American
Journal
of Computational Linguistics
r i t r o f i 2 5N A 4 T U R A L L A N G U A G E
AS A
S P E C I A L
C A S E
OF
P R O G R A M M I 0 N G
L A N G U A G E S
Geoffrey Sampson
Department of Lingui&tics
university of Lancaster
Lancaster LAI-4YT
England
SUMMARY
I
o f f e ra
tentativeanswer
t o a quesCion poaed by Leo$poetel: 'what t y p e of
automata
would produce and use struct-ures such
88natural
languages rpossess3 ' ?loam
ChowIcy hae pointed o u t that natural languages sharecertain
commonstructural
caaracteriatics, and he argues t h a tthese 1ing~ierkl.c universals have implications for our under- standing
of
hum- menta.1 processes.In
my
--
The Borm o$ ME-(1975),
I
8ug~est that we should develop a model of humanmental machinem by'deaigning an abstract automaton which
accepts progrm-3 haviag the
range
of
structures universallyfound
in
theeemaatic
analysesof sentences of
natural
langu- ages. !Phis article makesconcrete
proposals about such anautomaton.
A n
automaton
ie
defined by specifying a s e t of s t a t e s ,a s e t
of
acceptable programs. an input function mapping p a i r s of program and prior s t a t e into new s t * t e s , and a successor- s t a t erebation
which permits the automaton to move spontane- ouslyfrom one
s t a t e t o another, either deterministically or non-deterninistically.In
an
automata-theoretic model of human rental processes, sentences will play the p a r t of pro-grams, automaton-&ate8 w i l l correspond t o structures o f know- ledge
or
b e l i e f , the input function will s p e o i f y how a person'sbelief-structure
is altered by the sentences he hears or ~ e a d s ,and the successor-state relation wil1,correspond to the rules
o f
inference
by which dne derivesnew
b e l i e f s from the b e l i e f sone
alread$
h a ,A computer is a physical r e a l i z a t i o n of an automaton; but
an
automaton modelling the behaviour of usersof
natural l m g u -and
concentraee
on semantic features
which appeart o
beconstant
for all
natural
langtaages .)!Che
model I
proposeturns
o u t ,as
an unexpected bonus, t oo f f e r
satisfying
solutions
t o
anumber of
controversial pointsof
philosophioal logic.
On
t h eother
hand, it remains to
beseen
whether the model
can
successfully be extended beyond thesubset
of
natural
language it
now
covers;I
conclude bylisting
TABm
OJ'
CONTENTS1.
Introduction
...
6
2.
Definition
of
automaton
...
7
3.
Grammars and inference
rules
f o r natural
Languages
...
9
4.
High-level
language$
v.
machine
codes...
10
5.
Asample
high-levellanguage:
API;...
126.
APLdefined in
terms
o f9APL-apeaking
automaton'
14
7.
1Perfarmance4
v.
'competence'
in
natural
and
programming
languages
*-. 218.
English
to
be
definedin
terms
of English-speaking auto-
maton
...
22
9.
Noan
phrases
a r eelements
o fan
automaton
s t a t e...
2510.
Elements
are
at
various
distances
from
a
focus
...
2919.
Proper
aames
and
common
nouns
...
30
1'2.
The
genitive
construction
.
32
13.
Deiotics
...
33
14.
Clauses
v,
noun
phrases
.
33
15.
Relative
clauses
...
39
'16.
Formalization
of the distance
metric
...
4017.
TheEnglieh-speaking
automaton
define4
...
4218.
Outputaof
the
Englieh-speaking
automaton
...
91
19.
Language
v,observation
asinput
...
5220.
Natural
and
programming languages
compared and contrasted
m * *
57
2-4;
Philosophical wattractions of the
theory
...
5822.
Unsolved
problems
...
$9
I. !Phis
article
proposes a t e n t a t i v eanswer t o
a questionposed by Apostel
(1971:
22) : ''what type of automata would pro-duce and use structures such as natural languages [possessll? I
Chomsky has pointed
out
thatn a t u r a l
languages show commonstructural characteristiss: each
natural
language is derived transformationally from a context-free phz?ase-structure langu- age.* Chomsky (e.g. 1968, and cf. Lenneberg 1967) argues t h a t thisshows
that we have innate psychological machinery for pro-cessing
language.I
have suggested
ampso son
1972a,
1975a:--
ch, 8) that an r r u i t f u x way to construct a theory of such psych-ological machinery
will
be t o view the relation between sent- ence and hearer as analogous t o t h a t between computer programand
computer.
HereI
wishto
o f f e r some concrete proposalsabout the ~sychological machinery involved in the comprehension
of
natnrgl
language, basedon
comparihg the structure of nat-ural
languagewith
that ofactual
computer
programminglangu-
3
ages
in
practical use.
'1
I
insert
q p o s s e s s ' , s i d eI
p r e f e r
to
speak of languasesstructures
rather than being structures.I
discussown
comments
onthis
question elsewhere (Sampson2
I
show elsewhereampso son
1973b)
that this i san
empir-i c a l
hypothesis, despite the findings of Peters & Bitchie and others that angrecursively
enumerable language can begenerA
ated bysome transformational
grammar.3~hhe
theory
t o
bepresented
here
is somewhat
comparable withthat of
Winograd(1972),
althoughconstructed independ-
ently. By comparison with WinogradI
am
less interestedin
thepractical
problemsof
cormaunicating
withan
automaton
in
idiom-a t i o ,
'surface-structurea
English, and mare interestedin
whatchqacteristiccs
o fthe
huinm language-processingautomatondare
2. It is usual to distinguish the terms automaton and
-
com- puter: an automaton is a mathematical abstraction of a certain kind, while a computer i s a p h y s i c a l object designed t o embodythe properties of a particular automaton (cf. Putnam
tl9603
1961:147),
as an ink line on a sheet of graph paper is des- igned t o embody the properties $of a continuous f u n c t i o n ; thuse.g. a computer 3 u t not an automaton, may break down, as a
graph, but not a function, may be smudged. Naturally, though,
the only automata Tor which there exist corresponding colpputers
are automata .which it is both p o s a i b l e ana u s e f u l to realize physically; so t h e class of computers represents a rather narrow subset of t h e class of automata as d e f i n e d below. W e
shall sometimes speak of 'computersv meaning 'automata of the class to which actual computers correspond1; category mistakes
need n o t bother us if we a r e a l e r t to t h e i r dangers.
W e may d e f i n e
an
automaton as a quadruple(
f,
9,
9 -Int,
-
S u c ) , in which9
is a ( f i n i t e or infinite) s e tof s t a t e s ,
&
is a (finite or infinite) language (i.e. set qfstrings of symbols),
-
I n t is a partial function from9
X2
(the Cartesian product of
9
with $) intof
(the input funct-ion), apd Suc is a relation on
- -
f
P,-e. a s u b s e t ofY X
( t h e successor.-pltate relattion).
8
is called t h e machine langu-age of
4 ;
a aember of&
i a a proecram.We t r e a t the flow of time as a -succession of disczlete
instants (corresponding to cycles of a c t u a l computers).
Between any adjacent p a i r of instants, t h e automaton i s i n some
s t a t e
-
S 89,
At any given instant, a program may be input.If
t h e automaton is in -... S and P L &&,
is i n p u t , the automatonmoves to the s t a t e -Int(S, I
-
XI);
if(g,
It)#
dom(Int), wa saythat
-
L
is undefined f o r-
6 (and no change of state occurs),such that
---
S Suc S t , provided t h e r e is such a s t a t e-
S t . (Other-wise, no
change of s t a t e occurs, and-
S is called a stoppings t a t e . )
If
-
Suo is a ( p a r t i a l ) - function (i.e. if f o r each-
St h e r e is at most one s t a t e
-
S t such t h a t- -
S Suc S ) , t h e auto-maton is deterministic
.
Bn
ordinary d i g i t a l computer is a deterministic automatonw h ~ s e s t a t e s are realized as different distributions
oq
e l e c t -~ i c a l charge (representing the d i g i t s 0 an& I) over t h e ' f e p r i t e
cores in a s t o r e together w i t h a s e t of working r e g i s t e r s and an add.ress counter. The number of s t a t e s of such an automaton
1 s
finite
but very large: a simple computerwith
a s t o r bcontaining 4096 words of 16 b i t s t o g e t h e r with a single working register would have on t h e order of
5
x 10 79736 states. heprograms of the machine language
of.
such an automaton w i l leonsist of sequences of machine words not exceeding the size oi the store, and thus t h e machine language w i l l again be
finite. The input of such a program containing, say,
-
n words w & l l cause the automaton to load these words 'in-t;o t h e first a places in it s t o r e , replacing the current contents, and t o-
set t h e address counter t o 7 . 'Phe successor-state function is determined by the number in the addzess-counter t o g e t h e r
with the code translating
machine
words into in$.%mct2ons;whenever the counzer contain8 the number
-
i the au-t;omatonch-es i t s s t a t e by executing the instruction in t h e I
-
ith p l a c ein seore and incrementing t h e :ounter by one, A proper subset
of the automaton's states a r e stopping states: whenever the storage word indicated by the address counter is not the code
of any instruction, t h e machine stops.
state function, beginning with
-
S and ending) (if the succession i s f i n i t e ) at a stopping-state.A
computer is arranged so t h a t ,on entering certain states, it performs certain output actions
( e . g . it prints a symbolic representation of p a r t of its inter- nal state
onto
paper). The art of programmingsuch
a computerconsists of finding
an
input program which moves t h e computer into a state, t h e succession of which causes the computer t o perform ~ c t i o n s constituting a solution to t h e programmer'sproblem, while being f i n i t e and as short as possible.
3
A natural language, such as English, is s p s c i f i e diiyntacfically and semantically by defining a s e t
$
constitut- ing the sentences of the laaguage together with a subsetk
o f,$*
x
%
((where' X * '
denotes the power set of ) , such that,
,
,
.
.
,
L
3
1-
I&iff&
is implied by the premisses4
L
L
4 4,
...)
- + -
L - ( n
2, 0 , -3.L.
E&
whenever 0 1-
i ~ n ) .-
(Jn
t h el i m i t i n g case,-the
n u l l
s z t $k
iff I& is analytic.)In
practice, the infinitely numerous members of&
are generatedby a finite set of context-free phrase-structure rules, together with syntactic transformations which operate
on
the s t r u c t u r e s defined by those rules. T h e infinitely numerous members ofw i l l be defined by a s p e c i f i c a t i o n of a r e l a t i o s between the seneences of
&
and a set of a r r a y s of symbols c a l l e dgsernantic representationsg of those sentences, together with
tr
finite set of
rules of inference, similar t o t h o s e o f e x t a n t formal logics, which permit the construction of a derivation containing the semantic representation of$
as conclusion andthe
semantic
representations of L,
.
5
as premisses-q4, -n
j u s t when
I&,,
,
.*., -aL
I-
&,
.
m e 'geneFative semantic--
istsq have argued that: the relation between sentences and their
semantic
represeatations
is defined by the transformationalrules
revealed by independently-motivated syntactic analysisfe.g. Poetal
L'l9701
1971 :252f.
) ; although this hypothesis i scertainly
not
a l t o g e t h e raorrect'
(see e.g.Partee
1971),
it seems. likely that the semantic representation o#' a sentence is some simple funetion of its.syn$actic deep structure and itss u r f a c e
structure.
Therules
ofiaference
fornatural
langu-
ages w i l l
no
doubtexhibit
the 'structure-dependence' charact-er'iatic of syntactic transformations, as do t h e rules of
inZerence of
formal
logics, cf. Sampson(1975a:
163-7,
f o r t h - coming) (thus, theterm
' X s Y '-
in
the standard rule of modusponens,
i.e.
'{x
-=IY,
O mX
+
.
Y
,
is
astrmcCura1
descriptionnot
of
allformulae
contaiaing
aninstance of
' 3 ' but only of thosein
which' '
isan
immediate c~natituent of the whole formula).For
discussion
o f the philosophicalproblems
involvedin
thisway of
describing natural-language semantic analysis, includingproblems relating
t o the aaalytic/synthetic distinction, cf.Sampson
(1970, 1973a,
1975a:
ch.7).
4.
It
is tempting t o view t h e mind of a speakel' of e.g.English
asan
automaton
in
tihe
definedsense,
with the sent-ences
of English as the programs of its machine language, and the rules of inference of English determining the successor-s t a t e
relatioa.
In
o t h e rwords, some
component
of
t h e mindof an English-speaker would be a d ~ v i c e capable of e n t e r i n g any
the
relation
between sentences and semantic representationsis
a
function. In
practiceit
w i l ln o t
be (ambiguoussentences
@ll have mope thanone
semantic representation), so 'the'one
of a (perhaps infinitely) large nuhlber of discrete s t a t e s ;hearing (or reading) a sentence w o u l d move this device from one
s t a t e t o another
in
accordance with d e f i n i t e rules; and otherwler;! related t o t h e rules of inference
of
English would govern'how
it passes
through different states when not immediately reactingto
speech ( i . , e . when the owner of the mind is think- ing).Although t h e analogy is tempting, extant computers and their machine languages are n o t promising as sources f o r a t h e o r y of the relation. between human minds and n a t u r a l langu- ages. The machine language sketched above is n o t at all
reminiscent of n a t u r a l languages. The l a t t e r typically con-
t a i n infinitely many sentences, only the simplest of which a r e
used
in
practice; the
machine language of 52 c o n t a i n s an enorm- ous but finite number of programs, and the programs which a r euseful in practice (those which compute important functions)
a r e
not
t y p i d a l l y 'simple'in
any obvious sense.Portunately, the machine languages of .thg various extant
computers are n o t t h e only artificial programming languages in use. Partly f o r the very reason that machine languages are s o
different from natural languages, most programs are written
P
not
in
machine languages b u t in so-called 'high-levtl' .pro-gramming languages, sudh as FORTRAN, SNOBOL, APL, PL/? (to name
a few among many). W e may think of a computer
AM
suppl jedwith
a compiler program f o r some high-level langu'figedH
asA
simulating the workings o f a v e r y different,computer, sgy E.
actually exists: high-level languagzs
No
such computer as8 r e n o t t y p i c a l l y me Zachi~le languages of any physical com-
puters, and there a r e Undoubtedly s'oupd engineering reasons for this. B u t the abstract automaton
4
may be d e ~ c r i b e d j u s t as precisely as the automaton4 w h i a underlies t h e r e a lcomputer. One who programs an
$
Isgstemr (i.e. c o n j u n c t i o nof computer with deg-compiler) c o k - o n l ~ thinks of the machine
he is dealing w i t h z s having t h e eroperties of
,
and may be q u i t e unaware of the properties .of the machine-AM w i t h-.
which he is in fact interacting.
High-level
lapguages, aad t h e abstract automata whose'machine languagest t h e y are, differ from one another in more
in-teresting ways
than
do real computers and their machinelanguages; and furthermore ( n o t surprisingly, since high-level languages a r e designed to be easily usable by human programm-
ers) they are much more comparable with human languages than
are
r e a l
machine languages. (Typically, a high-level pro-gramming language is a context-free phrase-structure language, f o r instance.)
I
shall suggest t h a t the relationship betweer high-level languages ahd their corresponding automata givesus much b e t t e r clues about human mental machinery than does that between real computers and machine languages.
50
Let
me fiitst give an example of a high-level language:I
shallchoose
t h e language APL (see e.g.Iverson
1962,Pakin 1968).
AP$
is interestbing For our purposes because itis
particularly high-level: 5.e. it is r e l a t e d more distantlyto
machine languages of real computers, and more c l o l e l y t o human langudges, than many other high-level languages.It
isa real-time rather thm batch-processing language, which means that it is designed to be used
in
such a way t h a t the r e s u l tof i n p u t t i n g a program will normally be crucially dependent
o n t h e prior @-bate
of
the system (in a batch-processing langu-age, programs a r e designed t o be unaffected by those remains
of t h e p r i o r state which
survive
their input): this isa b l y the e f f e c t
on
a person of hearing a sentence deperidsin
,--
general
on
his
p r i o r system of knowledge and b e l i e f.'
! B e complete language
APL includes many features which
are
i r r e l e v a n t t o our analogy. F o r instance, there is a largeamount
of apparatusf o r
making and breaking contact with the system, and the like; we shall ignore this, ~ u s t as we shallignore
t h e fact t h a tin
human speech the effect of an utter- ance on a person depends among o t h e r things on whether the6
person is awake. Also,
APL
provides what amounts t o a methoduf using the language t o alter itself by adding new vocabulary; to discuss this would again complicate t h e issues we are i n t e r -
e s t e d
inm7
W e shall assume t h a t programmer and system arepermanently
contact
one
another,and
shallrestrict
our attention to a subset of APL to be defined below: raeherthan resorting t o a subscript to distinguish the restricted
language
from
APL in i t s f u l l complexity, we shall understand'gPLr to mean t h e subset of APL under consideration.
'The practicing computer user may find my definition the real-time/batch-processing distinction idiosyncratic; difference I describe is t h e only one relevant f o r o u r p r
of the esent purposes, but it is far rrom the most salient difference in
practice.
6
In
AP'L terms,we
ignore a l l system ins~ructions, i.e.words
beginning withA,
Note t h a t we usew
m
underlinin
(corresponding
to
bold type i n p r i n t )t o
quote b s s e q u -encee of
symbols from an object-language, whether this isan
artificial
language such as ATL or a natural language such asEnglish.
'hn
BPL
terms, we i g n o r e the dqyinition I-
mode and the use6. We begin by defining t h e s e t
9
APL of states of &APL.F i r s t , we recursively define a set of APL-prop&ties:
any p o s i t i v e
or
negative r e a l number is a numeric-
APL-property of dimension
#;
any character
on
t h e APL keyboard (i.e. any of a - f i p i t es e t of characters whose i d e n t i t y does not concern us) is a literal &property of dimension @;
f o r any integer I n and integer-string
-
D, any-
n-length stringover t h e s e t of numerio (literal) APL-properties of d i m e d i o n
-
D
is A a numeric ( l i t e r a l ) APL-property ofdimension
- -
D
%
.
'
P o r any finitg string .
D over the
I integers, any numeric or lit- eral APL-property of dimension-
D
is an APL-property, andnothing e l s e is guch. Clearly, t h e r e are infinitely many APL- properties.. The length of the dimension of an APL-property
is the
-
rank of that APL-property. !Phus, a number is a rank4numeric APL-property; a four-letter word, e.g.
-
LOVE,
is a rank- 1 literal -property; a 2 by3
matrlx of numbers,e m g o
3.9
2 l2 is a rank-!? numeric DL-property, etc.0 4 . 6 937'
Bn APGidentifier is any rank-? literal string beginning
'The symbol stands f o r concatenation (a dimension is
always an integer-string). Concatenation is a function from
so
we should strictly
write 'DAN9 (where N i ss e t 8 &d any integeE
n
5 ~ : - i e use the terms-5-tu le of h e -mentz of S' and '1enntE-n' s t r i n p : over S
'
interc&
angea 1~ for anyfunctrdn
from the sewam, 2,.:.
,
n)
of th; n a t k a lnumbers
i n t o
S;note
t h a tthe
n u l l
s e t0
i z t h e r e f o r e thewith
an
alphabeticcharacter:
t h e r e & r e therefore infinitelymany
APL-identifiers.
W e define Ident as the s e t includingall
-identifiers
t o g e t h e r with an e n t i t y , assumed t o be dis-tinct
f r o m all the A P L i d e n t i f i e r s , delloted by. t h e symbol-
0 ,
An DL-object is a p a i r i n g of any member o f s I d e n t w i t h an A P E
property;
we call
thefirst
memberof
an
APL-object t h e ident-i f i e r
of
the object and the second memher t h e p r o p e r t y of t h e--
-
object.
An
APEstateis
a finite s e t of APL-objects in which no distinct o b j e c t s b e a r t h e same identifier. (We may t h u s thinkof
an
k P E s t P t ' e as a function from a finite subset o f I d e n ti n t o
the s e t of A P E p r o p e r t i e s . ) We write IqAPL1
for the s e tof
all - s t a t e s : c l e a r l y , *APL is infinite.we
now
define txe lanwagezAPL
ofAAPL'
de,m
i s gen- era$ed by t h e context-free grammar on p. 16. The i n i t i a lsymbol
of that grammar is
-
a s s t ( f o r 'assignmentt). Sincec a p i t a l l e t t e r s
occur
among the terminal symbols of$
we useminiscules
as non-terminals; terminal symbols of2:;
asst
-+
+
-
-
dscrdscr
+
-
numname litname
deic
-
mf dscr
- -
dscr df dscr- - -
dscr tf dscr
ascr
-
-id [any APEidentifier]
-
numname -t [any number or string of numbers, denoting the
corresponding rank-0 or rank-1 numeric APL-property]
9
litname + Cany characteror
string of characters betweeninverted commas, denoting the corresponding rank-0 or
rank-1
literalmf Cany of a l a r g e finite s e t of symbols b r symb-01-strings
-
denoVXng p a r t i a l monadic functions on the set of A P E p r o p e r t i e s 1 11
df
-+
[any of a large finite set of symbol(- string)^ denoting-
p a r t i a l dyadic functiohs on the s e t of APL-properties] tf [aqy of a finite s e e of symbol(- string)^ d e n o t i n g
-
partial t r i a d i c functions
on
the s e t of APL-properties] 12 deic+
[any of a small f i n i t e s e t of symbol-strings denoting-
t o t a l monadic functions from
the
s e t of p o s s i b l e program-ing-acts
i n t o
t h e s e t of APL-properties]13
91n
practiceone
cannot write a length-0 string, and oneFhe sentehces
of
dm-,
a r e
the strings defined bythe
abovegrammar,
disambiguated by t h e use of round brackets (withassoc@tion
t o the r i g h t where l o t indicated by bracketing).The
sequence of
symbolsm+
may optionally be deleted wheni n i t -
MlmC
ial
in
a sentence.
l4 Clearly there&re
infinitely many sent- encesin
&APL.
A.sentence
o fhL
isan
APL-program.We
now
go 0x1 t o specMy t h efunction
-
IntApL
f r o maeapL
i n t o
which specifies
t h e *change ofAPE
s t a t e brought about by a g i ~ e nAPL-program.
To
determine the new s t a t e arrivedat
froman arbitrary
I
ignore
these practical complications f o r the sake of simplic- ity."1
rgnore
complications
relatingto
strings containingthe inverted
comma
character,
'l'l
Some
of
these function^,and their
~ a m e s , arecommon
toall
'dialects*
of
APL: e.g.5,
which denotes
thefunction
taking
integers
i n t o
their factorials,
strings
of integers i n t othe
oorresponding strings
of f a ~ t o r i a l a , etc., and which is1undefined
0.g.for
literalAPL-properties.
!Phe f a c i l i t y of'user-definition'
(cf.
note7)
permits a programmer to alterAPL+by
adding newfunctions.
' 1 2 A P ~
cantaznsno
triadic functions other than user- definedones.
' ' ~ . ~ r
denotes
t h e
f u n c t i o n
taking anyprogramming
a c t
i n t o
aetring
of integers representing the time of day at whichit
occurs.
14
There are
a numberof
syntacticcomplications,
a k i n
toeyntactic transformations
in
natural
languages,concerning
aGadic functf
on
c a l l e dindex,
whichis
denoted - by square brack-e t s ;
we
ignore these c o a a t i o n s , and shallnot
considercurrent s t a t e on input of an arbitrary program, we consider
the phrase-marker of which that program is the terminal string.
Beginning at
the leaves and working towards the r o o t , and eval-uatinq the rightmoat node whenever there is a choice, we assoc-
iate each
-
dacr node with an APL-property as i t s denotation and each-
aest node with a change to be made to the current APE-s t a t e : the
new
APL-stateis
theone
thatresults from
the olds t a t e by making
a l l
the changes associated with the variousa s s t
nodes in
the order mentioned, terminating with the change-
associated with the r o o t
-
asst node (which may of course be t h eonly one).
If
at any p o i n t a-
dacr node c a ~ o t b e assigned a denotation (e.g. because it is realized asan
A P E i d e n t i f i e rwhich is
not
the identifier of any ob$ectin
the current state), the etate-changes already made (if any) are the t o t a l changes achieved by that program.The rules for evaluating nodes a r e as follows:
A
-
dscr node realized as an identifier denotes t h e A P L property, if any, paired with thaa identsfkr in thecurrent
state;
a
-
dser node rewritten as numname or litname denotes t h eAPGproperty denoted by its 'expopent' (i.e. the terminal mat-
erial it dominates);
a
-
dear node r e w r i t t e n as-
deic denotes t h e APL-property given by applying the function denoted. by i t s exponent t o thecurrent programminpc-aot;
when a
-
dscr node +d dominates an mf node-
n
d f o l l o w e d bya
-
decr node d+, if d denotes some monadic function f and d2-1
-
-
denotes
an
U E p r o p e r t y 2 then%
denotes the APL-propertyf(~), provided
g
e
dom(f); the extension to dscr nodes rewrit--
-
-
ten
---
dscr df dscr and dscr tf dscr-
dscr is obvious.by 6 , followed by a dscr node denoting an APL-property
E,
adds*
-
a
new
&PLobject (i,-
E)
t o
t h e current state, destroying anyobject with the identifjer
-
i
which may already exist in t h ecurr-
ent
stat&-;if
Ii
is-
a,
a
representation of2
i s printed out;15
a
-
dscr uode imediately,dominating an-
a e s t node which hascreated an
B P E o b j e o t with the p r o p e r t yE
denotes2.
As
a( t r i v i a l )
exampleof
t h e operation o f these rules, consider the programinput t o
d f L
i n s t a t e {(A, (k 1 1 I ) , (B, k.r 10)). This programhas
t h econstituent structure
which appears in Pig. 'I on thenext
gage(in
which-
dscr
and
-
asst nodes
are
numberedin the
order they are
to
be evaluated).Suppose t h e program is i n p u t
i n
the morning, say a t11.30
a.m.
Then dscr
1-will
denote
t h estring 11
30 0. Thef u n c t i o n
>
takes (12 0 0, I 1 30 0,) i n t o 1 0 0, which becomes the denot-w
a t i o n
of dscrin
fact dscr will denote 1 0 0 whenever the-+3
1311CCIL3
program i s
i n p u t
i n
t h emorning
and 0 0 0whenever
it is i n p u tin
theafternoon
(when the hour integer will be 1 4 or more). The monadic function+/
-
adds t h e numbers in a string, so ifdscr
denotes 'I 0 0 then dscr,, denotes 1. Dscr denotes 10-3
-5
( i d e n t i f i e d by
3,
sodscr,
also
denotes 10. Accordingly,'21n
t h e fullversion of APL. a - c a n
.
-
oocur as a rewrite of dscr,in
which case dscris
assignedan
APL-property inputby
t h e p r o g r a m e r
at
t h n m e dscris evaluated by
t h e system,We
ignore this,since
it
i n t e r m s
with
the analogy with nat-ural
language.IL
the fullversion it is
also p o s s i b l eto
output
symbol-str'ingswhich do
not
represent individual APEdscr
-2
-
df-
dscrldeic
asst
adds an object (,
10) t o the current s t a t e and prints-
7
out
10.
The monadic function
gives t h e dimendionof
any &PEMJ MI
property, and
ascr,
denotes 1 -1 1, so d ~ denotes ~ r3 ,
~andhence
dsordenotes
13.Pinally,
a s s t addasan o b j e c t(Q, 13)
-10 1- 1
-
t o
the
current
s t a t e .In
other
words,if
the program iainput
in
t h e morning andthe prior s t a t e is as quoted, the final s t a t e will be
{(A, I ,II),
(2,
lo),
(,
lo),
(Q, 13)), whereas if it were(u tw
input
in the
afternoon t oAAPL
in
the same p r i o r s t a t e ther e s u l t a g s t a t e
would
beC(A,
rn 1 1 I ) ,(2,
lo),
( lCrr,
0),
(Q,
3 ) ) .
m
To define
f u l l y it remains only to specify the rel- ation Suc,,, On 4LPJi whichcontrols
the changes-of-state& r undergoes- spontaneously.
SucdpL is
the empty relation:every - s t a t e is a stopping state. A programmer working in
BPL
hasno
wishfor
tihe systemto
take actions beyond thoses p e c i f i e d by his programs: by d e f i n i n g monadic, dyadic, ,or
triadic functions
of
any complexity he wishes, he can g e t t h eanswers
t o hiequestions
simply by carryingout
the s t a t e -changes s p e c i f i e d in
his
program. (1n t h e maohine language of a.genuine
computer,on
t h e o t h e r hand, the state-changes broughtabout
by grograme are ofno
intrinsicr
interest,
and the i n p u to f a program
ie of
valueonly in
tha* it brings the computert o a s t a t e
from
w h i c h i t proceeds spontaneously toperform
actions
useful
t oits programmer.
)7.
It
may seem.contradictory to say that a real d i g i t a lcomputer,
whichwill
have only f i n i t e l y many s t a t e s andposs-
i b l e programs, canbe
made t osimulate
an
automaton
suchas
which
has i n f i n i t e l ym a n y
s t a t e s and programs. And, ofan
-state
maycontain
any
number of
o b j e c t s , for. anyAPL
computer/compiler
system t h e r e w i l l be af i n i t e
l i m i ton
thenumber of objects
in
a s t a t e ; although any real number m a y bean
BPL-property,in
a practical APL system real numbers are approximated t o a fini-te tolerance. The m a t i o n is q u i t e ana-logous to the case of natural language, where the individual's
tperfomance
'
i e an imperfect r e a l i z a t i o n of an ideal* tcompet- ence',in
one sense of t h a t distinction; j u s t as in linguist-i c s , so
in
the caseof
high-level programming languages it i s normalto
give a description of the ideal system separatelyfrom
a statement of the limitationson
t h e realizat5,on of t h a tsystem
in practice,
which
w i l l d i f f e rf r o m
one
personto
anotherin
thenatural
language case,from
one
computer/compiler pairto another in
the programming language case.Other high-level programming languages d i f f e r from
APL
not onlyin terms
oftheir sentences
butin
terms
of t h enature of
the states on which t h e i ~ sentences act. Thus in s t a t e s of e.g.SNOBOL, all objects a r e character strings; in
PL/1,
o b j e c t sinclude
not
only arrays of theAPL
kind but a l s o trees, trees of arrays, arrays oftrees,
e t c . Ijpace doea n o t permit asurvey of t h e differences between high4Level languages w i t h respect t o t h e nature of t h e i r states.
8. A t this point
we
are readyto
begin t o answer Apostel'squestion,
about
whatsort
of automata n a t u r a l languages a r eences are; but we have
seen
t h a t there is good reason to think the two may hs similar, and we can make more or lesa d e t a i l e d conjectures about t h e i rform.
In
my exgositionI
shall make various assumptions about aemantic representations, some of whiah have already been made f o r independent reasons by o t h e rscholars.
Insofar
as my theory dependson
theseassumptions,
a refutation of t h e l a t t e r refutes the theory--
this is oneof
the respectsin
which my theory is falsifiable, i . e . scient-i f i c ,
I
shall present my theoryin
a *relajxLvelyinformal,
intuit-
i v e Way t o begin with, and formalize it more carefully later.9
What we are looking f o r is a specifica-tAon of a s e t
Erin -
of s t a t e s , which we can
interpret
as s t a t e s ofsome
subpartof the mind of an English-speaker, such that semantic repre-
sent\ations
ofEnglish
seqtences a r er a t h e r
natural devicesfor
moving
this p a r t of the mind!. fromone
of i t s s t a t e s toanother.
It
will beconvenient
t o have some name f o r t h a t part of ahuman's
t o t a l
psychological make-up which is described byspeoifging ,
In
earlier, unpublished workI
have calledt h i a t h e
topicon
(coinedon
the analogy of 'lexicong), sinceI
envisage it as coneaining a s e t o f entities correspondingt o the
objects o f whichita
owner is aware, andto
which ha cantherefore take a definite description to refer.
Ln,
then, ist o
be a s e t of p o s s i b l e topicon-staeea. me s e t 8 of topicon- s t a t e savailable
to
speakers ofnatural
languagee other thanEnglish w i l l differ from ( f
17
below), but not inrespect of t h e properties
on
chich thia paper will concentrate. Note that a topicon-state is c e r t a i n l ynot
t o be equatedwith
a
% t a t e of mind'or
tpsychological stateq: atopicon
ise.g. the human may be happy
or
sad, asleepor
awake--
without implying any differencein
topicon-state.Just as
an
APEstatecontains
a s e tof
A P L o b j e c t s withproperties
drawnfrom
afixed clase,
so atopicon-state
willcontain
aset
of o b ~ e c t sI
shall
c a l l referents.
'6
supposesome
person-
P knows
ofthe existence of
a red c a r-
C;
then P 1 s 111)topicon
will
include
ar e f e r e n t
-
ccorresponding t o
-
C.Thq
referent
a cwill
be-
P 1 s 'Idea1of
-
C, in
Gehchtsterms
(1957).
The possible
properties
f o rreferents
will
be determined by t h evocabulary of
-
P 1 slanguage,
in
this
case English: each lexicalitem
of
Englishwill correspond to a
referent-property.I
shall
use
Geachlsoperator
5(
)(1957:
52)to
form names ofreferent-properties
from
lexical
items:if
-
P
knows
t h a t LC
is
a
red
car
then
-
c w i l lhave
the properties §(red) MhJand
§(ear).
MMI(An
element
of a mental s t a t ecannot
be r e d , buti t c a n
beP f s
-
topicon
will
include
not
onlyreferents
representing
physical
obdects
but
referents
f o rany
entities
of ~ h i c h-
P isaware
an8
whichhe
can
take definite
descriptions( r e f e r e n t i a l
NPs)
to
denote:
therewill
ber e f e r e n t s
for characters in
f i c t i o n ,
f o rabstractions like
t h e
centre
ofthis circle
e t c .( W l h - - A - . ' . A ~ '
eto.
But,
at anygiven time,
-
P 1 s t o p i c o n willcontain
only af i n i e e
number of referents.Given
enough
time,
of
course,
*here
is
no limit to
thenumber
of o b j e c t swhose
existence
P
coulddeduce
or
imagine;
andI
shall suggest that f o rP
t o-
-
'%ere
and
below,
rather thancoining neologisms
I
use
deduce or imagine t h e existence of some entity L
B is
f o r-
P'stopicon t o acquire a new referent representing (
B.
I k t deduct-ion and imagination take time: i n a f i n i t e amount of time u P a s
t o p i c o n will have acquired only finitely many referents.
90
Consider sentences (2a) and (2b) addressed to-
P (and let us simplify things initially by supposing that-
P
does not pre-viously know of any red cars
--
we s h a l l consider t h e moregeneral case in 510):
(2a) b s a-- a red car - y
I
aold the red car today.---
The
HP
a red i n (2a) w i l l create a r e f e r e n t with the pro-r v -
gerties §(red)
-
and $(oar) cIM*r in-
P a s topicon. On t h e o t h e r hand,when
he, hears (2b) theNP
*he---
red car will p i c k o u t t h e refer-ent
which a---
red car has already created (in order to a c ton
itin
ways which will be discussed later).In
o t h e r words, thedistinction
between the ,Arvrr.MccH- red car and a red c a r is quite parallelN - -
t o the distinction between
-
dscr and-
asst c o n s t i t u e n t s , reapect-ively
,
t h e s e l e c t s from the currents t a t e , the l a t t e r adds an object t o the current s t a t e . Let us
c a l l natural-language expressions which act i n t h e former way
'identifying expressionst
(IEs),
and expressions which a c t i n t h e latter way aestabliahing expressionsa (323s). Clearly theIE/EE distinction
is
related t o t h e traditional d i s t i n c t i o nbetween
:definiteq and 'indefinitea W e .However,
I
donot
claim t h a t - / a l l d e f i n i t e and indefinite MP8 count as IEs o r EXs
respectively. Consider, for instance, the
--
de d i c t o/
--
de re(or
opaquereferents
/
transparent reference) ambiguity exhib-I
am -1 foran
( 3 )
4,- -
In
the--
de dicto sense of-
ah-,
( 3 )
does not imply t h a t there are any elephante, although in the- -
de re senseit
implies that there ia at l e a s t one. Only in the--
de re sense is w - an ele-hant
in
( 3 )
anEE in
my t a m s , though p t a c t i c a l l y ane
L
-
ant
is
clearly an
'indefinite
NPt
in
both cases. On the otherw---
hand,
in
sentences containing quantifiers,
definiselBPB
mayn o t
always be IEs: thus,in
(4) the definiteNP
the-
does
not denote
aparticular
object (andtherefore,
perhaps,does
not
pickout
a particularone
of the hearer's referents).j u s t as the
indefinite
NP
cH. a doesn o t
seemto
establishthe
existence
of- a single book:(4) Whenever I
b s a bookI
remove the d-- A / N 4 - -
-I
shall develop mytheory
with aview
to handling t h e sub-set of
Englieh which excludes quantification and intensionaloontexts,
andi n
whioh
'definite' and 'indefinite1NPs
do coin- cide withIEa
andEEs
respectively-.
LaterI
s h a l l considersome of *he aspects of EnglLah which my theory does