perm filename FOO.XGP[ESS,JMC] blob
sn#144967 filedate 1975-02-11 generic text, type T, neo UTF8
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␈↓␈↓↓␈↓α␈↓
␈↓ ↓H
␈↓ pAN EXAMPLE FOR NATURAL LANGUAGE UNDERSTANDING AND THE AI PROBLEMS IT RAISES
␈↓ ↓H
␈↓ ↓H
␈↓ ↓H
␈↓ α_The␈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
␈↓ ↓H
␈↓ ↓Hlanguage␈α∞understander.␈α∞The␈α∞story␈α∞is␈α∞about␈α∞a␈α∞real␈α∞world␈α∞event␈α∞and␈α∞therefore␈α∞the␈α∞intentions␈α∞of␈α
the
␈↓ ↓H
␈↓ ↓Hauthor␈α
are␈α
less␈α
relevant␈α
for␈α
answering␈α
questions␈α
than␈α
in␈α
the␈αcase␈αof␈αthe␈αstory␈αabout␈αTad␈αdiscussed
␈↓ ↓H
␈↓ ↓Hearlier␈αin␈αthe␈αnatural␈αlanguage␈αseminar.␈α␈↓αThe␈αmain␈αgoal␈αof␈αthis␈αdiscussion␈αis␈αto␈αsay␈αwhat␈αa␈αperson
␈↓ ↓H
␈↓ ↓Hknows␈α
who␈α
has␈α
understood␈α
the␈α
story.␈α
This␈α
seems␈α
to␈α
me␈αto␈αbe␈αpreliminary␈αto␈αmaking␈αprograms
␈↓ ↓H
␈↓ ↓Hthat␈α
can␈α
understand.␈↓
␈↓ ↓H
␈↓ ↓H
␈↓ α_"A␈α
61-year␈α
old␈α
furniture␈αsalesman␈αwas␈αpushed␈αdown␈αthe␈αshaft␈αof␈αa␈αfreight␈αelevator␈αyesterday
␈↓ ↓H
␈↓ ↓Hin␈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
␈↓ ↓H
␈↓ ↓Helevator␈α
car␈α
because␈α
they␈α
were␈α
dissatisfied␈α
with␈α
the␈α
$1,200␈α
they␈α
had␈α
forced␈α
him␈α
to␈α
give␈α
them.
␈↓ ↓H
␈↓ ↓H
␈↓ α_The␈αbuffer␈αsprings␈αat␈αthe␈αbottom␈αof␈αthe␈αshaft␈αprevented␈αthe␈αcar␈αfrom␈αcrushing␈αthe␈αsalesman,
␈↓ ↓H
␈↓ ↓HJohn␈α
J.␈α
Hug,␈α
after␈α
he␈α
was␈α
pushed␈α
from␈α
the␈α
first␈α
floor␈α
to␈α
the␈α
basement.␈α
The␈α
car␈αstopped␈αabout␈α12
␈↓ ↓H
␈↓ ↓Hinches␈α
above␈α
him␈α
as␈α
he␈α
flattened␈α
himself␈α
at␈α
the␈α
bottom␈α
of␈α
the␈α
pit.
␈↓ ↓H
␈↓ ↓H
␈↓ α_Mr.␈αHug␈αwas␈αpinned␈αin␈αthe␈αshaft␈αfor␈αabout␈αhalf␈αan␈αhour␈αuntil␈αhis␈α
cries␈α
attracted␈α
the␈α
attention
␈↓ ↓H
␈↓ ↓Hof␈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␈α
chain.
␈↓ ↓H
␈↓ ↓H
␈↓ α_Mr.␈αHug␈αwas␈αremoved␈αby␈αmembers␈αof␈αthe␈αPolice␈αEmergency␈αSquad␈αand␈αtaken␈αto␈αLong␈αIsland
␈↓ ↓H
␈↓ ↓HCollege␈αHospital.␈αHe␈αwas␈αbadly␈αshaken,␈αbut␈αafter␈αbeing␈αtreated␈αfor␈αscrapes␈αof␈αhis␈αleft␈αarm␈αand␈αfor␈αa
␈↓ ↓H
␈↓ ↓Hspinal␈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.
␈↓ ↓H
␈↓ ↓H
␈↓ α_He␈α
has␈α
worked␈αfor␈αseven␈αyears␈αat␈αthe␈αstore,␈αon␈αthe␈αcorner␈αof␈αNevins␈αStreet,␈αand␈αthis␈αwas␈αthe
␈↓ ↓H
␈↓ ↓Hfourth␈αtime␈αhe␈αhad␈αbeen␈αheld␈αup␈αin␈αthe␈αstore.␈αThe␈αlast␈αtime␈αwas␈αabout␈αone␈αyear␈αago,␈αwhen␈α
his␈α
right
␈↓ ↓H
␈↓ ↓Harm␈α
was␈α
slashed␈α
by␈α
a␈α
knife-wielding␈α
robber."
␈↓ ↓H
␈↓ ↓H
␈↓ α_An␈α
intelligent␈α
person␈α
or␈α
program␈α
should␈α
be␈α
able␈α
to␈α
answer␈αthe␈αfollowing␈αquestions␈αbased␈αon
␈↓ ↓H
␈↓ ↓Hthe␈α
information␈α
in␈α
the␈α
story:
␈↓ ↓H
␈↓ ↓H
␈↓ α_1.␈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
␈↓ ↓H
␈↓ ↓Hrobbers␈αmight␈α
have␈α
been␈α
waiting␈α
for␈α
him,␈α
but␈α
if␈α
so,␈α
this␈α
would␈α
have␈α
probably␈α
been␈α
stated.␈α
What␈α
did
␈↓ ↓H
␈↓ ↓Hthe␈α
porter␈α
say␈α
to␈α
the␈α
robbers?␈α
Nothing,␈α
because␈α
the␈α
robbers␈α
left␈α
before␈α
he␈α
came.
␈↓ ↓H
␈↓ ↓H
␈↓ α_2.␈α
Who␈α
was␈α
in␈α
the␈α
store␈α
during␈α
the␈α
attempt␈α
to␈α
kill␈α
Mr.␈α
Hug?␈α
Mr.␈α
Hug␈α
and␈α
the␈α
robbers.
␈↓ ↓H
␈↓ ↓H
␈↓ α_3.␈α
Who␈α
had␈α
the␈α
money␈α
at␈α
the␈α
end?␈α
The␈α
robbers.
␈↓ ↓H
␈↓ ↓H
␈↓ α_4.␈α
Is␈α
Mr.␈α
Hug␈α
alive␈α
today?␈α
Yes,␈α
unless␈α
something␈α
else␈α
has␈α
happened␈α
to␈α
him.
␈↓ ↓H
␈↓ ↓H
␈↓ α_5.␈α
How␈α
did␈α
Mr.␈α
Hug␈α
get␈α
hurt?␈α
Probably␈α
when␈α
he␈α
hit␈α
the␈α
bottom␈α
of␈α
the␈α
shaft.
␈↓ ↓H
␈↓ ↓H
␈↓ α_6.␈α∞Where␈α∞is␈α∞Mr.␈α∞Hug's␈α∞home?␈α∞(A␈α∞question␈α
whose␈α
answer␈α
requires␈α
a␈α
literal␈α
understanding␈α
of
␈↓ ↓H
␈↓ ↓Honly␈α
one␈α
sentence␈α
of␈α
the␈α
stories.)
␈↓ ↓H
␈↓ ↓H
␈↓ α_7.␈α
What␈α
are␈α
the␈α
names␈α
and␈α
addresses␈α
of␈α
the␈α
robbers?␈α
This␈α
information␈α
is␈α
not␈α
available.
␈↓ ↓H
␈↓ ↓H
␈↓ α_8.␈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.
␈↓ ↓H
␈↓ ↓H
␈↓ α_9.␈αWhat␈αwould␈αhave␈αhappened␈αif␈αMr.␈αHug␈αhad␈αnot␈αflattened␈αhimself␈αat␈α
the␈α
bottom␈α
of␈α
the␈α
pit?
␈↓ ↓H
␈↓ ↓HWhat␈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?
␈↓ ↓H
␈↓ ↓H
␈↓ α_10.␈α
Did␈α
Mr.␈α
Hug␈α
want␈α
to␈α
be␈α
crushed?␈α
No.
␈↓ ↓H
␈↓ ↓H
␈↓ α_11.␈α
Did␈α
the␈α
robbers␈α
tell␈α
Mr.␈α
Hug␈α
their␈α
names?␈α
No.
␈↓ ↓H
␈↓ ↓H
␈↓ α_12.␈α
Were␈α
the␈α
robbers␈α
present␈α
when␈α
the␈α
porter␈α
came?␈α
No.
␈↓ ↓H
␈↓ ↓H
␈↓ α_13.␈α
Did␈α
Mr.␈α
Hug␈α
like␈α
the␈α
robbers,␈α
and␈α
did␈α
they␈α
like␈α
him?
␈↓ ↓H
␈↓ ↓H
␈↓ α_14.␈α⊂Why␈α⊂did␈α⊂the␈α⊂robbers␈α⊂leave␈α⊂without␈α⊂killing␈α⊂Mr.␈α⊂Hug?␈α∂Perhaps,␈α∂they␈α∂thought␈α∂they␈α∂had
␈↓ ↓H
␈↓ ↓Hkilled␈αhim,␈αand␈αperhaps␈αtheir␈αanger␈αwas␈αappeased␈αby␈αthe␈αactions␈αthey␈αhad␈αperformed,␈αand␈αperhaps
␈↓ ↓H
␈↓ ↓Hthey␈αhad␈αtaken␈αall␈αthe␈αtime␈αthey␈αdared,␈αand␈αperhaps␈αsomething␈αspecific␈αhappened␈αto␈αfrighten␈αthem
␈↓ ↓H
␈↓ ↓Haway.
␈↓ ↓H
␈↓ ↓H
␈↓ α_15.␈α
What␈α
would␈α
have␈αhappened␈αif␈αMr.␈αHug␈αhad␈αtried␈αto␈αrun␈αaway?␈αPerhaps␈αhe␈αwould␈αhave
␈↓ ↓H
␈↓ ↓Hsucceeded,␈αbut␈αmore␈αlikely␈αthey␈αwould␈αhave␈αinjured␈αor␈αkilled␈αhim␈αsince␈αprobably␈αthey␈αhad␈αweapons,
␈↓ ↓H
␈↓ ↓Hand␈α
there␈α
were␈α
three␈α
of␈α
them.
␈↓ ↓H
␈↓ ↓H
␈↓ α_16.␈αWhat␈αcan␈αMr.␈αHug␈αdo␈αto␈αavoid␈αthis␈αin␈αthe␈αfuture?␈αNo␈αsolution␈αis␈αentirely␈αsatisfactory.␈αHe
␈↓ ↓H
␈↓ ↓Hcould␈αcarry␈αa␈αgun␈αor␈αhe␈α
could␈α
quit␈α
or␈α
he␈α
could␈α
get␈α
his␈α
employers␈α
to␈α
install␈α
an␈α
alarm␈α
system␈α
or␈α
maybe
␈↓ ↓H
␈↓ ↓Hhe␈α
will␈α
be␈α
lucky.
␈↓ ↓H
␈↓ ↓H
␈↓ α_17.␈α
Did␈α
Mr.␈α
Hug␈α
know␈α
he␈α
was␈α
going␈α
to␈α
be␈α
robbed?␈α
Does␈α
he␈α
know␈α
that␈α
he␈α
was␈α
robbed?
␈↓ ↓H
␈↓ ↓H
␈↓ α_18.␈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
␈↓ ↓H
␈↓ ↓Hformer␈α
was␈α
a␈α
year␈α
ago.
␈↓ ↓H
␈↓ ↓H
␈↓ α_19.␈α
How␈α
did␈α
the␈α
robber␈α
try␈α
to␈α
crush␈α
him␈αwith␈αthe␈αcar?␈αBy␈αpressing␈αthe␈αbuttons␈αor␈αoperating
␈↓ ↓H
␈↓ ↓Hthe␈α
control␈α
lever␈α
to␈α
make␈α
the␈α
car␈α
go␈α
to␈α
the␈α
bottom␈α
of␈α
the␈α
shaft.
␈↓ ↓H
␈↓ ↓H
␈↓ α_20.␈αWhy␈αdid␈αMr.␈αHug␈αyell␈αfrom␈αthe␈αbottom␈αof␈αthe␈αelevator␈α
shaft?␈α
So␈α
as␈α
to␈α
attract␈α
the␈α
attention
␈↓ ↓H
␈↓ ↓Hof␈α
someone␈α
who␈α
would␈α
rescue␈α
him.
␈↓ ↓H
␈↓ ↓H
␈↓ α_21.␈α
How␈α
long␈α
did␈α
the␈α
events␈α
take?␈α
More␈αthan␈αhalf␈αan␈αhour␈αbut␈αless␈αthan␈αa␈αday.␈αMost␈αof␈αthe
␈↓ ↓H
␈↓ ↓Htime␈α
was␈α
spent␈α
by␈α
Mr.␈α
Hug␈α
filling␈α
out␈α
forms␈α
in␈α
the␈α
hospital.
␈↓ ↓H
␈↓ ↓H
␈↓ α_22.␈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
␈↓ ↓H
␈↓ ↓Hnormally␈αanswered␈αon␈αthe␈αbasis␈αof␈αsuch␈αa␈αstory,␈αsince␈αthe␈αpolice␈αreport␈αof␈αthe␈αincident␈αwas␈αprobably
␈↓ ↓H
␈↓ ↓Hthe␈α∩basis␈α∩of␈α∩the␈α∩␈↓↓New␈α∩York␈α∩Times␈↓␈α∩story.␈α∩Robbery,␈α∩possibly␈α∩assault␈α∩with␈α∩a␈α⊃deadly␈α⊃weapon,␈α⊃and
␈↓ ↓H
␈↓ ↓Hattempted␈α∞murder␈α∞are␈α∞the␈α∞more␈α
obvious␈α
crimes.␈α
One␈α
might␈α
specifically␈α
challenge␈α
natural␈α
language
␈↓ ↓H
␈↓ ↓Hsystems␈α
to␈α
answer␈α
this␈α
question.
␈↓ ↓H
␈↓ ↓H
␈↓ α_The␈αabove␈αlist␈αof␈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
␈↓ ↓H
␈↓ ↓Hthe␈αstory.␈αIt␈αwould␈αbe␈αworthwhile␈αto␈αtry␈αto␈αmake␈αup␈αa␈αlist␈αof␈αquestions␈αthat␈αdoes␈αcover␈αsubstantially
␈↓ ↓H
␈↓ ↓Hall␈αaspects␈αof␈αthe␈αstory␈αin␈αorder␈αto␈αget␈αas␈αcomplete␈αas␈αpossible␈αan␈αintuitive␈αidea␈αof␈αwhat␈αcapabilities
␈↓ ↓H
␈↓ ↓Hare␈α
involved␈α
in␈α
understanding␈α
such␈α
a␈α
story.
␈↓ ↓H
␈↓ ↓H
␈↓ α_Note␈αthat␈αthe␈αstory␈αis␈αabout␈αa␈αreal␈αevent␈αso␈αthat␈α
such␈α
a␈α
question␈α
as␈α
what␈α
does␈α
the␈α
"J"␈α
in␈α
"John
␈↓ ↓H
␈↓ ↓HJ.␈α∞Hug"␈α∞stand␈α
for␈α
has␈α
an␈α
answer.␈α
In␈α
the␈α
story␈α
about␈α
Tad,␈α
the␈α
question␈α
of␈α
what␈α
was␈α
Tad's␈α
middle
␈↓ ↓H
␈↓ ↓Hname␈α
or␈α
what␈α
year␈α
the␈α
story␈α
occurred␈α
in␈α
does␈α
not␈α
necessarily␈α
have␈α
an␈α
answer.
␈↓ ↓H
␈↓ ↓H
␈↓ α_I␈αthink␈αthat␈αartificial␈αintelligence␈αis␈α
not␈α
very␈α
close␈α
to␈α
being␈α
able␈α
to␈α
understand␈α
such␈α
stories␈α
in␈α
a
␈↓ ↓H
␈↓ ↓Hgenuine␈αway.␈αTherefore,␈αI␈αwould␈αlike␈αto␈αsneak␈αup␈αon␈αit␈α
gradually␈α
by␈α
dividing␈α
the␈α
problem␈α
into␈α
parts
␈↓ ↓H
␈↓ ↓Hwhich␈α
can␈α
be␈α
attacked␈α
separately.␈α
Here␈α
are␈α
some␈α
of␈α
the␈α
components:
␈↓ ↓H
␈↓ ↓H
␈↓ α_1.␈αA␈αformalism␈αcapable␈αof␈αexpressing␈αthe␈αassertions␈αof␈αthe␈αsentences␈αfree␈αfrom␈αdependence␈αon
␈↓ ↓H
␈↓ ↓Hthe␈α∂grammar␈α∂of␈α∂the␈α∂English␈α∂language.␈α∂A␈α∂good␈α∂test␈α∂for␈α∂such␈α∂a␈α∂formalism␈α∂would␈α∂be␈α∞to␈α∞produce␈α∞a
␈↓ ↓H
␈↓ ↓Hprogram␈α
for␈α
translating␈α
from␈α
the␈α
formalism␈α
into␈α
any␈α
of␈α
several␈α
natural␈αlanguages.␈αMore␈αweakly,␈αit
␈↓ ↓H
␈↓ ↓Hshould␈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
␈↓ ↓H
␈↓ ↓Htranslate␈α
from␈α
one␈α
known␈α
natural␈α
language␈α
to␈α
another.
␈↓ ↓H
␈↓ ↓H
␈↓ α_The␈α⊃grammar␈α⊂of␈α⊂such␈α⊂a␈α⊂language␈α⊂would␈α⊂be␈α⊂trivial␈α⊂and␈α⊂mathematical␈α⊂in␈α⊂character.␈α⊂There
␈↓ ↓H
␈↓ ↓Hwould␈αbe␈α
an␈α
"English"␈α
version␈α
of␈α
the␈α
formalism␈α
in␈α
which␈α
English␈α
words␈α
were␈α
used␈α
as␈α
identifiers,␈α
but
␈↓ ↓H
␈↓ ↓Hthere␈αwould␈αstill␈αhave␈αto␈αbe␈αa␈αglossary␈α
that␈α
gives␈α
the␈α
precise␈α
meaning␈α
of␈α
the␈α
identifiers.␈α
There␈α
would
␈↓ ↓H
␈↓ ↓Halso␈αbe␈αa␈αGerman␈αand␈αa␈αJapanese␈αversion.␈αThe␈αtranslation␈αfrom␈αthe␈αEnglish␈αversion␈αto␈αthe␈αGerman
␈↓ ↓H
␈↓ ↓Hor␈αJapanese␈αversion␈αwould␈αbe␈αa␈αsimple␈αsubstitution␈αfor␈αidentifiers,␈αand␈αa␈αGerman␈αor␈αJapanese␈αwho
␈↓ ↓H
␈↓ ↓Hhad␈α∂learned␈α∂the␈α∂grammar␈α∂could␈α∂then␈α∂translate␈α∂into␈α∂his␈α∂language␈α∂with␈α∞the␈α∞aid␈α∞of␈α∞the␈α∞German␈α∞or
␈↓ ↓H
␈↓ ↓HJapanese␈α
glossary.
␈↓ ↓H
␈↓ ↓H
␈↓ α_This␈αidea␈αhas␈αsome␈αresemblance␈αto␈αthe␈αidea␈αof␈α"deep␈αstructure",␈α
but␈α
I␈α
have␈α
some␈α
doubts␈α
about
␈↓ ↓H
␈↓ ↓Hwhether␈α
that␈α
idea␈α
is␈α
well␈α
enough␈α
defined␈α
to␈α
say␈α
definitely␈α
whether␈α
it␈α
meets␈α
the␈α
above␈α
criteria.
␈↓ ↓H
␈↓ ↓H
␈↓ α_2.␈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
␈↓ ↓H
␈↓ ↓Hdata␈αstructure,␈αit␈αwould␈αbe␈αdefinite␈αwhich␈αrobber␈αpushed␈αMr.␈αHug␈αfirst,␈αand␈αwhat␈αthe␈αrobbers␈αsaid
␈↓ ↓H
␈↓ ↓Heven␈α
though␈α
it␈α
is␈αnot␈αstated␈αin␈αthe␈αstory.␈αClearly␈αsome␈αcompromise␈αis␈αnecessary␈αhere,␈αsince␈αthe␈αdata
␈↓ ↓H
␈↓ ↓Hstructure␈α
need␈α
not␈α
be␈α
able␈α
to␈α
express␈α
positions␈α
and␈α
velocities␈α
of␈α
molecules.
␈↓ ↓H
␈↓ ↓H
␈↓ α_The␈αbasis␈αof␈αthis␈αdata␈αstructure␈αmight␈αbe␈αvarious␈αnetworks␈αof␈αnodes␈αdescribed␈αby␈αsentences␈α
in
␈↓ ↓H
␈↓ ↓Hthe␈αpredicate␈αcalculus.␈αSome␈αof␈αthe␈αsentences␈αwould␈αassert␈αthat␈αcertain␈αprograms␈αapplied␈αto␈αthe␈αdata
␈↓ ↓H
␈↓ ↓Hstructures␈αwould␈αanswer␈αcertain␈αquestions.␈αWhen␈α
such␈α
sentences␈α
existed,␈α
reasoning␈α
would␈α
include␈α
the
␈↓ ↓H
␈↓ ↓Hoperation␈α
of␈α
the␈α
programs.␈α
In␈α
this␈α
way,␈α
we␈α
would␈α
expect␈αto␈αavoid␈αthe␈αextreme␈αprolixity␈αthat␈αarises
␈↓ ↓H
␈↓ ↓Hwhen␈α
we␈α
attempt␈α
to␈α
do␈α
even␈α
simple␈α
calculations␈α
by␈α
pure␈α
predicate␈α
calculus␈α
deduction.
␈↓ ↓H
␈↓ ↓H
␈↓ α_The␈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
␈↓ ↓H
␈↓ ↓Hdeduce␈α
the␈α
answers␈αto␈αthe␈αabove␈αquestions␈αusing␈αa␈αproof␈αchecker.␈αMost␈αof␈αthe␈αproof-checker␈αwould
␈↓ ↓H
␈↓ ↓Hbe␈α
straightforward,␈α
but␈α
there␈α
is␈α
a␈α
major␈α
problem␈αconcerned␈αwith␈αwhen␈αit␈αis␈αpossible␈αto␈α"jump␈αto␈αa
␈↓ ↓H
␈↓ ↓Hconclusion".
␈↓ ↓H
␈↓ ↓H
␈↓ α_3.␈α
I␈α
see␈α
each␈α
of␈α
the␈α
following␈α
problems␈α
as␈α
a␈α
difficult␈α
AI␈α
problem:
␈↓ ↓H
␈↓ ↓H
␈↓ α_a.␈α
A␈α
"parser"␈α
that␈α
takes␈α
English␈α
into␈α
the␈α
"syntax␈α
free␈α
language".
␈↓ ↓H
␈↓ ↓H
␈↓ α_b.␈α
An␈α
"understander"␈α
that␈α
constructs␈α
the␈α
"facts"␈α
from␈α
a␈α
text␈α
in␈α
the␈α
"syntax␈α
free␈α
language".
␈↓ ↓H
␈↓ ↓H
␈↓ α_c.␈α∪Expression␈α∪of␈α∩the␈α∩"general␈α∩information"␈α∩about␈α∩the␈α∩world␈α∩that␈α∩could␈α∩allow␈α∩getting␈α∩the
␈↓ ↓H
␈↓ ↓Hanswers␈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
␈↓ ↓H
␈↓ ↓H"general␈α∪information"␈α∪would␈α∪also␈α∪contain␈α∩non-sentence␈α∩data␈α∩structures␈α∩and␈α∩procedures,␈α∩but␈α∩the
␈↓ ↓H
␈↓ ↓Hsentences␈α
would␈α
tell␈α
what␈α
goals␈α
can␈α
be␈α
achieved␈α
by␈αrunning␈αthe␈αprocedures.␈αIn␈αthis␈αway,␈αwe␈αwould
␈↓ ↓H
␈↓ ↓Hget␈α
the␈α
best␈α
of␈α
the␈α
sentential␈α
and␈α
procedural␈α
representations␈α
of␈α
knowledge.
␈↓ ↓H
␈↓ ↓H
␈↓ 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␈αthe␈α"facts".␈αWe
␈↓ ↓H
␈↓ ↓Himagine␈α∞the␈α∞questions␈α∞to␈α∞be␈α∞expressed␈α∞in␈α∞the␈α∞"fact"␈α
language␈α
and␈α
expect␈α
the␈α
answers␈α
in␈α
the␈α
"fact"
␈↓ ↓H
␈↓ ↓Hlanguage,␈α∞i.e.␈α∞we␈α∞avoid␈α∞grammar␈α∞problems␈α
in␈α
both␈α
understanding␈α
the␈α
questions␈α
and␈α
in␈α
expressing
␈↓ ↓H
␈↓ ↓Hthe␈α
answers.
␈↓ ↓H
COMMENT ⊗ VALID 00002 PAGES
␈↓ ↓H
C REC PAGE DESCRIPTION
␈↓ ↓H
C00001 00001
␈↓ ↓H
C00002 00002␈↓ β8␈↓ ∧λWhen my understander has digested the story of Mr. Hug, it
␈↓ ↓H
C00015 ENDMK
␈↓ ↓H
C⊗;
␈↓ ↓H
␈↓ α_When my understander has digested the story of Mr. Hug, it
␈↓ ↓H
will have added one or more predicate calculus sentences to its data
␈↓ ↓H
base. One sentence will do if it has the form
␈↓ ↓H
␈↓ ↓H
␈↓ α_∃ e p1 p2 g1 g2 e1 e2 ... . event(e) ∧ person(p1) ∧ name(p1)
␈↓ ↓H
= "John. J. Hug" ∧ g1 ⊂ Robbers ∧ ... etc.
␈↓ ↓H
␈↓ ↓H
␈↓ ↓H
In this form, all the entities involved in expressing the facts of
␈↓ ↓H
the story are existentially quantified variables. The only constants
␈↓ ↓H
in the formula would have been present in the system previously.
␈↓ ↓H
However, it is probably better to use a collection of sentences
␈↓ ↓H
introducing a collection of individual constants. In this case,
␈↓ ↓H
there will be 20 or so new individual constants representing people,
␈↓ ↓H
groups of people, the main event and its sub-events, places,
␈↓ ↓H
organizations, etc.
␈↓ ↓H
␈↓ ↓H
␈↓ α_1. In representing the robbers, the system has a choice of
␈↓ ↓H
representing them by three individual constants, R1, R2, and R3 or by
␈↓ ↓H
using a single symbol G1 to represent the group of robbers. A good
␈↓ ↓H
system will probably use both. If the number of robbers were not
␈↓ ↓H
specified, we would have to use a constant for the group. We have to
␈↓ ↓H
identify the robber who operated the elevator while the others pushed
␈↓ ↓H
Mr. Hug into the shaft. We shall call him R1. The other two are not
␈↓ ↓H
discriminated in the story, but there is no harm in our calling them
␈↓ ↓H
R2 and R3, even if there is no information to discriminate them. If
␈↓ ↓H
there were 20 robbers, it would be a mistake to give them all
␈↓ ↓H
individual names. Suppose it had further been stated that as the
␈↓ ↓H
robbers left one of them threatened to return and kill Mr. Hug later
␈↓ ↓H
but that it was not stated whether this robber was the same one who
␈↓ ↓H
operated the elevator. We could designate this robber by R4, but we
␈↓ ↓H
would not have sentences asserting that R4 was distinct from R1, R2
␈↓ ↓H
and R3; instead we would have a sentence asserting that R4 was one of
␈↓ ↓H
these. It is tempting to identify the group of robbers with the set
␈↓ ↓H
{R1,R2,R3}, but we may want to give the group some properties not
␈↓ ↓H
enjoyed by the set of its members. Sentences with plural subjects
␈↓ ↓H
express some rather tricky concepts. Thus, the group robbed the
␈↓ ↓H
store, and this is not an assertion that each member robbed the
␈↓ ↓H
store.
␈↓ ↓H
␈↓ ↓H
␈↓ α_The "members of the police emergency squad" presents a
␈↓ ↓H
similar problem. We don't want to assert how many there were. In
␈↓ ↓H
this connection, it may be worthwhile to distinguish between what
␈↓ ↓H
happened and what we wish to assert about what happened. A language
␈↓ ↓H
adequate to describe what happened would not have to leave the number
␈↓ ↓H
of policemen present vague and could give them each a name. In my
␈↓ ↓H
old jargon, such a language would be metaphysically adequate though
␈↓ ↓H
not epistemologically adequate. Devising a language that is only
␈↓ ↓H
metaphysically adequate may be a worthwhile stage on the way to an
␈↓ ↓H
epistemologically adequate system. By "devising a language" I mean
␈↓ ↓H
defining a collection of predicate and constant symbols and
␈↓ ↓H
axiomatizing their general properties. This language should not be
␈↓ ↓H
peculiar to the story of Mr. Hug, but we should not require that it
␈↓ ↓H
be completely general in the present state of the science.
␈↓ ↓H
␈↓ ↓H
␈↓ α_2. It is not obvious how to express what we know when we are
␈↓ ↓H
told that Mr. Hug is a furniture salesman. A direct approach is to
␈↓ ↓H
define an abstract entity called Furniture and a function called
␈↓ ↓H
salesmen and to assert
␈↓ ↓H
␈↓ ↓H
␈↓ α_Hug ε salesmen(Furniture).
␈↓ ↓H
␈↓ ↓H
This will probably work although the logical connection between the
␈↓ ↓H
abstract entity Furniture and concrete chairs and tables needs to be
␈↓ ↓H
worked out. It would be over-simplified to identify Furniture with
␈↓ ↓H
the set of furniture in existence at that time, because one could be
␈↓ ↓H
a salesman of space shuttles even though there don't exist any yet.
␈↓ ↓H
In my opinion, one should resist a tendency to apply Occam's razor
␈↓ ↓H
prematurely. Perhaps we can identify the abstract Furniture with the
␈↓ ↓H
an extension of the predicate that tells us whether an object should
␈↓ ↓H
be regarded as a piece of furniture, perhaps not. It does no harm to
␈↓ ↓H
keep them separate for the time being. This case looks like an
␈↓ ↓H
argument for using second order logic so that the argument of
␈↓ ↓H
␈↓↓salesmen␈↓ could be the predicate ␈↓↓furniture␈↓ that tells
␈↓ ↓H
whether an object is a piece of furniture. However, there are
␈↓ ↓H
various techniques for getting the same result without the use of
␈↓ ↓H
second order logic.
␈↓ ↓H
␈↓ ↓H
␈↓ α_3. Occam's razor. After reading the story, one is prepared
␈↓ ↓H
to answer negatively the question of whether there was someone else
␈↓ ↓H
besides Mr. Hug and the robbers present. However, sentences
␈↓ ↓H
describing such another person could be added to the story without
␈↓ ↓H
contradiction. Our basis for the negative answer is that we can
␈↓ ↓H
construct a model of the facts stated in the story without such a
␈↓ ↓H
person, and we are applying Occam's razor in order to not ␈↓↓multiply
␈↓ ↓H
entities beyond necessity␈↓. This could be attributed to the fact
␈↓ ↓H
that the ␈↓↓New York Times␈↓ tells the whole story when it can, but
␈↓ ↓H
I think that by putting Occam's razor into the system, we can get
␈↓ ↓H
this result without having to formalize the ␈↓↓New York Times␈↓.
␈↓ ↓H
␈↓ ↓H
␈↓ α_This suggests introducing the notion of the minimal
␈↓ ↓H
completion of a story expressed in the predicate calculus. The
␈↓ ↓H
minimal completion of the story is also a set of sentences in the
␈↓ ↓H
predicate calculus, but it contains sentences asserting things like
␈↓ ↓H
"The set of people in the store while the robbers were trying to
␈↓ ↓H
crush Mr. Hug consists of Mr. Hug and the robbers". These sentences
␈↓ ↓H
are to be obtained from the original set by the application of a
␈↓ ↓H
process formalizing Occam's razor. This process works from a set of
␈↓ ↓H
sentences and is not logical deduction although it might be
␈↓ ↓H
accomplished by deduction in a meta- language that contained
␈↓ ↓H
sentences about sets of sentences. As I have pointed out elsewhere,
␈↓ ↓H
the process cannot be deduction, because it generates sentences that
␈↓ ↓H
contradict sentences that are consistent with the original set of
␈↓ ↓H
sentences.
␈↓ ↓H
␈↓ ↓H
␈↓ α_A number of the questions given in the previous section have
␈↓ ↓H
answers that can be formally deduced from the minimal completion but
␈↓ ↓H
not from the original list.
␈↓ ↓H
␈↓ ↓H
␈↓ α_It has been suggested that probabilistic reasoning should be
␈↓ ↓H
used to exclude the presence of other people rather than Occam's
␈↓ ↓H
razor. The problem with this is that the number of additional
␈↓ ↓H
entities that are not logically excluded is limited only by one's
␈↓ ↓H
imagination so that it is not clear how one could construct a
␈↓ ↓H
probabilistic model that took these possibilities into account only
␈↓ ↓H
to exclude them as improbable. If one wants to introduce
␈↓ ↓H
probabilities, it might make more sense to assign a probability to
␈↓ ↓H
the correctness of the minimal completion of a ␈↓↓New York Times␈↓
␈↓ ↓H
story based on its past record in finding the relevant facts of
␈↓ ↓H
robberies.
␈↓ ↓H
␈↓ ↓H
␈↓ α_Another problem in constructing the completion is the
␈↓ ↓H
isolation of the story from the rest of the world. The members of
␈↓ ↓H
the Police Emergency Squad all have mothers (living or dead), but we
␈↓ ↓H
don't want to bring them in to the completion.
␈↓ ↓H
␈↓ ↓H
␈↓ α_To recapitulate: The original set of predicate calculus
␈↓ ↓H
sentences can be generated from the story as one goes along. Each
␈↓ ↓H
sentence is generated approximately from a sentence of the story with
␈↓ ↓H
the aid of general knowledge and what has been generated from the
␈↓ ↓H
previous sentences. (This will usually be the case if the story is
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well told although there are sometimes cases in which the correct way
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to express a sentence will depend on what follows - but this is not
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good writing). The completion, however, will depend on the whole of
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the story.
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␈↓ α_It might be interesting to consider what can be determined
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from a partial reading of the story - even stopping the reading
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in the middle of a sentence since what has appeared so far in a
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sentence often must be understood in order to even parse the rest of
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the sentence.
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