coMPUT'll'iTELLv o L .3 . t 9 t 7
I 14
cccdings of rhc ?th IntcrnationalJoint Confercnccon Anificial
t n t c l l i g l n c c , V a n c o u v e r8. . C . , p p . 3 3 1 - 3 3 7 '
1981. Narural languageProccssint:crucible for compuu'
rional theories of cognirfn.-Procecdings of rlc 8th Intcrnational
Karlsruhc'WcstGer'
on AnificialIntclli-ecncc,
JointConfercncc
p
P
.
l
l
8
0
1
1
8
6
.
many.
S r - r c u i ,i . n . t S Z t . A n i f i c i a li n t e l l i g c n c teh: e h e u r i s t iPc r o g r a m McGnu''Hill. Ncw York' NY'
mingapproach,
Two lessonsof logic
Bmrx Cexrrvett Stqlrn
PaloAIto'CA 94304'1J'S'A'
Center,
XerorPalo AItoResearch
ond
CA 94305' tl'S'A'
SranJord'
Centerforr,c srud.rof LanguagcandInJomatiotr,SrartfurdUniyarrig"
C m p n . l n r c l l .3 . ? l { - 2 l t
(19t7)
In particular
bc eleanedfrom is rulesand reprcsenlalions'
l. Background
results
(incompleteness
."ri, thit canbe madequiteconcrete
daredto 1879'rThis means for arithrnetic,for example),but the lessonitself is gencra'l'
Modernlogicis mostreasonably
toform'
hadmorcthana cenluryto studya Panicu-- For discussion,
of content
tharlogicians-have
I'tl call itthe irreducibili4'
m.uclt
surprisingly'
Not
systemsindependent
formal
so-called
somewhat
of
two
f"triifv
to
distinguish
iui
To getat it, we need
of anysymbolsystem'
of the enormousamounttheyhavelearnedis peculiarto their uroi.tt or dimensions
about rhc foundationsof mathematics'
rpr"in" assumptions
WhatI'll call the,frsr/actor of a symbolsysteminvolvesthe
however,areunivenal.holdingfor any shapesof rhesymbols,thewaysthey canbe put togetherand
Stme of theirinsights,
or sentences.
symbols,
signs,
of
system
mkin apart, and tlre behaviouror operationsdehnedover
'
logic's
of
many
that
to
see
come
Particular
letlers,and modusponensin
has
predicate
McDermott
them. Exprcssions,
By
humanreasoning'
in comto general
operations
aren'tapplicable
corresponding
and
ryP€s
dau
assumPtions
Iogic;absiract
- thatsonof thing.You canthink of this*'hole
and laige I think he's right, andI aerecthattheconsequences pulerscience
a combina'
system'smechanics:
"t a tiitte appalling.Bui McDermoitgoeson to imply f"t y.'
tackaeeasa rcprcsentational
AI'
for
basis
a
as
least
whole.
al
ovcr
defined
as
a
logic
ntions
rcjeir
ope
dynamic
and
mustthercfore
iion oiitt staticsrntctures
and
AI
bctween
affair
in a
love
realized
end
the
dircctjl'
what
bc
suggests,-to
must
he
time,
is
also
factor
It's
rhem.Ttrefint
work'
any
do
going
to
is
if
the
system
logic.
substrate,
-No*
"logic" 'physical
t:q'
mean' l
I don't carc too much about the term
s1'mbols
what the
the s)'mDols
with what
to do
do with
has'to
second
Tlre
Tlresecond
facror has
factor
wherherwe shoulduseit, broadlyconstrued'for the full range what they'rc aLout- their content.Interpretation(in thc.logi- |
of rationalbelief revision(roughly,\'hat you shouldor arc cian's sense!)is a secondfactor phenomenon,as arc truth ano I
wc
likely to belicvenext, if you bclievel- no.*), or whetherrefercnce. the latter in the senseof the rclation bdwe-enthc t
to
it
confining
logic in
"McDermon" and a personwho works at Yale' Shadcs
rto"ia foUowtraditionalmathematical
name
i
thc enrailmentrelation(roughty,what follows, if P is true)' of the old declarativc/proceduraldistinction (bur only shades:
J
andadopta moregeneralretm iot thehumancasc'(As I say'I
198?).
I'll usc sec Smith
ultimatesense,but in whatfollows
don't carc, in som-e
logic dretwo storiesarecalledprooftheory
mathematical
In
"thought"
''togic" for thenarrow!entailment
for
serse,and
and modeltheorj, rispcctivcly;semanticsis talicnto bc thc
- *re storyabout
what we do.)
lanir. Funhermorc,semantics
we can srudyof-rhe
What I do careaboutis this:thatwc learncvel,ything
s1'stemgin this
these
about
maners
wha(
rcally
is
.on,Lnt
"more equal" thanthefirst factoraccount'There'sa
history.Morespecifically'
from those100yean of intellectual
it's
sense
I worry thatMcbermon,in rejectinglogic'sparticularassumP- reasonfor thisasymmetry:
Witiout somesecondfactoraspecu'
tions, is also discardingsomeof its universallessons'Tu'o you couldn'tbc sureyou hauea symbolsystemat all' Everylessons,in panicular'
lhing t'"t a mechaniialnature'to put rhis anotherwa1';it's
prior (that'swhy ! called-itfint)' Havingconto
meriphysically
I.l. Issson one: theirreducibiliryof conrent form
to a
and thereforebeing amenable
The firsr lessonI take to be the deepcsttnrth that logicians tent,'on rlre other hand'
rEPreor
symbolic
is whatdistinguishes
havc uncovered:thattherc'smorcto a symbolsyslemtlrancan secondfacrorana-lysis,
(what philosophencall intentional)systemslikc
sentational
and compulersfrom ordinaryphysicalobjeculike
''Thc ycar 1879wasrhepublicationdateof Frcge'sBegrifsschrilt' lansuages
-pucks
foundation
logical
a
hoc-ky
develop
to
'ntst and oii refineries.
thc firsisrep in his life-longancmPt
lessonof logic.then,canbe suted in termsof the
ffre
for marhcmatics.AhhoughI will arguethat wc shouldreuin thc
"second
wo*
Frcgc's
that
rigour and precisionof ihe enormoJstradition
factor": the cJntentof a symbol,at lcastin general'
it' butarises
proximate
inipircd. I bclievcthar the inruitionsand insighuof variouscarlicr isn'tan inrrinsic
or causally
ProPen)'of
Peirce.art rt
For
domain'
espcciallyCharlcsSanders
other
wrirerson symbolicsyslems.
and
some
iyirem
thc
between
asa relation
in
Icast as rcic.'"nr to AI's .oni.-s. From our point of vicw it's
ANE'?'
Pt
of thesymbol
or reference
.irrpt.. rhemeaning
durdcvelopmcnt.
unfomrnatctharthe vastmajoriryof mathematical
er
LaGuardia'
or
rnffic
air
of ihis morning's
purcly"mathe- "n axiomatization
ing rhis cenruly.hasbcendevotcdto tbc narrower,
ol
20@ft up' No amount
aiqplanc.
actual
some
would
involve
maticel." case.
PnmJ
o C:nrb
, lmnnc
ru Crnr!
COITTTIEYIARIES
i n v c s t i g a t i n gh o w t h e s y m b o l P L A N E , ' i s u s e dw i t h i n t h e a i r '
traffic iontrol syslemcould ever tell you what planc it refen
r o . T o 8 e l t o t h e p l a n ei t s e l f y o u ' d h a v et o l o o k o u t s i d ct h es y s t c m . t o s e e h o w i t w a s c o n n e c t e du p t o , a n d u s e di n , i t s e n v i '
ronment. Or imaeine tr;'ine to determinethe tnrth of a repon
claiming that 70% of all doctorsrecommendCrest toothpastc'
You woutdn't bring out your microscopeto studythe paperthe
regort was written on. or submit it for rypognphic analysis;
around and acruallytalk to doctors.
'vou would drive
Cont.n,, in other words, doesn'thang arounda symbolsystcm, like a nervousleenaserafraid to leave thc house;it's out
thcrc, in the world. Nor can the secondfactor be deducedfrom
thc first. Funhermore (this is perhapsthe most surprisingthing
of all) this externaliryof content doesn't arise only for rcalrime iystems, like air-traffic control systems.It holdseven for
as absiract, circumstantially independent,causallyinen, and
completely disembodied a system as formal arithmetic.
that contentrela'
Ir's a major corroltary to this first lesson
"Povungnituk" to
tions arcn't computed. lf I use the name
rcfcr lo a small town on Hudson's Bay, for example,a content
relation holds between my uneranceand a major sourceof
Inuit stone carvings. But. jusr like the Propertyof being the
avemge age in a collection of pcople, this relationjust is; no
to hold- Adminedly' in
*ork-neeJs to be done in order for it "comPutc"
sometling,
you
may
unefiInce.
my
interprerine
but the purPose of your comPutation will only bc to arrange
yourself lo stand in something like the same kjnd of (nonlompured) content retation to the town that I did, when I said
it. Tirc town itself. which is a part of the contentrelation,is not
"proximate" cause
a part - not what the philosophen call a
. - of any comPutationalactiviry of saying or undentanding'
In conirasr with the first factor, to Put this anotberway, the
second facror of a symbol syslem doesn't needdirect physical
realization. Therc is no way the Inuits could deploya sensorin
Povungniruk to detect whether their town was being rcferrcdto
by an arbitnry speaker in an arbitrarily remote location'
It should beadmined that how this dl works - how symbols
"'reach out and touch someone" - remains an almost total
mystery. Some people (Winograd. for example).argue that
thly only do through human use; others (I'm in this category)
belicvc that human interpretation is sufficient' but no( neccssary. But whatever one's view, the facts that theseviews have
to dcal with are impressivc. To sun with, refercnceoutstriPs
causaliry, at lcast locally; with four simple leners I can rcfer lo
e composer who hasn't existed for more than 200 years not
to a set-theoreticmodel of him, to his name, or lo your comprehcnsion of him. but to his very hean and soul (eventhough'
untite Povungniruk. he doesn't exist any more)' Referencc
relations arcntl even constrainedby'the light-cbne;as Church
"sPeed of logic"' In fact
oncc pur it,r semanticstravels at lhc
refcrence almost outstriPs comprehension; if we didn't know
that tanguage works, we would sPurn rumoun of its long. distance capabilities.
Whar's more. the linle we do know isn't reassuring,at least
I for AI. To take just one example, it seemsthat the axioms of
'
arithmetic musr be connecled to thc numbers-(ratherthan to
I other nonstandard inlerpreutions) not by anyrhing intrinsic to
I them. but by us humans. It seems,that is. that agentsarc what
I mancr. for semantical connection. But lhat only shifu thc
i mystery - squarely onto AJ's subject maner: cognitive agen1.
i interprcrers (igain. in the philosophical sensel)of the symbols
:CSLI scminar.l"lay 3. t98{.
!
E
_q
1 l \
a n ds i g n s .
But if we don't know low rcferenceand content g.ork. ar
leastwe know tAal they work, and that therc is more to it all
rhan proof theory, Funhermorc, I take it to bc the job of
y n d e r s t o o dt o. e x p l a i n .i n a s
s e m a n r i c sa.t l e a s l a s c l a s s i c a l l u
way
a
as. possible, the interplar'
rigorous
and
systematic
"formal" (i.e., fint factorr) propenics.on thc onc
betwecn
rela'
hand,and theserclatively more mysterioussecond-factor
tionsof meaningand content,on the other.Admittcdll', in the
face of considerableignorancc,we can't yct fill in all the
details(though we do what we can - which, to date, mostlv
meansenumeratingtlre relata, but somedaymore should be
possible).What matlers- what logic's ftnt lessonrc:Iy tclls
us - is that the second factor conlentstory must bc told.
].2. I-essonneo: a single theoreticalsrance
Logic's second lesson is a theoreticalone, in the scnseof
being about theory - about how symbolic systemsshould be
expliined. Related to the ftnt, it arisesfrom the recognition
theory and model theory, in the
that the two factors (p*f
related,
in spiteof bein-econceprua.lly
be
must
case)
traditional
distinct.This is the role, in logic's case,playedby completenessproofs,notionsofsoundnessandvalidity,etc' ln conLrast,
you could aJsoargue that therc are two storiesto bc told about
money: one about is physical embodiment,one about is
socialandeconomic import. But, at leaston the surfacc,there
is no obviousreasonwhy the storiesshouldrelate;engineenat
the FranUin Mint dcsigning new dollar bills probablydon't
need to k-now Gresham's law (that bad money drives out
good).In logic, however, the connectionis morc direct' You
Iouldn't really claim to have a (lirst-factor)inferenceregimen
if you couldn'r relate it Pretty directly to (second'factor)
semanticinterPrctation.
Becauseof r-hisglobal but crucialconnection,logicianshave
developeda single theoreticalstanccfrom which to tell both
stories. The stories, furthermore, overlap in vocabulary: the
samerlieoretician'sgrammar that spcllsout the linguistic regularities of logical formulae is usedby proof tieoretician and
model theorelician alikc. And thc overlap is necessarl"That
logic's two facton arc rclatively independent(more on this in a
m6ment), and yet must ultimately be related,can onJybc said
from a vanhge point from which t}ey can borh bc scen'
In laying thcse things out it is importantnot to confuscthe
.on..pru"l-distinctnesi of facton, or the singlenessof tbcorttical sranapoint,with the questionof how relatedthc rwo factors
arc. By inalogy, Seometrydistinguishestengrh and area. but
thengoeson to tie them stronglytogelhertin the familiar rr'ay'
Simil-arty,both classical and relativisticmechanicsview rime
and spaie as concePruallydistinct; the two rheories diffcr in
what *rey then say about tlre notiors - whetherthey are inde'
pendent(the classical case) or intimatelyrclated (relativistic)'
io th. n"*t section I will claim that the frnt and secondfactors
of rhought should be intimately ard constantlyrelated.but it
doesn't follow that I rhink they are the samething.
How, then, does the second lesson relate to thc first?
just
Becausewe'rc now talking about theoriesof logic. not
penicuIn
aboutlogic iaelf, things gci a linle bit complicatcd.
lar, sinCe *rese theories Qike rhe logica.l syslems tbcy arc
abour) are themselves intentional phcnomena,we haYe rwo
tTheclaimthat formaliry,in rhecnd.rcduces
to firstfactornotiors
by B'-C'
book
in.prepantioo
a
in
.tgu.d
is
of physicalrcalizabiliry
bv Thc
Sm'irh.cntided Is CompurarionForma?(To bc Publishcd
MA.)
MIT Press/ABndford Book. Cambridge.
216
voL. l. l9E?
lr.,TELL.
co\{PLrT.
of representa'
(tu'ospecies
andmodellinS
3, Tharlaneuage
iifferently'
Thg
completely
rion,I uke iil sh'ouldbe lreated
malter
primary
subject
the
is
relation
reference
lineuisric
familiar
such
engendering
nontransitive,
to be strictly
asiumed
of meta'
hierarchies
distinction,
astheuse/menrion
conslructs
(of
otherhand
on the
T' Modelling,
andconvention
languages,
quadruples'
of
sets
the-soi that treatsTuring machinesas
iruth andFalsiryas0 and l. andso forrh)is not onJytakento
"frcc," in thesenset'hatyou
buialso
bctransitive,
3P 4l-o*:d
io rr. t modelof X in placcof X irself(evento identifythe
two) with theoreticalabandon'
"Tarskian
I don'tkrow exactly*'hat McDermonmeansby
sincehe ctearlyintendsit to be broadenoughto
semantics,"
(on
languages
of programming
analyses
includedenotational
whichmorebelow),butltakeittomeanroughlyasemantic
At anyrate
accountthatadoptsall threeof theseassumPtions'
herc.
I'll usethatdefinition
2. Human cognitionand logic'sassumptions
positioncannowbe statedin termsof thefint
McDermon's
what two assumptions:
of
much
with
agrce
thatlogicmakesthem'thatAI
that
I
indicated
he recognizes
already
I'vc
pas'
of this
over
consequences
deduction
purc
mustrejecir-hem,and thai therheorerical
McDermon siys: thatrationalityisn't
of
aspectinextricable
use
an
is
that
aredaunting'
rejecdon
ti* itgi""l forrnulae,
for the strengthof his
all tharstuff. But let'sgo a linle slowly' to seejust
i "gr... I've also got real synrPathy
f"o*iJg",
'llet go of ' or a]tered'as
a
to
go
back
let's
easily
be
In
can
lead.
theie
of
agreements
none
rcact[n:
Panicular,
whcrc th-esc
if ,h", *"r" a minor adjustmentto what remainsbasicallya
oit
--erin historY.
"logical" enterprise.
soassumpmodcrn
of
Thereare foundational
tugg.tted at the outset,the originators
furely
"TJrmal" logic - Frege,Russell,Whitehead'Carnap' iions,with all thatthat imPlies.
called
To makethat concrete,a few more wordsabouteach'To
^nJ to on - ',".rc-primarilylxploring(or at leastmotivated
conthings
All
mathematics'
of
foundations
thc
in
start with, the central intuition underlyingthe -so-called
ty) issues
iisiru.t.d';language
projectat CSLI involves
andcomputation
sidercd,rheYdid an excellentjob.
a co.m'
descentheir
We,
exactoPPo.site:
with
its
the linr assumption
replacing
Unfortunarely,though,theyalsodied'
we're
to
develop
is
goal
$tat
The
use.
achievement
langu.g.
by their
*in.o ^io dircctfocuson
dcnts,have beenso impressed
mustbc
of thinkingthattheydehnedwhatsemantics
ne* rheori.sand semanti.J fome*orks that analyzeindii;;;g.t
question
the
to
related
thecrucialroleof circumsunce
andembrace
a
t,ro-stag"'ptoblem,
raises
"idualunerances,
itit
iif..
and
parricular
andcontext.To takejust oneexample,thisinvolvesdiagnos*i*O ", rhe ourselabourihc-relationberween
their
facton:
accePt
to
liable
we
are
of all peninentcontextud
ine the relevantstRrcture
unir"oA insigbts.At fint blush,
"lt's 4:00
why
us
wherc
tcll
to
place
(such
the
around
ai
them
having
facts
too-glibly, not
t i"urnt background
o.*Jt
'tlr;;;it
(thal
strucrure
djscourse
theieciiions theydid. Then,oncewe discover*rat p.r.;' o* tl"id;, pt"tuppositions,
we'rc
for our Purposes'
i,elpresolvePronouns,foiexample),factsaboutthelanguage
O.ir p"ni.ular choicesarc untenable
of rlrCsubjectmaneror describcd
in a^ig.t of throwingthe wholething away,babycumbath- U.i'ngus"d, ih. tt..tut
which
linguisticand cognitivcprowater,
"
situriion,with respectro
that
werc
made'
that
choices
murualbclicf stnrctures
all
the
canvass
strucrured,
to
rurn'be
";" in
i"ti,.t rhantrying
;;;;
cogniforabout
facts
traditional
internd
underlying
said,
can't
be
assumPtions
and
three
can
liit
what
explain
lcimc simply
of internal
for AI' The following'in
t.i"i ^Ict,i,..trc that penain to the interprctadon
rnJ togi. tf,"t I U.ti"". areunienable
just
onesetof
is
this
and so on ind so forrh.And
structures,
otlrer words, arc tenetswc must,gq,t:
dozensof
had
has
CSLI
be
considered,
iit".i ,rt"i have to
l. That use can be ignorcd' This premise leads logic to
yean so far - and' from
4
project
for
this
on
people
oorking
'riiitt.
ignore agents and procesiing, to setaside-context,andto focus
In
peripectiue''lttrint it's makinggoodprogress'
It
unerances'
individual
or
on sentence rypes tnsteadoftokens
subsomething
bc
nJ, rot thananother4 yean thercshoutd
also suggeststh"t a s.nt.nce must rePresentis whole content
stantidto show.
could
sincc no other resourcesare licensed that
.ifu"iif!,
- thatfirst andsecondfaclorsarc
Tlre secondassumPtion
nafural
from
-"'f." ",i.,it contribudons. This is quite different
just asdeeP;I.alsothinkthisis the
goes
IocJiy ina.p"ndent
where dynamic and contixrual factorsoften implic'
i*gu"g",
He claimsthattheculprit
sobereJM.D.*on.
so
l"r ifirt has
for
itf .o""ttiuute to the content (the time of unerance'
only to prov'
(inference
"nowl')'
deduction
of
notion
its
is
loeicism
of
"a""t.q"ences),
for the word
"i'^*pf", provides an inter,preration
connection
semantical
but if a different
rUf.
Z. if,"i iocaily the two symbolic factors can be treatedindca way
such
in
defineable
(sav.
were
semantically
abduciion)
pcnOentty. even though (as suggestedabove) they must ultisemanfrom
cleft
be
(fint
could
factor)
role
procedural
ii'"i it.
marely bc globally related. In panicular, proof. theory or
senseto
tical imporr(secondfactor),thenit would still make
(secono
or
semantlcs
model
theory
(fint
and
factor)
inferencc
putathe
second
"at the
;"'"-,hi"Bt iown first, andbuildProgTms
factor) are tied together, for any given system',only
are
subtleties:
thesc
But
enrttprise'
theorems'From step r;". .ts.n-.. of thelogicist
end,'i with soundnessand completeness
and I don't believe
indepindencc,
l6cal
assume
'formai"
Jo"t
i"gi.
proceto step, in a
Proof, the (first-factor) inference
'thousht
that.
like
is
dure iannot dependon or affect (second-factor)semanticinterthisone,hasbeento usecomin attacking
"formal" is taken to mean, by
V! o*n strategy,
pretation. (In iact this is what
asa
andintrospection
puuiionallyinreiialnotionsof reflection
I
notjust one' Lotsof peoplehave
s)'slemsto consider,
-Jresrtea
symbol
o'irh ho* theyrelate:fromTanki, in settinguPP.rc
T, to Quinc' worrylng
conditionson satisryingConvention
But theovcrall
translation'
of
"Uort tf,. radicalindereiminacy
second
The
'
enough
ilear
is
factori*.*t
-ron,rr, of rheconnection
of
content
the
(for
eiamplc'
accounr
rhe
rheoretical
of
complete
yd
thc
include
musr
papc'r)
first
1963
Kripk.'s'
(the
underinvestiSdtion
of thesysrem
triLna Torrordime'nsions
in
logic'
modal
of
."n,"*. p*f rclations.andmodelstructures
is
theory
the
that
just
say
whatir is to
That's
l{i';k.'I;;.).
abin the systemunderinvestigation'
--inougt,
intricacies'What malrersherc is that a single'uniof both factors'I takethis
mustprovideaccounts
thcory
ficd
pointto
vantage
,."oenition of the'needfor a singletheoretical
great
contributions'
bc d;'csecondof logic's
l-et's turn to McDermon'
So much for background.
theorisrs as diverse as Fodor and Martin-Lof.)
\
+r
i
t
in u'hichto u,orkour virblealrcm;rrives.
Thepoinr'of
ffi,Wf-lUte
t |i€-Lisp.Smith (1981)in prrticular,
wasto showrhatevcn\r,ar"
t horseprogramminglaneuages
arebestundentoodin termsof
l o c a l l y i n t c n w i n e d f a c t o r s .A s i r h a p p c n s 2. - L i s p i g n o r e dc o n ( textual aspecls of use (by design) - thereby drawing somethin,eof a distinction between the l'int and secondassumptions
t - bur at the same tirne maUn_sits architecturelessgenenliz.
I
ablc than one mi-ehtlike. I hardly needadd tharlots more *'ork
is necessary herc.
I'
Similarly the third - that lan_euage
and modellingare caret gorically distinct. Although McDermon doesn't addressthis
t
premisc explicitly, it stands in equal need of reconsrruction.
c ttglg_lg
th eqgcs--gI-IePrEsenIation' a nd c orresno nd ence w i ll
t,
bc required (see Smith 19E7 for some inirial ana.lyses).
Therc
a arc two reasons this revamping is urgent: panly to e.rplain
c computational practice (see below), and parrJyro clarify our
standardtheoretical apparatus.In particular,althoughpromisri
cuous modclling may be helpful in answering large-scaleand
n hencc rather coarse-grainedquestions(such as whethera given
n formula is true, decidable, computable),it can be pernicious
Ir whcn one asks fine-grained questionsabout control, inrena sional identity, and the use olfinire rcsources.Also, currenr
u computational systems involve representationalstnrcruresof
i r a.ll kinds. ranging continuously from linguisricexpressions
to
b vimrdly iconic isomorphisms like bit maps and simulation
structurcs- This is a large area where rhe panicular assumpc tions of math,ematicallogic haveled ro unrenablemethodologiir cal practices (for AI theorisrs),as well as to unrenableclaims
?
on our primaly subject maner.
All in all- in other words. I agreewirh McDermon drarrhc
consequenccs of rejecting these assumptionsare enormous.
sr And yes, rhey certainJy underminethe coherenceof the "logift cist" program. Writing knowledgedown in advance,rvirhout
P rcgand to use, is a conceptual error doomed to failurc.
b
3. \4tat then?
and this is really whereI've beendriving- whararc
But
wc
do
insread?Insteadof abandoning
to
hopcandreveninsro
rl
unconstraincd
symbolmongering.
surelythi raskis ro develop
h
si aJternarivetheoreticalframeworks.
Now McDerrnon doesn't really argue for pure symbol
tc
"procedunlisr" paraci mongering,but he doessuggestthatthc
digm
thc
only
game
is
other
in
rown,
insinuaring
tharrhere
e
couldn'l
Why
be
any
others.
should
rhat
be
true?
For
example,
tc
flesh
n r why shouldn't we develop a full-scalerheoryof usc Y
u l out lhc projecr that the philosophyof scicncehas only jusr
rhatmust
re staned, for example - and uncovcrthe regularities
ol undcrlie integratedconrenrand behaviour?Fromthe factthar
rt usc and co{rrentare inexrricablylinked it doesn'tfollow that
r-h mtionaliry is random. And if ir isn't random,we can undercreed).
d i standit (at lcast thar seemslikc a plausibleinrellecrual
Sce, this is rcally whar I think's got McDermon'sgoat.
t^ Compurationalpracdce whatour programsacruallydo, not
what
- doesn't honour logic's threc
we
about
sav
them
AI
as
ot assumprionslaid out above;it mixesbehaviourandconrent
rh richly and rhickly as we do. The only rigoroussemanrical
m theorieswe have, on the otherhand.do-makethosercsrrictive
areunlenm assumptions-McDermott seesdratthe assumptions
able.
and
correcdy
notes
that
there
proposals
aren't
orher
any
in
around (" - . - it must have a semantics:
so it musrhavea
Tarskiansemanrics.because
thereis no orhercandidarc").
So
he's forccd ro taud pracrice.Bur then in virruallythe same
brcathhe admirs rhai rhat makeshim uncomforrible.
So he
Rq
H
Obcysthrcc
c l a s s i c aa
l ssumptions
Thcore
ticrl
fnmcwork
Logic and scr rhcory
Spcifrc
applicat
ion
A x i o m a r i z a r i oonfs
l i q u i d sr.r a f f i c , . . .
Rlquircd
rorni I,
c o S n r t t v sc c i e n c e
Qualirrtivcmodelsof
physicd rcrsoning
Frc. l. Appropriare
theorcrical
fnmcwo*s.
endsup somervhat
confused.
Whathe shouldendonc (it sayshere)isn.tpracticeitself,
bvt theoreticalframero.rks that do justicero'tharpractice'.
Thatis, what we want is a conceptuat
backdrop
in'te.msoi
whichto undentandForbus'swork in thesamewayrhatlogic
and model theory form a conceprualbackdropio, ttrylsi
re.search_on-rhe-o.nto-logy
of liquids.This siruation
is picruredin
Fig. l. To be fair, McDermonsaysa lor of thingsiu.ssestin;
thathe agreeswirh the generalthmstof rhisdiagram::.tl,.ri
arelargeclassesof programsrharlack any kind of theoretical
"AI progralns
underpinning:."
arenororious
for beingimpen_
etnblycomplex. . ., bul a modeltharwe don.rundei:rand
is
nota modelar all," "whar's reallybothering
meis rharthese
(diagnosis)
programembodytacittheories
ofabduction,"erc.
Wbathedoesn'rsuggesri
at leastsufficienrJy
cxplicitly,is thar
we needrheoriesto do jusricero programsin jusr rheway rhat
logicprovidestheoriesthardo justiceto lmirhemaricalj
scntences.
The question,that is. is how we are goingro fill in rhe
missing
quadranr.
It seemsrharthere,r* tio o=buious
sugges_
rions.We could uke loeic and set theory,andtry ro molify
them.Or we could rhrow away logic and s"r iheory, "ni
simplysrudyrhe pracdceirself, like enromologisrs
srudying
becs.
With respecr
to modifyingiogic andsertheory,I've a,lready
saida UnleaboutwharI rhinkwouldbe required
ftuild in the
opposire
of rherhreeassumprions
listedabove).And I.ve said
it will be hand.I agreewi$ Isracl(and,I takcit, McDermon)
that incremenralvariantslike nonmonoticlogic are nothing
likestrongenough(Israel1980).Theproblem
is rharonccyoi
startrcvampingthis muchof logic's foundarions,
ir's notciear
whatremains.It's easyto say t-hatone mustundersrand
just
whataspecrs
of classicallogic are parricular(i.c., spccifii ro
metamathematics),
which are universal- bur thai doesn't
male it easyro do. So far I've only suggested
rwo universal
lessons:
external(noncomputed!)
conrent.anda singletheoreticalvanragepoinr. But therc'sa lot morework to do.
I-alsohavegreatrcspeclfor the orlrersuggesrion:
srudying
and.reconstrucring
pracrice.We shoutd..-,rlinty unden-tni
architecrurc,
physicalembodiment,rcsourceallocarion- all
thc usualsruff, In facr rhis is wheremostof my own workhas
concentrated.
But it is also wberc my origina.lworry comes
backro roosr:rhe worry r}at logic's two giar lessoniwill bc
lost.ln factrhis worry can be seenas a triplcthrcar.
- Fint, becauseit porenriallyconfusespracticeirself wirh
t-heories
thatdojusticeto suchpracticc,I'm afraidrhatMcDermon's papcr will lead peoplero discardlogic's r-heoredcal
stancecomplerely,and focustoo muchon thepracricalside.
To be honest.I don'r rhink McDermonhimselfwill do this
(he'stoo unreminingly
theorerical),
but a casualreadercould
mistake
his inrenrions.
Second,
if youjust look at programs,
andtry ro makesense
\
C O N I P U Tl .^ " T E L L ,\ ' O L . l . l 9 E ?
218
Spccificationvicw:
(rypical in theorctical
computcr science)
, Program
,.,nantiar*l
I
Ingrcdicnt view:
(typical in AI)
Frc. 2. Two readings
of "prognm".
out of what they are doing, you will be liable to focussolelyon
l'irst-factor aspectsof systems, for a simple reason:The first
factor. as we said above, is tlre one that needsto be realizedin
thc machinc. And since the point of programsis to conjure up
an otherwise unorganized state machine into appropriateform
to exhibit reasoning, the program only needsto concentrateon
first-factor problems: strucrures, operations, behaviour. ln
general, as.we saw at the outset, the contenl isn't in the
machine at oll.
The third problem arisesfrom a curious fact abouthow practice is currently undentood. It's hard to tell exactly rvhat
"program" and "denonMcDermon means, but the words
tional semanlics," when uttered in one sentence,ineviubly
bring to mind the denotationalsemanticstraditionin compuler
science, as illustrated by Gordon, Plotkin, etc. (see, for
cxample, Gordon 1979). Now I firmly believe that all current
computational systems - from Amord to Zetalisp - blend
both factors we talked about earlier. The only factot of compu'ational systems that.computer scienceulks about,however,is
,c Frrst: procedural role, I believe this is true, curiously
"semailfcs." What is
cnough, even when people usethe lenn
"denotational semantics"
calleil
in computerscienceis in fact
a mo'del-theoreticanalysis of first-factor proceduralmlc, for a
rcason that depends on an ambiguiry in the use of the word
"program,"
suggestedin Fig. 2. I bave tried to explainthese
in Smith (1987);
diagrams, and some of their consequences,
the main insight is that programs, as understoodin theoretical
computer science, arc rypically vieu'ed as specificationsof
computational behaviour, whereasAI (McDermon is clearlyof
this view) takes them to be constituenrswithin it. On the fint
(computer science) view, the content of a prograrnis the computation specified;hence, the computationitselfis what denotational semantics takes its subject mauer lo bc.
Note, in passing,that all sortsof otherotherwiseodd things
are explained by this analvsis.To begin with, it explainswhy
pmgramming language semanticistsuse term models,initial
a-l-ecbras,and all the resr: they individuatetheir semantical
models (remember the rhird assumpdonl)so finely because
they are really modelling (the behaviourof; computational
processesthemselves.Iryaddirion. since 1,ouarc supposedto be
/'/'
a b l er o i n s r a n t i a raec o m p u t a t i o ns. i v e na p r o g r a ms p c c i f fi n gi r
" p r e s c r i p t i o n s . "a s u ' e l l a s " d e s c r i p t r o n s . "
( p r o g r a m sa r e
ro
u s eN 1 ' g a a r d 'psh r a s e )t,h e s e m a n t i c ar le l a t i o ni s c o n s t n i n e dr o
be effccrivein a u,ay that the contentrelation,for naturallan.
s u a g e a n d A I . i s c l e a r l i ' n o t ( r e m e m b e rt h e f i n t l e s s o n l l .
F u r t h e r m o r e ,o p e r a t i o n a la n d d e n o t a t i o n a ls e m a n t i c s ,i n
theoreticalcomputerscience.are t\\'o differentkinds of analrsis of rhe samerelation;Ihat's u'hy 1'ouseeequivalenceproofs
betweenthem (tle distinctionbetweenoperetionaland denoktional semantics,in otlrer words, is completelydifferentfrom
the one we've been talking about betu'eenfirst and secondfacton). Finally. note tlat, under this view, a computerreally
does interprct a program, in the philosopher'ssense!
Bur enough about someoneelse's worries. Thc imponant
point hereis that the contentrelationthat AI needsto study,as
opposed to thc case just considered, is the one that holds
berweenthe computational process and the world outsidc it.
"ingredient" view of programs,this wouldjust be the
On rhe
semanricsof the program itself; on the specifrcation(computer
science)view, it would be lhe semanticsof the senunticsoJ the
program (i.c., two levels of reference).Whicheverway you
go, threethings should be rememberedabout it: it will (at leasi
in general)reachoutsidethe machine,it won'I (again,in general) bc effectivc, and it won't ever be computed.
trr'i get back to McDermon. We had noted that a thorough'
eoing reconstruclion from first principles was an eno[nous
rheoreticaltask, and were looking at lhe other way of proceeding - by reconstructin-ePractice. With respectto the latter
alernativc, I had three u'orries. First, if (as a casualreaderof
McDermon)you just endone practice,you are liableto remain
a-rheoretical.Second, if you try to reconstructPracticcde
nol,o. you arcTdl-only faced with an enorrnoustask, but art
liable to see only first'factor asPects,sincc those are the onJy
onesthat arc implemented(content.remember,doesn'taPPcar
in rhe program at all). And tlren third. the rwister: if you
bonow techniquesfrom theoreticalcomputerscience,you will
be led to focus on the wrons relationcompletely.Funhermore,
not only doesn't it focus on the semanticalrelationwe'rc intcresredin, for somewhat -sraruitousreasons(the fact that programsarc prescriptive); it also ignoreslogic's first lesson:the
ineducibiliryof contentto form.
No matterhow you do it. in olher words, there'sa danger
that you'll miss out on logic's rwo grcatlessons.And that- I
hopg McDermon will agrcc - would be tragic.
of prognmminglan'
description
Gonpox.M. l9?9. The dcnoutiona.l
Ncw Yo*' NY.
Springer-Vedag,
an introduction.
-euagcs:
logic?ProccedIsn,rrt,D. 1980.Whal'su'rongwith non-monotonic
on Anificial Intelliingsof thc Fint Annualn'ationalConfcrencc
g c n c cS. u n f o r dC
, A. pp.99-101.
on modallogic' Acta
Krupxl, S. 1963.Scmanticalconsiderations
Fennica,l6: 83-9a.
Philosophica
in Lisp. Confcrcncc
Surrn. B. C. l9&4. Reflcctionand scmantics
of
on Principlcs
Rccordof rhc ElevcnthAnnualACM Symposium
Salt [:]ic City, UT, pp. 23-35. Also
Prognmmingl-angua-ecs,
CenterIntelligcntSystcms
availablcas Xcrox PaloAho Research
TechnicalRcponISL-S,PaloAIto, CA, 1984.
Laboratory
asPedsof
/n Theorctical
t986. Varicriesof self-rcfcrcncc.
about knowledee.Editedb.r JosephHalpcrn,Mor-ean
reasoning
in Anificial
Los Altos.CA. pp. l9-{3. Alsoto appcar
Kaufman,
Inrclligence'
continuum.CSU Tcchnical
1987.Thc correspondencc
ReponCSLI'8?'71. Sunfod Univeniry,Sunford,CA. Also
of the SixrhCanrdianConference
wirh thc Procecdings
appcarcd
Intclligence.
)"lontreal.
on-Artificial
Qucbec,\{arch1986,andto
in AnificialIntclligcnce.
appear