/LMAR=0/XLINE=3/FONT#0=BAXL30/FONT#1=BAXM30/FONT#2=BASB30/FONT#3=SUB/FONT#4=SUP/FONT#5=BASL35/FONT#6=NGR25/FONT#7=MATH30/FONT#8=FIX25/FONT#9=GRKB30
␈↓ α∧␈↓␈↓ u1


␈↓ α∧␈↓α␈↓ β;AN EXAMPLE FOR NATURAL LANGUAGE UNDERSTANDING

␈↓ α∧␈↓α␈↓ ∧zAND THE AI PROBLEMS IT RAISES



␈↓ α∧␈↓␈↓ αTThe␈α∞following␈α
story␈α∞from␈α
the␈α∞␈↓↓New␈α
York␈α∞Times␈↓␈α
is␈α∞my␈α
candidate␈α∞for␈α
a␈α∞target␈α
for␈α∞a␈α
natural
␈↓ α∧␈↓language␈αunderstander.␈α The␈αstory␈αis␈αabout␈αa␈α
real␈αworld␈αevent,␈αand␈αtherefore␈αthe␈αintentions␈αof␈α
the
␈↓ α∧␈↓author␈α
are␈αless␈α
relevant␈αfor␈α
answering␈αquestions␈α
than␈α
for␈αmade␈α
up␈αstories.␈α
 ␈↓αThe␈αmain␈α
goal␈αof␈α
this
␈↓ α∧␈↓αdiscussion␈αis␈αto␈αsay␈αwhat␈αa␈αperson␈αwho␈αhas␈αunderstood␈αthe␈αstory␈αknows␈αabout␈αthe␈αevent.␈α This
␈↓ α∧␈↓αseems to me to be preliminary to making programs that can understand.␈↓

␈↓ α∧␈↓␈↓ αT"A␈α∪61-year␈α∀old␈α∪furniture␈α∪salesman␈α∀was␈α∪pushed␈α∀down␈α∪the␈α∪shaft␈α∀of␈α∪a␈α∀freight␈α∪elevator
␈↓ α∧␈↓yesterday␈α
in␈α
his␈α
downtown␈α
Brooklyn␈α
store␈α
by␈α
two␈α
robbers␈α
while␈α
a␈α
third␈α
attempted␈α
to␈α
crush␈αhim
␈↓ α∧␈↓with␈α
the␈αelevator␈α
car␈αbecause␈α
they␈αwere␈α
dissatisfied␈αwith␈α
the␈α␈↓∧1␈↓1,200␈α
they␈αhad␈α
forced␈αhim␈α
to␈αgive
␈↓ α∧␈↓them.

␈↓ α∧␈↓␈↓ αTThe␈α
buffer␈α
springs␈α
at␈α
the␈α
bottom␈α
of␈α
the␈α
shaft␈α
prevented␈α
the␈α
car␈α
from␈α
crushing␈α
the␈α
salesman,
␈↓ α∧␈↓John␈αJ.␈α
Hug,␈αafter␈αhe␈α
was␈αpushed␈α
from␈αthe␈αfirst␈α
floor␈αto␈α
the␈αbasement.␈α The␈α
car␈αstopped␈αabout␈α
12
␈↓ α∧␈↓inches above him as he flattened himself at the bottom of the pit.

␈↓ α∧␈↓␈↓ αTMr.␈α⊃Hug␈α⊂was␈α⊃pinned␈α⊃in␈α⊂the␈α⊃shaft␈α⊃for␈α⊂about␈α⊃half␈α⊂an␈α⊃hour␈α⊃until␈α⊂his␈α⊃cries␈α⊃attracted␈α⊂the
␈↓ α∧␈↓attention␈α∪of␈α∪a␈α∪porter.␈α∪ The␈α∪store␈α∪at␈α∩340␈α∪Livingston␈α∪Street␈α∪is␈α∪part␈α∪of␈α∪the␈α∪Seaman's␈α∩Quality
␈↓ α∧␈↓Furniture chain.

␈↓ α∧␈↓␈↓ αTMr.␈α⊂Hug␈α∂was␈α⊂removed␈α∂by␈α⊂members␈α∂of␈α⊂the␈α∂Police␈α⊂Emergency␈α∂Squad␈α⊂and␈α∂taken␈α⊂to␈α∂Long
␈↓ α∧␈↓Island␈αCollege␈αHospital.␈α He␈αwas␈αbadly␈αshaken,␈αbut␈αafter␈αbeing␈αtreated␈αfor␈αscrapes␈αof␈αhis␈αleft␈αarm
␈↓ α∧␈↓and␈α∂for␈α∂a␈α∂spinal␈α∂injury␈α∞was␈α∂released␈α∂and␈α∂went␈α∂home.␈α∞ He␈α∂lives␈α∂at␈α∂62-01␈α∂69th␈α∂Lane,␈α∞Maspeth,
␈↓ α∧␈↓Queens.

␈↓ α∧␈↓␈↓ αTHe␈α
has␈αworked␈α
for␈αseven␈α
years␈αat␈α
the␈αstore,␈α
on␈α
the␈αcorner␈α
of␈αNevins␈α
Street,␈αand␈α
this␈αwas␈α
the
␈↓ α∧␈↓fourth␈α
time␈α
he␈αhad␈α
been␈α
held␈αup␈α
in␈α
the␈αstore.␈α
 The␈α
last␈αtime␈α
was␈α
about␈αone␈α
year␈α
ago,␈α
when␈αhis
␈↓ α∧␈↓right arm was slashed by a knife-wielding robber."

␈↓ α∧␈↓␈↓ αTAn␈α
intelligent␈αperson␈α
or␈α
program␈αshould␈α
be␈α
able␈αto␈α
answer␈α
the␈αfollowing␈α
questions␈αbased␈α
on
␈↓ α∧␈↓the information in the story:

␈↓ α∧␈↓␈↓ αT1.␈α
Who␈α
was␈α
in␈α
the␈α
store␈α
when␈α
the␈α
events␈α
began?␈α
 Probably␈α
Mr.␈α
 Hug␈α
alone.␈α
although␈αthe
␈↓ α∧␈↓robbers␈αmight␈αhave␈αbeen␈αwaiting␈αfor␈αhim,␈αbut␈α
if␈αso,␈αthis␈αwould␈αhave␈αprobably␈αbeen␈αstated.␈α
 What
␈↓ α∧␈↓did the porter say to the robbers?  Nothing, because the robbers left before he came.

␈↓ α∧␈↓␈↓ αT2. Who was in the store during the attempt to kill Mr.  Hug?  Mr. Hug and the robbers.

␈↓ α∧␈↓␈↓ αT3. Who had the money at the end?  The robbers.

␈↓ α∧␈↓␈↓ αT4. Is Mr. Hug alive today?  Yes, unless something else has happened to him.

␈↓ α∧␈↓␈↓ αT5.  How did Mr. Hug get hurt?  Probably when he hit the bottom of the shaft.
␈↓ α∧␈↓␈↓ u2


␈↓ α∧␈↓␈↓ αT6.␈α Where␈αis␈αMr.␈α Hug's␈αhome?␈α (A␈αquestion␈αwhose␈αanswer␈αrequires␈αa␈αliteral␈αunderstanding
␈↓ α∧␈↓of only one sentence of the stories.) Does Mr. Hug live in Brooklyn?  No, he lives in Queens.

␈↓ α∧␈↓␈↓ αT7. What are the names and addresses of the robbers?  This information is not available.

␈↓ α∧␈↓␈↓ αT8.␈α⊂Was␈α∂Mr.␈α⊂Hug␈α⊂conscious␈α∂after␈α⊂the␈α⊂robbers␈α∂left?␈α⊂ Yes,␈α∂he␈α⊂cried␈α⊂out␈α∂and␈α⊂his␈α⊂cries␈α∂were
␈↓ α∧␈↓heard.

␈↓ α∧␈↓␈↓ αT9.␈α What␈αwould␈αhave␈αhappened␈αif␈αMr.␈α Hug␈αhad␈αnot␈αflattened␈αhimself␈αat␈αthe␈αbottom␈αof␈αthe
␈↓ α∧␈↓pit?␈α∂ What␈α∞would␈α∂have␈α∞happened␈α∂if␈α∞there␈α∂were␈α∞no␈α∂buffer␈α∞springs?␈α∂Mr.␈α∞Hug␈α∂would␈α∂have␈α∞been
␈↓ α∧␈↓crushed?

␈↓ α∧␈↓␈↓ αT10. Did Mr. Hug want to be crushed?  No.

␈↓ α∧␈↓␈↓ αT11. Did the robbers tell Mr. Hug their names?  No.

␈↓ α∧␈↓␈↓ αT12. Were the robbers present when the porter came?  No.

␈↓ α∧␈↓␈↓ αT13. Did Mr. Hug like the robbers, and did they like him?

␈↓ α∧␈↓␈↓ αT14.␈α Why␈αdid␈αthe␈αrobbers␈αleave␈αwithout␈αkilling␈αMr.␈α Hug?␈α Perhaps,␈αthey␈αthought␈αthey␈αhad
␈↓ α∧␈↓killed␈α∩him,␈α∩and␈α∩perhaps␈α∩their␈α∩anger␈α∩was␈α⊃appeased␈α∩by␈α∩the␈α∩actions␈α∩they␈α∩had␈α∩performed,␈α⊃and
␈↓ α∧␈↓perhaps␈α∂they␈α⊂had␈α∂taken␈α∂all␈α⊂the␈α∂time␈α∂they␈α⊂dared,␈α∂and␈α∂perhaps␈α⊂something␈α∂specific␈α⊂happened␈α∂to
␈↓ α∧␈↓frighten them away.

␈↓ α∧␈↓␈↓ αT15.␈α∂What␈α∞would␈α∂have␈α∞happened␈α∂if␈α∞Mr.␈α∂ Hug␈α∞had␈α∂tried␈α∞to␈α∂run␈α∞away?␈α∂Perhaps␈α∂he␈α∞would
␈↓ α∧␈↓have␈α
succeeded,␈α
but␈αmore␈α
likely␈α
they␈αwould␈α
have␈α
injured␈αor␈α
killed␈α
him␈αsince␈α
probably␈α
they␈αhad
␈↓ α∧␈↓weapons, and there were three of them.

␈↓ α∧␈↓␈↓ αT16.␈αWhat␈αcan␈α
Mr.␈αHug␈αdo␈α
to␈αavoid␈αthis␈α
in␈αthe␈αfuture?␈α
 No␈αsolution␈αis␈α
entirely␈αsatisfactory.
␈↓ α∧␈↓He␈αcould␈αcarry␈αa␈αgun␈αor␈αhe␈αcould␈αquit␈αor␈αhe␈αcould␈αget␈αhis␈αemployers␈αto␈αinstall␈αan␈αalarm␈αsystem␈αor
␈↓ α∧␈↓maybe he will be lucky.

␈↓ α∧␈↓␈↓ αT17. Did Mr. Hug know he was going to be robbed?  Does he know that he was robbed?

␈↓ α∧␈↓␈↓ αT18.␈α
Was␈α
Mr.␈αHug's␈α
right␈α
arm␈α
slashed␈αbefore␈α
his␈α
left␈α
arm␈αwas␈α
scratched?␈α
 Yes,␈α
because␈αthe
␈↓ α∧␈↓former was a year ago.

␈↓ α∧␈↓␈↓ αT19.␈α
How␈α
did␈α
the␈α
robber␈α
try␈α
to␈α
crush␈αhim␈α
with␈α
the␈α
car?␈α
 By␈α
pressing␈α
the␈α
buttons␈αor␈α
operating
␈↓ α∧␈↓the control lever to make the car go to the bottom of the shaft.

␈↓ α∧␈↓␈↓ αT20.␈α⊂Why␈α∂did␈α⊂Mr.␈α∂Hug␈α⊂yell␈α∂from␈α⊂the␈α∂bottom␈α⊂of␈α∂the␈α⊂elevator␈α∂shaft?␈α⊂ So␈α∂as␈α⊂to␈α⊂attract␈α∂the
␈↓ α∧␈↓attention of someone who would rescue him.

␈↓ α∧␈↓␈↓ αT21.␈α
How␈αlong␈α
did␈αthe␈α
events␈αtake?␈α
 More␈αthan␈α
half␈αan␈α
hour␈αbut␈α
less␈αthan␈α
a␈αday.␈α
 Most␈αof
␈↓ α∧␈↓the time was spent by Mr. Hug filling out forms in the hospital.

␈↓ α∧␈↓␈↓ αT22.␈α∞What␈α∞crimes␈α∞were␈α∞committed?␈α
 This␈α∞question␈α∞has␈α∞the␈α∞advantage␈α
that␈α∞it␈α∞is␈α∞one␈α∞that␈α
is
␈↓ α∧␈↓normally␈α⊃answered␈α⊃on␈α∩the␈α⊃basis␈α⊃of␈α∩such␈α⊃a␈α⊃story,␈α∩since␈α⊃the␈α⊃police␈α∩report␈α⊃of␈α⊃the␈α∩incident␈α⊃was
␈↓ α∧␈↓␈↓ u3


␈↓ α∧␈↓probably␈αthe␈αbasis␈α
of␈αthe␈α␈↓↓New␈αYork␈α
Times␈↓␈αstory.␈α Robbery,␈αpossibly␈α
assault␈αwith␈αa␈αdeadly␈α
weapon,
␈↓ α∧␈↓and␈α⊂attempted␈α∂murder␈α⊂are␈α∂the␈α⊂more␈α∂obvious␈α⊂crimes.␈α∂ One␈α⊂might␈α∂specifically␈α⊂challenge␈α∂natural
␈↓ α∧␈↓language systems to answer this question.

␈↓ α∧␈↓␈↓ αTThe␈α∃above␈α∀list␈α∃of␈α∃questions␈α∀is␈α∃rather␈α∀random.␈α∃ I␈α∃doubt␈α∀that␈α∃it␈α∀covers␈α∃all␈α∃facets␈α∀of
␈↓ α∧␈↓understanding␈α
the␈α
story.␈α It␈α
would␈α
be␈αworthwhile␈α
to␈α
try␈α
to␈αmake␈α
up␈α
a␈αlist␈α
of␈α
questions␈α
that␈αdoes
␈↓ α∧␈↓cover␈αsubstantially␈αall␈αaspects␈αof␈αthe␈αstory␈αin␈αorder␈αto␈αget␈αas␈αcomplete␈αas␈αpossible␈αan␈αintuitive␈αidea
␈↓ α∧␈↓of what capabilities are involved in understanding such a story.

␈↓ α∧␈↓␈↓ αTNote␈α
that␈α∞the␈α
story␈α∞is␈α
about␈α∞a␈α
real␈α∞event␈α
so␈α∞that␈α
such␈α∞a␈α
question␈α∞as␈α
what␈α∞does␈α
the␈α∞"J"␈α
in
␈↓ α∧␈↓"John␈α
J.␈α
 Hug"␈αstand␈α
for␈α
has␈αan␈α
answer.␈α
 In␈αa␈α
made-up␈α
story,␈αquestions␈α
about␈α
middle␈α
names␈αor
␈↓ α∧␈↓what␈α
year␈α
the␈α
story␈α
occurred␈α
in␈α
do␈α
not␈α
necessarily␈α
have␈α
an␈α
answer,␈α
and␈α
an␈α
intelligent␈α
person␈α
or
␈↓ α∧␈↓program would know that too.

␈↓ α∧␈↓␈↓ αTI␈α
think␈α
that␈α
artificial␈α
intelligence␈α
is␈α
not␈α
very␈α
close␈α
to␈α
being␈α
able␈α
to␈α
understand␈α
such␈α
stories␈α
in
␈↓ α∧␈↓a␈αgenuine␈αway.␈α Therefore,␈αI␈αwould␈αlike␈αto␈αsneak␈αup␈αon␈αit␈αgradually␈αby␈αdividing␈αthe␈αproblem␈αinto
␈↓ α∧␈↓parts which can be attacked separately. Here are some of the components:

␈↓ α∧␈↓␈↓ αT1.␈α
A␈αformalism␈α
capable␈αof␈α
expressing␈αthe␈α
assertions␈αof␈α
the␈αsentences␈α
free␈α
from␈αdependence
␈↓ α∧␈↓on␈αthe␈αgrammar␈αof␈αthe␈αEnglish␈αlanguage.␈α A␈αgood␈αtest␈αfor␈αsuch␈αa␈αformalism␈αwould␈αbe␈αto␈αproduce
␈↓ α∧␈↓a␈α
program␈α
for␈α
translating␈α
from␈α
the␈α
formalism␈α
into␈α
any␈α
of␈α
several␈α
natural␈α
languages.␈α More␈α
weakly,
␈↓ α∧␈↓it␈α
should␈α
be␈α
as␈α
easy␈α
for␈α
a␈α
human␈α∞to␈α
translate␈α
from␈α
the␈α
formalism␈α
into␈α
a␈α
natural␈α
language␈α∞as␈α
to
␈↓ α∧␈↓translate␈α⊂from␈α⊂one␈α⊂known␈α⊂natural␈α⊂language␈α⊃to␈α⊂another.␈α⊂ Let's␈α⊂call␈α⊂this␈α⊂formalism␈α⊃an␈α⊂␈↓↓artificial
␈↓ α∧␈↓↓natural language␈↓ - ANL for short.

␈↓ α∧␈↓␈↓ αTThe␈α
grammar␈α
of␈α
ANL␈α
should␈α
be␈α
trivial␈α
and␈α
mathematical␈α
in␈α
character.␈α
 There␈α
would␈αbe␈α
an
␈↓ α∧␈↓"English"␈α
version␈α
in␈α
which␈α
English␈α
words␈α
were␈α
used␈α
as␈α
identifiers,␈α
but␈α
there␈α
would␈α
still␈α
have␈αto␈α
be
␈↓ α∧␈↓a␈αglossary␈α
that␈αgives␈α
the␈αprecise␈α
meaning␈αof␈α
the␈αidentifiers.␈α
 There␈αwould␈α
also␈αbe␈α
a␈αGerman␈αand␈α
a
␈↓ α∧␈↓Japanese␈α
version.␈α The␈α
translation␈αfrom␈α
the␈αEnglish␈α
version␈αto␈α
the␈αGerman␈α
or␈α
Japanese␈αversion
␈↓ α∧␈↓would␈α
be␈α∞a␈α
simple␈α
substitution␈α∞for␈α
identifiers,␈α
and␈α∞a␈α
German␈α
or␈α∞Japanese␈α
who␈α
had␈α∞learned␈α
the
␈↓ α∧␈↓grammar could then translate into his language with the aid of the German or Japanese glossary.

␈↓ α∧␈↓␈↓ αTThis␈α∞idea␈α∞has␈α∞some␈α∂resemblance␈α∞to␈α∞the␈α∞idea␈α∞of␈α∂"deep␈α∞structure",␈α∞but␈α∞I␈α∞have␈α∂some␈α∞doubts
␈↓ α∧␈↓about whether either idea is well enough defined to say.

␈↓ α∧␈↓␈↓ αT2.␈α
 A␈α
data␈α
structure␈α
for␈α
expressing␈α
the␈α
facts␈α
(apart␈α
from␈α
expressing␈α
the␈α
sentences).␈α
 In␈α
such␈α
a
␈↓ α∧␈↓data␈α
structure,␈α
it␈α
would␈α
be␈α
definite␈α
which␈αrobber␈α
pushed␈α
Mr.␈α
Hug␈α
first,␈α
and␈α
what␈α
the␈αrobbers␈α
said
␈↓ α∧␈↓even␈α∞though␈α∞it␈α∞is␈α∞not␈α∞stated␈α∞in␈α∞the␈α∞story.␈α∞ Clearly␈α∞some␈α∞compromise␈α∞is␈α∞necessary␈α∞here,␈α∞since␈α
the
␈↓ α∧␈↓data␈α∪structure␈α∀need␈α∪not␈α∪be␈α∀able␈α∪to␈α∪express␈α∀positions␈α∪and␈α∪velocities␈α∀of␈α∪molecules.␈α∀ Like␈α∪the
␈↓ α∧␈↓PLANNER␈αlanguages,␈α
as␈αMoore␈α
(1976)␈αhas␈α
characterized␈αthem,␈α
the␈αdescriptions␈α
would␈αcontain␈α
no
␈↓ α∧␈↓disjunctions,␈α⊃and␈α⊃might␈α⊃be␈α⊃a␈α⊃collection␈α⊂of␈α⊃relations␈α⊃with␈α⊃constants␈α⊃as␈α⊃arguments␈α⊃where␈α⊂every
␈↓ α∧␈↓relation not asserted (in a certain class) is automatically denied.

␈↓ α∧␈↓␈↓ αTAlternatively,␈αthe␈αbasis␈αof␈αthis␈αdata␈αstructure␈αmight␈αbe␈αvarious␈αnetworks␈αof␈αnodes␈αdescribed
␈↓ α∧␈↓by␈α
sentences␈αin␈α
the␈αpredicate␈α
calculus.␈α Some␈α
of␈αthe␈α
sentences␈αwould␈α
assert␈αthat␈α
certain␈αprograms
␈↓ α∧␈↓applied␈α⊃to␈α⊃the␈α⊃data␈α⊃structures␈α⊃would␈α⊃answer␈α⊃certain␈α⊃questions.␈α⊃ When␈α⊃such␈α⊃sentences␈α⊃existed,
␈↓ α∧␈↓reasoning␈α
would␈α
include␈α∞the␈α
operation␈α
of␈α
the␈α∞programs.␈α
 In␈α
this␈α
way,␈α∞we␈α
would␈α
expect␈α∞to␈α
avoid
␈↓ α∧␈↓the␈α
extreme␈αprolixity␈α
that␈α
arises␈αwhen␈α
we␈α
attempt␈αto␈α
do␈α
even␈αsimple␈α
calculations␈α
by␈αpure␈α
predicate
␈↓ α∧␈↓calculus deduction.
␈↓ α∧␈↓␈↓ u4


␈↓ α∧␈↓␈↓ αTThe␈α
test␈α
of␈α
success␈α
for␈α
the␈α
"data␈α
structure"␈α
would␈α
be␈α
that␈α
a␈α
human␈α
could␈α
readily␈αformally
␈↓ α∧␈↓deduce␈α⊂the␈α⊂answers␈α⊂to␈α⊂the␈α⊂above␈α⊂questions␈α⊂using␈α⊂a␈α⊂proof␈α⊂checker.␈α⊂Most␈α⊂of␈α⊃the␈α⊂proof-checker
␈↓ α∧␈↓would␈α∂be␈α∂straightforward,␈α∂but␈α∂there␈α∞is␈α∂a␈α∂major␈α∂problem␈α∂concerned␈α∞with␈α∂when␈α∂it␈α∂is␈α∂possible␈α∞to
␈↓ α∧␈↓"jump to a conclusion".

␈↓ α∧␈↓␈↓ αT3. I see each of the following problems as a difficult AI problem:

␈↓ α∧␈↓a. A "parser" that takes English into ANL.

␈↓ α∧␈↓b. An "understander" that constructs the "facts" from a text in the ANL.

␈↓ α∧␈↓c.␈αExpression␈αof␈αthe␈α"general␈α
information"␈αabout␈αthe␈αworld␈αthat␈α
could␈αallow␈αgetting␈αthe␈αanswers␈α
to
␈↓ α∧␈↓the␈α
questions␈α
by␈α
formal␈α
reasoning␈α
from␈α
the␈α
"facts"␈α
and␈α
the␈α
"general␈α
information".␈α
 The␈α"general
␈↓ α∧␈↓information"␈α∞would␈α∞also␈α∞contain␈α∞non-sentence␈α∞data␈α∞structures␈α∞and␈α∞procedures,␈α∞but␈α∂the␈α∞sentences
␈↓ α∧␈↓would␈αtell␈αwhat␈αgoals␈αcan␈αbe␈αachieved␈αby␈αrunning␈αthe␈αprocedures.␈α In␈αthis␈αway,␈αwe␈αwould␈αget␈αthe
␈↓ α∧␈↓best of the sentential and procedural representations of knowledge.

␈↓ α∧␈↓d.␈α∂A␈α∂"problem␈α∂solver"␈α∂that␈α⊂could␈α∂answer␈α∂the␈α∂above␈α∂questions␈α⊂on␈α∂the␈α∂basis␈α∂of␈α∂the␈α⊂"facts".␈α∂ We
␈↓ α∧␈↓imagine␈αthe␈αquestions␈αto␈αbe␈αexpressed␈αin␈αthe␈α"fact"␈αlanguage␈αand␈αexpect␈αthe␈αanswers␈αin␈αthe␈α"fact"
␈↓ α∧␈↓language,␈αi.e.␈αwe␈αavoid␈αgrammar␈αproblems␈αin␈αboth␈αunderstanding␈αthe␈αquestions␈αand␈αin␈αexpressing
␈↓ α∧␈↓the answers.

␈↓ α∧␈↓Note of June 1980:

␈↓ α∧␈↓␈↓ αTMuch␈α∪of␈α∪the␈α∪reasoning␈α∪involved␈α∩in␈α∪answering␈α∪the␈α∪above␈α∪questions␈α∪is␈α∩non-monotonic.
␈↓ α∧␈↓There␈α
is␈α
a␈α
hint␈α
about␈αthis␈α
is␈α
the␈α
paper,␈α
but␈α
the␈αtreatment␈α
requires␈α
revision␈α
to␈α
take␈α
into␈αaccount
␈↓ α∧␈↓circumscription and other modes of non-monotonic reasonin.

␈↓ α∧␈↓John McCarthy
␈↓ α∧␈↓Computer Science Department
␈↓ α∧␈↓Stanford University.
␈↓ α∧␈↓␈↓ u5


␈↓ α∧␈↓NOTES ON AN "UNDERSTANDER"

␈↓ α∧␈↓␈↓ αTWhen my understander  has digested the  story of Mr.  Hug, it
␈↓ α∧␈↓will have added  one or more predicate calculus sentences to its data
␈↓ α∧␈↓base.  One sentence will do if it has the form

␈↓ α∧␈↓␈↓ αT∃ e p1 p2 g1 g2 e1 e2 ...  . event(e) ∧ person(p1) ∧ name(p1)
␈↓ α∧␈↓= "John. J. Hug" ∧ g1 ⊂ Robbers ∧ ... etc.


␈↓ α∧␈↓In this form,  all the entities  involved in expressing the  facts of
␈↓ α∧␈↓the story are existentially quantified variables.  The only constants
␈↓ α∧␈↓in the  formula would  have been  present in  the system  previously.
␈↓ α∧␈↓However,  it is  probably better  to  use a  collection of  sentences
␈↓ α∧␈↓introducing  a collection  of  individual constants.   In  this case,
␈↓ α∧␈↓there will be 20 or so new individual  constants representing people,
␈↓ α∧␈↓groups  of  people,  the  main  event  and  its  sub-events,  places,
␈↓ α∧␈↓organizations, etc.

␈↓ α∧␈↓␈↓ αT1. In representing  the robbers, the  system has a  choice of
␈↓ α∧␈↓representing them by three individual constants, R1, R2, and R3 or by
␈↓ α∧␈↓using a single symbol G1 to  represent the group of robbers.  A  good
␈↓ α∧␈↓system will  probably use  both. If  the number  of robbers  were not
␈↓ α∧␈↓specified, we would have to use a constant for the group.  We have to
␈↓ α∧␈↓identify the robber who operated the elevator while the others pushed
␈↓ α∧␈↓Mr. Hug into the shaft.  We shall call him R1.  The other two are not
␈↓ α∧␈↓discriminated in the story, but there is no harm in our calling  them
␈↓ α∧␈↓R2 and R3, even if there is no information  to discriminate them.  If
␈↓ α∧␈↓there  were  20 robbers,  it  would be  a  mistake to  give  them all
␈↓ α∧␈↓individual names.  Suppose it  had further  been stated  that as  the
␈↓ α∧␈↓robbers left one of them threatened  to return and kill Mr. Hug later
␈↓ α∧␈↓but  that it was not stated whether this  robber was the same one who
␈↓ α∧␈↓operated the elevator.  We could designate this robber  by R4, but we
␈↓ α∧␈↓would not have  sentences asserting that R4 was  distinct from R1, R2
␈↓ α∧␈↓and R3; instead we would have a sentence asserting that R4 was one of
␈↓ α∧␈↓these.  It is tempting to identify the group  of robbers with the set
␈↓ α∧␈↓{R1,R2,R3},  but we may  want to give  the group  some properties not
␈↓ α∧␈↓enjoyed by the set  of its members.   Sentences with plural  subjects
␈↓ α∧␈↓express  some rather  tricky concepts.   Thus,  the group  robbed the
␈↓ α∧␈↓store,  and this  is  not an  assertion that  each member  robbed the
␈↓ α∧␈↓store.

␈↓ α∧␈↓␈↓ αTThe  "members  of  the police  emergency  squad"  presents  a
␈↓ α∧␈↓similar  problem. We don't  want to assert  how many there  were.  In
␈↓ α∧␈↓this connection,  it may be  worthwhile to  distinguish between  what
␈↓ α∧␈↓happened and what we wish to  assert about what happened.  A language
␈↓ α∧␈↓adequate to describe what happened would not have to leave the number
␈↓ α∧␈↓of policemen present vague  and could give them  each a name.   In my
␈↓ α∧␈↓old jargon,  such a language would be  metaphysically adequate though
␈↓ α∧␈↓not epistemologically adequate.   Devising  a language  that is  only
␈↓ α∧␈↓␈↓ u6


␈↓ α∧␈↓metaphysically adequate may  be a worthwhile  stage on the way  to an
␈↓ α∧␈↓epistemologically adequate  system.  By "devising  a language" I mean
␈↓ α∧␈↓defining  a  collection  of   predicate  and  constant  symbols   and
␈↓ α∧␈↓axiomatizing their general  properties.  This language  should not be
␈↓ α∧␈↓peculiar  to the story of Mr. Hug, but  we should not require that it
␈↓ α∧␈↓be completely general in the present state of the science.

␈↓ α∧␈↓␈↓ αT2. It is not obvious how to express what we  know when we are
␈↓ α∧␈↓told that Mr.  Hug is a furniture salesman.   A direct approach is to
␈↓ α∧␈↓define an  abstract entity  called Furniture  and a  function  called
␈↓ α∧␈↓salesmen and to assert

␈↓ α∧␈↓␈↓ αTHug ε salesmen(Furniture).

␈↓ α∧␈↓This will probably  work although the logical connection  between the
␈↓ α∧␈↓abstract entity Furniture  and concrete chairs and tables needs to be
␈↓ α∧␈↓worked out.  It would  be over-simplified to identify Furniture  with
␈↓ α∧␈↓the set of furniture in existence  at that time, because one could be
␈↓ α∧␈↓a  salesman of space shuttles even though  there don't exist any yet.
␈↓ α∧␈↓In my opinion,  one should resist a  tendency to apply Occam's  razor
␈↓ α∧␈↓prematurely.  Perhaps we can identify the abstract Furniture with the
␈↓ α∧␈↓an extension of the predicate that tells us whether an object  should
␈↓ α∧␈↓be regarded as a piece of furniture, perhaps not.  It does no harm to
␈↓ α∧␈↓keep  them separate  for the  time being.   This  case looks  like an
␈↓ α∧␈↓argument for  using  second  order  logic so  that  the  argument  of
␈↓ α∧␈↓␈↓↓salesmen␈↓  could be  the  predicate  ␈↓↓furniture␈↓ that  tells
␈↓ α∧␈↓whether  an  object is  a  piece of  furniture.   However,  there are
␈↓ α∧␈↓various techniques  for getting the  same result  without the use  of
␈↓ α∧␈↓second order logic.

␈↓ α∧␈↓␈↓ αT3. Occam's razor.   After reading the story, one  is prepared
␈↓ α∧␈↓to answer  negatively the question of whether  there was someone else
␈↓ α∧␈↓besides  Mr.  Hug  and  the  robbers  present.    However,  sentences
␈↓ α∧␈↓describing such  another person could  be added to the  story without
␈↓ α∧␈↓contradiction.  Our  basis for  the negative  answer  is that  we can
␈↓ α∧␈↓construct a model  of the facts  stated in the  story without such  a
␈↓ α∧␈↓person, and we are applying Occam's razor in order to not ␈↓↓multiply
␈↓ α∧␈↓↓entities beyond necessity␈↓.  This could be  attributed to the  fact
␈↓ α∧␈↓that the ␈↓↓New York Times␈↓ tells the whole  story when it can, but
␈↓ α∧␈↓I  think that by  putting Occam's razor  into the system,  we can get
␈↓ α∧␈↓this result without having to formalize the ␈↓↓New York Times␈↓.

␈↓ α∧␈↓␈↓ αTThis  suggests   introducing  the   notion  of  the   minimal
␈↓ α∧␈↓completion  of a  story  expressed in  the predicate  calculus.   The
␈↓ α∧␈↓minimal completion of  the story is  also a set  of sentences in  the
␈↓ α∧␈↓predicate calculus,  but it contains sentences  asserting things like
␈↓ α∧␈↓"The  set of  people in the  store while  the robbers  were trying to
␈↓ α∧␈↓crush Mr. Hug consists of Mr. Hug and the  robbers".  These sentences
␈↓ α∧␈↓are  to be obtained  from the  original set by  the application  of a
␈↓ α∧␈↓process formalizing Occam's razor.  This process works from a set  of
␈↓ α∧␈↓␈↓ u7


␈↓ α∧␈↓sentences  and  is  not  logical  deduction   although  it  might  be
␈↓ α∧␈↓accomplished  by   deduction  in  a  meta-  language  that  contained
␈↓ α∧␈↓sentences about sets of sentences.  As I have pointed  out elsewhere,
␈↓ α∧␈↓the process cannot be deduction,  because it generates sentences that
␈↓ α∧␈↓contradict  sentences that  are consistent  with the original  set of
␈↓ α∧␈↓sentences.

␈↓ α∧␈↓␈↓ αTA number of the questions given in  the previous section have
␈↓ α∧␈↓answers that can  be formally deduced from the minimal completion but
␈↓ α∧␈↓not from the original list.

␈↓ α∧␈↓␈↓ αTIt has been suggested that  probabilistic reasoning should be
␈↓ α∧␈↓used  to exclude  the presence  of other  people rather  than Occam's
␈↓ α∧␈↓razor. The  problem  with  this  is that  the  number  of  additional
␈↓ α∧␈↓entities that  are not  logically excluded is  limited only  by one's
␈↓ α∧␈↓imagination  so  that  it is  not  clear how  one  could  construct a
␈↓ α∧␈↓probabilistic model that  took these possibilities into  account only
␈↓ α∧␈↓to   exclude  them  as   improbable.  If   one  wants   to  introduce
␈↓ α∧␈↓probabilities, it might make  more sense to  assign a probability  to
␈↓ α∧␈↓the correctness of the  minimal completion of a ␈↓↓New  York Times␈↓
␈↓ α∧␈↓story  based on  its past  record  in finding  the relevant  facts of
␈↓ α∧␈↓robberies.
␈↓ α∧␈↓Many of the problems of minimal completions are discussed in
␈↓ α∧␈↓MINIMA[F76,JMC], and those results will hopefully be integrated into
␈↓ α∧␈↓a future draft of this note.

␈↓ α∧␈↓␈↓ αTAnother  problem  in  constructing  the  completion  is   the
␈↓ α∧␈↓isolation of the  story from the rest  of the world.   The members of
␈↓ α∧␈↓the Police  Emergency Squad all have mothers (living or dead), but we
␈↓ α∧␈↓don't want to bring them in to the completion - not to speak of
␈↓ α∧␈↓bringing in more remote ancestors all of whom can be asserted to exist
␈↓ α∧␈↓on the basis of axioms about people.

␈↓ α∧␈↓␈↓ αTTo  recapitulate: The  original  set  of  predicate  calculus
␈↓ α∧␈↓sentences can  be generated from the  story as one goes  along.  Each
␈↓ α∧␈↓sentence is generated approximately from a sentence of the story with
␈↓ α∧␈↓the aid  of general knowledge  and what has  been generated  from the
␈↓ α∧␈↓previous sentences.   (This will usually be the  case if the story is
␈↓ α∧␈↓well told although there are sometimes cases in which the correct way
␈↓ α∧␈↓to express a sentence  will depend on what follows -  but this is not
␈↓ α∧␈↓good writing).   The completion, however, will depend on the whole of
␈↓ α∧␈↓the story.

␈↓ α∧␈↓␈↓ αTIt might be interesting to consider what can be determined
␈↓ α∧␈↓from a partial reading of the story - even stopping the reading
␈↓ α∧␈↓in the middle of a sentence since what has appeared so far in a
␈↓ α∧␈↓sentence often must be understood in order to even parse the re...

␈↓ α∧␈↓This draft of MRHUG[S76,JMC]@SU-AI was PUBbed on April 13, 1981.