈αeffect␈αof␈α
a
␈↓ α∧␈↓␈↓ βDsubroutine␈α⊂is␈α⊂not␈α⊂usually␈α∂good␈α⊂or␈α⊂bad␈α⊂in␈α∂itself.␈α⊂ Therefore,␈α⊂the␈α⊂mechanism␈α∂that
␈↓ α∧␈↓␈↓ u3


␈↓ α∧␈↓␈↓ βDselects␈α∪subroutines␈α∪should␈α∪have␈α∪concepts␈α∪of␈α∪interesting␈α∪or␈α∪powerful␈α∩subroutine
␈↓ α∧␈↓␈↓ βDwhose application may be good under suitable conditions.

␈↓ α∧␈↓␈↓ αTOf␈α∞the␈α
5␈α∞points␈α
mentioned␈α∞above,␈α∞our␈α
work␈α∞concentrates␈α
mainly␈α∞on␈α
the␈α∞second.␈α∞ We␈α
base
␈↓ α∧␈↓ourselves␈αon␈αthe␈αidea␈αthat:␈α␈↓↓In␈αorder␈αfor␈αa␈αprogram␈αto␈αbe␈αcapable␈αof␈αlearning␈αsomething␈αit␈αmust␈αfirst
␈↓ α∧␈↓↓be␈αcapable␈αof␈αbeing␈αtold␈αit.␈↓␈αIn␈αfact,␈αin␈αthe␈αearly␈αversions␈αwe␈αshall␈αconcentrate␈αentirely␈αon␈αthis␈αpoint
␈↓ α∧␈↓and␈α⊂attempt␈α∂to␈α⊂achieve␈α∂a␈α⊂system␈α∂which␈α⊂can␈α∂be␈α⊂told␈α∂to␈α⊂make␈α∂a␈α⊂specific␈α∂improvement␈α⊂in␈α⊂in␈α∂its
␈↓ α∧␈↓behavior␈αwith␈α
no␈αmore␈α
knowledge␈αof␈α
its␈αinternal␈α
structure␈αor␈α
previous␈αknowledge␈α
than␈αis␈α
required
␈↓ α∧␈↓in␈αorder␈αto␈αinstruct␈αa␈αhuman.␈α Once␈αthis␈αis␈αachieved,␈αwe␈αmay␈αbe␈αable␈αto␈αtell␈αthe␈α␈↓↓advice␈αtaker␈↓␈αhow
␈↓ α∧␈↓to learn from experience.

␈↓ α∧␈↓␈↓ αTThe␈αmain␈αdistinction␈αbetween␈αthe␈αway␈αone␈αprograms␈αa␈αcomputer␈αand␈αmodifies␈αthe␈αprogram
␈↓ α∧␈↓and␈α
the␈α
way␈α
one␈α
instructs␈α
a␈α
human␈α
or␈α
will␈α
instruct␈α
the␈α
␈↓↓advice␈α
taker␈↓␈α
is␈α
this:␈α
A␈α
machine␈αis␈α
instructed
␈↓ α∧␈↓mainly␈αin␈αthe␈αform␈αof␈αa␈αsequence␈αof␈αimperative␈αsentences;␈αwhile␈αa␈αhuman␈αis␈αinstructed␈αmainly␈αin
␈↓ α∧␈↓declarative␈α⊂sentences␈α⊂describing␈α⊂the␈α⊂situation␈α⊂in␈α⊂which␈α⊂action␈α⊂is␈α⊂required␈α⊂together␈α⊂with␈α⊃a␈α⊂few
␈↓ α∧␈↓imperatives␈α⊂that␈α⊂say␈α⊂what␈α⊂is␈α⊂wanted.␈α⊂ We␈α⊂shall␈α∂list␈α⊂the␈α⊂advantages␈α⊂of␈α⊂of␈α⊂the␈α⊂two␈α⊂methods␈α∂of
␈↓ α∧␈↓instruction.

␈↓ α∧␈↓␈↓↓Advantages of Imperative Sentences␈↓


␈↓ α∧␈↓␈↓ β∧1.␈↓ βDA procedure described in imperatives is already laid out and is carried out faster.

␈↓ α∧␈↓␈↓ β∧2.␈↓ βDOne␈α
starts␈α
with␈α
a␈α
machine␈α
in␈α
a␈α
basic␈α
state␈α
and␈α
does␈α
not␈α
assume␈α
previous␈α
knowledge
␈↓ α∧␈↓␈↓ βDon the part of the machine.

␈↓ α∧␈↓␈↓↓Advantages of Declarative Sentences␈↓


␈↓ α∧␈↓␈↓ β∧1.␈↓ βDAdvantage can be taken of previous knowledge.

␈↓ α∧␈↓␈↓ β∧2.␈↓ βDDeclarative␈α∂sentences␈α∂have␈α∂logical␈α∂consequences␈α∂and␈α∂it␈α∂can␈α∂be␈α∂arranged␈α∂that␈α∂the
␈↓ α∧␈↓␈↓ βDmachine␈α∞will␈α∞have␈α∞available␈α∞sufficiently␈α∞simple␈α∞logical␈α∞consequences␈α∞of␈α∞what␈α∞it␈α∞is
␈↓ α∧␈↓␈↓ βDtold and what it previously knew.

␈↓ α∧␈↓␈↓ β∧3.␈↓ βDThe␈αmeaning␈α
of␈αdeclaratives␈α
is␈αmuch␈αless␈α
dependent␈αon␈α
their␈αorder␈α
than␈αis␈αthe␈α
case
␈↓ α∧␈↓␈↓ βDwith imperatives.  This makes it easier to have after-thoughts.

␈↓ α∧␈↓␈↓ β∧4.␈↓ βDThe␈αeffect␈αof␈αa␈αdeclarative␈αis␈αless␈αdependent␈αon␈αthe␈αprevious␈αstate␈αof␈αthe␈αsystem␈αso
␈↓ α∧␈↓␈↓ βDthat less knowledge of this state is required on the part of the instructor.

␈↓ α∧␈↓␈↓ αTThe␈α∂only␈α∂way␈α∂we␈α∂know␈α∂of␈α∂expressing␈α∂abstractions␈α∂(such␈α∂as␈α∂the␈α∂previous␈α∂example␈α∂of␈α∞the
␈↓ α∧␈↓opposition␈αin␈αcheckers)␈αis␈αin␈αlanguage.␈α That␈αis␈αwhy␈αwe␈αhave␈αdecided␈αto␈αprogram␈αa␈αsystem␈αwhich
␈↓ α∧␈↓reasons verbally.

␈↓ α∧␈↓␈↓ ¬α␈↓αThe Construction of the Advice Taker␈↓

␈↓ α∧␈↓␈↓ αTThe ␈↓↓advice taker␈↓ system has the following main features:
␈↓ α∧␈↓␈↓ u4


␈↓ α∧␈↓␈↓ β∧1.␈↓ βDThere␈αis␈αa␈αmethod␈αof␈αrepresenting␈αexpressions␈αin␈αthe␈αcomputer.␈α These␈αexpressions
␈↓ α∧␈↓␈↓ βDare␈αdefined␈αrecursively␈α
as␈αfollows:␈αA␈α
class␈αof␈αentities␈αcalled␈α
terms␈αis␈αdefined␈α
and␈αa
␈↓ α∧␈↓␈↓ βDterm␈α⊗is␈α∃an␈α⊗expression.␈α∃ A␈α⊗sequence␈α∃of␈α⊗expressions␈α∃is␈α⊗an␈α⊗expression.␈α∃ These
␈↓ α∧␈↓␈↓ βDexpressions are represented in the machine by list structures (␈↓↓ref.1␈↓).

␈↓ α∧␈↓␈↓ β∧2.␈↓ βDCertain␈αof␈α
these␈αexpressions␈αmay␈α
be␈αregarded␈αas␈α
declarative␈αsentences␈αin␈α
a␈αcertain
␈↓ α∧␈↓␈↓ βDlogical␈α
system␈α
which␈α
will␈α
be␈α
analogous␈α
to␈α
a␈α
universal␈α
Post␈α
canonical␈α∞system.␈α
 The
␈↓ α∧␈↓␈↓ βDparticular␈α∀system␈α∪chosen␈α∀will␈α∪depend␈α∀on␈α∪programming␈α∀considerations␈α∀but␈α∪will
␈↓ α∧␈↓␈↓ βDprobably␈α∪have␈α∪a␈α∪single␈α∪rule␈α∪of␈α∪inference␈α∪which␈α∪will␈α∪combine␈α∀substitution␈α∪for
␈↓ α∧␈↓␈↓ βDvariables␈α
with␈αmodus␈α
ponens.␈α
 The␈αpurpose␈α
of␈α
the␈αcombination␈α
is␈α
to␈αavoid␈α
choking
␈↓ α∧␈↓␈↓ βDthe machine with special cases of general propositions already deduced.

␈↓ α∧␈↓␈↓ β∧3.␈↓ βDThere␈α
is␈α
an␈α∞␈↓↓immediate␈α
deduction␈α
routine␈↓␈α∞which␈α
when␈α
given␈α∞a␈α
set␈α
of␈α∞premises␈α
will
␈↓ α∧␈↓␈↓ βDdeduce␈α∞a␈α
set␈α∞of␈α
immediate␈α∞conclusions.␈α
 Initially,␈α∞the␈α
immediate␈α∞deduction␈α
routine
␈↓ α∧␈↓␈↓ βDwill␈α
simply␈αwrite␈α
down␈αall␈α
one-step␈αconsequences␈α
of␈αthe␈α
premises.␈α Later,␈α
this␈αmay
␈↓ α∧␈↓␈↓ βDbe␈α
elaborated␈α
so␈α
that␈α
the␈α
routine␈α
will␈α
produce␈α
some␈α
other␈α
conclusions␈α
which␈αmay␈α
be
␈↓ α∧␈↓␈↓ βDof␈α∂interest.␈α∂ However,␈α∂this␈α∂routine␈α∂will␈α∂not␈α∂use␈α∂semantic␈α∂heuristics;␈α⊂i.e.,␈α∂heuristics
␈↓ α∧␈↓␈↓ βDwhich depend on the subject matter under discussion.

␈↓ α∧␈↓␈↓ αT␈↓ βDThe␈αintelligence,␈αif␈αany,␈αof␈αthe␈αadvice␈αtaker␈αwill␈αnot␈αbe␈αembodied␈αin␈αthe␈αimmediate
␈↓ α∧␈↓␈↓ βDdeduction␈α⊃routine.␈α⊂ This␈α⊃intelligence␈α⊃will␈α⊂be␈α⊃embodied␈α⊂in␈α⊃the␈α⊃procedures␈α⊂which
␈↓ α∧␈↓␈↓ βDchoose␈α⊂the␈α⊃lists␈α⊂of␈α⊂premises␈α⊃to␈α⊂which␈α⊃the␈α⊂immediate␈α⊂deduction␈α⊃routine␈α⊂is␈α⊃to␈α⊂be
␈↓ α∧␈↓␈↓ βDapplied.␈α⊂ Of␈α⊃course,␈α⊂the␈α⊃program␈α⊂should␈α⊃never␈α⊂attempt␈α⊃to␈α⊂apply␈α⊃the␈α⊂immediate
␈↓ α∧␈↓␈↓ βDdeduction␈α∂routine␈α∂simultaneously␈α∂to␈α∂the␈α∂list␈α∂of␈α∂everything␈α∂it␈α∂knows.␈α∂ This␈α∂would
␈↓ α∧␈↓␈↓ βDmake the deduction routine take too long.

␈↓ α∧␈↓␈↓ β∧4.␈↓ βDNot␈α
all␈α
expressions␈α
are␈α
interpreted␈αby␈α
the␈α
system␈α
as␈α
declarative␈α
sentences.␈α Some␈α
are
␈↓ α∧␈↓␈↓ βDthe␈αnames␈αof␈αentities␈αof␈αvarious␈αkinds.␈α Certain␈αformulas␈αrepresent␈α␈↓↓objects␈↓.␈α For␈αour
␈↓ α∧␈↓␈↓ βDpurposes,␈αan␈α
entity␈αis␈α
an␈αobject␈α
if␈αwe␈α
have␈αsomething␈α
to␈αsay␈α
about␈αit␈α
other␈αthan␈α
the
␈↓ α∧␈↓␈↓ βDthings␈α∞which␈α∞may␈α∞be␈α∞deduced␈α∞from␈α∞the␈α∞form␈α∞of␈α∞its␈α∞name.␈α∞ For␈α∞example,␈α∂to␈α∞most
␈↓ α∧␈↓␈↓ βDpeople,␈αthe␈αnumber␈α3812␈αis␈αnot␈αan␈αobject:␈αthey␈αhave␈αnothing␈αto␈αsay␈αabout␈αit␈αexcept
␈↓ α∧␈↓␈↓ βDwhat␈α
can␈α
be␈α
deduced␈αfrom␈α
its␈α
structure.␈α
 On␈α
the␈αother␈α
hand,␈α
to␈α
most␈αAmericans␈α
the
␈↓ α∧␈↓␈↓ βDnumber␈α∩l776␈α∩is␈α∩an␈α∪object␈α∩because␈α∩they␈α∩have␈α∪filed␈α∩somewhere␈α∩the␈α∩fact␈α∪that␈α∩it
␈↓ α∧␈↓␈↓ βDrepresents␈α⊂the␈α⊂year␈α⊂when␈α⊂the␈α⊂American␈α⊂Revolution␈α⊂started.␈α⊂ In␈α⊂the␈α⊃␈↓↓advice␈α⊂taker␈↓
␈↓ α∧␈↓␈↓ βDeach␈α
object␈α
has␈α
a␈α
␈↓↓property␈α
list␈↓␈α
in␈αwhich␈α
are␈α
listed␈α
the␈α
specific␈α
things␈α
we␈α
have␈αto␈α
say
␈↓ α∧␈↓␈↓ βDabout␈αit.␈α Some␈αthings␈αwhich␈αcan␈αbe␈αdeduced␈αfrom␈αthe␈αname␈αof␈αthe␈αobject␈αmay␈αbe
␈↓ α∧␈↓␈↓ βDincluded␈αin␈αthe␈αproperty␈αlist␈αanyhow␈αif␈αthe␈αdeduction␈αwas␈αactually␈αcarried␈αout␈αand
␈↓ α∧␈↓␈↓ βDwas difficult enough so that the system does not want to carry it out again.

␈↓ α∧␈↓␈↓ β∧5.␈↓ βDEntities␈α
other␈α
than␈αdeclarative␈α
sentences␈α
which␈α
can␈αbe␈α
represented␈α
by␈α
formulas␈αin
␈↓ α∧␈↓␈↓ βDthe system are individuals, functions, and programs.

␈↓ α∧␈↓␈↓ β∧6.␈↓ βDThe␈αprogram␈αis␈α
intended␈αto␈αoperate␈αcyclically␈α
as␈αfollows.␈α The␈αimmediate␈α
deduction
␈↓ α∧␈↓␈↓ βDroutine␈α⊂is␈α⊂applied␈α⊃to␈α⊂a␈α⊂list␈α⊂of␈α⊃premises␈α⊂and␈α⊂a␈α⊂list␈α⊃of␈α⊂individuals.␈α⊂ Some␈α⊃of␈α⊂the
␈↓ α∧␈↓␈↓ βDconclusions␈αhave␈αthe␈αform␈αof␈αimperative␈αsentences.␈α These␈αare␈αobeyed.␈α Included␈αin
␈↓ α∧␈↓␈↓ βDthe␈α⊂set␈α⊂of␈α⊂imperatives␈α⊃which␈α⊂may␈α⊂be␈α⊂obeyed␈α⊃is␈α⊂the␈α⊂routine␈α⊂which␈α⊃deduces␈α⊂and
␈↓ α∧␈↓␈↓ βDobeys.

␈↓ α∧␈↓␈↓ αT␈↓ βDWe␈α⊂shall␈α∂illustrate␈α⊂the␈α⊂way␈α∂the␈α⊂␈↓↓advice␈α∂taker␈↓␈α⊂is␈α⊂supposed␈α∂to␈α⊂act␈α∂by␈α⊂means␈α⊂of␈α∂an
␈↓ α∧␈↓␈↓ u5


␈↓ α∧␈↓␈↓ βDexample.␈α∞ Assume␈α∞that␈α∞I␈α∞am␈α∞seated␈α∞at␈α∞my␈α
desk␈α∞at␈α∞home␈α∞and␈α∞I␈α∞wish␈α∞to␈α∞go␈α∞to␈α
the
␈↓ α∧␈↓␈↓ βDairport.␈α My␈αcar␈αis␈αat␈αmy␈αhome␈αalso.␈α The␈αsolution␈αof␈αthe␈αproblem␈αis␈αto␈αwalk␈αto␈αthe
␈↓ α∧␈↓␈↓ βDcar␈αand␈αdrive␈αthe␈αcar␈αto␈αthe␈αairport.␈α First,␈αwe␈αshall␈αgive␈αa␈αformal␈αstatement␈αof␈αthe
␈↓ α∧␈↓␈↓ βDpremises␈αthe␈α
␈↓↓advice␈αtaker␈↓␈α
uses␈αto␈α
draw␈αthe␈α
conclusions.␈α Then␈α
we␈αshall␈α
discuss␈αthe
␈↓ α∧␈↓␈↓ βDheuristics␈αwhich␈αcause␈αthe␈α␈↓↓advice␈αtaker␈↓␈αto␈αassemble␈αthese␈αpremises␈αfrom␈αthe␈αtotality
␈↓ α∧␈↓␈↓ βDof␈α
facts␈α
it␈α
has␈α
available.␈α
 The␈α
premises␈α
come␈α
in␈α
groups,␈α
and␈α
we␈α
shall␈α∞explain␈α
the
␈↓ α∧␈↓␈↓ βDinterpretation of each group.

␈↓ α∧␈↓␈↓ β∧␈↓ βD1.␈↓ ∧∧First,␈α⊃we␈α⊂have␈α⊃a␈α⊂predicate␈α⊃"␈↓↓at␈↓".␈α⊃"␈↓↓at(x,y)␈↓"␈α⊂is␈α⊃a␈α⊂formalization␈α⊃of␈α⊂"␈↓↓x␈α⊃is␈α⊃at␈α⊂y␈↓".
␈↓ α∧␈↓␈↓ βDUnder this heading we have the premises

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧1.␈↓ ∧D␈↓↓at (I, desk)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧2.␈↓ ∧D␈↓↓at (desk,home)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧3.␈↓ ∧D␈↓↓at (car, home)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧4.␈↓ ∧D␈↓↓at (home,county)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧5.␈↓ ∧D␈↓↓at (airport, county)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βDWe␈α∞shall␈α∂need␈α∞the␈α∞fact␈α∂that␈α∞the␈α∂relation"␈↓↓at␈↓"␈α∞is␈α∞transitive␈α∂which␈α∞might␈α∂be␈α∞written
␈↓ α∧␈↓␈↓ βDdirectly as

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧6.␈↓ ∧D␈↓↓at(x,y), at(y,z) → at(x,z)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βDor alternatively we might instead use the more abstract premises

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧6'.␈↓ ∧D␈↓↓transitive (at)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧7'.␈↓ ∧D␈↓↓transitive (u) → (u(x,y), u(y,z) → u(x.z))␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βDfrom which 6. can be deduced.

␈↓ α∧␈↓␈↓ β∧␈↓ βD2.␈↓ ∧∧There are two rules concerning the feasibility of walking and driving.

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧8.␈↓ ∧D␈↓↓walkable(x), at(y,x), at(z,x), at(I,y) → can(go(y,z, walking))␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧9.␈↓ ∧D␈↓↓drivable(x), at(y,x), at (z,x), at(car,y), at(I,car → can(go(y,z, driving))␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βDThere are also two specific facts

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧10.␈↓ ∧D␈↓↓walkable (home)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧11.␈↓ ∧D␈↓↓drivable (county)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD3.␈↓ ∧∧Next we have a rule concerned with the properties of going.

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧12.␈↓ ∧D␈↓↓did(go(x,y,z)) → at(I,y)␈↓
␈↓ α∧␈↓␈↓ u6


␈↓ α∧␈↓␈↓ β∧␈↓ βD4.␈↓ ∧∧The problem itself is posed by the premise:

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧13.␈↓ ∧D␈↓↓want(at(I,airport))␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD5.␈↓ ∧∧The␈α
above␈α
are␈α
all␈α
the␈α∞premises␈α
concerned␈α
with␈α
the␈α
particular␈α∞problem.␈α
 The
␈↓ α∧␈↓␈↓ βDlast group of premises are common to almost all problems of this sort.  They are:

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧14.␈↓ ∧D␈↓↓(x → can(y)), (did(y) → z) → canachult[x,y,z)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βDThe␈αpredicate␈α␈↓↓"canachult(x,y,z)"␈↓␈αmeans␈αthat␈αin␈αa␈αsituation␈αto␈αwhich␈α␈↓↓x␈↓␈α
applies,␈αthe
␈↓ α∧␈↓␈↓ βDaction␈α∞␈↓↓y␈↓␈α∞can␈α∞be␈α∞performed␈α∞and␈α∞ultimately␈α∞brings␈α∞about␈α∞a␈α∞situation␈α∞to␈α∞to␈α∞which␈α∞␈↓↓z␈↓
␈↓ α∧␈↓␈↓ βDapplies.  A sort of transitivity is described by

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧15.␈↓ ∧D␈↓↓canachult(x,y,z), canachult(z,u,v) → canachult(x,prog(y,u),v).␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βDHere␈α
␈↓↓prog(u,v)␈↓␈α
is␈αthe␈α
program␈α
of␈αfirst␈α
carrying␈α
out␈α␈↓↓u␈↓␈α
and␈α
then␈α␈↓↓v␈↓.␈α
 (Some␈α
kind␈αof
␈↓ α∧␈↓␈↓ βDidentification␈α
of␈α
a␈α
single␈α
action␈α
␈↓↓u␈↓␈α∞with␈α
the␈α
one␈α
step␈α
program␈α
␈↓↓prog(u)␈↓␈α∞is␈α
obviously
␈↓ α∧␈↓␈↓ βDrequired,␈αbut␈α
the␈αdetails␈α
of␈αhow␈αthis␈α
will␈αfit␈α
into␈αthe␈αformalism␈α
have␈αnot␈α
yet␈αbeen
␈↓ α∧␈↓␈↓ βDworked out).

␈↓ α∧␈↓␈↓ αT␈↓ βDThe final premise is the one which causes action to be taken.

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧16.␈↓ ∧D␈↓↓x,canachult(x,prog(y,z),w), want(w) → do(y)␈↓

␈↓ α∧␈↓␈↓ αT␈↓ βDThe␈αargument␈α
the␈α␈↓↓advice␈α
taker␈↓␈αmust␈α
produce␈αin␈α
order␈αto␈α
solve␈αthe␈αproblem␈α
deduces
␈↓ α∧␈↓␈↓ βDthe following propositions in more or less the following order:

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧1.␈↓ ∧D␈↓↓at(I,desk) → can(go(desk,car,walking))␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧2.␈↓ ∧D␈↓↓at(I,car) → can(go(home,airport,driving))␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧3.␈↓ ∧D␈↓↓did(go(desk,car,walking)) → at(I,car)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧4.␈↓ ∧D␈↓↓did(go(home,airport,driving)) → at(I,airport)␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧5.␈↓ ∧D␈↓↓canachult(at,(I,desk), go(desk,car,walking, at(I,car))␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧6.␈↓ ∧D␈↓↓canachult(at(I,car), go(home,airport,driving), at(I,airport))␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧7.␈↓ ∧D␈↓↓canachult(at(I,desk),␈α4prog(go(desk,car,walking),␈α4go(home,airport,
␈↓ α∧␈↓↓␈↓ βDdriving)) → at(I,airport))␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βD␈↓ ∧∧8.␈↓ ∧D␈↓↓do(go(desk,car,walking))␈↓

␈↓ α∧␈↓␈↓ β∧␈↓ βDThe deduction of the last proposition initiates action.

␈↓ α∧␈↓␈↓ αTThe␈αabove␈αproposed␈αreasoning␈αraises␈αtwo␈αmajor␈αquestions␈αof␈αheuristic.␈α The␈αfirst␈αis␈αthat␈αof
␈↓ α∧␈↓how␈αthe␈αl6␈αpremises␈αare␈αcollected,␈αand␈αthe␈αsecond␈αis␈αthat␈αof␈αhow␈αthe␈αdeduction␈αproceeds␈αonce␈αthey
␈↓ α∧␈↓are␈α∞found.␈α∂ We␈α∞cannot␈α∞give␈α∂complete␈α∞answers␈α∞to␈α∂either␈α∞question␈α∞in␈α∂the␈α∞present␈α∞paper;␈α∂they␈α∞are
␈↓ α∧␈↓␈↓ u7


␈↓ α∧␈↓obviously␈αnot␈αcompletely␈αseparate␈αsince␈αsome␈αof␈αthe␈αdeductions␈αmight␈αbe␈αmade␈αbefore␈αsome␈αof␈αthe
␈↓ α∧␈↓premises are collected.  Let us first consider the question of where the l6 premises came from.

␈↓ α∧␈↓␈↓ αTFirst␈α∞of␈α∞all,␈α∞we␈α∂assert␈α∞that␈α∞except␈α∞for␈α∞the␈α∂13th␈α∞premise␈α∞␈↓↓want(at(I,airport))␈↓,␈α∞which␈α∂sets␈α∞the
␈↓ α∧␈↓goal,␈α∩and␈α∩the␈α⊃1st␈α∩premise␈α∩␈↓↓(at(I,desk)␈↓␈α⊃which␈α∩we␈α∩shall␈α⊃get␈α∩from␈α∩a␈α⊃routine␈α∩which␈α∩answers␈α⊃the
␈↓ α∧␈↓question␈α␈↓↓"where␈αam␈αI")␈↓,␈α␈↓↓all␈αthe␈αpremises␈αcan␈αreasonably␈αbe␈αexpected␈αto␈αbe␈αspecifically␈αpresent␈αin␈αthe
␈↓ α∧␈↓↓memory␈↓␈αof␈αa␈αmachine␈αwhich␈αhas␈αcompetence␈αof␈αhuman␈αorder␈αin␈αfinding␈αits␈αway␈αaround.␈α That␈αis,
␈↓ α∧␈↓none␈α∂of␈α∂them␈α∂are␈α∂so␈α∂specific␈α∂to␈α∂the␈α∂problem␈α∂at␈α∂hand␈α∂that␈α∂assuming␈α∂their␈α∂presence␈α∂in␈α∂memory
␈↓ α∧␈↓constitutes␈α∂an␈α∂anticipation␈α⊂of␈α∂this␈α∂particular␈α⊂problem␈α∂or␈α∂of␈α∂a␈α⊂class␈α∂of␈α∂problems␈α⊂narrower␈α∂than
␈↓ α∧␈↓those␈αwhich␈αany␈αhuman␈αcan␈αexpect␈αto␈αhave␈αpreviously␈αsolved.␈α We␈αmust␈αimpose␈αthis␈αrequirement
␈↓ α∧␈↓if we are to be able to say that the ␈↓↓advice taker␈↓ exhibits ␈↓↓common sense␈↓.

␈↓ α∧␈↓␈↓ αTOn␈αthe␈αother␈α
hand,␈αwhile␈αwe␈αmay␈α
reasonably␈αassume␈αthat␈αthe␈α
premises␈αare␈αin␈α
memory,␈αwe
␈↓ α∧␈↓still␈α∞have␈α∞to␈α∂describe␈α∞how␈α∞they␈α∂are␈α∞assembled␈α∞into␈α∂a␈α∞list␈α∞by␈α∂themselves␈α∞to␈α∞which␈α∂the␈α∞deduction
␈↓ α∧␈↓routine␈α
may␈αbe␈α
applied.␈α
 Tentatively,␈αwe␈α
expect␈α
the␈α␈↓↓advice␈α
taker␈↓␈α
to␈αproceed␈α
as␈α
follows:␈αinitially,␈α
the
␈↓ α∧␈↓sentence␈α␈↓↓"want(at(I,airport))"␈↓␈αis␈αon␈α
a␈αcertain␈αlist␈α␈↓↓L␈↓,␈α
called␈αthe␈αmain␈αlist,␈α
all␈αby␈αitself.␈α The␈α
program
␈↓ α∧␈↓begins␈αwith␈αan␈αobservation␈αroutine␈αwhich␈αlooks␈αat␈αthe␈αmain␈αlist␈αand␈αputs␈αcertain␈αstatements␈α
about
␈↓ α∧␈↓the␈α∞contents␈α∞of␈α
this␈α∞list␈α∞on␈α∞a␈α
list␈α∞called␈α∞"observations␈α
of␈α∞the␈α∞main␈α∞list".␈α
 We␈α∞shall␈α∞not␈α∞specify␈α
at
␈↓ α∧␈↓present␈α
what␈α
all␈α∞the␈α
possible␈α
outputs␈α
of␈α∞this␈α
observation␈α
routine␈α
are␈α∞but␈α
merely␈α
say␈α
that␈α∞in␈α
this
␈↓ α∧␈↓case␈α
it␈α
will␈α
observe␈α
that␈α
"the␈α
only␈α
statement␈αon␈α
␈↓↓L␈↓␈α
has␈α
the␈α
form␈α
␈↓↓'want(u(x))'."␈↓␈α
(We␈α
write␈α
this␈αout␈α
in
␈↓ α∧␈↓English␈αbecause␈αwe␈αhave␈αnot␈αyet␈αsettled␈αon␈αa␈αformalism␈αfor␈αrepresenting␈αstatements␈αof␈αthis␈αkind).
␈↓ α∧␈↓The␈α∞"deduce␈α∂and␈α∞obey"␈α∞routine␈α∂is␈α∞then␈α∞applied␈α∂to␈α∞the␈α∞combination␈α∂of␈α∞the␈α∞"observations␈α∂of␈α∞the
␈↓ α∧␈↓main␈α
list"␈α∞list,␈α
and␈α
a␈α∞list␈α
called␈α∞the␈α
"standing␈α
orders␈α∞list".␈α
 This␈α∞list␈α
is␈α
rather␈α∞small␈α
and␈α∞is␈α
never
␈↓ α∧␈↓changed,␈α
or␈α
at␈α
least␈α
is␈α
only␈α
changed␈α
in␈α
major␈α
changes␈α
of␈α
the␈α
advice␈α
taker.␈α
 The␈α
contents␈α∞of␈α
the
␈↓ α∧␈↓"standing␈α∞orders"␈α∞list␈α∂has␈α∞not␈α∞been␈α∞worked␈α∂out,␈α∞but␈α∞what␈α∞must␈α∂be␈α∞deduced␈α∞is␈α∞the␈α∂extraction␈α∞of
␈↓ α∧␈↓certain␈α
statements␈α
from␈α
property␈α
lists.␈α
 Namely,␈α
the␈α
program␈α
first␈α
looks␈α
at␈α␈↓↓"want(at(I,airport))"␈↓␈α
and
␈↓ α∧␈↓attempts␈α∞to␈α∂copy␈α∞the␈α∞statements␈α∂on␈α∞its␈α∞property␈α∂list.␈α∞ Let␈α∞us␈α∂assume␈α∞that␈α∞it␈α∂fails␈α∞in␈α∂this␈α∞attempt
␈↓ α∧␈↓because␈α␈↓↓"want(at(I,airport))"␈↓␈αdoes␈αnot␈αhave␈αthe␈αstatus␈α
of␈αan␈αobject␈αand␈αhence␈αhas␈αno␈αproperty␈α
list.
␈↓ α∧␈↓(One␈α⊂might␈α⊂expect␈α⊂that␈α⊂if␈α⊂the␈α⊂problem␈α⊂of␈α⊂going␈α⊂to␈α⊂the␈α⊂airport␈α⊂has␈α⊂arisen␈α⊂before,␈α∂␈↓↓"want(at(I,
␈↓ α∧␈↓↓airport))"␈↓␈α∀would␈α∀be␈α∀an␈α∀object,␈α∀but␈α∀this␈α∀might␈α∀depend␈α∀on␈α∀whether␈α∀there␈α∀were␈α∀routines␈α∀for
␈↓ α∧␈↓generalizing␈αprevious␈αexperience␈αthat␈α
would␈αallow␈αsomething␈αof␈αgeneral␈α
use␈αto␈αbe␈αfiled␈αunder␈α
that
␈↓ α∧␈↓heading).␈α∞ Next␈α∞in␈α∞order␈α∞of␈α∞increasing␈α∂generality␈α∞the␈α∞machine␈α∞would␈α∞see␈α∞if␈α∞anything␈α∂were␈α∞filed
␈↓ α∧␈↓under␈α∂␈↓↓"want(at(I,x))"␈↓␈α⊂which␈α∂would␈α⊂deal␈α∂with␈α∂the␈α⊂general␈α∂problem␈α⊂of␈α∂getting␈α⊂somewhere.␈α∂ One
␈↓ α∧␈↓would␈αexpect␈αthat␈αpremises␈α6,␈α(or␈α6'␈αand␈α7'),␈α8,␈α9,␈α12,␈αwould␈αbe␈αso␈αfiled.␈α There␈αwould␈αalso␈αbe␈αthe
␈↓ α∧␈↓formula

␈↓ α∧␈↓␈↓ ¬␈↓↓want(at(I,x)) → do(observe(where am I))␈↓

␈↓ α∧␈↓which␈α∂would␈α∂give␈α∂us␈α∂premise␈α∂1.␈α∂ There␈α∂would␈α∂also␈α∂be␈α∂a␈α∂reference␈α∂to␈α∂the␈α∂next␈α∂higher␈α∂level␈α∂of
␈↓ α∧␈↓abstraction␈αin␈αthe␈αgoal␈αstatement␈αwhich␈αwould␈αcause␈αa␈αlook␈αat␈αthe␈αproperty␈αlist␈αof␈α␈↓↓"want(x)"␈↓.␈α This
␈↓ α∧␈↓would give us 14, 15, and 16.

␈↓ α∧␈↓␈↓ αTWe␈αshall␈αnot␈αtry␈αto␈αfollow␈αthe␈αsolution␈αfurther␈αexcept␈αto␈αremark␈αthat␈αon␈αthe␈αproperty␈αlist␈αof
␈↓ α∧␈↓␈↓↓"want(at(I,x))"␈↓␈α
there␈α∞would␈α
be␈α∞a␈α
rule␈α∞that␈α
starts␈α
with␈α∞the␈α
premises␈α∞␈↓↓at(I,y)"␈↓␈α
and␈α∞␈↓↓"want(I,x)"␈↓␈α
and
␈↓ α∧␈↓has␈αas␈α
conclusion␈αa␈α
search␈αfor␈α
the␈αproperty␈α
list␈αof␈α
␈↓↓"go(y,x,z)"␈↓.␈α This␈α
would␈αpresumably␈α
fail,␈αand
␈↓ α∧␈↓then␈αthere␈αwould␈αhave␈αto␈αbe␈αheuristics␈αthat␈αwould␈α
initiate␈αa␈αsearch␈αfor␈αa␈α␈↓↓y␈↓␈αsuch␈αthat␈α␈↓↓"at(I,y)"␈↓␈α
and
␈↓ α∧␈↓␈↓↓"at(airport,yy)"␈↓.␈α⊃ This␈α⊃would␈α⊂be␈α⊃done␈α⊃by␈α⊂looking␈α⊃on␈α⊃the␈α⊂property␈α⊃lists␈α⊃of␈α⊂the␈α⊃origin␈α⊃and␈α⊂the
␈↓ α∧␈↓destination␈α
and␈α
working␈α
up.␈α
 Then␈α
premise␈α
9␈α
would␈α
be␈α
found␈α
which␈α
has␈α
as␈α
one␈α
of␈α
its␈αpremises
␈↓ α∧␈↓␈↓↓at(I,car)␈↓.␈α⊂ A␈α⊃repetition␈α⊂of␈α⊃the␈α⊂above␈α⊂would␈α⊃find␈α⊂premise␈α⊃8,␈α⊂which␈α⊂would␈α⊃complete␈α⊂the␈α⊃set␈α⊂of
␈↓ α∧␈↓␈↓ u8


␈↓ α∧␈↓premises␈α∪since␈α∪the␈α∪other␈α∪␈↓↓"at"␈↓␈α∪premises␈α∪would␈α∪have␈α∪been␈α∪found␈α∪as␈α∪by-products␈α∀of␈α∪previous
␈↓ α∧␈↓searches.

␈↓ α∧␈↓␈↓ αTWe␈αhope␈αthat␈αthe␈α
presence␈αof␈αthe␈αheuristic␈αrules␈α
mentioned␈αon␈αthe␈αproperty␈αlists␈α
where␈αwe
␈↓ α∧␈↓have␈αput␈αthem␈αwill␈αseem␈αplausible␈αto␈αthe␈αreader.␈α It␈αshould␈αbe␈αnoticed␈αthat␈αon␈αthe␈αhigher␈αlevel␈αof
␈↓ α∧␈↓abstraction␈αmany␈αof␈αthe␈αstatements␈αare␈αof␈αthe␈αstimulus-response␈αform.␈α One␈αmight␈αconjecture␈αthat
␈↓ α∧␈↓division␈α⊃in␈α⊂man␈α⊃between␈α⊂conscious␈α⊃and␈α⊃unconscious␈α⊂thought␈α⊃occurs␈α⊂at␈α⊃the␈α⊃boundary␈α⊂between
␈↓ α∧␈↓stimulus-response␈α
heuristics␈α
which␈α
do␈α
not␈α
have␈α∞to␈α
be␈α
reasonsed␈α
about␈α
but␈α
only␈α
obeyed,␈α∞and␈α
the
␈↓ α∧␈↓others which have to serve as premises in deductions.

␈↓ α∧␈↓␈↓ αTWe␈α⊂hope␈α∂to␈α⊂formalize␈α⊂the␈α∂heuristics␈α⊂in␈α∂another␈α⊂paper␈α⊂before␈α∂we␈α⊂start␈α⊂programming␈α∂the
␈↓ α∧␈↓system.




␈↓ α∧␈↓␈↓ βz␈↓↓DISCUSSION OF THE PAPER BY DR. J. MCCARTHY␈↓

␈↓ α∧␈↓PROF.␈αY.␈α
BAR-HILLEL:␈αDr.␈α
McCarthy's␈αpaper␈α
belongs␈αin␈α
the␈αJournal␈α
of␈αHalf-Baked␈αIdeas,␈α
the
␈↓ α∧␈↓creation␈α
of␈α
which␈α
was␈α
recently␈α
proposed␈α
by␈α
Dr.␈α
I.␈α
J.␈α
Good.␈α
Dr.␈α
McCarthy␈α
will␈α
probably␈α
be␈α
the␈α
first
␈↓ α∧␈↓to␈αadmit␈αthis.␈α Before␈αhe␈α
goes␈αon␈αto␈αbake␈αhis␈α
ideas␈αfully,␈αit␈αmight␈αbe␈α
well␈αto␈αgive␈αhim␈αsome␈α
advice
␈↓ α∧␈↓and␈αraise␈αsome␈αobjections.␈α He␈αhimself␈αmentions␈αsome␈αpossible␈αobjections,␈αbut␈αI␈αdo␈αnot␈αthink␈αthat
␈↓ α∧␈↓he treats them with the full consideration they deserve; there are others he does not mention.

␈↓ α∧␈↓␈↓ αTFor␈α∞lack␈α∞of␈α∂time,␈α∞I␈α∞shall␈α∂not␈α∞go␈α∞into␈α∂the␈α∞first␈α∞part␈α∂of␈α∞his␈α∞paper,␈α∂although␈α∞I␈α∞think␈α∂that␈α∞it
␈↓ α∧␈↓contains␈α
a␈α
lot␈αof␈α
highly␈α
unclear␈α
philosophical,␈αor␈α
pseudo-philosophical␈α
assumptions.␈α
 I␈αshall␈α
rather
␈↓ α∧␈↓spend␈α
my␈αtime␈α
in␈α
commenting␈αon␈α
the␈αexample␈α
he␈α
works␈αout␈α
in␈αhis␈α
paper␈α
at␈αsome␈α
length.␈α Before␈α
I
␈↓ α∧␈↓start,␈α∃let␈α∀me␈α∃voice␈α∀my␈α∃protest␈α∃against␈α∀the␈α∃general␈α∀assumption␈α∃of␈α∀Dr.␈α∃McCarthy␈α∃-␈α∀slightly
␈↓ α∧␈↓caricatured␈α∀-␈α∀that␈α∀a␈α∀machine,␈α∀if␈α∀only␈α∪its␈α∀program␈α∀is␈α∀specified␈α∀with␈α∀a␈α∀sufficient␈α∀degree␈α∪of
␈↓ α∧␈↓carelessness, will be able to carry out satisfactory even rather difficult tasks.

␈↓ α∧␈↓␈↓ αTConsider␈α∩the␈α∩assumption␈α∪that␈α∩the␈α∩relation␈α∪he␈α∩designates␈α∩by␈α∪␈↓↓at␈↓␈α∩is␈α∩transitive␈α∪(page␈α∩81).
␈↓ α∧␈↓However,␈α∞since␈α
he␈α∞takes␈α∞both␈α
␈↓↓"at(I,desk)"␈↓␈α∞and␈α
␈↓↓"at(desk,home)"␈↓␈α∞as␈α∞premises,␈α
I␈α∞presume␈α∞-␈α
though
␈↓ α∧␈↓this␈αis␈αnever␈αmade␈αquite␈αclear␈α-␈αthat␈α␈↓↓"at"␈↓␈αmeans␈αsomething␈αlike␈αbeing-a-physical-part-or-in-the-
␈↓ α∧␈↓immediate-spatial-␈α
neighborhood-of.␈α
 But␈α
then␈αthe␈α
relation␈α
is␈α
clearly␈α
not␈αtransitive.␈α
 If␈α
A␈α
is␈αin␈α
the
␈↓ α∧␈↓immediate␈αspatial␈αneighborhood␈αof␈αB␈αand␈αB␈αin␈αthe␈αimmediate␈αspatial␈αneighborhood␈αof␈αC␈αthen␈αA
␈↓ α∧␈↓need␈αnot␈αbe␈α
in␈αthe␈αimmediate␈α
spatial␈αneighborhood␈αof␈αC.␈α
 Otherwise,␈αeverything␈αwould␈α
turn␈αout
␈↓ α∧␈↓to␈α∞be␈α
in␈α∞the␈α
immediate␈α∞spatial␈α∞neighborhood␈α
of␈α∞everything,␈α
which␈α∞is␈α
surely␈α∞not␈α∞Dr.␈α
McCarthy's
␈↓ α∧␈↓intention.␈α Of␈α
course,␈αstarting␈α
from␈αfalse␈α
premises,␈αone␈α
can␈αstill␈α
arrive␈αat␈α
right␈αconclusions.␈α We␈α
do
␈↓ α∧␈↓such␈α
things␈αquite␈α
often,␈αand␈α
a␈αmachine␈α
could␈αdo␈α
it.␈α
 But␈αit␈α
would␈αprobably␈α
be␈αbad␈α
advice␈αto␈α
allow
␈↓ α∧␈↓a machine to do such things consistently.

␈↓ α∧␈↓␈↓ αTMany␈αof␈α
the␈αother␈α
23␈αsteps␈α
in␈αDr.␈αMcCarthy's␈α
argument␈αare␈α
equally␈αor␈α
more␈αquestionable,
␈↓ α∧␈↓but␈α∞I␈α∂don't␈α∞think␈α∂we␈α∞should␈α∞spend␈α∂our␈α∞time␈α∂showing␈α∞this␈α∞in␈α∂detail.␈α∞ My␈α∂major␈α∞question␈α∂is␈α∞the
␈↓ α∧␈↓following:␈αOn␈αpage␈α83␈αMcCarthy␈αstates␈αthat␈αa␈αmachine␈αwhich␈αhas␈αa␈αcompetence␈αof␈α
human␈αorder
␈↓ α∧␈↓in␈αfinding␈αits␈αway␈αaround␈αwill␈αhave␈αalmost␈αall␈αthe␈αpremises␈αof␈αthe␈αargument␈αstored␈αin␈αits␈αmemory.
␈↓ α∧␈↓I␈αam␈αat␈αa␈αcomplete␈αloss␈αto␈αunderstand␈αthe␈αpoint␈αof␈αthis␈αremark.␈α If␈αDr.␈αMcCarthy␈αwants␈αto␈αsay␈αno
␈↓ α∧␈↓more␈αthan␈αthat␈αa␈αmachine,␈αin␈αorder␈αto␈αbehave␈α
like␈αa␈αhuman␈αbeing,␈αmust␈αhave␈αthe␈αknowledge␈αof␈α
a
␈↓ α∧␈↓human␈αbeing,␈αthen␈αthis␈αis␈αsurely␈αnot␈αa␈αvery␈αimportant␈αremark␈αto␈αmake.␈α But␈αif␈αnot,␈αwhat␈αwas␈αthe
␈↓ α∧␈↓intention of this remark?
␈↓ α∧␈↓␈↓ u9


␈↓ α∧␈↓␈↓ αTThe␈α
decisive␈α
question␈α
how␈α
a␈α
machine,␈αeven␈α
assuming␈α
that␈α
it␈α
will␈α
have␈α
somehow␈αcountless
␈↓ α∧␈↓millions␈α∂of␈α∂facts␈α∂stored␈α∂in␈α∂its␈α∞memory,␈α∂will␈α∂be␈α∂able␈α∂to␈α∂pick␈α∞out␈α∂those␈α∂facts␈α∂which␈α∂will␈α∂serve␈α∞as
␈↓ α∧␈↓premises␈α∞for␈α∞its␈α∞deduction␈α∞is␈α∞promised␈α∞to␈α
receive␈α∞its␈α∞treatment␈α∞in␈α∞another␈α∞paper,␈α∞which␈α∞is␈α
quite
␈↓ α∧␈↓right for a half-baked idea.

␈↓ α∧␈↓␈↓ αTIt␈α
sounds␈α
rather␈α
incredible␈α
that␈α
the␈α
machine␈α
could␈α
have␈α
arrived␈α
at␈α
its␈α
conclusion␈α
-␈α
which,␈α
in
␈↓ α∧␈↓plain␈α
English,␈α
is␈α
"Walk␈α
from␈α
your␈α
desk␈α
to␈α
your␈α
car!"␈α
-␈α
by␈α
sound␈α
deduction.␈α
 This␈αconclusion␈α
surely
␈↓ α∧␈↓could␈α∂not␈α∂possibly␈α∂follow␈α⊂from␈α∂the␈α∂premise␈α∂in␈α∂any␈α⊂serious␈α∂sense.␈α∂ Might␈α∂it␈α∂not␈α⊂be␈α∂occasionally
␈↓ α∧␈↓cheaper␈α
to␈α
call␈α
a␈α
taxi␈α
and␈α
have␈α
it␈α
take␈α
you␈α
over␈α
to␈α
the␈α
airport?␈α
 Couldn't␈α
you␈α
decide␈α
to␈αcancel␈α
your
␈↓ α∧␈↓flight␈αor␈αto␈αdo␈αa␈αhundred␈αother␈αthings?␈α I␈α
don't␈αthink␈αit␈αwould␈αbe␈αwise␈αto␈αdevelop␈αa␈α
programming
␈↓ α∧␈↓language␈α∞so␈α
powerful␈α∞as␈α
to␈α∞make␈α∞a␈α
machine␈α∞arrive␈α
at␈α∞the␈α
conclusion␈α∞Dr.␈α∞ McCarthy␈α
apparently
␈↓ α∧␈↓intends it to make.

␈↓ α∧␈↓␈↓ αTLet␈α⊃me␈α⊃also␈α⊃point␈α⊃out␈α⊃that␈α⊃in␈α⊃the␈α⊃example␈α⊃the␈α⊃time␈α⊃factor␈α⊃has␈α⊃never␈α⊃been␈α⊃mentioned,
␈↓ α∧␈↓probably␈αfor␈αthe␈α
sake␈αof␈αsimplicity.␈α
 But␈αclearly␈αthis␈αfactor␈α
is␈αhere␈αso␈α
important␈αthat␈αit␈α
could␈αnot
␈↓ α∧␈↓possibly␈α∂be␈α∂disregarded␈α∂without␈α∂distorting␈α∂the␈α∂whole␈α∂argument.␈α∂ Does␈α∂not␈α∂the␈α∂solution␈α∞depend,
␈↓ α∧␈↓among␈αthousands␈α
of␈αother␈αthings,␈α
also␈αupon␈αthe␈α
time␈αof␈α
my␈αbeing␈αat␈α
my␈αdesk,,␈αthe␈α
time␈αat␈αwhich␈α
I
␈↓ α∧␈↓have to be at the airport, the distance from the airport, the speed of my car, etc.

␈↓ α∧␈↓␈↓ αTTo␈αmake␈αthe␈αargument␈αdeductively␈αsound,␈αits␈αcomplexity␈αwill␈αhave␈αto␈αbe␈αincreased␈αby␈α
many
␈↓ α∧␈↓orders␈αof␈αmagnitude.␈α So␈αlong␈αas␈αthis␈αis␈αnot␈αrealized,␈αany␈αdiscussions␈αof␈αmachines␈αable␈αto␈αperform
␈↓ α∧␈↓the␈α
deductive␈α
-␈α
and␈α
inductive!␈α
-␈α
operations␈αnecessary␈α
for␈α
treating␈α
problems␈α
of␈α
the␈α
kind␈αbrought
␈↓ α∧␈↓forward␈α∃by␈α∃Dr.␈α∃McCarthy␈α∃is␈α⊗totally␈α∃pointless.␈α∃ The␈α∃gap␈α∃between␈α∃Dr.␈α⊗ McCarthy's␈α∃general
␈↓ α∧␈↓programme␈α(with␈αwhich␈αI␈α
have␈αlittle␈αquarrel,␈αafter␈α
discounting␈αits␈α"philosophical"␈αfeatures)␈αand␈α
its
␈↓ α∧␈↓execution␈α∞even␈α
in␈α∞such␈α∞a␈α
simple␈α∞case␈α∞as␈α
the␈α∞one␈α∞discussed␈α
seems␈α∞to␈α∞me␈α
so␈α∞enormous␈α∞that␈α
much
␈↓ α∧␈↓more␈α
has␈αto␈α
be␈αdone␈α
to␈α
persuade␈αme␈α
that␈αeven␈α
the␈αfirst␈α
step␈α
in␈αbridging␈α
this␈αgap␈α
has␈αalready␈α
been
␈↓ α∧␈↓taken.

␈↓ α∧␈↓DR.␈αMCCARTHY␈α
(in␈αreply):␈α
Prof.␈αBar-Hillel␈α
has␈αcorrectly␈αobserved␈α
that␈αmy␈α
paper␈αis␈α
based␈αon
␈↓ α∧␈↓unstated␈αphilosophical␈α
assumptions␈αalthough␈αwhat␈α
he␈αmeans␈α
by␈α"pseudo-philosophical"␈αis␈α
unclear.
␈↓ α∧␈↓Whenever␈αwe␈αprogram␈αa␈αcomputer␈αto␈αlearn␈αfrom␈αexperience␈αwe␈αbuild␈αinto␈αthe␈αprogram␈αa␈αsort␈αof
␈↓ α∧␈↓epistemology.␈α
 It␈αmight␈α
be␈αargued␈α
that␈αthis␈α
epistemology␈α
should␈αbe␈α
made␈αexplicit␈α
before␈αone␈α
writes
␈↓ α∧␈↓the␈α∞programme,␈α∞but␈α∞epistemology␈α∞is␈α∞in␈α∞a␈α
foggier␈α∞state␈α∞than␈α∞computer␈α∞programming␈α∞even␈α∞in␈α
the
␈↓ α∧␈↓present␈α
half-baked␈α
state␈α
of␈α
the␈α
latter.␈α
 I␈α
hope␈α
that␈α
once␈α
we␈α
have␈α
succeeded␈α
in␈α
making␈αcomputer
␈↓ α∧␈↓programs␈α∂reason␈α∂about␈α∂the␈α∂world,␈α∂we␈α∂will␈α⊂be␈α∂able␈α∂to␈α∂reformulate␈α∂epistemology␈α∂as␈α∂a␈α⊂branch␈α∂of
␈↓ α∧␈↓applied mathematics no more mysterious or controversial than physics.

␈↓ α∧␈↓␈↓ αTOn␈α⊂re-reading␈α∂my␈α⊂paper␈α⊂I␈α∂can't␈α⊂see␈α⊂how␈α∂Prof.␈α⊂Bar-Hillel␈α∂could␈α⊂see␈α⊂in␈α∂it␈α⊂a␈α⊂proposal␈α∂to
␈↓ α∧␈↓specify␈α∂a␈α∂computer␈α∂program␈α∂carelessly.␈α∂ Since␈α∂other␈α∂people␈α∂have␈α∂proposed␈α∂this␈α∂as␈α∂a␈α⊂device␈α∂for
␈↓ α∧␈↓achieving "creativity", I can only conclude that he has some other paper in mind.

␈↓ α∧␈↓␈↓ αTIn␈αhis␈αcriticism␈αof␈αmy␈αuse␈αof␈αthe␈αsymbol␈α"at",␈αProf.␈αBar-Hillel␈αseems␈αto␈αhave␈αmisunderstood
␈↓ α∧␈↓the␈αintent␈αof␈αthe␈αexample.␈α First␈αof␈αall,␈αI␈αwas␈αnot␈αtrying␈αto␈αformalize␈αthe␈αsentence␈αform,␈αA␈αis␈αat␈αB,
␈↓ α∧␈↓as␈α∂it␈α∞is␈α∂used␈α∂in␈α∞English.␈α∂ ␈↓↓"at"␈↓␈α∂merely␈α∞was␈α∂intended␈α∂to␈α∞serve␈α∂as␈α∂a␈α∞convenient␈α∂mnemonic␈α∂for␈α∞the
␈↓ α∧␈↓relation␈α
between␈α
a␈α
place␈α
and␈αa␈α
sub-place.␈α
 Second,␈α
I␈α
was␈αnot␈α
proposing␈α
a␈α
practical␈α
problem␈αfor␈α
the
␈↓ α∧␈↓program␈α∩to␈α∩solve␈α∩but␈α∩rather␈α∩an␈α∩example␈α∩intended␈α∩to␈α∩allow␈α∩us␈α∩to␈α∩think␈α∩about␈α∩the␈α∩kinds␈α∩of
␈↓ α∧␈↓reasoning involved and how a machine may be made to perform them.

␈↓ α∧␈↓Prof.␈αBar-Hillel`s␈αmajor␈αpoint␈αconcerns␈αmy␈αstatement␈αthat␈αthe␈αpremises␈αlisted␈αcould␈αbe␈αassumed␈αto
␈↓ α∧␈↓␈↓ f10


␈↓ α∧␈↓be␈α⊗in␈α⊗memory.␈α∃ The␈α⊗intention␈α⊗of␈α⊗this␈α∃statement␈α⊗is␈α⊗to␈α⊗explain␈α∃why␈α⊗I␈α⊗have␈α⊗not␈α∃included
␈↓ α∧␈↓formalizations␈αof␈αstatements␈αlike,␈α"it␈αis␈αpossible␈αto␈αdrive␈αfrom␈αmy␈αhome␈αto␈αthe␈αairport"␈αamong␈αmy
␈↓ α∧␈↓premises.␈α
 If␈αthere␈α
were␈α␈↓↓n␈↓␈α
known␈αplaces␈α
in␈α
the␈αcounty␈α
there␈αwould␈α
be␈α␈↓↓n(n-1)/2␈↓␈α
such␈αsentences␈α
and,
␈↓ α∧␈↓since␈α
we␈α
are␈α
quite␈α
sure␈α
that␈α
we␈α
do␈α
not␈αhave␈α
each␈α
of␈α
them␈α
in␈α
our␈α
memories,␈α
it␈α
would␈α
be␈αcheating␈α
to
␈↓ α∧␈↓allow the machine to start with them.

␈↓ α∧␈↓␈↓ αTThe␈α
rest␈α
of␈α∞Prof.␈α
Bar-Hillel`s␈α
criticisms␈α∞concern␈α
ways␈α
in␈α∞which␈α
the␈α
model␈α∞mentioned␈α
does
␈↓ α∧␈↓not␈α
reflect␈αthe␈α
real␈αworld;␈α
I␈αhave␈α
already␈αexplained␈α
that␈αthis␈α
was␈αnot␈α
my␈αintention.␈α
 He␈αis␈α
certainly
␈↓ α∧␈↓right␈α⊂that␈α∂the␈α⊂complexity␈α∂of␈α⊂the␈α∂model␈α⊂will␈α∂have␈α⊂to␈α∂be␈α⊂increased␈α∂for␈α⊂it␈α∂to␈α⊂deal␈α⊂with␈α∂practical
␈↓ α∧␈↓problems.␈α⊂ What␈α⊂we␈α⊂disagree␈α⊂on␈α⊂is␈α⊃my␈α⊂contention␈α⊂that␈α⊂the␈α⊂conceptual␈α⊂difficulties␈α⊂arise␈α⊃at␈α⊂the
␈↓ α∧␈↓present␈αlevel␈α
of␈αcomplexity␈αand␈α
that␈αsolving␈α
them␈αwill␈αallow␈α
us␈αto␈αincrease␈α
the␈αcomplexity␈α
of␈αthe
␈↓ α∧␈↓model easily.

␈↓ α∧␈↓␈↓ αTWith␈αregard␈α
to␈αthe␈αdiscussion␈α
between␈αProf.␈αBar-Hillel␈α
and␈αOliver␈αSelfridge␈α
-␈αthe␈α
logic␈αis
␈↓ α∧␈↓intended␈α
to␈αbe␈α
faultless␈α
although␈αits␈α
premises␈αcannot␈α
be␈α
guaranteed.␈α The␈α
intended␈α
conclusion␈αis
␈↓ α∧␈↓␈↓↓"do(go(desk,are,walking))"␈↓␈α⊂not,␈α⊃of␈α⊂course,␈α⊃␈↓↓"at(I,airport)"␈↓.␈α⊂ The␈α⊂model␈α⊃oversimplifies␈α⊂but␈α⊃is␈α⊂not
␈↓ α∧␈↓intended to oversimplify to the extent of allowing one to deduce one's way to the airport.