Esa Itkonen
Is There a 6Computational Paradigm' within Linguistics?
The advent of computers has considerably changed the landscape of linguistics, as shown by the increasing number of publications and conferences devoted solely
to
computational linguistics. The emergenceof this
subdisciplineis not
dueto the fact that
aheretofore
neglectedrealm of linguistic
phenomena wouldfinally
have attainedthe recognition that it
deserves(as
hashappened e.g. with neurolinguistics or
pidgin-and-creole studies).If this were the
case,then
computational linguisticswould simply
occupy one moreor
less well-defined subdomainwithin the overall field of
linguistics. However, computationallinguistics purports to investigate those some
phenomena(roughly:
sentences and texts) that have been investigated sincethe
inceptionof
linguistics.The
questionnow
hasto be
askedwhether this new way of
seeingdiffers from the old
onesufficiently much to
justify
speakingof
a paradigma.ticshift
(cf .Winograd
1983: 13-22).Before proceeding any farther, however,
I
haveto
answer apossible objection. It is
sometimesclaimed ttrat a
giventheoretical
framework,
whetheror not we
chooseto call it
a'paradigm', literally
constitutesits own
data.As
canbe
seenfrom
the preceding paragraph,I do not
sharethis view.
(Thisentails that
in my
opinion Saussure assertedonly
a haH+ruthin claiming
that "c'est lepoint
de vuequi
créeI'objet".) There
is always an atheoretical (or pretheoretical) level at whichit
makesperfect
senseto
speakof differenr theories (or
'paradigms') dealingwith
the samedata.In
practiceno
one has ever doubtedthis,
evenif in one's
philosophical momentsone might
feelof the different
frameworks(cf. Itkonen
1991:325428). For
instance,it
would be perverseto
deny that one and the same setof
sentencesmay be analyzed in dissimilar ways
by representativesof
different schools.Now let us see whether there is any justification for speaking of a computational paradigm. In presenting my
argument,I
shall make useof
avery
simpleartificial
languagel,
namelya
language whose sentencesare of the form
(aå)".(This is, in the
presentcontext, the 'same data' which
thedifferent
typesof
description haveto
cometo grips with.) I
donot think, however, that the simplicity of my
example underminesmy
argument.That is, I
donot think
that makingthe
example increasinglymore complex would at any
point bring aboutaqualítatíve changein
the mutual relations between the types of descriptions thatI
shall discuss.Already in the
'pre-computational' days linguists made useof rewriting
rules. Thus, when we haveto
presenta
grammarfor L within
theframework of
mainstream, non-computational linguistics,it
lookslike
this:I)
11: S-+
abS12:S+ab
A
sentencelike
abababis
generatedin
three steps, namelyby
applying therule r,
twice, and thenby
applying therule r, (cf. figure 1).
s
ab ab
Figure
1.An
evenolder formalism for describng L is provided
by predicate logic (plus the notionof
set-membership).Inthis
caseihe grammai contains one universally quantified
implication
and one singular statement:II) Vx(xe
Sabe
Sl abx
e
S)The
senteneæabafub (or, more precisely, the truth
that abababis a
sentence)is
generatedby two joint
applicationsof
Universal Instantiation and Modus Ponens:
Vx(xeS>abxeS)
abe
S ababe
SVx(xe S = abxe
S)abab
e
Sababab
e
SThe grammars
I
andII
are testedin
the samgway'
namely-by finding
out whether they generateall
andonly
sentencesof
¿.
Ttresetwo
aspects cofrespondto
ttre notionsof
completeness and sound.ness, ãs they are usedin the theory of logic. On
the one hand,we
havea
sentenceof l,
andwe
askwhether it
isgenerated
by
our gra¡nmar.If
the answeris
'yes' every!þe
weãsk this queition, ihe grammar generates
a//
sentencesof L,
andis therefore complete. On the other hand, we have our
graÍrmar, and we ask whether whatit
generatesis
a sentenceof
l. lt the
answeris 'yes' every time we
askthis
question,our
grammar generates only sentencesof L,
andis
therefore sound.(It is of ño
consequence thatL
happensto be
sosimple
as tomake,
in reality,
any questioning superfluous.)The
notions(or viewpoints) of
soundness and completeness conespondto
the notionsof
'prediction' and 'explanation', as they are usedin
the philosophyof
the natural sciences(cf. Itkonen
1978:4-9,254-
2s3).
All
natural-languagegrammars are tested as to their
soundness
and
completeness,with the qualification that
anadditional criterion is
constitutedby the 'adequacy' of
thestructural descriptions (whatever concrete interpretation
isgiven to this difficult notion). A
natural-languagegrammar
is concernedwith
the(intuitive)
correctnessof
sentenceswhile
an axiomatizationof formal logic is
concemedwith the (intuitive) validity of formulae. But
apartfrom this difference, they
are testedexactly in the
samervay. It is crucially important
to understandthat,
apartfrom
such simple cases as propositionalor
predicatelogic, a logical
axiomatizationis falsified if it,
although
provably
sound and complete,fails to be íntuitively
sound and/or complete,i.e. if it
generatesintuitively
non-valid formulae and/orfails to
generateintuitively valid formulae. In this
respect, axiomatizationsof natural
sciencesdiffer from
either grammaticalor logical
axiomatizations.They purport
to generateall
and onlyempirícally true
sentences(of
the relevantdomain), but empirical truth, unlike intuitive
correctnessor intuitive validity, is a property which
cannotbe
assignedto
a sentence just by inspectingit
(cf. Itkonen 1978:n6-287).
Next, we
shall considera
computationalgrammar of /,. I
submit that computers are taken
to
have inaugurateda
new erain
linguistics,mainly
becausethey
seemto
enableus to
havedynamíc
descriptions,where we previously had orùy
static descriptions.Previously we
investigatedlinguistic
structures;but now we
investigatelinguistic
processe,s,more
precisely processesof
speakingand
understanding.(Notice that
since cognitive-computational processes applyto structures-and
are indeed represented asjust
successionsof structures-, it
would bemore
accurateto
speakof
'structures-and-processes', ratherthan of just
'processes'.)As a
consequence,it is particularly
important to determine the extent to which this idea of
am) s(ab(x)):-s(x).
s(ab).
As inputs, the grammar may be given two types of
'questions', exemplified here by
A
and B:1In
responseto A,
the grammar producesthe output
'yes.' (which means that ababab has theproperty of
being a sentence).In
response toB, it
produces thefollowing
oulput:'dynamic
tum'
isjustified.
I shall
choose PRoLoGas the language in which
the computational grammar ofL
is couched. The grammar containsone'rule'
and one 'fact':X:
ab;X:
ab(ab);X:
ab(ab(ab));It is
clear thatA
andB
exemplify sentence-recognition and sentence-generation, respectively.They may be
considered as loose analogues of the corresponding psycholo gical proces ses.A
comparisonof
the grammarsI, II,
andIII
reveals bothsimilaritiesìnd
dissimilarities. On the one hand, the structureof
the grammarlll
is exactly the same asthat of the
grammarII
(and,
by implication,
thatof the
grammarI). On the other, in
the casèof
ttre grammarsI
andII, it
is the grammarian(or
thelogician) hímself who
hasto perform the
tasksof
sentence-geãeration and sentsnce-recognition, whereas
in
the caseof
theltamma. III,
the grammarian needsonly to give the input in
))
s(ab(ab(ab
s(x).
?
?
A)
B)t I disregard the questions involving the'anonymous variable' (-).
form of the
relevant questions;after this, it is the
grammarwhich performs
the tasksof
sentence-generation and sentence- recognition.It
seemsclear to me that, from the viewpoint of
actual descriptivepractice, the
dissimilaritiesare
outweighedby
thesimilarities. Writing the graÍrmar III is an
undertakingqualitatively similar to writing the grammars I and II. Of
course, the grammar
III
containsthe
ideaof a
machine which performs the tasks assignedto it, but from
the viewpointof
thegrammarian this idea remains hidden. The affinity with
mainstream linguistics is enhancedby
thefact that
thepRoloc
notation may be replacedby
therewriting
notation, resultingin
the'definite
clausegrammar' (cf.
Pereira&
Shieber1987:70-
7e).
Finally, we
shall considera grammar which is literally
amachine.I
have chosen theTuring
machinefor this
purpose.This choice may need some justification.
First, Turing
machinesare norrnally
regarded as abstract machines defining mathematical functions;but it is
also possibleto
regard them as machinesin
theliteral
senseof
theword. In fact, it is quite
convenientto illustrate the notion of
causalitywith the aid of a (concrete) Turing machine. On
thisinterpretation,
the symbolwhich
the machine readsat t is
anexternal ca.use, while the state
in
which the machineis
atr
is an internal cause. The combination of these two causes brings about oneinternal
effect, namely the statein
which the machineis
att+l,andtwo
external effects, namely the symbol which, having been printedin
lieuof
the earlier symbol,will
be on the tape att+1,
and the movementeither to the left or to the right (or,
perhaps, the halting) which the machine
will
have performed att +
1
(cf . Itkonen 1983: 22, 287 -288).Second, the language
I is so simple that it could
also be describedby
a finite-state machine.At
present, however,I
amnot interested
in
conceptual parsimony, butrather in
conceptualclarity;
and, as I just noted, the Turing machineis well
suited to illustrate the functioningof
a causal process.Third, the
grammarwhich I am
aboutto
present handlesonly the aspect ofsentence-recognition (cf. table 1)'
ry) {o 9r \z
A
a b B
R
Qt,
R
Qz,
R
1, stop92,
R
Qo, R 0, stop
R
R
0, stop
Table 1.
In the
'machine-table' (seetable 1)
the column outside the rectangle contains the 'external causes',i.e. the
symbols.on
the tup",õhrt
as the row outside the rectangle contains the 'intemalðäor"r', i.e. the
machine-states.The
effectsof
thesepairs of
causes are located inside the rectangle,
in
sucha way that
non- changes arenot explicitly
mentioned.For
instance, the machinestaft; in
eo, reading.A.-As a result, it
replaces4 Uy.A (i'e'
leaves
it
unchangeð), enters Q"(i.e.
remainsin it),
and moves one stepto
therigtri.-
Theonly
new_ symbols that. are printedii" fi"" of B) ãre 1 and 0, which mean 'yesr and 'no',
respectively.
Let us
iee
how the grammarIV
recognizes that abababis
asentence, whereas abbaba, aababa, and
a
arenot
sentences(cf.
table 2).
when
thereis a conect
sentenceon
the tape, the machine movesfrom A to B, while alternating
between Qo aurrd Q,,replaces
B by 1, and
stopg.snr9l the
machine encounters an.iror, i.e.
whenit
readsèittrer b in
qoor
¿in q,, it
entets q,,,"rnuint in it until it
reachesB,
replacesB by 0,
and stops' The sentence ø,which
entails readingB h q,,
constitutesan error
type
of
its own.AabababÉ
1t'ItttìrrrttIt
Qo
Qo9r 9o I'
QoI'
QoA a b b a b t'rtr'.ìrrrrttt "&
9o 9o I'
Qo9¿ Q, Q.
Q¿Aaababaä^
t'trrtìrìrttIt
9o
QoI'
QzQ. 9. 9"
Q.A trs "&
Qo 9o
Q'Table 2.
'When
we
comparethe grammar IV to the other
threegrammars, we finally discover a genuine dissimilarity.
The grammarIV is
dynamic,in the
senseof
describinga
temporal process;it
incorporatesthe notion of
chnngeof state.
Bycontrast, the grammars
I, II,
andIII
describe static, atemporal structures; any processes, whetherthey are perfomed by
the grammarianor by
the computer, remain hidden.To put it in
a nutshell,I claim
that the notionof
a computational paradigmin
linguistics is justified only to the extent that
computer-based descriptions resemble the grammarfV.
Once
I have
statedmy basic claim, I must
immediatelyqualify it
Somewhat.It
is quite clear that PRoLoG programming¡mpl¡c¡tly contains the idea
of
a process. Answeringa
question means eitherproving
the sentence asked (asin
'understanding') orproving
the sentences resulting from replacing the. variaþle($in
ihe
senience askedby
constants (asin 'production');
and thishappens by searching and fínding facts that qualify
asinJtantiations of the bodies of rules (i.e. of the antecedent clauses
of
universalimplications). The programmer knows that
rules are readfrom top
to bottom and that conjunctionsin
the bodiesof
rules are readfrom left to right;
and observingthe
correctorder
may make the difference between aprogram
that worksand one that
doesnot. This knowledge may, however,
be incorporatedinto
the grammatical conventions. Thereforeit still
remainsthe
casethat it is
possibleto practice
PRoloc-based grammatical description without having any very clear notionof
the computational processss involved.
The point
thatl
have made hererather informally
has been made quiteexplicitly,
and at amore
generallevel, by
Petre&
Windei
(1990). They discuss rhe difference between declarative and imperative computer languages, whichroughly
correspondsto the, difference
-betweenour grammars III and IV. A
declarative language specifies what is the problem
to
be solved,without indicaiing how it is
solved. Because"declaration,
by nature, excludesãlgorithm" (p.
176),the
solutionof
the how- question is defenedto
the language implementation. Imperative|ãnguages,
by
contrast,still
reflect the basic machine operations:as ã sei
of
instructions, they show the processof
computation.Between
pure types of imperative and
declarative languages there are intermeãiate types,i.e.
declarative languageswith
an"expression
of
algorithmicintent". Now it
is precisely Petre&
\Miider's
(1990)-claim that the 'imperative vs.
declarative'distinction should be thought of as
^ continuum; and
they proceedto
placevarious
programming -languageson it. For
instance,FoilrRAN is a typical imperative
language;LIsr
issituated exactly at the 'imperative vs. declarative'
divide;PRoLoc
lies
somewhere betweenLrsp and typical
declarative languages.Peter &
'Winder reachthis
conclusion:"The
basic difference between programming styles liesin
thehiding of
thecomputational model" (p. 180). This entails,
interestinglyenough, that it is questionable whether
pRot.oc-baseddescrþtions should be
consideredas part of
computational linguistics at all.Thus, whether or not
computershave brought about
a changeof
perspectivewithin
linguistics,is a
matterof
degree, and thisin a twoþld
sense.First,
one language (e.g.rnor-oc) may
bemore
'conseryative'than
another(e.9. r.rsr).
Second, evenwithin
one and the same language the grammarian may bemore or
less awareof
the (moreor
less) hidden computational process.I submit that the gradunl nature of this
changeof perspective does not agree too well with the way
that paradigmatic shifts are generally conceivedof. More
precisely, some computerlinguists (i.e.
thoseoperating with
languagesclose to the imperative end of the continuum) may
have experienceda genuine paradigmatic shift in their way of
thinking, but others may not.
I shall
concludethis
paperwith a few
remarksof a
more generalnature, relating the
preceding resultsto
questionsof
languageuse and
pragmatics.First, the distinction
betweendeclarative and imperative
languagesis
analogousto
that betweenlogical,
set-theoretic semanticsand algorithmic or procedural
semantics.In Itkonen (1983: 149-L51,311-313) I
argued ttrat, in terms of
psychologicalimport,
algorithmicmodels are more informative than logical ones; and
this conclusionmay now be
generalizedso as to apply to
the distinction between imperative and declarative languages.Second,
algorithmic
semanticsis
a misnomerto
the extent thatthe
computational processesare
meantto be
even rough analogues of cognitive processes, simply because this amounts to committing the psychologistic fallacy (op.cit. p.
313). That thisfallacy is nearþ
ubiquitousin
today'scognitive
science, doesnothing to
lessenits
objectionable character.This
also meansthat any comparison between
Turing
and ÏVittgenstein (see e.g.Leiber
1991:81-88) is
misconceived, unless the processes that the machineperforms
are thoughtof
as (embeddedin) public
actions governed by socially valid norms.Third, Leiber's (1991: Ch.10)
attemptto align
Chomskywith Turing
and Wittgensteinis
misconceivedtout court. Iî
addition to the fact that he is interested
in
mental structure, notin
mental process(cf.
Jackendoff 1987:38-39),
Chomsky has consistently denied the relevanceof
behavioral,public criteria,
thusexplicitly
opposing ttre V/ittgensteinian position(cf.
Itkonen1983 : 227
-233,
243-248).It
is often said that computers may simulate processesof
anykind, whether
physical, psychological,or
social.It
should beclearly understood, however, that computers may be,
andtypically
are, quite unable to simulate those surroundings and/or accompaniments which, to a large extent, constitute a process as whatit
is. Therefore a program alone is seldom enough.References
Itkonen, Esa (1978) Granv¡aticøl Theory a.nd Metascienc¿. Amsterdam:
Benjamins.
Itkonen, Esa (1983) Causality in Linguistic Theory.I¡ndon: Croom Helm.
Itkonen, Esa (1991) Universal History of Linguistics: India, Chinø, Arabía,
E urope. Amsterdam: Benj amins.
Jackendoff, Ray (1987) Consciousness and the Computationnl Mínd.
Cambridge, MA: MIT Press.
Leiber, Justin (1991) An Invitation to Cognitive Science. Oxford: Blackwell.
Pereira, Fernando
&
Shieber, Stuart (1987) Prolog and Natural-LangwgeA naly si s. Stanford: CSLI.
Petre, Márian
&
tWinder,R.
(1990)On
Languages, Models, and Programming Styles. The Computer Journal33: 173-180.Winograd" Terry (1983) Language as a Cognitive Process. Reading, Mlt:
Addison-Wesley.
Esa Itkonen
Deparrnent of Linguistics Henrikinkatu 4a
FIN-20014 University of Turku Finland
E-mail eitkonen@utu.fi