American Journal of Computational Linguistics ritrofi 2 5 
NA4TURAL LANGUAGE 
AS A 
SPECIAL CASE 
OF 
PROGRAMMI0NG LANGUAGES 
Geoffrey Sampson 
Department of Lingui&tics 
university of Lancaster 
Lancaster LAI-4YT 
England 
Copy~ipht 1975 by the Association for Computational LinguisGics 
SUMMARY 
I offer a tentative answer to a quesCion poaed by Leo 
$poetel: 'what type of automata would produce and use struct- 
ures such 88 natural languages rpossess3 '? 
loam ChowIcy hae pointed out that natural languages share 
certain common structural caaracteriatics, and he argues that 
these 1ing~ierkl.c universals have implications for our under- 
standing of hum- menta.1 processes. In my The Borm o$ ME- 
-- 
(1975), I 8ug~est that we should develop a model of human 
mental machinem by'deaigning an abstract automaton which 
accepts progrm-3 haviag the range of structures universally 
found in the eemaatic analyses of sentences of natural langu- 
ages. !Phis article makes concrete proposals about such an 
automaton. 
An automaton ie defined by specifying a set of states, 
a set of acceptable programs. an input function mapping pairs 
of program and prior state into new st*tes, and a successor- 
state rebation which permits the automaton to move spontane- 
ously from one state to another, either deterministically or 
non-deterninistically. In an automata-theoretic model of 
human  rental processes, sentences will play the part of pro- 
grams, automaton-&ate8 will correspond to structures of know- 
ledge or belief, the input function will speoify how a person's 
belief-structure is altered by the sentences he hears or ~eads, 
and the successor-state relation wil1,correspond to the rules 
of inference by which dne derives new beliefs from the beliefs 
one alread$ ha, 
A computer is a physical realization of an automaton; but 
an automaton modelling the behaviour of users of natural lmgu- 
age will certainlx be very different from the automata which 
and concentraee on semantic features which appear to be constant 
for all natural langtaages .) 
!Che model I propose turns out, as an unexpected bonus, to 
offer satisfying solutions to a number of controversial points 
of philosophioal logic. On the other hand, it remains to be 
seen whether the model can successfully be extended beyond the 
subset of natural language it now covers; I conclude by listing 
some unsolved problems. 
TABm OJ' CONTENTS 
1. Introduction ... 6 
2. Definition of automaton ... 7 
3. 
Grammars and inference rules for natural Languages ... 9 
4. High-level language$ v. machine codes ... 10 
5. A sample high-level language: API; ... 12 
6. APL defined in terms of 9APL-apeaking automaton' 14 
7. 1Perfarmance4 v. 'competence' in natural and programming 
languages *-. 21 
8. English to be defined in terms of English-speaking auto- 
maton ... 22 
9. Noan phrases are elements of an automaton state ... 25 
10. Elements are at various distances from a focus ... 29 
19. 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 ... 40 
17. The Englieh-speaking automaton define4 ... 42 
18. 
Outputa of the Englieh-speaking automaton ... 91 
19. Language v, observation as input ... 52 
20. 
Natural and programming languages compared and contrasted 
m** 57 
2-4; Philosophical w attractions of the theory ... 58 
22. Unsolved problems ... $9 
23.. Conclusion . . . 67 
Reference8 .@. 68 
I. 
!Phis article proposes a tentative answer to a question 
posed by Apostel (1971: 22) : ''what type of automata would pro- 
duce and use structures such as natural languages [possessll? 
I 
Chomsky has pointed out that natural languages show common 
structural 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 that 
this shows that we have innate psychological machinery for pro- 
cessing language. I have suggested  ampso son 1972a, 1975a:-- 
ch, 8) that an rruitfux way to construct a theory of such psych- 
ological machinery will be to view the relation between sent- 
ence and hearer as analogous to that between computer program 
and computer. Here I wish to offer some concrete proposals 
about the ~sychological machinery involved in the comprehension 
of natnrgl language, based on comparihg the structure of nat- 
ural language with that of actual computer programming langu- 
3 
ages in practical use. 
'1 
I insert qpossess', side I prefer to speak of languases 
structures rather than being structures. I discuss 
own comments on this question elsewhere (Sampson 
2 
I show elsewhere  ampso son 1973b) that this is an empir- 
ical hypothesis, despite the findings of Peters & Bitchie and 
others that ang recursively enumerable language can be generA 
ated by some transformational grammar. 
3~hhe theory to be presented here is somewhat comparable 
with that of Winograd (1972), although constructed independ- 
ently. By comparison with Winograd I am less interested in the 
practical problems of cormaunicating with an automaton in idiom- 
atio, 'surface-structurea English, and mare interested in what 
chqacteristiccs of the huinm language-processing automatondare 
suggested by those features of English which appear to be 
universal, 
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 is a physical object designed to embody 
the properties of a particular automaton (cf. Putnam tl9603 
1961: 147), as an ink line on a sheet of graph paper is des- 
igned to embody the properties $of a continuous function; thus 
e.g. a computer 3ut 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 posaible ana useful to realize 
physically; so the class of computers represents a rather 
narrow subset of the class of automata as defined below. We 
shall sometimes speak of 'computersv meaning 'automata of the 
class to which actual computers correspond1; category mistakes 
need not bother us if we are alert to their dangers. 
We may define an automaton as a quadruple 
( f, 9, 9- Int, - Suc), in which 9 is a (finite or infinite) set 
of states, & is a (finite or infinite) language (i.e. set qf 
strings of symbols), - Int is a partial function from 9 X 2 
(the Cartesian product of 9 with $) into f (the input funct- 
ion), apd Suc is a relation on 
- - f P,-e. asubset of YX 
(the successor.-pltate relattion). 8 is called the machine langu- 
age of 4; a aember of & ia a proecram. 
We treat the flow of time as a -succession of disczlete 
instants (corresponding to cycles of actual computers). 
Between any adjacent pair of instants, the automaton is in some 
state - S 8 9, At any given instant, a program may be input. 
If the automaton is in -... S and P L & &, is input, the automaton 
moves to the state -I Int(S, - XI); if (g, It) # dom(Int), wa say 
that - L is undefined for - 6 (and no change of state occurs), 
If no program is input, the automaton moves to some state - 8' 
such that --- S Suc St, provided there is such a state - St. 
(Other- 
wise, no change of state occurs, and - S is called a stopping 
state.) If - Suo is a (partial) - 
function (i.e. if for each - S 
there is at most one state - St such that -- S Suc S), the auto- 
maton is deterministic . 
Bn ordinary digital computer is a deterministic automaton 
wh~se states are realized as different distributions oq elect- 
~ical charge (representing the digits 0 an& I) 
over the 'feprite 
cores in a store together with a set of working registers and 
an add.ress counter. The number of states of such an automaton 
1s finite but very large: a simple computer with a storb 
containing 4096 words of 16 bits together with a single working 
register would have on the order of 5 x 10 79736 states. 
 he 
programs of the machine language of. such an automaton will 
eonsist of sequences of machine words not exceeding the size 
oi the store, and thus the machine language will again be 
finite. The input of such a program containing, say, - n words 
w&ll cause the automaton to load these words 'in-t;o the first 
a places in it store, replacing the current contents, and to 
- 
set the address counter to 7. 'Phe successor-state function 
is determined by the number in the addzess-counter together 
with the code translating machine words into in$.%mct2ons; 
whenever the counzer contain8 the number - i the au-t;omaton 
ch-es its state by executing the instruction in the I - ith place 
in seore and incrementing the :ounter by one, A proper subset 
of the automaton's states are stopping states: whenever the 
storage word indicated by the address counter is not the code 
of any instruction, the machine stops. 
For any state - S of a deterministic automaton, we may use 
the term succession of S for the seauence of states the auto- 
-- 
maton will pass through under th~ control .of its successor- 
state function, beginning with - S and ending) (if the succession 
is finite) at a stopping-state. A computer is arranged so that, 
on entering certain states, it performs certain output actions 
(e.g. it prints a symbolic representation of part of its inter- 
nal state onto paper). The art of programming such a computer 
consists of finding an input program which moves the computer 
into a state, the succession of which causes the computer to 
perform ~ctions constituting a solution to the programmer's 
problem, while being finite and as short as possible. 
3 A natural language, such as English, is spscified 
iiyntacfically and semantically by defining a set $ constitut- 
ing the sentences of the laaguage together with a subset k of 
,$* x % ((where 'X*' denotes the power set of ), such that 
, , , . . , L 3 1- I& iff & is implied by the premisses 
4 
L L 4 4, ...) -+- L-(n 2, 0, -3. L. E & whenever 0 1 - i ~n). - 
(Jn the 
limiting case,-the null szt $ k iff I& is analytic.) In 
practice, the infinitely numerous members of & are generated 
by a finite set of context-free phrase-structure rules, together 
with syntactic transformations which operate on the structures 
defined by those rules. The infinitely numerous members of 
will be defined by a specification of a relatios between 
the seneences of & and a set of arrays of symbols called 
gsernantic representationsg of those sentences, together with 
tr finite set of rules of inference, similar to those of extant 
formal logics, which permit the construction of a derivation 
containing the semantic representation of $ as conclusion and 
the semantic representations of L , . 5 as premisses 
-q4, -n 
just when I&,, , .*., -a L 
I- &, . 
me 'geneFative semantic- 
- 
4t!Ibe semantic representation(*), on the assumption 'that 
istsq have argued that: the relation between sentences and their 
semantic represeatations is defined by the transformational 
rules revealed by independently-motivated syntactic analysis 
fe.g. Poetal L'l9701 1971 : 252f. ) ; although this hypothesis is 
certainly not altogether aorrect' (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 its 
surface structure. The rules of iaference for natural langu- 
ages will no doubt exhibit the 'structure-dependence' charact- 
er'iatic of syntactic transformations, as do the rules of 
inZerence of formal logics, cf. Sampson (1975a: 163-7, forth- 
coming) (thus, the term 'XsY' - in the standard rule of modus 
ponens, i.e. '{x -Om =IY, X + . Y 
, is a strmcCura1 description not 
of all formulae contaiaing an instance of '3' but only of those 
in which '' is an immediate c~natituent of the whole formula). 
For discussion of the philosophical problems involved in this 
way of describing natural-language semantic analysis, including 
problems relating to the aaalytic/synthetic distinction, cf. 
Sampson (1970, 1973a, 1975a: ch. 7). 
4. It is tempting to view the mind of a speakel' of e.g. 
English as an automaton in tihe defined sense, with the sent- 
ences of English as the programs of its machine language, and 
the rules of inference of English determining the successor- 
state relatioa. In other words, some component of the mind 
of an English-speaker would be a d~vice capable of entering any 
the relation between sentences and semantic representations is 
a function. In practice it will not be (ambiguous sentences 
@ll have mope than one semantic representation), so 'the' 
should read 'one of the ... (respectively)'. 
one of a (perhaps infinitely) large nuhlber of discrete states; 
hearing (or reading) a sentence would move this device from one 
state to another in accordance with definite rules; and other 
wler;! related to the rules of inference of English would govern' 
how it passes through different states when not immediately 
reacting to speech (i.,e. when the owner of the mind is think- 
ing). 
Although the analogy is tempting, extant computers and 
their machine languages are not promising as sources for a 
theory of the relation. between human minds and natural langu- 
ages. The machine language sketched above is not at all 
reminiscent of natural languages. The latter typically con- 
tain infinitely many sentences, only the simplest of which are 
used in practice; the machine language of 52 contains an enorm- 
ous but finite number of programs, and the programs which are 
useful in practice (those which compute important functions) 
are not typidally 'simple' in any obvious sense. 
Portunately, the machine languages of .thg various extant 
computers are not the only artificial programming languages in 
use. Partly for the very reason that machine languages are so 
different from natural languages, most programs are written 
P 
not in machine languages but in so-called 'high-levtl' .pro- 
gramming languages, sudh as FORTRAN, SNOBOL, APL, PL/? (to name 
a few among many). We may think of a computer AM suppl jed 
with a compiler program for some high-level langu'fige dH as 
A 
simulating the workings of a very different,computer, sgy 
E. 
actually exists: high-level languagzs 
No such computer as 
8re not typically me Zachi~le languages of any physical com- 
puters, and there are Undoubtedly s'oupd engineering reasons 
for this. 
But the abstract automaton 4 may be de~cribed 
just as precisely as the automaton4 whia underlies the real 
0 
computer. 
One who programs an $ Isgstemr (i.e. conjunction 
of computer with deg-compiler) cok-onl~ thinks of the machine 
he is dealing with zs having the eroperties of , and may 
be quite unaware of the properties .of the machine-AM with 
-. 
which he is in fact interacting. 
High-level lapguages, aad the abstract automata whose 
'machine languagest they are, differ from one another in more 
in-teresting ways than do real computers and their machine 
languages; and furthermore (not surprisingly, since high-level 
languages are designed to be easily usable by human programm- 
ers) they are much more comparable with human languages than 
are real machine languages. (Typically, a high-level pro- 
gramming language is a context-free phrase-structure language, 
for instance.) I shall suggest that the relationship betweer 
high-level languages ahd their corresponding automata gives 
us much better 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 shall choose the language APL (see e.g. Iverson 1962, 
Pakin 1968). AP$ is interestbing For our purposes because it 
is particularly high-level: 5.e. it is related more distantly 
to machine languages of real computers, and more clolely to 
human langudges, than many other high-level languages. It is 
a real-time rather thm batch-processing language, which means 
that it is designed to be used in such a way that the result 
of inputting a program will normally be crucially dependent 
on the prior @-bate of the system (in a batch-processing langu- 
age, programs are designed to be unaffected by those remains 
of the prior state which survive their input): this is 
appropriate for an analogy with human language, singe presum- 
ably the effect on a person of hearing a sentence deperids in 
,-- 
general on his prior system of knowledge and belief .' 
!Be complete language APL includes many features which 
are irrelevant to our analogy. For instance, there is a large 
amount of apparatus for making and breaking contact with the 
system, and the like; we shall ignore this, ~ust as we shall 
ignore the fact that in human speech the effect of an utter- 
ance on a person depends among other things on whether the 
6 
person is awake. Also, APL provides what amounts to a method 
uf using the language to alter itself by adding new vocabulary; 
to discuss this would again complicate the issues we are inter- 
ested inm7 We shall assume that programmer and system are 
permanently contact one another, and shall restrict 
our attention to a subset of APL to be defined below: raeher 
than resorting to a subscript to distinguish the restricted 
language from APL in its full complexity, we shall understand 
'gPLr to mean the subset of APL under consideration. 
'The practicing computer user may find my definition 
the real-time/batch-processing distinction idiosyncratic; 
difference I describe is the only one relevant for our pr 
of 
the 
esent 
purposes, but it is far rrom the most salient difference in 
practice. 
6 
In AP'L terms, we ignore all system ins~ructions, i.e. 
words beginning with A, Note that we use wm underlinin 
(corresponding to bold type in print) to quote bssequ- 
encee of symbols from an object-language, whether this is an 
artificial language such as ATL or a natural language such as 
English. 
'hn BPL terms, we ignore the dqyinition I - mode and the use 
of characters V A : + . 
6. 
We begin by defining the set 
9 APL of states of &APL. 
First, we recursively define a set of APL-prop&ties: 
any positive or negative real number is a numeric - APL- 
property of dimension #; 
any character on the APL keyboard (i.e. any of a-fipite 
set of characters whose identity does not concern us) 
is a literal &property of dimension @; 
for any integer I n and integer-string - D, any - n-length string 
over the set of numerio (literal) APL-properties of 
dimedion - D is A a numeric (literal) APL-property of 
dimension -- D%.' 
Por any finitg string .I D over the integers, any numeric or lit- 
eral APL-property of dimension - D is an APL-property, and 
nothing else is guch. Clearly, there 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 rank4 
numeric APL-property; a four-letter word, e.g. LOVE, is a rank- 
- 
1 literal -property; a 2 by 3 matrlx of numbers, 
emgo 
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 for concatenation (a dimension is 
always an integer-string). Concatenation is a function from 
so we should strictly write 'DAN9 (where N is 
set 8 &d any integeE n 5 ~:-ie use the terms-5-tu le of he- 
mentz of S' and '1enntE-n' strinp: over S ' interc & angea 1~ for 
any functrdn from the sewam, 2, .:. , n) of th; natkal 
numbers into S; note that the null set 0 iztherefore the 
length4 strgg- overany set. 
with an alphabetic character: there &re therefore infinitely 
many APL-identifiers. We define Ident as the set including 
all -identifiers together with an entity, assumed to be dis- 
tinct from all the APLidentifiers, delloted by. the symbol 
- 0, 
An DL-object is a pairing of any member ofsIdent with an APE 
property; we call the first member of an APL-object the ident- 
ifier of the object and the second memher the property of the 
-- - 
object. 
An APEstate is a finite set of APL-objects in which no 
distinct objects bear the same identifier. (We may thus think 
of an kPEstPt'e as a function from a finite subset of Ident 
into the set of APEproperties. ) We write I qAPL1 for the set 
of all -states: clearly, *APL is infinite. 
we now define txe lanwage zAPL of AAPL' 
de,m is gen- 
era$ed by the context-free grammar on p. 16. The initial 
symbol of that grammar is - asst (for 'assignmentt). Since 
capital letters occur among the terminal symbols of $ we 
use miniscules as non-terminals; terminal symbols of 2:; 
are wavy-underlined (cf. note 6, p. 3, whether they are 
letters or other characters, 
asst -+ + dscr 
- - 
dscr + 
- 
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 character or string of characters between 
inverted commas, denoting the corresponding rank-0 or 
rank-1 literal 
mf Cany of a large finite set of symbols br symb-01-strings 
- 
denoVXng partial monadic functions on the set of APE 
properties1 
11 
df -+ [any of a large finite set of symbol(- string)^ denoting 
- 
partial dyadic functiohs on the set of APL-properties] 
tf 
[aqy of a finite see of symbol(- string)^ denoting 
- 
partial triadic functions on the set of APL-properties] 
12 
deic + [any of a small finite set of symbol-strings denoting 
- 
total monadic functions from the set of possible program- 
ing-acts into the set of APL-properties] 13 
91n practice one cannot write a length-0 string, and one 
cgnnot distinguish a length-? string from a rank-0 property; but 
Fhe sentehces of dm-, are the strings defined by the above 
grammar, disambiguated by the use of round brackets (with 
assoc@tion to the right where lot indicated by bracketing). 
The sequence of symbols m+ may optionally be deleted when init- 
MlmC 
ial in a sentence. l4 Clearly there &re infinitely many sent- 
ences in &APL. A.sentence of hL is an APL-program. 
We now go 0x1 to specMy the function - IntApL from 
aeapL 
into which specifies the *change of APE 
state brought about by a gi~en APL-program. 
To determine the new state arrived at from an arbitrary 
I ignore these practical complications for the sake of simplic- 
ity. 
"1 rgnore complications relating to strings containing 
the inverted comma character, 
'l'l 
Some of these  function^, and their ~ames, are common to 
all 'dialects* of APL: e.g. 5, which denotes the function 
taking integers into their factorials, strings of integers into 
the oorresponding strings of fa~toriala, etc., and which is1 
undefined 0.g. for literal APL-properties. !Phe facility of 
'user-definition' (cf. note 7) permits a programmer to alter 
APL+by adding new functions. 
'12AP~ cantazns no triadic functions other than user- 
defined ones. 
''~.~r denotes the function taking any programming 
act into a etring of integers representing the time of day at 
which it occurs. 
14 
There are a number of syntactic complications, akin to 
eyntactic transformations in natural languages, concerning a 
Gadic functf on called index, which is denoted - by square brack- 
ets; we ignore these coaations, and shall not consider 
'index' apart from the other dyadic function$. 
current state on input of an arbitrary program, we consider 
the phrase-marker of which that program is the terminal string. 
Beginning at the leaves and working towards the root, and eval- 
uatinq the rightmoat node whenever there is a choice, we assoc- 
iate each - dacr node with an APL-property as its denotation and 
each - aest node with a change to be made to the current APE- 
state: the new APL-state is the one that results from the old 
state by making all the changes associated with the various 
asst nodes in the order mentioned, terminating with the change 
- 
associated with the root - asst node (which may of course be the 
only one). 
If at any point a - dacr node ca~ot be assigned a 
denotation (e.g. because it is realized as an APEidentifier 
which is not the identifier of any ob$ect in the current state), 
the etate-changes already made (if any) are the total changes 
achieved by that program. 
The rules for evaluating nodes are as follows: 
A - dscr node realized as an identifier denotes the APL 
property, if any, paired with thaa identsfkr in the current 
state; 
a - dser node rewritten as numname or litname denotes the 
APGproperty denoted by its 'expopent' (i.e. the terminal mat- 
erial it dominates); 
a - dear node rewritten as - deic denotes the APL-property 
given by applying the function denoted. by its exponent to the 
current programminpc-aot; 
when a - dscr node d+ dominates an mf node d followed by 
- n 
a - decr node d+, if d denotes some monadic function f and d2 
-1 - - 
denotes an UEproperty 2 then % denotes the APL-property 
f(~), provided g e dom(f); the extension to dscr nodes rewrit- 
- - - 
ten --- dscr df dscr and dscr tf dscr dscr is obvious. 
- 
An - aset node dominating a member - i of Ident, followed 
by 6, followed by a dscr node denoting an APL-property E, adds 
* 
- 
a new &PLobject (i, - E) to the current state, destroying any 
object with the identifjer - i which may already exist in the curr- 
ent stat&-; if I i is - a, a representation of 2 is printed out; 15 
a - dscr uode imediately,dominating an - aest node which has 
created an BPEobjeot with the property E denotes 2. 
As a (trivial) example of the operation of these rules, 
consider the program 
input to dfL in state {(A, (k 1 1 I), (B, k.r 10)). This program 
has the constituent structure which appears in Pig. 'I on the 
next gage (in which - dscr and - asst nodes are numbered in the 
order they are to be evaluated). 
Suppose the program is input in the morning, say at 11.30 
a.m. Then dscr will denote the string 11 30 0. The function 
-1 
> 
takes (12 0 0, I1 30 0,) into 1 0 0, which becomes the denot- 
w 
ation of dscr in fact dscr will denote 1 0 0 whenever the 
-+3 1311CCIL3 
program is input in the morning and 0 0 0 whenever it is input 
in the afternoon (when the hour integer will be 14 or more). 
The monadic function +/ adds the numbers in a string, so if 
- 
dscr denotes 'I 0 0 then dscr,, denotes 1. Dscr denotes 10 
-3 -5 
(identified by 3, so dscr, also denotes 10. Accordingly, 
'21n the full version of APL. a-can oocur as a rewrite 
. - 
of dscr, in which case dscr is assigned an APL-property input 
by theprogramer at thnme dscr is evaluated by the system, 
We ignore this, since it interms with the analogy with nat- 
ural language. IL the full version it is also possible to 
output symbol-str'ings which do not represent individual APE 
properties; again we ignore this. 
dscr 
-2 - 
dscrl 
df - 
deic 
- 
asst 
adds an object ( , 10) to the current state and prints 
-7 
out 10. The monadic function gives the dimendion of any &PE 
MJ 
MI 
property, and ascr, denotes 1 -1 1, so d~~r~ denotes 3, and 
hence dsor denotes 13. Pinally, asst addasan object (Q, 13) 
-10 -1 1 - 
to the current state. 
In other words, if the program ia input in the morning and 
the prior state is as quoted, the final state will be 
{(A, I ,I I), (2, lo), ( , lo), (Q, 13)), whereas if it were 
(u tw 
input in the afternoon to AAPL in the same prior state the 
resultag state would be C(A, rn 1 1 I), (2, lo), ( lCrr , 0) , (Q, 3)). 
m 
To define fully it remains only to specify the rel- 
ation Suc,,, 
On 4LPJi 
which controls the changes-of-state 
&r undergoes- spontaneously. SucdpL is the empty relation: 
every -state is a stopping state. A programmer working in 
BPL has no wish for tihe system to take actions beyond those 
specified by his programs: by defining monadic, dyadic, ,or 
triadic functions of any complexity he wishes, he can get the 
answers to hie questions simply by carrying out the state- 
changes specified in his program. (1n the maohine language of 
a .genuine computer, on the other hand, the state-changes brought 
about by grograme are of no intrinsicr interest, and the input 
of a program ie of value only in tha* it brings the computer 
to a state from whichit proceeds spontaneously to perform 
actions useful to its programmer. ) 
7. 
It may seem.contradictory to say that a real digital 
computer, which will have only finitely many states and poss- 
ible programs, can be made to simulate an automaton such as 
which has infinitely many states and programs. And, of 
oouree, in practice the simulation ie,not perfect. Although 
an -state may contain any number of objects, for. any APL 
computer/compiler system there will be a finite limit on the 
number of objects in a state; although any real number may be 
an BPL-property, in a practical APL system real numbers are 
approximated to a fini-te tolerance. 
The mation is quite ana- 
logous to the case of natural language, where the individual's 
tperfomance ' ie an imperfect realization of an ideal* tcompet- 
ence', in one sense of that distinction; 
just as in linguist- 
ics, so in the case of high-level programming languages it is 
normal to give a description of the ideal system separately 
from a statement of the limitations on the realizat5,on of that 
system in practice, which will differ from one person to another 
in the natural language case, from one computer/compiler pair 
to another in the programming language case. 
Other high-level programming languages differ from APL not 
only in terms of their sentences but in terms of the nature of 
the states on which thei~ sentences act. Thus in states of e.g. 
SNOBOL, all objects are character strings; in PL/1, objects 
include not only arrays of the APL kind but also trees, trees 
of arrays, arrays of trees, etc. Ijpace doea not permit a 
survey of the differences between high4Level languages with 
respect to the nature of their states. 
8. At this point we are ready to begin to answer Apostel's 
question, about what sort of automata natural languages are 
appropriate programming languages for. Any answer,to such a 
novel question must' obviously be very speculative; but the 
ideas that follow seam plausible enough to be worth consider- 
ation. We do not know with any certainty evbn what the sem- 
antic representations or syntactic deep structures of our sent- 
ences are; but we have seen that there is good reason to think 
the two may hs similar, and we can make more or lesa detailed 
conjectures about their form. In my exgosition I shall make 
various assumptions about aemantic representations, some of 
whiah have already been made for independent reasons by other 
scholars. Insofar as my theory depends on these assumptions, 
a refutation of the latter refutes the theory -- this is one 
of the respects in which my theory is falsifiable, i.e. scient- 
ific, 
I shall present my theory in a *relajxLvely informal, intuit- 
ive Way to begin with, and formalize it more carefully later. 
9 
What we are looking for is a specifica-tAon of a set 
Erin 
- 
of states, which we can interpret as states of some subpart 
of the mind of an English-speaker, such that semantic repre- 
sent\ations of English seqtences are rather natural devices 
for moving this part of the mind!. from one of its states to 
another. It will be convenient to have some name for that part 
of a human's total psychological make-up which is described by 
speoifging , In earlier, unpublished work I have called 
thia the topicon (coined on the analogy of 'lexicong), since 
I envisage it as coneaining a set of entities corresponding 
to the objects of which ita owner is aware, and to which ha can 
therefore take a definite description to refer. 
Ln, then, 
is to be a set of possible topicon-staeea. me set8 of topicon- 
states available to speakers of natural languagee other than 
English will differ from (f 17 below), but not in 
respect of the properties on chich thia paper will concentrate. 
Note that a topicon-state is certainly not to be equated 
with a %tate of mind' or tpsychological stateq: a topicon is 
claimed to be only one small part of a human's mental machinery, 
and there will be many way8 in which the latter can vary -- 
e.g. the human may be happy or sad, asleep or awake -- without 
implying any difference in topicon-state. 
Just as an APEstate contains a set of APLobjects with 
properties drawn from a fixed clase, so a topicon-state will 
contain a set of ob~ects I shall call referents. '6 
suppose 
some person - P knows of the existence of a red car - C; then P1s 111) 
topicon will include a referent - c corresponding to - C. 
Thq 
referent a c will be - P1s 'Idea1 of - C, in Gehchts terms (1957). 
The possible properties for referents will be determined by the 
vocabulary of - P1s language, in this case English: 
each lexical 
item of English will correspond to a referent-property. 
I 
shall use Geachls operator 5( ) (1957: 52) to form names of 
referent-properties from lexical items: 
if - P knows that L C is 
a red car then - c will have the properties §(red) MhJ and §(ear). MMI 
(An element of a mental state cannot be red, but itcan be 
Pfs - topicon will include not only referents representing 
physical obdects but referents for any entities of ~hich - P is 
aware an8 which he can take definite descriptions (referential 
NPs) to denote: there will be referents for characters in 
fiction, for abstractions like the centre of this circle etc. 
(Wlh--A-.'.A~' 
eto. But, at any given time, - P1s topicon will contain only 
a finiee number of referents. Given enough time, of course, 
*here is no limit to the number of objects whose existence 
P could deduce or imagine; and I shall suggest that for P to 
- - 
'%ere and below, rather than coining neologisms I use 
terms having established uaages in philosophy and logic in- 
senses which claeh with their normal use; in such~cases I use 
the term only in the sense I define. 
deduce or imagine the existence of some entity L B is for - P's 
topicon to acquire a new referent representing (I B. kt deduct- 
ion and imagination take time: in a finite amount of time u Pas 
topicon 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 shall consider the more 
general case in 510): 
(2a) 
bs a red car y- 
a-- 
I aold the red car today. 
------ 
The HP a red in (2a) will create a referent with the pro- 
rv- 
gerties §(red) - and $(oar) cIM*r in - Pas topicon. On the other hand, 
when he, hears (2b) the NP *he red car will pick out the refer- 
--- 
ent which a red car has already created (in order to act on it 
--- 
in ways which will be discussed later). In other words, the 
distinction between the ,Arvrr.MccH- red car and a red car is quite parallel 
N-- 
to the distinction between - dscr and - asst constituents, reapect- 
ively , the selects from the 
current 
state, the latter adds an object to the current state. 
Let us 
call natural-language expressions which act in the former way 
'identifying expressionst (IEs), and expressions which act in 
the latter way aestabliahing expressionsa (323s). Clearly the 
IE/EE distinction is related to the traditional distinction 
between :definiteq and 'indefinitea We. However, I do not 
claim that-/all definite and indefinite MP8 count as IEs or EXs 
respectively. Consider, for instance, the -- de dicto / -- de re 
(or opaque referents / transparent reference) ambiguity exhib- 
ited by 9s in 'intensional contextst (see s.g. Quine 1960: $30; 
I am 1- for an 
(3) 4, -- 
In the -- de dicto sense of - ah -, (3) does not imply that 
there are any elephante, although in the -- de re sense it implies 
that there ia at least one. Only in the -- de re sense is an ele- 
w- 
hant in (3) an EE in my tams, though ptactically an e 
L - 
ant is clearly an 'indefinite NPt in both cases. On the other 
w--- 
hand, in sentences containing quantifiers, definise lBPB may not 
always be IEs: thus, in (4) the definite NP the - 
does not denote a particular object (and therefore, perhaps, 
does not pick out a particular one of the hearer's referents). 
just as the indefinite NP cH. a does not seem to establish 
the existence of- a single book: 
(4) Whenever I bs a book I remove the d- 
-A/ N4--- 
I shall develop my theory with a view to handling the sub- 
set of Englieh which excludes quantification and intensional 
oontexts, and in whioh 'definite' and 'indefinite1 NPs do coin- 
cide with IEa and EEs respectively-. Later I shall consider 
some of *he aspects of EnglLah which my theory does not handle 
successfully as it stands. 
men in the subset of Englisli considered here, not all 
definite NPa will in fact refer to referents already in the 
hearer's topicon. For instance, a chi= may come home from 
school at-the beginning of a new term and say to his mother: 
(5) 
I saw the new teacher 
rr-EAM.-- 
It may be that the mother does not know that there is a new 
teacher, i.e, it may be that her topicon contains no referent 
for which the phrase the new teacher is appropriate; but in 
AMh-- 
practice she is likely to work out from her child's sentence 
that there is a new teacher, and to understand that the child 
saw him. other words, this phrase 
the 
- 
teacher acts as an EE to create a new referent in the mother's 
7 
topicon. However, it seem8 plausible to say that this is in 
some sense not the central use of a phrase such as the new 
w- 
teacher; it-would be more appropriate, if the mother does not 
- 
how about the new teacher, for the child to say something like: 
(6) 
There is a new teacher at school and I saw him t- 
~Eks.eb--lIMCl-MWItv-~ 
in-which the referent denoting the teacher is first introduced 
by anaEE aad only then re-identified by an IE. Notice that 
the mother may react to (5) by sayin6 something like: 
(7) What new teacher? I didn't know there was one. 
--- ff-v--JIMMV(, 
which would not be a poasible reaction to a sentence using the 
EE a new teacher. 
-- - 
What happens when the mother successfully acquires a new 
referent-in response to (5), I suggest, is that she imagines 
some clrcurnscance in which the new teacher would succeed in 
A-wv-7 
picking ref eren-t; her topicon -- for instance, if there 
were a new teacher at her child's school -- and, in imagining 
these circumstances, creates the *referent; after which the 
sentence operates on her topicon in the normal way. The APL 
system d~es not work like this: if one inputs the sentence 
A + B to an APL-state lacking an object named B, the system 
AhAmmrJ & 
prints out a message pointing out one's error but does not 
change state. It is natural enough, though, that human lingu- 
istic behaviour shows more initiative than the behaviour of 
artificial automata. A programmer has complete control over 
the automaton he programs, and it is easier to require the 
programmer to get his programs right than to equip the automaton 
with routines to guess what the programmer means by defective 
sentences. A human speaker, on the other ,had, has no way of 
knowing exactly what state his hearer's topicon is in, so it is 
all to the good if the hearer can comp6ffgate in simple cases 
for defects in the speaker's sentences. 
Gince-I shall frequently be speaking of the relations 
between linguistic sqressions, topicon-referents, and th'e ent- 
ities in the outside world which the linguistic expressions 
denots, let me lay down some tsrminolog&cal conventions, I shall 
use denotation for the relation between an'IE and  he thing 
which a hearer takes that IE to correspond to; my theory asserts 
that denotation i8 a composition of two relations, a relation 
of reference between linguistic expressions and topicon refer- 
ents, and a relation of representation between topicon-refer- 
ents and things. Thus, if the phrase your car said to P now 
-- 
- 
picks out a ref erenti =, in - P's topicon, and if - P owns exactly 
one car - C, then your car refers - to 2, and denotes - C, and s, 
represents - C. We say' that =, is the referent -4 of and - C the 
denotatum of, = car (on this occasion), 
hlCkV 
Notice that an IE may refer, without denoting: if - P has 
Crime Punishment, then his 
will two 
referents, say 3 and q, such-that 
refers to E~ 
and ~lana Ivanovna refers to r even though neither of these 
-- -3) 
NPs denotes anything (and, correspondingly, 3 and g, will both 
L... 
have the property S(f ictional) ) . 
Furthermore, identhy of the 
P 
denotata of two IEs does not imply identity of their referents. 
Thus, if - P knows that I have exactly one brother and that he 
is the new doc%or, then the IEs the new doctor and 
--- 
brother will refer to the same referent in Pfs topicon, and 
7 - 
henoe also denote the same man (the details of reference by 
means of the genitive construction are discussed in 912 below); 
but if - P knows that I have one brother and that there is a new 
doctor, but does not realize that they are the same man, then 
the two IEs will refer to different referents in - Pgs topicon, 
even though each of these referents will in fact represent the 
(10. So far we have assumed that, when a hearer hears an IE 
auuh as the red car, his topicon contains only one referent 
--- 
~5th the properties $(red) - and $(car). H Clearly this will not 
in general (or even usually) be so: when one hears an IE, it 
will often be the case that one knows of a number of objects 
In 
fitting the description. 'l One who hears the red car will take 
--v 
the phrase to refer to one among the various red cars of which 
he is aware which is in some way closer than the others to the 
'7~f Russellg s theory of descriptions  u us sell K19051 
1949: 1051 Whitehead & Russell 1927: 30) were an accurate sem- 
antic desclription of English (which Russell did not, of course, 
claim- it to be -- cf. his 119573 1969 : 335-7), then most Eng- 
lish sentences uttered in practice would be simply false because 
they_contain IEs asserting the ungqueness of objects fitting 
descriptions which in fact are multiply instantiated. Philo- 
sophers who have discussed reference have treated it as a simple 
relation between expressions and things, rather than as the 
compoaite relation for which I argue; but they have succeeded 
in this only by devotiag undue attention to NPs, such as Soc- 
rates or 
- 
which perhaps have only one 
p-le to be quite rare in pract- 
ice. 
focus of his attention. This will translate iatm our theory 
as the notion that the referents in a topicon are arrayed in 
some kind of space, one point of which constitutes the focus 
of attention at any given time, 
The nature of this space, and 
the factors which determine the position of the referents and 
focus of attention in it,, will be considered in 916 below; for 
the moment, let us simply assume fhat the notion can be made 
precise. 
Then we can say that any IE consisting of the word 
the followed by a series x, ;1 ... w 
of adjectives and noun 
AEH* -n 
will refer to the nearest referent t5 the hearer% focus of 
attention having all the properties ( ) , () . . . , and 
5%) 
Thus, the car will refer to the nearest $(car) referent 
hM/- - 
to %he focus, while the red car will refer to the nearest refer- 
--- 
ent to the hearer's focus which is both §(red) and %car), 
18 
IWw AM/ 
One would expect that the nearest referent of all to the focus 
in any topicon-state should be referred to as the* in English 
-3 
a eyntactic rule replaces the as a complete NP by he, she, or 
M - /r*c*k 
it. 
A13 
ad, In &PL, object8 :an be referred to by their identifiers. 
The oUvious candidates as natural-language equivalents of ident- 
ifiers are proper names. However, although some logicians have 
di~cussed proper names, under the label sinmlar - terms, as if 
181 can offer no explanation of the syntactic distinction 
between nouns and adjectives, which serves no obvious semantic 
mction; however, since the distinction appears to be univer- 
sal in natural laaguagGs, my account of English semantiq repre- 
sentations will incorporate it. 
(We solution to this puzzle 
ray have to do with the fact that Borne adjectives are 'syncat- 
egorematic' in a way which nouns never are: a 'goad actor' is 
not necessarily good though he is necessarily an actor.) 
tney are the equivalent of APL identifiers (for a summary of 
the alternative views, see Oheng 1968), English proper names 
in fact do not behave in this way. In APL, a state in which 
two distinct objects bear the same identifier is simply not a 
well-formed state. In English, on the other hand, locutions 
like : 
(8) 
Do you mean our Charles or your Charles? 
-*H*J(HICICYr---/CCH(- 
The London in En- iz ba than the London in 
(9) - , ---#us- 
occur frequently enough: although many proper nouns apply only 
to one referent in an average topicon, many apply to more than 
one. Superficially, proper nouns seem syntactically distinct 
from common nouns in that IEs containing proper nouns lack - the: 
the car, but not *the London. However, Gloat (1969) has argued 
WIICChS. -- 
convincingly that in deep syntactic structure proper nouns are 
preceSded by the, and that proper and common nouns are syntact- 
- 
ically quite parallel in the base. We shall take it that pro- 
per nouns correspopd to properties for referents in just the 
same way as commol nouns: London refers to the nearest 
/Hrycrcrch, 
§(London) referent to the hearer's fo,cus, as the car refers 
- Mh/\ML 
to the nearest §(car) ~mh referent. (me problems of how the pairs 
of IEs in (8) and (9) succeed in referring to distinct refer- 
ents will be answered in 912 and $15 respectively.) 
Clearly 
there is a disttnction between names and common nouns in that 
the applicability of a name to an object is more 'arbitraryt 
than that of a common noun. But this distinction is gradient 
rather than all-or-none; e.g. a schoolboyts nickname, such as 
Fm, will be intermediate in arbitrariness (a boy called 
Ps will probably be fat, but not all fat boys will be called 
12. A somewhat more complicated situation arises in conn- 
ection with IEs involving genitive constructions. The 'basic' 
sense of the genitive is commonly taken to be possession, as 
in John's car; however, the genitive often represeats other 
7- 
relationships+ as in John's father, John's c, John's God 
-- 7 - -9 
the 
of the problem, the dm of the U&u& etc. etc. 
w #v--- - /ur- 
Even in a case where the genitive NP denotes a person and the 
head NP denotes an inanimate ouect, such as -- John1a car, although 
on many occasions of use the NP will be paraphrasable as - the 
bar which John owns the same NP will surely be used equally 
--.--wP--* 
frequently in other situati-fins in which the appropriate para- 
phrases would be the car which we saw ni miss - 
-w-(Wdv-v - 
John down, the car which John km he'd like to bx if 
hwu--- --- Lr+rc 
he on& had the -, or other expressions of urely idiosyn- 
w -A&-'- 
cratio and epheieral relationships between the denotatum of the 
geniiive HP and that of the head NP, 
The device of the topicon space permits a neat account of 
this situation. 
In an NP of the form A's B or the B of A (e.g. 
-w - -I.-- 
John's car, the roof of the house), A will as usual pick out 
-- --&-bat---- II 
the referent the hearer ' s focus having the 
properties corresponding to the lexical items of r, n while the 
NP as a whole will pick out the nearest referent - to & having 
the properties corresponding to the lexical items of B. - Thus 
in the case of John's car, John will pick out the nearest refer- 
-* - 
ent to the hearer's focus having the property $(John) and, if 
- 
that referent is gl, John's car will pick out the nearest refer- 
-- 
ent to 2, having the property §(car). 
The latter referent need 
w 
not be the nearest §(car) referent to the he arerls focus; if it 
(\rur 
is not, the car and John's car will have different reference 
rchmr- -- 
for him. As we shall see when we discuss the organization of 
the topicon-space in 916, ownership is only oneof the factors 
that may cause a §(man) referent to be close to a particular 
- 
#(car) referent in a topicon. 
- 
13. Certain English words, known as deictics or token- 
reflexives., correspond to the terms labelled - deic in APL: 
these include I, m, now, here, etc. 
hl - - 
l9 Deictics, like other 
IEs, pick out referents of the hearer's topicon; but their ref- 
erents depend on characteristics of the spe'ech act in which 
they are used, and are independent of the arrangement or prop- 
erties of referents in the hearer's topicon. For this reason, 
deictics neve? occur as the head of a genitive construction, 
and there are no phrases like %he you (with 's 
- - * 
as genitive rather than short for is); will refer to the 
- 
same referent on a given occasion (namely the referent repre- 
senting the addressee of the speech act -- the owner the 
topicon, unless he is overhearing words addressed to someone 
else) whatever other referents are in the vicinity, so it would 
be otiose to modify a deictic with a genitive NP. 
34. So far I have discussed only referents corresponding 
to ndun-phraaes in syntax, and representing individuals in the 
outside world. However, some referents will represent what 
would more normally be called 'facts' or 'events' than 'individ- 
uals'. Ordinary predicate logic distinguishes sharply between 
individuals on the one hand, and facts or events on the other: 
the former are translated into singular terms, the latter into 
'g~inguiats do not usually include the first and second 
person pronouns among the 'deictics', but logically they are of 
the same category. 
arrays of predicate followed by arguments, 
and the syntax of 
the predicate calculus does not permit one to occur in place 
of the other. However, in English, if e.g. John - b-t -- the car 
has the semantic representation 'f(a, -- 
.LI b)' (where - f is the pred- 
icate bs and - a and a b are singular terms standing for John and 
$he car), then presumably the semantic representation of: 
(10) It surprised Mary that John the car. 
-uw--- w- 
will have to have 'f(a, 3- - b)' as one of the arguments of the pre- 
dicate su rise -- (10) will have to be represented as some- 
& 
thing like 'g( f(a, 3L - b), ), where g is and c stands 
for Mary (tense is discussed later in this section). 20- If 
''liosenbaum (1967) has shown that in deep syntax, before 
the application of a transformation called 'Extraposition', 
(10) has the normal subject-verb-object structure with that 
- 
ab- the car - as subject. The need to permit proposlt- 
ions as arguments of predicates is discussed by Leech (1969: 
25-6). In the *selnan$ic representations' given here, I arrange 
the predicate-symbol to the left of all the arguments, in order 
to clarify the c~mparison with standard logical notation. It 
is by a quite arbitrary choice, however, that formal logic 
writes 
'f(a, 2)' rather than 'a f b', and when I define & 
Qelow I azll adopt the orderiiig-which more closely 
Eng 
reflects the surface stzmcture of English. (Ct is a moot point 
within linguistics whether the dee structures of English sent- 
ences have 'the ordering subject-ver _% -obJect or verb-subject- 
object.) 
- 
facts, as well as things, may be denoted by suitable linguistic 
expressions, then suppose that topicon contains refer- 
ents representing facts (propositional referents) as well as 
referents representing things (individual referents). We will 
suppose further that the referents in a topicon are linked in 
a graph structure in which propositional referents dominate 
n-tuples of (propositional or individual) referents, corresp- 
- 
onding to the arguments of the respective propositions. Con- 
sider e.g. one who knows that someone called John bought a car: 
his topicon will contain a structure of the following form: 
In (11) nodes stand for referents, which I shall call 'r ' 
-1 
* etc. (N.B. I shall always use 'rm for nodes of topicon- 
'g2 9 cI 
states, as opposed to 'dl - for nodes of phrase-markers of sent- 
ences). The lowest-level referents are unlabelled, while the 
higher-level referents are each labelled with an English word. 
'Phe referents =, and g2 represent respectively John and the car, 
while represents the fact that John bought the car. The 
referent r represents the fact that the thing represented by 
-5 
4 
is a car, while r 
represents the fact that the thing repre- 
-3 
sented by 2, is a John ('is called "Johnu1. as we usually say 
in the case of proper names). 
To say that a referent, say I&, 
has the property §(car), - is to say that there is some referent , 
in this case r which dominates the I-tuple r,-+ and which is 
-5' 
labelled car. 
rcNvc 
A sentence acts as an EE for the establishing of propos- 
itional referents, as an indefinite NP such as a car is an EE 
hA- 
for establishing individual referents. 5us, suppose - P1s 
topicon contains the structure of (I?), together with a 9( 
referent, say (that is, is dominated by a propositional 
referent z7 labelled Mary): then P's hearing (or reading) the 
- 
- 
sentence (j~), i.e. It Mary that John bought the car 
I*N - -----I 
will create in P1s - 
topicon a new propositional referent, say 
%* 
labelled and dominating the 2-tuple (3, ): - P1s 
new topicon-state will contain the structure shown as (12) on 
the next page. 
In (12), broken lines show the new structure created by 
sentence (10). Notice that propositional referents, like indi- 
vidual referents, may be referred to by pronouns; if r+ is 
close enough to - Pgs focus of attention, the same effect will 
be achieved by the sentence: 
'(13) It surprised Mary. 
*-- 
The number of referents dominated by a given referent in 
a topicon will corrdlate with the label of the latter referent. 
An unlabelled referent will be an individual referent and will 
dominate nothing; a referent labelled with an - n-adic predicate 
will dominate an I n-tuple of referents. 5us a referent labelled 
with a noun will dominate one referent; a referent labelled 
with a verb taking subject, direct object, and indirect obaect 
will dominate a 3-tuple of refiirents; and so on. In natural 
languages the distinctions between the different arguments of 
a verb are shown sometimes by ordering, sometimes by preposit- 
ions (to /HS or case endings (Johami), etc. 
- 
I assume that some individual referents represent points 
of time, and that one of the arguments of most verbs in natural 
languages is the time at which the action in question occurred. 
mere a verb in the preterite occurs with no phrase overtly 
denoting a point of time, I take it that the nearest time ref- 
erent t;o the hearer's current focus of attention becomes the 
respective argument of the new propositional referent: one 
would not normally say e.g. - John bat the mW.-- car unless the 
hearer can be expected to know what occasion one is speaking 
about. In other words, preterite tense picks out the nearest 
§(time) - 
referent as CHh he picks out the nearest §(male) - referent. 
McCawley (1971) has argued that preterite tense and pronouns 
have a cornon syntactic origin, a finding which renders my 
-A 
semantic approach all the more appealing. 
c I 
Although I assume time arguments for verbs, to avoid clut- 
ter I shall not include them on diagrams. 
That - clauses may be used to refer to propositional refer- 
ents either as IEs or as EEs, without the distinction being 
markeii syntactically. Sentence (10) (It - md that - 
John b-t the car) is equally appropriate whether or not 
w w- 
the hearer already knows that John bought the 
car. !Phus, if 
P's topicon contains the structure of (17) (p. 35), the phrase 
- 
that John b- the car in (10) will pick out and create 
-- UlWC- 
the extra structure of (12); but if - P's topicon lacks r+, then 
the same phrase will create a referent labelled- ba and domin- 
ating - rq (and a time referent) before the rest of the 
L'I 
A verb in the perfect, as in John has bou ht the car, 
-+ 
- 
will act as an EE for a time referent , as a ver 1n preter2 
ite acts as an IE. These remarks might, however, have to be 
modiiiea to handle American usage: one of the characteristics 
of American English is that it permits the preterite in circum- 
etances where the perfect would be obligatory -- in British usage. 
sentence creates a node labelled su_lprise dominating this new 
node, , and a time referent. The absence of syntactic di9- 
tinction between phrases establishing propositional referents 
ad phraseril identifying them can readily be explained. Either 
John bought the car at the time in question or he did not; 
there will never be two referents both labelled bs and domin- 
ating the same 3-tuple of individual referents, so if - P's 
topicon contains (11) and he hears the phrase that John 
-7 
the car then he knows that this must refer to r+ rather than 
Ccrru"- 
calling for the creation of a new propositional referent. 
22 
If there were no distinction between the car and a car, on the 
NHmA#@-.. (vr- 
other hand, he would have no way of knowing, on hearing the 
IP car, whether 9 or some new §(car) referent was intended. 
ow--& - 
I take it that. languages lacking definite and indefinite art- 
icles mark the IE/EE distinction for individual referents by 
some other syntactic devices. 
15. 
The graph structure into which an individual referent 
enters can be used to pick out that referent by mebs of relat- 
ive clauses. Thus if the car refers to g2, then the IE: 
-- 
(14) 
the man who bought the car 
-wwNHrcmclY-- 
will reEarto the nearest referent, say r , to the hearer's 
--x 
focus such that r has the property §((man7 and such that some 
-ex - 
22 
It is convenient to speak of a topicon's owner as 'know- 
ing' facts about his topicon, just as it is convenient to anthro- 
pomorphize a computer program and speak of it 'knowingt vari- 
ous facts; these locutions are, of course, literally nonsense, 
but they could easily be replaced by longer paraphrases which 
did not commit category mistakes. 
referent labelled 
dominates a 3-tuple including - r,, 2, and 
the nearest time referent. 
If - P knotvs that the denotzbam of 4 r 
is a man (i.8. if his topicon includes, in addition to the 
structure diagrammed in (12) (p. 37), a referent labelled - man 
and dominating g,), and if there are no tense problems, then 
(14), the man who the car will refer to g,, 
e-- &--- -3 
However, note the distinction between restrictive and 
appositive relative clauses (cf. Bach 1968), A restrictive 
relative clause, e. g, who - bm Ee czr in (I4), is part of 
an IE: it gives a property of the target referent. An appos- 
itive relative clause, on the other hand, as in ('l5), acts as 
an EE: 
'Phe man, who b- the car is old. 
--- --- 
In (15), the man acts as a complete IE; when (15) is input to 
w- 
a topicon, the man will pick out the nearest §(man) referent 
w- h*Hrr 
to the focus (say &), and then the mgositive relative will 
create a new referezt labelled buy and dominating & and the 
- 
referent of the car, before the main clause creates-a referent 
labelled old dominating G. The function of appositive relat- 
hmc 
ive clauses in natural lGguages is thus quite comparable to 
that of embedded - ass* clauses in APL, 
16. The principle that each sentence received by a hearer 
creates a new referent in the hearer's topicon suggests a nat- 
ural way of reconstructing within the theory the notion of a 
focus of attention9, which varies with the topics being dis- 
cussed: we may define the focus of attention as the most rec- 
ently-created referent at any given time. The graph structure 
associated with propositional referents offers a way of formal- 
izing the notion of distance between referents in the topicon: 
we may define the distance between any two referents as the 
minimum number of edges (e Unes which link nodes) that must 
be traversed t"o get from one referent to the other. Thus, con- 
sider the sequence of sentences: (ihJ John - a car. 
- -- 
(ii) me car hit a man. (iii) He dial-e police. Assume 
--4A*m-- -- 
the hearer's topicon already containe $ referent, say g,, with 
the properties S(~0b.n) - and §(man). Amr hearing sentences (i) 
w 
and (ii) but before (iii) the hearer's topicon will include 
the structure of (16), with the focus at 5 (the referent cre- 
ated by (ii)): 
(16) contains two referents to which he - could refer, namely g,, 
apd I+; r+ is one edge from the focus and ;, is three edges 
away. 
Therefore the theory predicts that he in (iii) will be 
- 
taken to refer to r+ rather than y,, and this prediction seems 
correct: he in (iii) will be taken to denote the man who has 
w 
been hit, rather than John. (Notice that this cannot be pre- 
dicted from the situation described: when a driver hits a ped- 
estrian, the driver is as likely as the pedestrian to call the 
police. ) 
1% 
We may no* define the automaton which I claim to repre- 
sent the mind of a speaker of English. !be grammar of the sub- 
set of English we are analysing is as follows: 
the - NP (of IE) 
- 
he it 
v-3 rwc 
Deic + I, you, now, . . . 
--Ae-n 
Noun + Mq, man, . . . 
- - 
Pr' red, real, ... 
h - - 
PP~ + love, k~~ow, ... 
- - 
The finite set of predicates of English, together with the 
phonetic shapes of particles such as the and .of, will be spec- 
- AAP 
ific to the English language. I would hypothesize that in 
other respects (17) generates the semantic representations of 
sentences in any natural language, though the rules which 
relate the phrase-markers generated by (17) to the correspond- 
ing surface forms will vary from languagsto language. 
Some of the latter rules which operate in English will be 
obvious. Thus, subordinate clauses (non-root 'Sf constituents) 
have that prefixed to them (replacing the in case the latter 
- w 
appears); nouns not preceded by the - are pupplied with -- a/=; 
'the NP of IEf may become 'IE's HE" in some cases; wh is real- 
+ - - I+IW 
ized as who, which, or that and is fronted. and he is realized 
Mmr - - h-, a 
z: 
as she - in certain circwstances; adjectives have the verb be - 
supplied, or are moved in front of their noun with the relative 
pronoun wh deleted; clauses outside an LE are given commas to 
IvlN 
mark them as appositive rather than restrictive relative 
clauses; etc. Is shall not attempt to render explicit every 
detail of the relation between my semantic representations and 
superficial structures of English sentences. 
We may define the set 9 of states of the automaton 
& 
Eh3 
mg 
as follows. Suppose Pred is the finite set of English 
7 2 
predicates, i.e. the, set - Pr u - Pr u . in (77). Then a pair 
24 
(M, - - Foc) in which (i) I, M is a aemiforest 
over - Pred such that 
23~ ,treat the distinction between he and s e as determined 
rather than as needing to be marked in %e seman + ic representat- 
ion: in the standard use of English pronouns (leaving out of 
account the special rules operating under contrastive stress), 
& is appropriate only if the intended referent is the nearest 
individual referent of all to the hea.rerfs focus, not merely 
the nearest of the #(male) referents. 
- 
24~ use semiforest as a generalization of the notion - tree: 
each node immediately dominating a length-n - string is labelled 
vith an 1 n-adic predicate and each leaf is unlabelled, and 
(ii) - Foc is3 a root of 1 M, is a member of 9 
Eng' 
The function Int 
--g 
which determines how a sentence of this 
moves a topicon from one state to another is specified 
by rules which associate subsets of the referents of the curr- 
ent topicon state with nodes in the structural description of 
the sentence; as in the APL case, certain nodes cause addit- 
ions to the current state. We shall write 'Ref' - for the part- 
fal function, specified by these rules, from nodes of the sent- 
ence into subsets of the topicon-referents; in the case where 
a conetituent refers (in our technical sense) to a ~eferent, 
fef will take the node dominating the constituent into the unit 
- 
aef aontaining that referent. 
The rules determining Inthg are as follows: (see aext page) 
a seniforest is allowed to have more than om rout, and nodes 
#we allowed to branch upwards as well as downwards. A semifor- 
est over a vocabulary V-is a triple (D, 6, #) where D is a set 
st oodea, 8 is a part-izl function of immediate domin'ce iron - D 
Sntxings over D such that every node is dodnated (not 
necessarily immedigtely -- dominate is the ancestral of 'imedi- 
stely dominate ' ) by at least one root (i. e. undominated node), 
anQ oc is a partial function of lamin from D into V. Nodes 
outside the domain of 6 are leaves --Y-+ or ermina'l: noded: Note 
teat, b$ defining the range '6s containing strings, I have 
built left-to-right ordering into my aefinition; semiforests 
as defined here are ~stringsemiforests.~ rather than 'setsemi- 
forests' in the sense of Sampeon (forthcoming). 
(R?) 
Whenever two nodes &, - d' of the phrase-marker are such 
that - d immediately dominates the length-I string -3 dt if -- Ref(dl) 
is defined then -- ~ef(d) r Ref(dR). -- 
(R2) 
If IE immediately dominates t& NP, then - Ref(1E) is the 
unit set containing the nearest member of - Ref(Np) to the curr- 
ent f acus . 25 (,NearestR a~ defined on p. 41.) 
(RJ) 
If IE immediately dominates the - NP of - IE' then - Ref(1E) is 
the unit set containing the nearest member of - Ref(NP) to the 
sole member of - Ref(IEb). 
(R4) 
-w Ref(fie) is the unit set containing the nearest individ- 
ual referent to the current focus not having the prOggrty 
I(inanimate); P --An Ref(it) is the unit set containing the nearest 
(propositional or individual) referent to the current focus 
not having the property §(human). 7 
(R5) 
If the speech-act being analysed is -9 A then -* Ref(1) is the 
unit set containing the referent representing the performer of 
A, F&ef(now) is the unit set containing the referent represent7 
- -- 
ing the time at which A - occurs, etc. 
'Pbe remaining rules depend on whether br not a given node 
is dominated (not necessarily immediately) by an IE node. 
(B6) 
I5 an S not dominated by IE immehiately dominates 
ED?, p&'NP2 . HPn (n - 3 I), where I?& is realized as A. P, 
then (see next pagz): 
25~trictly, R2 should read: *If a node d labelled IE 
imrPeUiately dominates the length-2 string db 8" in which dR is 
labelled th . (etc.)': the abbreviatio=ed &re shzld 
be self-erp 3 anatory. (Cf. also the prime on 'IE1 in rule R3, 
used to distinguish two nodes each labelled IE.) 
(i) if 
is the left sister of S and some NPi 
(1 
- i < - n) is realized as wh, w then - Ref(NP.) 1 = - R~~(NP~)T 
(ii) 
if there is a referent la6elled A# P and immedi- 
ately dominating g, . . . r where irql = Ref (NP,) , = 
-31' - 
- Ref(m2), ... , and 
= R~T(w n ) , then - Ref (s) = 1%) ; 
(iii) if no zuch referefit as in (ii) exists, then 
it is created, and - ~ef (S) = {+3 . 
(~7) 
If an S dominated by an IE node immediately dominates 
NPl P& NP2 ... NP 
(n ) I), where P& is realized as P, and 
n - 
N 
if, for some n i (1 
- i 
- n), mi is realized as wh, then Ref(S) 
r\yr 
- 
I 
is the set of all referents such that, for some referent % 
labelled P and immediately dozinating some string of referent6 
w 
, 
... , zLe Ref(NP.) - if 16 ;id n - and a# - i and r 
= gX 
iL D -2. - 
if a = - i. 
(R8) 
If BIP immediately dominates NPf 8, then - Ref(~l?) = - Flef(NP8) 
if NP is not dominated by an IE node; otherwise - R~~(NP) = 
Ref (W * ) n Ref (S) . 
- - 
(Rg) 
If a Noun node realized as N is not dominated by an IE 
ad 
node then Noun creates an individual referent - r and a referent 
labelled a N immediately dominating -3 r and - ~ef (~oun) = {gj ; 
otherwise - ~ef(Noun) is the set ~f all §(N) referents in the 
N 
topicon. 
(~10) 
Whenever a new referenk is created it becomes the curr- 
ent foc.us. 
Po illustrate the op&ration of Int 
-mg ' 
1 shall consider 
a sample sentence and a sample topicon-state. The sentence is: 
(18) 
Be man wno c- JohnB s fish, who was bald, knew' that 
hhMr-- ------- 
you love the teacher who bought a horse. 
+------- 
Sentence (18) has the foil-owing semantic representation (as 
usual I ignore tense for simplicity). I omit the superscripts 
from 'Pr' nodes, since they are obvious, and I subscript cer- 
tain nodes for later discussion. 
The topicon state to which (19) is input is assumed to be 
as in (20) below (without the material drawn in dotted lines), 
with the current focus at r 
(indicated by concentric circles): 
45 
The- owner of the topicon diagrammed in (20), to whom (19) is 
addressed, is represented in (20) by g5: he is a man called 
Dick who has caught and eaten a fish, and who loves the denot- 
atum of s7, who is a woman teacher who has bought a horse. 
The denotatum of g2 is a man called John who has also bought 
a horse and has eaten a fish which was caught by the denotatum 
'of El,, a man teacher called Tom, who loves the same woman as 
Dick. 
We now use mles Rl-R10 to interpret the nodes of (?9), 
beginning with the leftmost interpretable leaf (since the mater- 
ial on the left of (19) is what is heard first). 
Nounl is dominated by IE, so by R9 - Ref(Noun,,) = iz,, , g53; 
hence by R1 - ~ef (NP2) is also jz1, z2, Similarly - ~ef (9) 
is Er2\, so, tripially, by R2 Ref(IE4) - is {r2'). . R~~(NP~) - is 
T 
r 2; by R3, since % is two edges from 2 while I& is 
-3' -6 
eight edges from - r2, - Ref (IE6) is fr3] - (John1 -- s fish denotes the 
fish that John ate, on this omasion). By R7, ~ef (S7) = is,) 
(only Tom caught the denotatum of 3); so, by R8, - R~~(NP~) 
= )E, 9 2, z53 n [z~], i*ea jgq) 
and by R2 and R1 - R~~(NP~) is 
also 3 II rl) . 
By B6i, - ~ef (NP,,~) = f g,) . 
Sq is not dominated by 
an IE node, so by R6iii r is created with the label bald 
-30 -9 
dominating gl, and by RIO- the focus shifts to -30' r 
BY R8 9 
~ef (NPq2) = Ref (NPq) = {g,]. 
- 
- 
You is a deictic which always refers to the referent repre- 
/YHC 
senting the addressee, so - Ref(NPq3> = . 
- ~ef (NPq4) = {q, g7]- 
- lief (qs) = is, +I; both cq8 
~9 dominate pairs of 
referents the second member of which belongs to _I R~~(NP?~), so, 
B7, Ref(Sq6) " { f?3, and by R8 - ~ef(NPq~) (and hence 
~ef(tXP,~)) = By RGii, Ref(S ) = {s5'J. Finally, by 
- - 49 
RGiii, SZ0 create's a referent q1 labelled know and dominating 
- 
) 
and the new focus is at r 
(9 45 9 -3'l 
Notice that8\, were it not for the appositive clause who 
- 
was bald, the phrase that you loved the yy teacher in (18) 
-- ---- - 
would be redundant. !he initial focus was at r (the previ- 
45 
ous sentence had been You love the ym teacher, say); the 
w-- P 
sentence !Che man who cst John's fish knew it would serve as 
-vb--- -7-- 
well as The man who cm John's fish knew that =love the 
--- ---- -- 
-teacher or ... that you love her to create the referent 
- NH.-ymr.-- 
+l 
However, the appositive clause who was bald shifts the 
--- 
focus to r 
-30 ' 
so my theory predicts that it in the sentence 
* 
The man who cat John's fish, who was bald, knew it will be 
&wv--- ------- 
taken to refer to r rae'her than to r 
-30 
-- 
-25 
i.e. to denote the 
Q 
fact of his baldness rather than that oS Dick's loving the 
teacher. Intuitively this prediction seems correct. 
The relation Suc 
-Eng ' 
which determines which possible next 
statis Jmg can move to from any given state independently of 
input, will correspond to the rules of inference in the semant- 
ic description of English. Thus, suppose there is a rule 
'x fish & g; catch x -+ x die a in English (i. e. suppose it is 
-- -- -- 
part of the meMng of the words fish, die, and catch that a 
- - - 
fish dies if it is caught); then the topicon of (20) will be 
liable at any time to acquire a referent labelled die and dom- 
/\hN. 
hating r or , since each of these have the property #(fish) 
-3 - 
and occur as second argument of a referent labelled em. 
Clearly, Lg will be a non-deterministic automaton: the 
single rulerof inference mentioned permits two alternative 
successor states for (20). Anydne with experience of construct- 
ing deductions in formal logic bows that there are typically 
a large (though finite) number of ways of continuing a given 
derivation; similarly, the rules of inference for a natural 
language will no doubt permit many.posaible successor-states 
for any given state. 
If the process of moving throue states 
under the control of the successor-stale relation is .to be the 
reconstruction within the topicon theory of the pretheoretical 
notion of thinkinq, this characteristic seems desirable: 
we 
do not feel that human thought flows along deterministic 
channels. 
26 
18. Although the effects of most changes of state in the 
cases of the machine-language discussed in 82 and of APL were 
confined to the automata themselves, in both cases certain 
state-changes were associated with action by the automaton on 
its environment. Thus, whenever an APL-state acquired an 
object named -3 a a representation of the property of that obj- 
ect was, printed by the system on an output sheet of paper. We 
may imagine that action is linked to thought in this way also 
in the human case. Suppose some referent in a topicon 
represents the person who owns that topicon; then it might be 
that whenever, during a sequence of state-changes controlled 
by the successor-state relation, the topicon acquires a refer- 
ent labelled assert and dominating % in subject position and 
- 
some proposi*ional referent E, in object position, the owner 
of the topicon utters a sentence which asserts the proposition 
represented by zq. And, supposing 9 represents some person, 
say John, if a hit referent is created dominating ( z2) then 
- 
26~ do not intend this paragraph to imply any position 
on the determinism/fsee-will issue. If determinism is correct, 
then there will presumably be laws deciding which out of the 
various successor states permitted by the rules of inference 
of its language a given topicon actually moves into at a given 
time. Such laws lie outside the scope of this article. 
the topicon-owner hits John. 
27 
19. There are two obvious problems Connected with the notion 
that the referents in a topicon, which are supposed to corre- 
spond to the entities of which the topicon-owner is aware and 
the propositions he believes, are created by input sentences. 
The first problem is that no allowance is made for the poss- 
ibility that speakers are not believed. Thus, if the topicon- 
owner hears John, the denotatum of s2, say I bat a car yest- 
td. IU- - 
erdag, then according to the rules I have laid down his top- 
icon acquires a §(oar) ~rhk referent representing John's new car. 
But in practice, obviously the topicon-owner may choose to dis- 
believe John; what happens to his topicon in this case? 
The second problem is that it is simply untrue that a 
person acquires beliefs about the existence of entities and the 
truth of propositions only by being told about them, I may 
come to believe that there exists a red car either because 
John tells me that he has bought a red car and I believe him, 
or because I see the red car; similarly, I may come to believe 
that John bought the red car either because he tells me so or 
because I watched the transaction take place. The car may 
subsequently be denoted by the phrase the red car, and the pro- 
w-- 
position about it by the clause that John bought the red car, 
hcum-Ncrk*Nc-~- 
irrespective of whether the referents rewt.seht~~ the car and the 
proposition were ere-ated in response to speech or observation, 
27~hesa remarks may sound as if I an! treating humans as 
mindless robots -- 'automata1 in the pejorative, deterministic 
sense -- but quite the reverse: remember that the referents 
whose creation correlates with the topicon-owner's actions are 
brought into being by the process we have identified with think- 
ing. There is nothing disrespectful to our species in suggest- 
ing that our actiens are controlled by our thought. 
The answers to these problems are related. 
I suggest 
that the sight of John buying a car ia the kind of input to a 
person that ha8 the effect on his topicon which I have so far 
attributed to the hearing of the sentence John b-t a car (or 
- #--- 
John b=t the car if the car is one of which the topicon 
- - -' 
owner is already'aware): in other words, this sight creates 
a referent labelled buy and dominating referents representing 
- 
John and the car. On the other hand, hearing, say, Mary utter- 
ing %he words John - bmt -- a car, or hearing John say I b-t 
#v- 
a car, has a more complex effect than I have been suggesting: 
c.L- 
it creates a node labelled assert dominating the referent 
7 
representing Mary (or John) together with a new buy referent 
28 
- 
as already mentioned. 
I diagram the two cases in (21) and (22), on the next page. 
The part of the diagram in solid lines is the same in each case, 
and represents part of the hearer's topicon before the change 
of state. In (21) the dotted lines represent the effect on 
the topica of aeeing John buy a car; in this case, since the 
topicon owner sees the car, re may assume that he adds some 
further facts about it (such as that it is red) to his topicon. 
In (22) the dotted lines show the result instead of hearing 
John say I bst a car. In this case, the referent represent- 
- NW 
ing the car will be dominated just by the car node and the 
- 
node, since the hearer has no independent information about it. 
2%oss (19'70) and others have claimed that there is actu- 
ally syntactic evidence that JJ bm %sr has a deep struct- 
ure something like I sert tfi John ou ht agar. Ross's 
+ arguments are attacEed by raser WO beyson (1970), Batth- 
ews (1972). My theory is intended to be independent 
of Ross's 
claim, although the latter, if accepted, would possibly make 
my theory seem more plausible, 


Notice that, if John tells you he has b~ught a car, you 
may well doubt that he has bought a car but you are not free 
in the same way to doubt that John has asserted that he has 
bought a car. You may, of course, doubt the latter also -- 
'Did he keally say the words I thought I heard him say?', 'Can 
I be sure it was really John speaking?' -- but this is to doubt 
the accuracy of one's observations, as one may doubt whether 
John bought a car after watching him buy it, rather than doubt- 
ing the truth of what is said to one. 
Clearly there are enormous problems about how observations 
via the senses of a complex and continuous environment result 
in topicon changes corres@onding to the input of a discrete 
sentence: why should my view of John handing over a cheque 
on the car-dealer's forecourt change my topicon in the way 
which corresponds to the sentence John bat a car, rather 
- -- 
than any of the (surely) infinitely many other propositions 
which could be corroborated on the evidence of my current 
visual, auditory, etc. inputs? However, these problems are in 
no sense created by the topicon theory: these are already 
familiar problems in psychology and in the philosophy of science. 
(Cf. e.g. Hanson 1948, Gregory 1970.) Some process of deriving 
discrete propositional beliefs from continuous sensory input 
must occur, if observation is to be relevant to propositional 
knowledge at all. Since this process is known to exist indep- 
endently of my theory, and since I can make no contribution to 
maerstanding is, I shall not consider it further. 
Once we agree to treat simple declarative sentences as 
creating propositional referents labelled assert, there is no 
- 
special diMiculty in handling sentences performing other illoc- 
rltionary acts; e.g. - Shut - the door! - will establish a command 
P 
referent dominating referents representing speaker, hearer, and 
the proposition that the hearer will shut the door. 
Rules of inference may permit referents representing facts 
about the world to be created on the basis of referents repre- 
senting facts about assertions. Suppose, for instance, that 
there is a rule of inference which we might state as 
'x - a-t ;e, -- x truthful -+ ;E true'; - then a topicon including 
referents representing the fact that John is truthful and me 
fact that John asserted that he bought a car will be able to 
move to a state in which the representation bf the proposition 
asserted by John is &true), - as shown: 
Similarly, one can imagine thaf there might be rules of infer- 
ence taking a topicon from the state created by the reception 
of Skt the door! to a state which causes the topicon-owner to 
--- 
shut the door. However, here we come close to 
the point at 
which my theory in its present state breaks down; 
I defer ais- 
cussing this 
20. According to the theom I have sketched, English as 
gram@ language is not dissimilar to DL, SNOBOL, etc, 
resembles the latter in that its states consist of arrays 
~bjects &awn from a specified class (although the precis 
structure of the arrays is different as between English a 
the artificial programming languages, as it ie between the 
latter themselves), and io. that the structural descriptions of 
Its sentences include a subclass of nodes which pick out obj- 
ects from the current state and another rsubclass which add new 
objects to the current state. English differs from &PL, SNO- 
BO&, etc., in lacking identifiers, and in using the property 
of distance between objects in a state in order to identify 
objects. 
My theory is certainly inadequate to account for many 
quite elementary facts about English and other natural langu- 
ages. If may be that its deficiencies are too great for the 
theory to merit consideration. 
However, I would argue that it 
is rlorth according my theorg the temporary immunity from fals- 
ifbation to which Lakatos (1970: 
179) suggests new =,search 
propammes are entitled, in Gaae anyone can suggest modific- 
ti*Xons wfiIcB preserve its-ga&goints while removing its 
4ef ects, 
21. 
Before discuseing the objections to it, let me mention 
a number of points to which my theory offers satisfactory 
soltatioas. 
In the first place, the theory is attractive simply becau- 
se it offers an answer (emn itthe answer eventually turns out 
to be wrong) to the question why humans should spend so much 
of' their time exchanging the abstract structures called 'sent- 
ences': unlike cultivating the ground or building houses, the 
utility of this occupation is not immediately apparent to the 
observer (Sampsan 1972a, 1975~ 133-6). In my theory, the 
exchange of sentences, like direct, observation 'of the environ- 
ment, helps humans build up a complex but finite 'map-' Or 
'model' of the world, a model whtch can be described in quite 
* 
concrete terms and which controls the human's actions in mys 
which, again, in prindiple should be quite explicitly defin- 
able. 
The notion tmodel' is of course g- central one in the most 
influential current view of what language is for -- the view 
which explicates natural-language semantics in terms of 'model 
theory'. BU~ the 'possible worlds ' of model theory, unlike 
the topicons of my theory, are infinitely complex entities 
which can hardxy be taken to represent characteristics of 
finite human minds. Burthemore, in the model-theoretic 
approach to nratural language, the point about a true sentence 
is that it aenotee the Bregean truth-value True (see e.g. wppes 
1973); but if we think of the act of uttering a true sentence 
as the act of aenating the Tme, then it is quite unclear why 
people sBou?d utter sentences (let alone why tneg should utter 
one true sentence rather than another). 29 [~ootnote on p.59a] 
In my theory, to utter a particular true sentence to a hearer 
is to .make a particular change to his mental model of the world 
which gives the hearer more premisses from which to predict the 
consequences of his actions; thus, the more true sentences a 
person hears, the more rational his actions can be. 
theory has some more specific points in its favour. 
It explicates neatly some syntactic/semantic dist'inctions which 
seem rather pervasive in natural language bdt which have res- 
isted other attempts at explication: the definite/indePinite 
distinction in noun-phrases, the restrictive/appo&ive distinct- 
ion in relative cxaflses. Also it neatly explains the genitive 
oonstruction. Acoounts of the genitive which treat it in terms 
of possessioh (e.g. Suppes 1973: 382-3) are simply Waithful 
to the facts; it seems that any relation between the denotatum 
of the head Ell? and that of the genitive NP in a genitive phrase 
can be used to upderatand such a phrase, but this makes sense 
only if, for a given hearer, there are a well-defined, limited 
set of relations between denotata -- as qoy theory asserts. 
My 
theory .shows how it can be that definite descriptions succeed 
in referring even thougb,, contrary to Russell's theory of 
descriptions, the properties they mention are typically not 
iniquely instantiated -- and, more remarkably, in the case of 
pronouns no properties of the denotatum are. specifies at all. 
My theory ie also satisfying in its treatment of presupp- 
oeitione. 
Although the fact that sentences typically embody 
preeuppoektions has by now received much discussion in linguist- 
ice, it has not been clear how the distinction between aasert- 
2%or objections to model theory as a means of explicating 
natural-1-a e semantics and pragmatics, cf. Sampson (1974, 
1975b), Patts f 4975), Jaraing & Jardine (1975). 
ions and presuppositions should be represented in terms of syn- 
tactic or semantic descriptions. One proposal (cf. Fillmore 
1969, .&&off 1969, Horn 1970) is that the semantic description 
of a sentence should be a pair of objects, one element repre- 
sentingX9qe proposition asserted and the other the proposition 
presupposed. This proposal is problematical, first because it 
seems arbitrary - why should a sgmantic description of a sent- 
ence consist of a pair of propositions rather than one propo- 
sition or a 5-tuple of propositions? -- and, more seriously, 
because it is not clear that there is in general dust one or 
even any fixed number of propositions presupposed by a sentence, 
as there is just one proposition asserted by a sentence. Thus, 
the sentence: 
(24) 
The car which John bought ie red. 
---rhMCCrCr-chM.- 
presupposes that John b- a car, but also presumably that 
(ChhM &- 
there ie someone called John; John's car perhaps presupposes 
-w----- -- 
that JohD bought a car, but perhaps alludes to the fact that 
John was almost mm down by a car, etc. etc. On my theory, 
failure of presupposition occurs when the input sentence is 
undefined for the current topicon-state. (24) will fail if 
there is no triple z,, , r-+ of referents in the current state 
such that % ie (S) , is §(car), vCMk z3 is labelled s, and 
%3 
immediately dominates ( 2). To say that (24) presupp- 
oses that John bet a ear corresponds to the fact that if 
-- ck- 
the latter phrase does not pick out any current referent; by the 
rules R4RIO which define the function Xnt 
-Eng ' 
then $he sent- 
ence (24)l Fail t-o create a node labelled assert - -- i.e. 
will fail to make an assertion. Presupposition-failure is 
quite &;in to the case in APL when a - dscr node is realized as 
an identifier belonging to no current object, or as a function 
together with a set of arguments falling outs'ide the domain of 
that function; in the APL case, higher - asst nodes will fail to 
create corresponding APL-objects, as the sentence (24) fails 
to create either a referent labelled red or one labelled assert 
nMh - 
in a topicon lacking zqe3. 
I have argued elsewhere (l972b) that the reason why the 
Liar paradox does not render English inconsistent is that, as 
a matter of observable fact, a definite description in a natural 
language ia never taken by naive native speakers to refer to 
a propoeition asserted by the sentence in whic*h that defihite 
deeoription occurs, whether or not paradox would result if it 
were. 'Phi@ immediately raises the question why natural langu- 
agee should have such a convenient property. My theory explains 
this simply: in natural languages, as in APL, interpretation 
of nodee takes place not simultaneously but sequentially, from 
the boetom upwards. At the time the referent of the NP what I 
-- 
am now ea is to be locafed, the referent ta be cr-aated by 
w- 
the, eentenas cwhat I am now a is false cannot yet have 
wwHw- -- 
been brought into existence, so the possibility that the two 
letgh'b be identiaal does not arise. 
%!he theory aleo explaine the puzzling fact that 
(25) Soott: is iientical to the author of 'Waverley'. 
-Chrc----- -- 
~an be a u~eful thing to say, while 
"(26) 
Saott is identical to 6cott. 
----- 
can hardLy be so (Bussell 7905: 108; cf. e.g. Linsky 1967: 26). 
(26) will pick out the same referent, say g,, twice, and create 
a referent labelled identical and dominating (r r ) but we 
- -1 ' -?I 
may assume that a rule of inference of English states that any- 
thing is identical to itself, i.e. that a referent labelled 
identical may always be created dominating (r r ) for any 
- -x' --x 
referent - rx. Therefore the input sentence acEievZs nothing 
that the s~ccessor-state relation could not have achieved inde- 
pendently of any input. In the case of (25), however, if the 
hearer does not know that Scott is the author of 'Waverleyf, 
then the two NPs will pick out different referents r,,, 3 in 
his topicon and will create an iaentical node dominating 
- 
clearly'no Ehglish rule of inference will do this. 
r 1, 
9 4 
30 
The composite nature of the denotation relation incorpor- 
ated within my theor;tr copes neatly with the fact that natural 
languages use exactly the same syntactic devices for discuss- 
ing characters in fiction, and the like, as for discussing real 
entities. Anyone who has read Crime - and Punishment will under- 
stand the sentences: 
(27) Raskolnikov killed Alena Ivanovria. 
---- 
(28) ~lka Ivanovna killed Raskolnikov. 
---- 
and will agree that the former is true and the latter false. 
30~trictly speaking, (25). will create an assert node ,dom- 
inating the ref @>pent representing the utterer m) and the 
tical --- node mentioned. We may assume that one of 
,a Sue,_ lays down that when two distinct node 
the rule 
phrases 
are identical) a new state may be formed in which r and r' are. 
replaced by a single referent connected with all tEe refEents 
to-which either - r-or - rt were linked. 
Yet, in the case of formulae of the predicate calculus such as 
f(a, b), f(b, a), if a or b lack denotation then the formulae 
-3 - IL - LI II) 
as wholes seem to be either both false or both meaningless, 
but not interestingly different. 
Reichenbach (1947: 549) has 
offered a logic which includes representations of sentences 
about fictional entities, but in his system the symbol-arrays 
corresponding to NPs having fictional referents are quite diff- 
erent in kind from those corresponding to NPs having real refer- 
ents. There is no trace of such a distinction in the syntax 
of natural languages. In my theory, the NPs Raskolnikov and 
Richard. Nixon work in exactly the same way as each other -- 
w- 
they each pick out one of the referents in the hearer's topicon 
-- so it is natural that the NPs are syntactically parallel. 
The fact that the referent of Baskolnikov will have the proper- 
ty $(fictional) while that of Richard Nixon has the property 
P -- 
§(real) - is no mode reason to distinguish sentences (27) and 
(28) from sentences about Richard Nixon and Spiro Agnew syntact- 
ically than is the fact that the referent of Raskolnikov has 
the property J(~ussian) while that of: - Nixon has the property 
§(~merican). - 
31 - 
3'~he topicon theory thus seams to make some sense of the 
ontological views of Meinong (79l3) and the early Russell (cf. 
Linsky 1967: 2). Meinong was troubled by the truth of e.g. 
(i) Pegasus does not exist. 
---- 
since, if Pegasus really does not exist, there appears to be 
nothing which (i] can be about, and thus (i) cannot make a true 
statement. Meinorig therefore suggested (382-3, 491) that, 
although it was true of only .some definite descriptions that 
their denotata actually existed, the denotatum of any'de~inite 
description had quasi-existence, and this was enough-for an 
entity to serve as the sub~ect of a statement. In our terms, 
to 'denote a quasi-existent object1 is to refer to a referent; 
to 'denote ,an existent~ob~ect~ is to refer to a referent having 
a denotatum. 
Finally, my theory suggests why there are three categories 
of Austinian 'speech acts'. Austin (1962) dist'inguished (not 
consistently, admittedly) between locutionary acts (speaking), 
illooutionary acts (doing something, e.g. giving an order, - in 
speaking), and perlocutionar~ acts (achieving some effect, e.g. 
causing the hearer to perform an action, through speaking). 
(A number of current commentators on Austin would not agree 
with presentation of his distinctions; however, 
believe 
my discussion is faithful to Austin's own views in much of - How 
to Do Things with Words.) Why should there be just three 
_1 - 
categories of speech act, rather than two or four? Some schol- 
ars have suggested that the three-category analysis is incorr- 
ect; but I would support it. Consider the various consequences 
speaking. the first level, sound produced ; the pro- 
duction of this sound is a locutionary act. If the sound is a 
well-formed sentence of English which is defined by the input 
function for the hearer's topicon state, then that sentence 
produce6 a specific effect on the hearer's topicoll: the pro- 
duction of this effect is an illocutionary act of the type 
defined by the label of the topmost new referent. Thus, if the 
sentence adds to the topicon a referent labelled assert the 
%Puw--' 
illocutionary act is one of assertion; the 'misfiring' of an 
illocutionary act, as when a sentence syntactically in declar- 
ative form fails -t:o make an assertion because one of its defin- 
ite descriptions fails to refer, corresponds to failure to 
create an assert referent in the hearer's topicon. (We have 
- 
seen that, when a subordinate node cannot be evaluated, process- 
ing of the phrase-marker stops.) The new topicon state may 
lead other t opicon states perhaps, to actions the 
hearer's part, via the successor-state relation: the product- 
ion of such effects may be identified with Austin's perlocution- 
ary acts. 
My theory predicts that the illocutionary force of 
a given sentence should be well-defined and drawn from a finite 
class of illocutionary types (corresponding to the possible 
labels of sentential phrase-marker roots), while 
(since 
ma; 
is non-deterministic) the perlocutionary effects may be many 
and various; this seems to accord with Austin's discussion. 
32 
22. 
Having presented my theory and discussed the respects 
in which it seems successful, I must now discuss its many inad- 
equacies. Some aspects of English have been omitted from the 
present account simply for the sake of brevity; I believe 
there is no difficulty of principle in expanding my account to 
handle e.g. plurality, co-ordination yvith and, prepositions, 
- 
adverbs, modality, and most subordinate clauses. But a number 
of English constructions present greater problems. These - 
include, for instance, negation and universal quantification. 33 
For negation, one might think of treating not.as a monadic 
- 
predicate whose argument is a proposition, so that, e.g., John 
- 
did not bz a car would have the same effect on a hearer's 
0vuu'-- M- 
topicon as - John ba a oar, followed by the creation of a 
0-MM 
32~n the framework of my theory, the ~locutionary/illocut- 
ionary distinction becomes rather parallel to the distinction 
between seein and seein as which exercised Wittgenstein and 
other ph d osop ears. *e duck-rabbit picture (cf. Hanson 
l958) if light reflectedprom that picture stimulates my optic 
I eee it as a duck, if this stimulation leads to the 
:::;ion of a ~(ZECI~) - re*erent in topicon. 
33The fact that these two constructions should both be 
problematic is no coincidence. We can handle sentences whose 
translations into predicate calculus involve existential'quant- 
ification, e.g. '&r)(c(x) & b(;i, 5))' for J bat a car; 
' -3x-@ is interchangeiibre wiFh x , 
80, i& could hgnG 
negarion, we should be able to ha'dle universal quantification. 
not referent dominating the bx referent just created. But 
F-f" 
then it would make sense to speak of the sr which John didn't 
hML 7-- 
bx , 
n 
whereas in its commoner sense John did not bs a car does 
--- -- 
not imply the existence of any particular unbought car. Again, 
one might think of interpreting e.g. All love John as 
0uu-- -- 
creating a love referent dominating each pair (r r ) of refer- 
- -1 ' -2 
ents in the hearer's topicon such that r is (r) and r 
-1 7 -2 
is the referent representing John. But this would be quite 
inadequate: the sentence is about, not the particular girls 
the hearer knows of when he hears it uttered, but all girls 
whatsoever. A related point is that the meory does not handle 
the generic sense of definite NPs, as* The ele_phant is a 
- .. - ML- 
noble beast. 
-- 
34 
Other difficulties are with yes/no questions, 
the between and interpret- 
ations of complement clauses (- d* - was uated v. 
dancin@; - was ) with trF-functional connectives 
such as if, or, with conjunctions such as but v. and, 
rm, An+ - - 
v. because whose appropriateness depends on a given proposition 
7 
constituting evidence for or against the truth of another, and 
with comparative and superlative constructions. 9> 
340ne approach to these problems might involve introducing 
referents representing muniversalsf (in the logical sense), so 
that for an individual referent to have the property §(girl) 
or g(e~) would be for that referent to be one of mun- 
ordere set of individual referents dominated by the referent 
representing the universal irl or e-t (in which case the 
notion of 'labelling' proposl % xonal referents might be dropped). 
Then the propositional referent created by All irls lov John 
would link the referent representing the unlversa -+?F wi h 
the individual referent $or John. It remains to be seen whether 
an adequate eolution can be produced along these lines. 
"I am not sure whether the opaque/transparent reference 
distinction belongs on this list. I am inclined to explain the 
Another deficiency of the present theory is that there 
are phrase-markers generated by (17) whose effects are not 
specified by R1-10, e.g. phrase-markers in which NP is rewrit- 
ten wh S. I hope that an account 
of the unexplained construct- 
ions in the above list may turn out to involve uses for the 
phrase-markers which are not handled by R1-10, 
but I have no 
idea whether this will be so, 
23. I am not at present clear how to adapt my theory to acc- 
ount for these constructions, and, since they include some very 
basic ones, my discussion of the nature of the automaton under- 
lying a hearer's linguistic abilities may be worthless. How- 
ever, although my theory may be rejected, it would seem that 
there must be some adequate theory of the human comprehension 
of language in terms of automata whose states are of finite 
complexity. An account "of natural-language semantics in terms 
of infinitely large sets of, in general, infinitely complex 
possible worlds cannot be the whole truth about how finite 
human beings understand language. I hope, therefore, that the 
inadequacies of the above account may spur others to improve on 
my work. 
two senses of e.g. John is lookin a the dean by saying that 
- -- 
the hearer's topicon wll~codreferents representing refer- 
ents in John's to icon (as well as referents representing- 
'F. 
ects m Ehetsl % e world). and that while. in the trans~arent 
- 
sense, the dean picks out- one of the ordink referents, in the 
-- 
opaque sense it picks out one of the referents. representing 
John's referents. But clearly this needs to be spelLed out 
more fully than I have done. A D. Phil. thesis currently being 
prepared by Ephraim Borowski of Hertford College, Oxford, incorp- 
orates some promising lines of attack on a number of these 
problems. 

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