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␈↓ 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∧␈↓␈↓ ε|1␈↓ ∧



␈↓ 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∧␈↓␈↓ ε|2␈↓ ∧



␈↓ 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∧␈↓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 no 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∧␈↓␈↓ ε|3␈↓ ∧



␈↓ 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∧␈↓␈↓ 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∧␈↓␈↓ ε|4␈↓ ∧



␈↓ α∧␈↓NOTES ON AN "UNDERSTANDER"

␈↓ α∧␈↓␈↓ αTWhen␈αmy␈αunderstander␈αhas␈αdigested␈αthe␈αstory␈αof␈αMr.␈α Hug,␈αit␈αwill␈αhave␈αadded␈αone␈αor␈αmore
␈↓ α∧␈↓predicate calculus sentences to its data base.  One sentence will do if it has the form

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

␈↓ α∧␈↓In␈α∪this␈α∪form,␈α∪all␈α∪the␈α∪entities␈α∪involved␈α∪in␈α∪expressing␈α∪the␈α∪facts␈α∪of␈α∪the␈α∪story␈α∪are␈α∪existentially
␈↓ α∧␈↓quantified␈α
variables.␈α
 The␈α
only␈α
constants␈α
in␈α
the␈αformula␈α
would␈α
have␈α
been␈α
present␈α
in␈α
the␈αsystem
␈↓ α∧␈↓previously.␈α However,␈αit␈αis␈αprobably␈αbetter␈αto␈αuse␈αa␈αcollection␈αof␈αsentences␈αintroducing␈αa␈αcollection
␈↓ α∧␈↓of␈αindividual␈αconstants.␈α In␈αthis␈αcase,␈αthere␈αwill␈αbe␈α20␈αor␈αso␈αnew␈αindividual␈αconstants␈αrepresenting
␈↓ α∧␈↓people, groups of people, the main event and its sub-events, places, organizations, etc.

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

␈↓ α∧␈↓␈↓ αTThe␈α"members␈α
of␈αthe␈α
police␈αemergency␈αsquad"␈α
presents␈αa␈α
similar␈αproblem.␈α
We␈αdon't␈αwant␈α
to
␈↓ α∧␈↓assert␈α
how␈α
many␈α
there␈α
were.␈α
 In␈α
this␈α
connection,␈α
it␈α
may␈α
be␈α
worthwhile␈α
to␈α
distinguish␈αbetween␈α
what
␈↓ α∧␈↓happened␈α∞and␈α
what␈α∞we␈α∞wish␈α
to␈α∞assert␈α∞about␈α
what␈α∞happened.␈α∞ A␈α
language␈α∞adequate␈α∞to␈α
describe
␈↓ α∧␈↓what␈αhappened␈αwould␈αnot␈α
have␈αto␈αleave␈αthe␈αnumber␈α
of␈αpolicemen␈αpresent␈αvague␈αand␈α
could␈αgive
␈↓ α∧␈↓them␈αeach␈αa␈αname.␈α In␈αmy␈αold␈αjargon,␈αsuch␈αa␈αlanguage␈αwould␈αbe␈αmetaphysically␈αadequate␈αthough
␈↓ α∧␈↓not␈αepistemologically␈αadequate.␈α Devising␈αa␈αlanguage␈αthat␈αis␈αonly␈αmetaphysically␈αadequate␈αmay␈αbe
␈↓ α∧␈↓a␈αworthwhile␈αstage␈αon␈αthe␈αway␈αto␈αan␈αepistemologically␈αadequate␈αsystem.␈α By␈α"devising␈αa␈αlanguage"
␈↓ α∧␈↓I␈α∂mean␈α∂defining␈α∂a␈α∞collection␈α∂of␈α∂predicate␈α∂and␈α∞constant␈α∂symbols␈α∂and␈α∂axiomatizing␈α∂their␈α∞general
␈↓ α∧␈↓properties.␈α∂ This␈α∂language␈α∞should␈α∂not␈α∂be␈α∞peculiar␈α∂to␈α∂the␈α∞story␈α∂of␈α∂Mr.␈α∞Hug,␈α∂but␈α∂we␈α∂should␈α∞not
␈↓ α∧␈↓require that it be completely general in the present state of the science.

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

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



␈↓ α∧␈↓␈↓ ε|5␈↓ ∧



␈↓ α∧␈↓This␈α
will␈α
probably␈αwork␈α
although␈α
the␈αlogical␈α
connection␈α
between␈αthe␈α
abstract␈α
entity␈αFurniture␈α
and
␈↓ α∧␈↓concrete␈α∩chairs␈α∩and␈α∩tables␈α∩needs␈α∩to␈α∩be␈α∩worked␈α∩out.␈α∩ It␈α∩would␈α∩be␈α∩over-simplified␈α∩to␈α∩identify
␈↓ α∧␈↓Furniture␈αwith␈α
the␈αset␈αof␈α
furniture␈αin␈αexistence␈α
at␈αthat␈αtime,␈α
because␈αone␈αcould␈α
be␈αa␈α
salesman␈αof
␈↓ α∧␈↓space␈αshuttles␈αeven␈αthough␈αthere␈αdon't␈αexist␈αany␈αyet.␈α In␈αmy␈αopinion,␈αone␈αshould␈αresist␈αa␈αtendency
␈↓ α∧␈↓to␈αapply␈αOccam's␈αrazor␈αprematurely.␈α Perhaps␈αwe␈αcan␈αidentify␈αthe␈αabstract␈αFurniture␈αwith␈αthe␈αan
␈↓ α∧␈↓extension␈α⊃of␈α⊃the␈α⊃predicate␈α⊃that␈α⊃tells␈α⊃us␈α∩whether␈α⊃an␈α⊃object␈α⊃should␈α⊃be␈α⊃regarded␈α⊃as␈α⊃a␈α∩piece␈α⊃of
␈↓ α∧␈↓furniture,␈α
perhaps␈α
not.␈α
 It␈α
does␈α
no␈α
harm␈α
to␈α
keep␈α
them␈α
separate␈α
for␈α
the␈α
time␈α
being.␈α
 This␈αcase␈α
looks
␈↓ α∧␈↓like␈α∂an␈α∂argument␈α⊂for␈α∂using␈α∂second␈α⊂order␈α∂logic␈α∂so␈α⊂that␈α∂the␈α∂argument␈α⊂of␈α∂␈↓↓salesmen␈↓␈α∂could␈α⊂be␈α∂the
␈↓ α∧␈↓predicate␈α
␈↓↓furniture␈↓␈α
that␈α
tells␈α
whether␈α
an␈α
object␈α
is␈α
a␈α
piece␈α
of␈α
furniture.␈α
 However,␈α
there␈αare␈α
various
␈↓ α∧␈↓techniques for getting the same result without the use of second order logic.

␈↓ α∧␈↓␈↓ αT3.␈α
Occam's␈α
razor.␈α After␈α
reading␈α
the␈αstory,␈α
one␈α
is␈α
prepared␈αto␈α
answer␈α
negatively␈αthe␈α
question
␈↓ α∧␈↓of␈αwhether␈α
there␈αwas␈α
someone␈αelse␈αbesides␈α
Mr.␈α Hug␈α
and␈αthe␈α
robbers␈αpresent.␈α However,␈α
sentences
␈↓ α∧␈↓describing␈αsuch␈αanother␈αperson␈αcould␈αbe␈αadded␈αto␈αthe␈αstory␈αwithout␈αcontradiction.␈α Our␈αbasis␈αfor
␈↓ α∧␈↓the␈α
negative␈α
answer␈α
is␈α
that␈α
we␈α
can␈α
construct␈α
a␈αmodel␈α
of␈α
the␈α
facts␈α
stated␈α
in␈α
the␈α
story␈α
without␈αsuch␈α
a
␈↓ α∧␈↓person,␈α
and␈αwe␈α
are␈αapplying␈α
Occam's␈α
razor␈αin␈α
order␈αto␈α
not␈α
␈↓↓multiply␈αentities␈α
beyond␈αnecessity␈↓.␈α
 This
␈↓ α∧␈↓could␈α
be␈α
attributed␈αto␈α
the␈α
fact␈α
that␈αthe␈α
␈↓↓New␈α
York␈α
Times␈↓␈αtells␈α
the␈α
whole␈α
story␈αwhen␈α
it␈α
can,␈α
but␈αI
␈↓ α∧␈↓think␈α∂that␈α∂by␈α∂putting␈α∂Occam's␈α∂razor␈α∂into␈α∂the␈α∂system,␈α∂we␈α∂can␈α∂get␈α∂this␈α∂result␈α∂without␈α∂having␈α∂to
␈↓ α∧␈↓formalize the ␈↓↓New York Times␈↓.

␈↓ α∧␈↓␈↓ αTThis␈αsuggests␈αintroducing␈αthe␈αnotion␈αof␈αthe␈αminimal␈αcompletion␈αof␈αa␈αstory␈αexpressed␈αin␈αthe
␈↓ α∧␈↓predicate␈αcalculus.␈α The␈αminimal␈αcompletion␈αof␈αthe␈αstory␈αis␈αalso␈αa␈αset␈αof␈αsentences␈αin␈αthe␈αpredicate
␈↓ α∧␈↓calculus,␈α
but␈α
it␈α∞contains␈α
sentences␈α
asserting␈α∞things␈α
like␈α
"The␈α∞set␈α
of␈α
people␈α∞in␈α
the␈α
store␈α∞while␈α
the
␈↓ α∧␈↓robbers␈αwere␈αtrying␈αto␈αcrush␈αMr.␈αHug␈αconsists␈αof␈αMr.␈αHug␈αand␈αthe␈αrobbers".␈α These␈αsentences␈αare
␈↓ α∧␈↓to␈α∞be␈α∞obtained␈α
from␈α∞the␈α∞original␈α∞set␈α
by␈α∞the␈α∞application␈α∞of␈α
a␈α∞process␈α∞formalizing␈α∞Occam's␈α
razor.
␈↓ α∧␈↓This␈α∂process␈α∂works␈α⊂from␈α∂a␈α∂set␈α⊂of␈α∂sentences␈α∂and␈α⊂is␈α∂not␈α∂logical␈α⊂deduction␈α∂although␈α∂it␈α⊂might␈α∂be
␈↓ α∧␈↓accomplished␈α
by␈α
deduction␈αin␈α
a␈α
meta-␈αlanguage␈α
that␈α
contained␈αsentences␈α
about␈α
sets␈α
of␈αsentences.
␈↓ α∧␈↓As␈α
I␈αhave␈α
pointed␈α
out␈αelsewhere,␈α
the␈α
process␈αcannot␈α
be␈α
deduction,␈αbecause␈α
it␈α
generates␈αsentences
␈↓ α∧␈↓that contradict sentences that are consistent with the original set of sentences.

␈↓ α∧␈↓␈↓ αTA␈αnumber␈αof␈αthe␈αquestions␈α
given␈αin␈αthe␈αprevious␈αsection␈α
have␈αanswers␈αthat␈αcan␈αbe␈α
formally
␈↓ α∧␈↓deduced from the minimal completion but not from the original list.

␈↓ α∧␈↓␈↓ αTIt␈αhas␈αbeen␈αsuggested␈α
that␈αprobabilistic␈αreasoning␈αshould␈αbe␈α
used␈αto␈αexclude␈αthe␈αpresence␈α
of
␈↓ α∧␈↓other␈αpeople␈αrather␈αthan␈αOccam's␈αrazor.␈αThe␈αproblem␈αwith␈αthis␈αis␈αthat␈αthe␈αnumber␈α
of␈αadditional
␈↓ α∧␈↓entities␈α
that␈αare␈α
not␈αlogically␈α
excluded␈α
is␈αlimited␈α
only␈αby␈α
one's␈α
imagination␈αso␈α
that␈αit␈α
is␈α
not␈αclear
␈↓ α∧␈↓how␈α∂one␈α∞could␈α∂construct␈α∞a␈α∂probabilistic␈α∞model␈α∂that␈α∞took␈α∂these␈α∞possibilities␈α∂into␈α∞account␈α∂only␈α∞to
␈↓ α∧␈↓exclude␈αthem␈αas␈αimprobable.␈α If␈αone␈αwants␈αto␈αintroduce␈αprobabilities,␈αit␈αmight␈αmake␈αmore␈αsense␈α
to
␈↓ α∧␈↓assign␈α
a␈α
probability␈αto␈α
the␈α
correctness␈α
of␈αthe␈α
minimal␈α
completion␈α
of␈αa␈α
␈↓↓New␈α
York␈α
Times␈↓␈αstory␈α
based
␈↓ α∧␈↓on its past record in finding the relevant facts of robberies.

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

␈↓ α∧␈↓␈↓ αTTo␈αrecapitulate:␈α
The␈αoriginal␈αset␈α
of␈αpredicate␈α
calculus␈αsentences␈αcan␈α
be␈αgenerated␈α
from␈αthe


␈↓ α∧␈↓␈↓ ε|6␈↓ ∧



␈↓ α∧␈↓story␈α
as␈α∞one␈α
goes␈α
along.␈α∞ Each␈α
sentence␈α
is␈α∞generated␈α
approximately␈α
from␈α∞a␈α
sentence␈α
of␈α∞the␈α
story
␈↓ α∧␈↓with␈α∂the␈α∂aid␈α∂of␈α⊂general␈α∂knowledge␈α∂and␈α∂what␈α∂has␈α⊂been␈α∂generated␈α∂from␈α∂the␈α⊂previous␈α∂sentences.
␈↓ α∧␈↓(This␈αwill␈αusually␈αbe␈αthe␈αcase␈αif␈αthe␈αstory␈αis␈αwell␈αtold␈αalthough␈αthere␈αare␈αsometimes␈αcases␈αin␈αwhich
␈↓ α∧␈↓the␈αcorrect␈αway␈αto␈αexpress␈αa␈αsentence␈αwill␈αdepend␈αon␈αwhat␈αfollows␈α-␈αbut␈αthis␈αis␈αnot␈αgood␈αwriting).
␈↓ α∧␈↓The completion, however, will depend on the whole of the story.

␈↓ α∧␈↓␈↓ αTIt␈α∞might␈α
be␈α∞interesting␈α∞to␈α
consider␈α∞what␈α
can␈α∞be␈α∞determined␈α
from␈α∞a␈α
partial␈α∞reading␈α∞of␈α
the
␈↓ α∧␈↓story␈α-␈αeven␈α
stopping␈αthe␈αreading␈αin␈α
the␈αmiddle␈αof␈αa␈α
sentence␈αsince␈αwhat␈αhas␈α
appeared␈αso␈αfar␈αin␈α
a
␈↓ α∧␈↓sentence often must be understood in order to even parse the rest of the sentence.








































␈↓ α∧␈↓␈↓ ε|7␈↓ ∧