I National Bureau of Standards Reference book not to be

t"':o n from

y.

^ecknical <Vtete 258

A PREREQUISITE

TO THE UTILITY OF MICROGRAMMARS

WILLIAM C. WATT

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards is a principal focal point in the Federal Government for assuring

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listing of its four Institutes and their organizational units. Institute for Basic Standards. Electricity. Metrology. Heat. Radiation Physics. Mechanics. Applied Mathematics. Atomic Physics. Physical Chemistry. Laboratory Astrophysics.* Radio Standards Laboratory: Radio Standards Physics; Radio Standards Engineering.** Office of Standard Ref- erence Data. Institute for Materials Research. Analytical Chemistry. Polymers. Metallurgy. Inorganic Materials. Reactor Radiations. Cryogenics.** Office of Standard Reference Materials. Central Radio Propagation Laboratory.** Ionosphere Research and Propagation. Troposphere

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NATIONAL BUREAU OF STANDARDS

Technical Note 258

ISSUED APRIL 19, 1965

A PREREQUISITE

TO THE UTILITY OF MICROGRAMMARS

William C. Watt

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, Government Printing Office

Washington, D.C., 20402 - Price 25 cents
CONTENTS

Pa^e

ABSTRACT 1

0. INTRODUCTION 1

1. EXTRAPOLATION, AND THE AVOIDANCE

OF ITS PITFALLS 3

2. CONCLUSION AND PROSPECT 20

REFERENCES 22

IX
A PREREQUISITE TO THE UTILITY OF MICROGRAMMARS

William C. Watt

This paper takes up the question of a hitherto-ignored

obstacle to the useful functioning of microgrammars in

artificial intelligence systems. This obstacle consists of the

difficulty of "staying within" the microgrammar in man-machine

communication, a condition rooted in the fact that microgrammars

produce a "language" which consists entirely of English sentences,

but of only some English sentences: and it is hard or even impossible for the microgrammar-user to remember which sentences

he is allowed to use. Besides raising this problem, and studying it in some detail, I indicate what steps may be taken to

overcome it; these are such steps as lend the microgrammar

more "extrapolative symmetry".

0. Introduction

Many people whose research makes essential use of large digital

computers can 'converse 1 freely with their machines without feeling

hampered by their being unable to converse in their native tongue.

For example, mathematicians presumably feel little need to express

in English their instructions for high-speed computation, since ALGOL

2 serves this purpose quite adequately ; nor would they react with anything but annoyance if the computer were given to responding in English,

rather than in mathematical expressions and organizations of such

expressions. However, in other situations, the unavailability of

1 This paper is one outgrowth of a long-term research project at the

National Bureau of Standards. The ideas presented here have been threshed

out in the course of numerous discussions with two other participants

in this project, Russell A. Kirsch and Robert W. Hsu, whose devil's

advocacies it is a pleasure to credit here.

The research on which this paper is based has been supported by the

National Institutes of Health, under agreement NB 05613-01. This support

is gratefully acknowledged.

2 I will continue to use ALGOL to exemplify the large multi-purpose

programming languages; obviously another, such as FORTRAN, would have

served about as well. In the same fashion, I will continue to use English as my example of a natural language.
English as a man-machine language is felt rather keenly, for either or

3 both of two reasons . First, there are many instructions (and queries)

which are better expressed in English than in ALGOL, and many answers more suitably phrased in English than in the form of data-structures.

And secondly, those who want to communicate with the machine may not

be conversant with any of the machine languages, and may (as is generally the case) be at a point in their professional careers where taking

off the time required to become proficient in such a language would be

out of the question.

Machine languages can be extended, of course: ALGOL could be

given the power to express more than it now does, and could perhaps

be progressively extended so that in the end it would be able to

express anything expressible in English. However, such a procedure

would have the secondary effect. of making ALGOL more and more difficult

to learn: we can lessen the first of ALGOL'S liabilities (its deficiency

in expressive power) only at the cost of greatly increasing the second

(its relative 'distance' from the user).

There are good reasons, then, for wishing that English were

available as a man-machine language. But for English to serve this

function it must first have been described by a quasi-complete grammar

((qcg)), roughly analogous to the syntax of ALGOL; and this qcg, moreover, must be in a model to which computers are accomodated. Despite

4 intensive efforts at more than one linguistic center this first

condition has not yet been met, though it may be in the relatively

near future ; enough is already known about English, however, to indicate

3 I will argue in another paper that this lack should be felt even more keenly, in these 'other situations', for more compelling reasons which as yet are not widely recognized.

4 Chiefly at the University of Pennsylvania, at Harvard, and at M.I.T.;

see especially ((3)) for results of the research at Penn. Numbers

in double parentheses (( )) refer to items in the appended list of

References

5 On the other hand, an 'English grammar' in the most inclusive sense

of this term--a device which simulates speaker-behavior in its linguistic

aspects (if these can be delimited) is hardly even contemplated at present, except to be shelved as being forbiddingly, perhaps impossibly,

difficult.
that meeting the second condition getting a qcg into the computer

may be extremely difficult, for English in its 'entirety' (probably

any natural language) requires a model of very powerful capacity . Inevitably, then, attention has occasionally turned toward the

practicability of constructing useful computer grammars for portions

of English. There is no doubt that such partial grammars can be

written such "microgrammars", as I will call them in fact

several, of varying sizes, are already in existence . I believe that

it is not generally realized, however, that there is a formidable

obstacle in the way of these microgrammars ' being of real use to a synthetic intelligence system.

This paper examines that obstacle and indicates how it may be overcome

1 . Extrapolation, and the Avoidance of Its Pitfalls .

A Microgrammar allows its user to employ English sentences in

communicating with the computer; but, by definition, it allows him to

employ only certain English sentences. The user is invited to speak

In his native tongue, but he is also enjoined to choose his sentences

carefully lest he express something which the microgrammar is powerless

6 This question has been widely treated in the literature, most

concisely in ((2)). I place the word "entirety" in quotes because the

boundary-line between 'English' and ' non-English' is by no means sharply

defined. Even when a large number of utterances have been satisfactorily ranked by decreasing grammaticality, it is not easy to set that

threshold below which the utterances are so ungrammat ical as to be

unEnglish.

7 Of those I am acquainted with the most highly developed are the large

microgrammar written by Jane J. Robinson at the RAND Corporation ((9)),

and the smaller PLACEBO IV, written by the present author at the National

Bureau of Standards ((11)) and ((12)). It should be emphasized that e.g.

((3)) covers much more English than either Robinson's grammar or PLACEBO

IV; but ((3)) shows not a microgrammar but hopefully a massive segment

of a qcg. The difference between these two types of algorithm is made

reasonably clear in ((11)).
to analyze: which therefore the machine is powerless to act on. Clearly then the user must somehow become familiar with the set of

allowable utterances.

To draw a comparison, let us suppose that an American archeologist

is introduced to a French colleague who he is told "speaks a little

English", "enough to conduct a conversation about archeology".

Realizing that he and the Frenchman share only a very small portion

of English, and wanting to waste as little time as possible, the

American will want to learn quickly what the limits of this shared

portion are. If he is sensible, rather than launching into a discussion

and taking his chances sentence by sentence that he will overstep the

portion's boundaries, the American may go about his task systematically.

Restricting himself first of all strictly to archeology, so as to limit

vocabulary, he may hazard one or two simple sentences; finding these

understood he may chance a few more along the same lines; and thus by

extending little by little the bounds of discourse, he may succeed

in gradually marking off an area of English within which he and the

Frenchman can converse, with but very few wasteful oversteps. The

intuitive 'system' he will have made use of is one which it would be

interesting to know more about; for the moment at least let us be

content with calling it one of 'rough extrapolation', a process exem- plified by the reasoning: "x and y_ are English sentences and are similar,

and x was within the bounds of the shared portion of English, therefore

_y. must be" . To illustrate the results of such extrapolation, let us glance

at the first sentences which such a hypothetical American might produce

when asked to summarize his own views on Maya-Toltec interactions.

1. "Teotihuacan strongly influenced the Guatemalan highlands."

2. "The Toltecs dominated the Yucatecan Maya."

3. "The dominance of the Toltecs decreased during the Mayapan

period ."

4. "This decrease coincided with the flowering of the Guatemalan

City-States, Iximche for example."
5. "Whether or not this coincidence was meaningful, is open to

question."

Note that, over this series of sentences, there is a progression

toward greater complexity: of structure and of relation to the

g preceding sentences . The first sentence typifies the English SubjectVerb-Object sentence, where both Subject and Object are nominals

The second sentence has the same structure. In the third, the Subject

is a nominalizat ion of the verb of the second sentence; the Subject of

the fourth sentence is a nominalizat ion of the Verb of the third. In

the fifth sentence, the Subject is in part a nominalizat ion of the

Verb of the fourth, but the subject has been complicated by the

"whether or not" construction. (Needless to say, this rough description

of these inters entential relations is not meant to be taken very

seriously.

)

It is fair to say, I think, that our hypothetical archeologist

9

did not do a bad job. He adhered to as simple a vocabulary as he could , and he kept his syntax 'simple' in some untutored meaning of that

term. I think it almost self-evident, however, that if he continued

the process much further, he would soon run afoul of the Frenchman's

limitations. In fact, he may have already done so in sentence five:

the Frenchman may be unable to parse the "whether or not..." Subject,

and may thus fail to understand this sentence . The American in this

8 Of course I do not mean to imply that, in an actual conversation

under the stated conditions, any such progression would appear so dramatically, in the span of five sentences. Still less do I claim that

in any conversation complexity could or would increase unendingly. I mean only to exemplify a process which we might well expect to find

in use under the stated circumstances. If this rather casual example

be taken as an hypothesis, it should not be a very hard one to test.

9 He can also be said to have profited from his knowledge of French,

in using the cognate "decrease" rather than the equally natural "wane".

10 The Frenchman's total inability to understand a sentence which

he can parse only in part, will be questioned below.
case would be forced to backtrack, to try a simpler way of conveying

his thought. There is no good reason to believe, in fact, that the

American will ever entirely cease to overstep the boundaries of the

Frenchman's portion of English, unless he restricts himself to so small a vocabulary, and so scrawny a syntax, as to render quite easy

his observance of the limits, but almost impossible his transmission

of information.

A microgrammar, too, 'understands' only a small set of English

sentences; and in this respect the user of a microgrammar is in the same fix as the American archeologist sketched above. He must watch

himself carefully lest he trespass on forbidden territory, while at

the same time uttering new sentences in order to get his message across. Naturally if the microgrammar is extremely small the user can simply

memorize the list of its allowable sentences; if it is moderately small

he may succeed in memorizing its grammatical rules, and perhaps

(this is less likely) in composing sentences which accord with those

11

rules . In fact, however, a microgrammar of such limited scope

could scarcely be useful as a vehicle of expression: it would

probably be no more useful as such than the sort of linguistic apparatus

12 one can acquire by thumbing through a tourist phrasebook . Short of

memorizing the sentences and/or the rules, the user must either

gradually infer the boundaries of allowable speech, as our archeologist

must; or he must be given a microgrammar which has been designed in

such a way as to have boundaries which the user very seldom oversteps.

11 No matter how small, of course, if the microgrammar contains

recursive loops the set of specified sentences, being infinite, cannot

be memorized as such.

12 Many computers have been programmed so that their users can type

in such instructions as 'PRINT' or 'COMPUTE' or whatever. Using English

words in this way hardly constitutes using a microgrammar, - if that

term is to mean anything - any more than a Dubuque housewife buying a 'chaise longue' is using French.
Of these two alternatives, clearly the second is preferable, for the

first would be at best a painful process, and in effect an interminable

13 one To point up the difference between microgrammars and ALGOL, we may

note that the Frenchman of our example has much less trouble staying

within the bounds of the portion of English he shares with the American

than the American does. That is, the Frenchman too will tend to

extrapolate into areas beyond the boundaries of that portion, both

on the basis of what English he knows and on the basis of French,

insofar as he feels that his fragmentary English "corresponds" to

French. And the Frenchman will, from time to time, by accident hit

on a well-formed English sentence. But obviously his situation is

quite different from the American's: he is extrapolating into a foreign language, on whatever basis, and is presumably almost always aware of the fact that in effect he is "creating" new and unfamiliar

14 expressions ; while the American, for his part, is comparing two

sentences from a language he is thoroughly familiar with, and deciding

that the second is enough 'like' the already-accepted first to

warrant trying it. The Frenchman I think will be less likely to

extrapolate, he will be more self-conscious about it; it should then

be far easier for him to stay within the boundaries of the English

portion he shares with the American. His situation is not unlike

13 Actually a third alternative might be thought of, one suggested by

our example of the American and the Frenchman. That is, just as the

Frenchman does not really have to understand a sentence in its entirety

to get the gist of what's being said, so too a microgrammar might be

able to analyze whatever it is equipped to, ignoring the rest or dealing

with the remainder in accordance with the portion previously parsed.

(In present practice if a sentence cannot be wholly digested, it's

disgorged.) This alternative is taken up again in a later paragraph, q.v.

14 More exactly, 'new and partly unfamiliar expressions' they must

be partly familiar in order for him to 'extrapolate' them.
that of someone who knows ALGOL: the ALGOL-user, too, must occasionally 'extrapolate 1 new pseudo-ALGOL expressions, on the basis of what

he knows about ALGOL; but in general he is less likely to do this

than the American is to extrapolate as 'within the shared portion 1

sentences he knows to be well-formed English utterances

In sum, the thesis presented here is that it is easier to

1 fi avoid extrapolating 'new' expressions than 'familiar' ones

If this is true, it will be easier to devise an ALGOL for careless

(i.e. human) users than to devise a microgrammar for such users:

fewer mistakes must be anticipated.

Which returns us to our main point: if a useful microgrammar is

to be provided, one must be devised which allows in advance for the

extrapolation it will inevitably provoke; a microgrammar which relies

15 This point should not be overemphasized, however; ALGOL-programmers

do after all make mistakes (not all of them extrapolative); the lesser

likelihood of their doing so is of no great service to them.

16 I should note that a point similar to the one I have made with

my hypothetical American and 'shared portion' of English, has been

made by F. W. Alt using for his example an English-speaker trying

to stay within Basic English. Thus, on page 137 of his Electronic

Digital Computers ((1)), Alt speaks of "Basic English, that artificial

language in which only a small number of English words are used:

it is easy to learn for someone who does not known (sic) English,

but it Is quite difficult for an English-speaking person to learn

to avoid the forbidden words." As opposed to Alt's emphasis on "forbidden words", however, I have tried to stress the element of

"forbidden structures". It is far easier to expand a microgrammar

so as to specify more "words" than it is to expand it so as to wellspecify more sentence-types. I should also point out that, although

both Alt's thesis (regarding words) and mine (regarding sentences)

are highly plausible, I know of no experimental verification of either, nor does Alt cite any. Such a test should be far from difficult to

devise, however.
on extrapolation as the only means of mastering it (since its rules

cannot be learned), must certainly provide for the liabilities of the

extrapolative process

To state this problem is to state in brief the problem of making

microgrammars which are already linguistically-adequate, useful for

artificial-intelligence systems.

What are the properties of an English portion which users can stay within — of "habitable" English fragments? One way of finding

out is to discover what 'extrapolative' mistakes are likeliest, for

this knowledge might be used to incorporate into a microgrammar the areas into which 'extrapolation' most often penetrates, thus making

18

the expanded 'anticipatory' microgrammar habitable

Without making any claim that there is an exact classification

of the kinds of 'extrapolation' to be expected, I think it might still

be profitable to distinguish between 'syntactic' extrapolation (often

19 paraphrastic) and 'lexical' extrapolation; and, under each of

these headings, between 'close' and 'loose' extrapolation.

17 The contradiction here is only apparent. If a microgrammar, no matter how much extrapolation it included, endlessly fomented further

extrapolation to the same degree, then our work would never be done,

and the 'extrapolation-including' microgrammar would be an impossibility.

From a given lexicon and a given set of rules, however, not all English

sentences are likely to be 'extrapolated'; very few, comparatively, are likely to be extrapolated often. On this assumption, at least, rests our hope of building a microgrammar which, 'providing for' high-frequency

extrapolations, facilitates the user's staying within the bounds of

its microlanguage.

18 It may also be possible to accommodate many types of non-extrapolative

mistakes — clerical errors and so on — but this possibility will not

be further discussed here.

19 But not always ('Here are some neurons' ^ 'Here is a neuron'); and

often a 'degree of paraphrase 1 must be admitted, informally, as in the

examples which follow.
Examples follow:

TYPE OF 'MISTAKE' EXTRAPOLATING FROM: TO:

1. Syntactic, close Is a neuron here? Is there a neuron here?

2. Syntactic, loose Is a neuron here? a. Are there any

neurons here?

b. Do there happen to

be any neurons

here?

cCan you fina any

neurons here?

a. Do you see anything in the way of

a neuron here?

3. Lexical, close Is a neuron here? Is an astrocyte here?

h. Lexical, loose Is a neuron here? a. Is a cell here?

b. Is a larynx here?

c. Is a gizzara here?

a. Is a zeppelin here?

I wouia rather not aevote very much attention to these aa-hoc

aistinctions, but a brief exposition might be in oraer. All of the

cases of 'syntactic' extrapolation are pariphrastic, at least to

20

a very high aegree: the user, on the basis of what the microgrammar

20 That is, their extensions largely overlap.

10
has already accepted, analogizes as equally acceptable a similar

sentence which to him means more-or-less the same thing, under

21

identical contextual conditions. In the case of 'close' syntactic

extrapolation, the paraphrase is first of all seemingly exact, and

is also extremely close in structure to the original; in fact, I 22

see only a stylistic difference "between them. I think these first

two sentences are also closer together semantically than are the

first and any of the 'loosely ' -extrapolated sentences; hut since

this point is unimportant I have not tried to devise any tests to

subject this claim to scrutiny. The 'loose' syntactic extrapolations are ranked by increasing 'laxity, ' or difference in form from

21 Many of the 'extrapolations' characteristic of the situations

here under view must be cases of analogy: for example, where

sentences 'a,' 'b, ' and 'c' are in the accepted portion, and

'b ' is similar to 'a' in some (naive) way, then an 'analogical

extrapolation' might produce some 'd, ' presumed also to be

within the accepted portion, on the analogy "a is to b as c is

to d." Or, between two forms only, the analogy might be taken

as "^a is to the accepted portion as (the similar) b is." I want to avoid taking this point much further here, both

because the term "extrapolation" is less specific than "analogy,"

and is thus more suitable to the present status of this

research; and also because I want to avoid the implication that

the 'extrapolative ' process here treated is to be identified

with the process of 'analogical change' as studied by

diachronists, e.g., in ((6)). There are, to be sure, some points of apparent similarity between the two processes, but

it would be premature to attempt to state their kinship

I have also wanted to avoid bearing down too hard on the

'paraphrastic' elements here alluded to; for a more serious

study of paraphrase, see e.g. ((5)).

22 On the other hand, it might be contended that sentences like

"Is a neuron here?" are so deviant as to be non-English: I have heard an eminent linguist defend this view, which may well

be valid for his idiolect.

11
the original. (2a) is rather close in form, and may he identical

in meaning. (2h) is rather distant in form, and seems to involve

additional meaning elements; (2c) is at least as distant in form,

and has added mention of the addressee ("you"); and (2d) is veryfar in form and is couched in extremely informal style.

The cases of 'lexical extrapolation' involve substitution of

one word (^lexical item) for another. -* In the example of 'close'

lexical extrapolation, 'neuron' is replaced by 'astrocyte: ' both are

names of cells found in e.g. the human brain. In the 'loose' lexical

extrapolations the substitutions can be intuitively judged to result

in greater semantic distance, (4a) substitutes 'cell,' which is

a generic term for the class one of whose members is 'neuron;

(4b) substitutes the name of a quite different body-part, though

still preserving medical terminology; (4c) substitutes, again, the

name of a body-part, but in the vernacular; and (4d) substitutes a 24

noun chosen practically at random.

23 In generative grammars like PLACEBO IV, the difference between

'syntactic' rules and 'lexical' ones is a difference only

between locations in the instantiative path: 'lexical' rules

are last to be actuated in generation, first in analysis

(parsing) . PLACEBO IV does not distinguish the lexical level

by pausing prior to reaching that level for a 'change -of -gears'

into a context-recognizing model; in fact only in the most

trivial sense can PLACEBO IV be said to have morphographemicizing

rules at all.

Even in grammars which do pause for context-recognition, however,

the difference between 'syntax' and 'lexis' needn't be verymarked, in the sense of there being artificial 'levels' imposed

on the grammar.

24 Or, more accurately, at random from the set of inanimate

count -nouns.

12
From the above discussion I think it is obvious that if no

constraints whatever were placed on the use of the microgrammar,

and if the user were at all inclined to stray into the areas

delimited above: that there would be little hope of containing him

within anything short of an English qcg. However, the user will

not normally be so reckless. Factors tending to restrain his

discourse are:

1. The fact that he is seated at a computer console;

2. His being there to discuss a given field of knowledge;

3. His having been warned that his addressee, like our

hypothetical Frenchman, 'understands a little English.'

The first and third factors will operate together with the

primary effect of limiting the syntactic rules the user calls into

play. In a formal situation he will be less casual than if he were

addressing an idler in the Courthouse Square; his discourse would

already be somewhat restrained if he were addressing a human

colleague. Also, seated at the keyboard, and hopefully being less

than a practiced typist, he will tend to avoid lengthy circumlocutions and convolute syntax. The brevity of his expressions will be

increased still more, perhaps, by his knowledge that the computer

he is addressing is an expensive interlocutor.

The first and third factors, in conjunction with the second,

should serve to restrict the user's vocabulary. The extent to which

the second factor plays a role in this regard may well depend, of

course, on which field of knowledge is at issue; but it would be

13
mere guesswork to attempt at this time to give even a crude ranking

of professional dialects with respect to how much English each calls

25

on.

All of the factors cited above can and should he exploited by

the microgrammarian as facilitating his task. In particular, these

factors should serve to reduce to the vanishing point some of the

'loose' extrapolations listed above: (2b), (2c), and (2d) should

no longer be problems, and certainly (kc) and (4d) should not be.

(Ij-b) may constitute a problem in inverse proportion to the degree of

specialization of the user, or of the subject he is concerned with;

a general practitioner might have more cause to use the word

'larynx' than a neuropathologist, for example. Left as principal

problems, then, are four kinds of extrapolation: 'close syntactic,

least-lax 'loose syntactic; ' 'close lexical, ' and least-lax

'loose lexical.' It is probable that all of these will plague the

microgrammarian: and, barring steps to overcome them, the user of

the system.

25 English may be regarded as being composed of, or manifested in,

many different dialects (each In turn composed of, or manifested

In, many different idiolects) . There are a number of ways of

subdividing English into its dialects; these ways are mutually

conflicting. Chiefly, one may delimit dialects of area, of

class, and of profession. The first of these Is under extensive

investigation the world over, in the form of the many 'Linguistic

Atlas' projects under way. The second has received somewhat

less attention. The third has received still less; though

studies are often published (as in the journal American Speech ) of professional and cant terms, I know of no study of the

varieties of syntax distinguished by various professional

dialects

Ik
The most obvious way of overcoming them, and the dullest and

least practical, is to station a linguist at the user's shoulder,

instructing him to expand the grammar whenever its limits are

exceeded. Next most obvious, and extremely challenging, is to

provide a mechanical device to perform this linguistic service.

This device would analyze as much of the sentence as it could,

then integrate the remainder into the grammar (instead of merely

26

suppressing it) and parse the sentence in its entirety. The most

elegant and satisfying way of overcoming the difficulties, and also

one of some linguistic or at least psycholinguistic interest, is to

anticipate them in the microgrammar itself . To continue the example

treated above, a microgrammar which specifies "Is a neuron here?"

should also specify "Is there a neuron here?", "Are there any neurons

here?", "Is an astrocyte here?", and "Is a cell here?". And

therefore, of course, also "Are there any neurons here?", "Is there

27 an astrocyte here?", and so on.

26 The Klein-Simmons program described in ((7)) can be looked on

as essentially a device of this kind. Its computations (from

sentential context) are quite limited in scope, however

(without questioning the efficacy claimed for them); and a much

more powerful program would be necessary to carry out the

operations necessary to allow the computer to surrogate the

'over-the -shoulder linguist.'

27 Before we close this subject, perhaps it should be remarked

that in practice we could expect syntactic and lexical

violations to occur simultaneously; a user might well

extrapolate from "Is a neuron here?" to "Are there any

astrocytes here?", for example.

15
It would seem not unreasonable to group all of these factors

together as comprising a single prerequisite of 'habitable' micro28

grammars: a prerequisite we might call 'extrapolative symmetry.'

I do not propose to define this term very exactly here, but its

meaning should be intuitively obvious from the preceding discussion:

a microgrammar which has 'extrapolative symmetry' will contain no

extrapolative gaps, such as the omission of "Is there a neuron here?"

in an algorithm including that sentence's fellows. Naturally no

microgrammar will possess complete extrapolative symmetry for in

any case the term has been left indefinite enough so that this

absolute quality might be hard to recognize ; but the measure to

which it approaches this ideal will be, I suggest, the measure of

29

its utility for human users.

28 Symmetry as a general property has been much discussed as among

the desiderata of linguistic analysis. Harris ((^)) has treated

this desideratum with regard to all levels of analysis; more often it is treated with regard solely to phonological analysis,

where the doctrine has recently become somewhat controversial,

as see e.g. ((8)) and ((10)).

29 If the process of 'extrapolation' had been defined with any

precision we could discover whether or not a microgrammar (or a natural language) could have complete extrapolative symmetry:

whether, that is, eventually a point may be reached where new

extrapolations produce only sentences already in the language

(or microlanguage) . I know of no evidence to support either

this conclusion or its converse.

In any case it should be pointed out that PLACEBO IV obviously

lacks complete extrapolative symmetry; so also will its successors. I hope only that it will ultimately be possible

to produce a microgrammar which approaches 'complete

extrapolative symmetry 1 closely enough to significantly reduce

the amount of trespassing that takes place during use and

also the number of Injunctions that must be kept in mind by

users.

16
I have argued that if a given microgrammar has 'extrapolative

symmetry' in large measure, and if the user of that microgrammar

is mindful of the general constraints placed on him: that he will

be able to make new sentences without often transgressing the limits

of the microlanguage . In this respect his behavior, and his freedom,

will resemble those of the speaker of English, who also makes new

sentences without often transgressing the limits of the language.

It may be tempting to draw the inference that the way in which

English-speakers form new English sentences is somewhat akin to

the way in which mi c rogrammar-users form new sentences in the

30 microlanguage: that is, that both use an extrapolatory process.

Such a conjecture however has no bearing on the point at hand, which

is that regardless of what processes are used, the English- speaker

30 On the other hand there are marked dissimilarities between

the behavior of English-speakers and the (expected) behavior

of microlanguage -users. Not least of these is the fact that

microlanguage -users necessarily create their sentences in an

artificial situation, without ever quite forgetting that

artificiality; whereas English-speakers are scarcely aware that they are 'using a grammar' to produce their sentences.

For this reason, and for others, I would like to stop short

of making the above-cited conjecture.

IT
must be enabled to carry over into his use of a mierolanguage some

31

of the same freedom he has enjoyed in his use of English.

In insuring that his microgrammar have 'extrapolative symmetry,

the linguist's first task will, obviously, be to make certain that

for each sentence structure in the microgrammar, all of the common

paraphrasing structures are also included in the microgrammar.

Thus, if the microgrammar specified sentences such as "A neuron is

to the left of an astrocyte," it should definitely include

sentences of the form "There is a neuron to the left of an astrocyte,"

"An astrocyte is to the right of a neuron," and so on. (With respect

to increasing the utility of the microgrammar, it does not matter

that we have only a rough idea of what 'paraphrases' are; as native

speakers of English our 'rough idea' is likely to correspond to the

user's, and in any case the microgrammar does not label (for the most

part) any sentences as paraphrastic, so that if the linguist merely

tries to include all common apparently-paraphrastic sentence -types,

31 In the unconstrained 'everyday' situation a speaker is almost

totally unaware of the restrictions placed by English on what

he wants to say. (Whether this is because English is beautifully

adapted to expressing what he wants to say, or because what he

wants to say is conditioned by English, is a moot question.)

But what is more immediate to our present concerns is the fact

that under the same circumstances that speaker is almost totally

unaware of the restrictions placed by English on how he will

express what he wants to say. It is surely an essential part

of our linguistic habits that we are not constantly fumbling

for the right grammatical rule, in our effort to express some- thing or to correct a malformed expression. This is to say,

without putting any weight on a gratuitous assumption about the

English-speaker 's 'extrapolative' activities, that if such

speakers did make all new sentences on an 'extrapolative' basis,

then English would, have to have a very large measure of what I have called 'extrapolative symmetry.

18
he can hardly go wrong . ) But this will not he enough, if our idea

of 'paraphrastic' is ' truth-preserving, ' for as I have gone to such

lengths to point out, the microgrammar-user may be expected to

extrapolate from "A neuron Is next to..." to "Neurons are next to...".

Thus, a secondary requirement must be met: that common nonparaphrastic extrapolations (or paraphrases which are only locally

(in the context at hand) truth-pre serving) be included in the

microgrammar. This requirement may boil down to a rule that certain

classes of transformational rules must be taken into account when

building a microgrammar, in that certain resulting transforms must

be included. Should this be true the process of building a

microgrammar of ' extrapolative symmetry' will have been made less

difficult, because more understood; but it is still too early to

venture a prediction on how likely the microgrammarian is to have

this good fortune.-1

32 Obviously, the more transformational relations a given transform

grammar recognizes, the more likely that grammar is to provide

the microgrammarian with information on what 'extrapolations'

his product ought to include. A transform grammar which ignores

the relation between "He kicked her" and "He gave her a kick,"

for example, would not suggest that a microgrammar including

the first should include the second. Generally speaking

transform grammarians of the Harrisian school feel more constrained to treat all intersentential relations of a transformational nature (though this insistence is due as much

to predilection as to doctrine); grammars from this school, then,

may be of greater usefulness to microgrammarians. This point

may also be taken as an argument against using any but the

transformational model for microgrammars. The argument is

cogent (as are others on this point); but for the moment it is

necessary to make do with what we have.

19
2. Conclusion and Prospect .

I hope to have shown that whereas against qcg microgrammars

have at least the immediate advantage that they can he made availahle

now, against e.g. ALGOL microgrammars have the permanent advantage

that they will allow their users to carry over some of their

general linguistic habits into their communication with computers.

I have suggested however that these same linguistic habits will

constitute a serious stumbling-block to the utility of microgrammar

unless these algorithms can offer, in extrapolative freedom, an

analog to the latitude which qcg seem to have. I have indicated how

this freedom may be possible of attainment, through its being

restricted in scope by the parameters of the using situation, and

through its being provided, when within these parameters, by a

Klein-Simmons type of auto -grammarizer and/or hy the incorporation

of extrapolative symmetry. I have sketched some guidelines for

suggested future research.

Some of this research is already underway. PLACEBO IV is

gradually being expanded, one of the chief objectives of this work

33

being provision of a microgrammar of high extrapolative symmetry.

33 It may well be that the end result of successively approximating

a given microgrammar to' maximal extrapolative symmetry' is

necessarily a qcg of English, or at best an English qcg less some of its terminals (e.g. 'zeppelin'). If true, this is

irrelevant, for the microgrammarian is not out to supply full

extrapolative symmetry, only enough to make the microgrammar

'hahitable. ' Knowing in advance how much 'symmetry' will be

necessary for this end would he extremely difficult, but such

knowledge will not be necessary; the linguist can test the microgrammar against user-habitability at many points during the time

of development; and he can, at some more-or-less arbitrary point,

decide (with the user's compliance) that the microgrammar has

"become habj table enough to warrant cutting off further development.

20
Experiments with informants are to be conducted to ascertain how

close to reaching habitability each stage of the microgrammar has

come, and to learn where informants overstep the microgrammar 's

hounds

It may turn out that my hope that microgrammars can be made

habitable is unfounded. In light of this possibility, I think it

must be said that enough is now known about microgrammars and about

the prerequisites for their utility, to predict that if they cannot

be designed in such a way as to permit transference to their use of

general linguistic habits, with little penalty for such transference,

they will necessarily be relegated to the status of curiosities.

21
REFERENCES

((]_)) Franz W. Alt, Electronic Digital Computers , pp. x, 336.

New York and London (1958)

((2)) Noam Chomsky, Syntactic Structures , pp. Il6.

Janua Linguarum, Studia Memoriae Nicolai Van Wijk Dedlcata, IV

' s Gravenhage (1957)

((3)) Zellig S. Harris, The Elementary Transformations , pp. 110.

University of Pennsylvania Transformations and Discourse

Analysis Papers, #54. ('Pre-publication copy').

Philadelphia (19&-).

((h)) Zellig S. Harris, Methods in Structural Linguistics , 1951;

Fourth Impression pp. xvi, 38^.

Chicago (i960).

((5)) Henry Hiz, The Role of Paraphrase in Grammar, pp. 12.

University of Pennsylvania Transformations and Discourse

Analysis Papers , #53T""

Philadelphia (19&0.

((6)) Henry M. Hoenigswald, Language Change and Linguistic

Reconstruction, pp. viii, 168.

Chicago (i960).

((7)) Sheldon Klein & Robert F. Simmons, "A Computational Approach

to Grammatical Coding of English Words."

J. ACM 10.33^-3^7 (1963).

((8)) Kemp Malone, "On Symmetry in Phonemic Analysis."

Lg 38.1^2-1^6 (1962).

((9)) Jane J. Robinson, Preliminary Codes and Rules for the

Automatic Parsing of English, pp. ix, 1^-0.

The RAND Corporation, Memorandum RM-3339-PR.

Santa Monica (1962).

((10)) W. Freeman Twaddell, "Uses and Abuses of Symmetry."

Studies in American English: Second Texas Conference on

Problems of Linguistic Analysis in English ; cited article

pp. 129-137, discussion pp. 137-150 and 162-163

Austin, Texas (1962).

((ll)) William C. Watt, General Properties of Microgrammars . (forthcoming)

((12)) William C. Watt, PLACEBO IV: Rules, Concordance, Sample

Computer Generation . NBS Technical Note 255

Washington ( 1965 )

22

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