A Few Steps Towards Computer Lexicometry

(1)

American

Journal

of

Computational

Linguistics

Nicholas V. F i n d l e r and

Heino

Viil

Department

of

Computer

Science

S t a t e

University

of

New

York

Buff

a10

M i c r o f i c h e 4

(2)

N i c h o l a s V. F i n d l b r and fleino V i i l Department o f L'omputcr S c i e n c e

S t a t e u n i v e r s i t y of New York a t U u f f a l o

We describe a branch of d i c t i o n a r y s c i e n c e , and recormend t h e

term lexicometry for i t , t h a t deals w i t h the m a t h e m a t i c a l and

statistical aspects of d i c t i o n a r i e s . I t i s related t o both and former de n o t incj the d e s c r i p t i o n

of l e x i c a l m a t e r i a l and t h e latter i t s a n a l y s i s and study.

Many problems i n computational l i n g u i s t i c s r e q u i r e the use of a stored d i c t i o n a r y easily a c c e s s i b l e t o a c o q u t w program. I n the course of an i n v e s t i g a t i o n , s u c h a d i c t i o n a r y may have to be

expanded, reduced, rcanrranged, o r modified in various ways o A l s o

several n o n l i n g u i s t i c disciplines using t h e c m p u t e r , such as psychology, biology, m e d i c i n e , and s o c i o l o g y , o f t e n n e e d a l a r g e d a t a base in t h e £ o m of a d i c t i o n a r y . The relevant s t r u c t u r a l properties of a d i c t i o n a r y , however, have n o t yet been s u f f i c i e n t l y and systematically i n v e s t i g a t e d . Research i n this area is needed i n order t o o p t i m i z e the construction af s t o r e d

dictionaries and t o manipulate them i n e f f i c i e n t ways.

1

A c o n s i d e r a b l y extended version of t h i s p a p e r w a s sUbmitted t o t h e S t a t e University of N e w York i n Buffalo in partial

s a t i s f a c t i o n of the r e q u i r e m e n t s for the dbcjree of of science of Ileino ~ i i l . T h e project r c p r e s e n : . ~ the continuation of an e a r l i e r work by 1Jickolas V. ~ i n d f e r . Ilmy ideas and a l l t h e p r o g ~ m m i n g effort i s due t o I i e i n o ~ i i l . The w r i t e - u p is a

o i n t e f f o r t . The work r e p o r t e d here w a s s u p p o r t e d by N a t i o n a l cience F o u n d a t i o n Grant G J - G 5 8 .

(3)

F ' i r s t

,

we

review c r i t i c a l l y t h e problems o f meaning and i t s

r e p r e s e n t a t i o n , t h e q u e s t i o n s r e l a t i n g t o l e x i c a l d e f i n i t i o n s . . t o

P O ~ Y S = ' ~ Y , homonymy, s e m a n t i c d e p l e t i o n . synonymy, and

l e x i c o g r a p h y and Lexicology i n g e n e r a l . We a l s o d i s c u s s the

c o n c e p t of l e x i c a l v a l e n c e

and

e l a b o r a t e a n o v e l idea, c o v e r a g e ,

which

i s o f b o t h t h e o r e t i c a l and p r a c t i c a l importance. I n t h i s

context, r e l a t i o n s h i p 6 are e s t a b l i s h e d among three v a r i a b l e s :

the

s i z e

of t h e covered set, t h e

s i r e

of t h e c o v e r i n g set, and

the maximum d e f b i t i o n l e n g t h . b o t h , t h e s i z e o f t h e c o v e r i n g

s e t and the

maximum

d e f i n i t i o n l e n g t h should be s m a l l for

economic c o n s i d e r a t i o n s . But decreasing one

w i l l

i n c r e a s e the other. I t i s t h e r e f o r e important t o e s t a b l i s h these

r e l a t i b n s h i p s e m p i r i c a l l y . T h e knowledge, s o g a i n e d w i l l c o n s t i t u t e a b a s i s f o r o p t h i z i n g the s t r u c t u r e of a d i c t i o n a r y f o r s p e c i f i e d size of t h e covered s e t and a s p e c i f i e d machine.

The p r e s e n t p i l o t project i n t h i s v i r g i n f i e l d has an o b j e c t i v e o f v e r i f y i n g some c o n j e c t u r e s . I t e s t a b l i s h e s some

principles

of c o n s t r u c t i n g , f o r m a t t i n g , and s t o r i n g a large d a t a

base i n d i c t i o n a r y form. it d e v e l o p s programs f o r d i s p l a y i n g , h a n d l i n g , and modifying such a d a t a base. T h e p a p e r o f f e r s an example how a c o n c e p t u a l l y c o n t i n u o u s o p e r a t i o h

on

large amounts of data

can

be reduded

ts

o p e r a t i n g

on

a

fraction

of the

whole

d a t a base a t a t i m e by s u c c e s s i v e s m a l l i n c r e m e n t s o f time. W e

f i n a l l y d e m o n s t r a t e t h e f e a s i b i l i t y o f solving l e x i c o m a t r i c problems on t h e computer and, a t t h e same time, show t h e c o s t

i n v o l v e d i n doing such

work

i n terms o f b o t h human e f f o r t and

machine time,

(4)

and

the r e s u l t s that

were obtained

. . .

2

.

C o n s t r u c t i o n of

the

data b a s e 29

3

.

The results of the computations

. .

. . .

42

Acknowledgement

. . .

51

References

. . . a .

- 5 1

Appendix I

Program DeVelopment

. . .

54

Appendix I1

Some ideas for the program to investigate the relatianship

(6)

INTRODUCTION

S i n c e t h e

early days

o f e l e c t r o n i c

computing, two

kinds

of

a s s o c i a t i o n s

have

existed between computers

and

d i c t i o n a r i e s

:

either

t h e

computer

uses,

for v a r i o u s purposes,

a

stored

d i c t i o n a r y

of some

sort

(lexicon,

vocabulary,

glossary,

thesaurus)

or

the

compuker

is

employed

for constructing

and

a n a l y z i n g

a

d i c t i o n a r y .

The

latter

a c t i v i t y

was

given a

s t r o n g

impetus

in

the

late

1950's

by the

formation

o f t h e c e n t r e

dlEtudes

du

Vocabulaire

Francais

and

its

p u b l i c a t i o n ,

the

Cahiers

de

Lexicologie.

Thus

lexicography

was among

t h e

first

ncn-mathematical disciplines

to make

use

of

the

symbol

manipulating

c a p a b i l i t y of

computers.

While

formal

theories

of

s y n t a x

have

been $uccessful

in

d e s c r i b i n g

t h e

rules

of gramnatical

accepeability

of

n a t u r a l

language

utterances,

the

study

of

meaning,

u s u a l l y

c a l l e d

semantics,

has

not yet

produced a

theory

of

the

semantic

structure

of

languages, based

on observation

and

a n a l y s i s .

It

is

beyond

the

scope

a f

t h i s

paper

to

d i s c u s s ,

even

s u p e r f i c i a l l y ,

the

various v i e w p o i n t s concerned

w i t h

the

concept

of

meaning.

One

of

us,

V i i l

(19741,

h a s ,

however,

compiled

a

reasonably

exhaustive

c r i t i c a l survey

of

the

relevant l i t e r a t u r e .

For

the

purposes

of

this

work,

it suffi-ces to present the

(7)

1 . Logical

meaning

a p p l i e s

to

such attempts to

deal

with meaning as symbolic l o g i c

and

mathematics.

The meanings with

which the

s i g n a l s of such systems

correlate

are unique

outside-world

referents

or

unique

meanings w i t h i n t h e l o g i c a l

system

t h a t

e v e n t u a l l y have o u t s i d e - w o r l d referents.

2. General-sernant'4c

meanings

are a l s o

uniqne

in

their

reference

to

o u t s i d e world, but the

semanticists

are

less

s t r i n g e n t

i n

scope than the l o g i c i a n s . N e v e r t h e l e s s , t h e i r

scope is

an

i d e a l i z e d language,

much

more

l i m i t e d than ordinary language.

3.

Communication-theory meaning

is

equivalent

to t h e

amount

of

information

t h a t

can

be transmitted per

u n i t

time

in

a comunication . s y s t e m .

4 . Lexicoqraphical meaning is t h a t

of

"words,

"

and

the

I

outside-world

reference

i s

what

w e

o r d i n a r i l y c a l l

meaning. 11

5.

Psycholoqical

meaning has so great a _{scope t h a t t h e} par&

involving

o r d i n a r y

language becomes

nearly

t r i v i

a1

.

It

encompasses

overt or

covert behavior of any organism as

responses to s t i m u l i .

6. Word-mind meaning h$q the scope e q u i v a l e n t to t h a t of

(8)

conceptual

c a t e g o r i e s . T o o r d i n a r y meanings ( i n t h e l e x i c a l s e n s e ) here c o r r e s p o n d s i g n a l s by which m e n t a l s t a t e s a r e a s c e r t a i n e d .

7. L i n q u i s t i c meaning refers t o s i g n a l s a s the p i e c e s

o u t

o f which l a n g u a g e i s made, i.e. m i c r o l i n g u i s t i c , p h ~ n o l o g i c a l , and s y n t a c t i c s i g n a l s .

In

the

framework

.of o u r

particular

topic

_{w e}

shall

be

mainly

c o n c e r n e d w i t h categories 4 and 7 .

A c c o r d i n g t o

Weinreich

(1 966 )

,

u n i l i n g u a l d e f l n i n g d i c t i o n a r i e s appear t o be based on a model that assumes a d i s t i n c t i o n

between

meaning p r o p e r ( s i g n i f i c a t i o n , comprehension, i n t e n s i o n ) and t h e t h i n g meant by a s i g n ( d e n o t a t i o n ,

reference,

e x t e n s i o n )

.

On the basis

of what

i s

meant

by a sign, Osgaod,

s u c i ,

and

Tannenbaum

( 1 9 5 7 )

distinguish three k i n d s

of

meaning.

1. Pragmatical ( s o c i o l o g i c a l ) meaning : the r e l a t i o n of

signs t o s i t u a t i o n s and behaviors.

2

.

( l i n a u i s t i c ) meaning :

the

r e l a t i o n of s i g n s

t o

other

signs.

3. S e m a n t i c a l meaning: the r e l a t i o n of signs t o t h e i r s i g n i f i c a t e s

.

I t

i s

easy to see that these classes are i n

(9)

Homing o n t o o u r primary t a r g e t , w e may now restrict

our

interests

somewhat

f u r t h e r and c o n c e n t r a t e on t h e t w o l a s t classes o f meaning, known u n d e r v a r i o u s d e s i g n a t i o n s b u t , b y t h e

m a j o r i t y

of

writers,

d i s t i n g u i s h e d as s t r u c t u r a l meaning and

lexical

meaning.

Mackey (19653 f i n d s

structural meanings

i n ( 1 )

structure

words, ( 2 ) i n f l e c t i o n a l f o r m s , and (31 types of word o r d e r .

Examples

of

structure

words

are

a r t i c l e s

and

prepoai

t i o n s ,

and

these, he i n s i s t s , a l t h o u g h o f t e n

called

m e a n i n g l e s s o r

empty,

may

have

a

large

number

o f

meanings.

S i m i l a r l y , the i n f l e c t i o n a l forms, s u c h as t h e g e n i t i v e case and p r e s e n t t e n s e ,

may

have a

number

of meanings, and

s o

may some types of

word

order.

L e x i c a l mefinings, on t h e o t h e r h a n d ,

refer

t o

the

meanings

of t h e c o n t e n t words, i n

which

the d i f f e r e n c e s i n meaning

are

most

easily

s e e n .

I n

R u s s e l l ' s v i m (1 9 6 7 )

the

s t r u c t u r e

words, such

as " t h a n , I&

"or,

"

" h o w e ~ e r , " have meaning o n l y

in

a suitable

verbal

c o n t e x t

and

c a n n o t

s t a n d

alone.

The

c o n t e n t

words,

which

he

c a l l s

object

words, s u c h as p r o p e r names, c l a s s names of animals, names of

c o l o r s , do

not

p r e s u p p o s e ~ t h e r

words and can

be used

i n

i s o l a t i o n . T h e i r meaning

i s

l e a r n t by c o n f r o n t a t i o n

with

o b j e c t s

that

are

what

they

mean

or

i n s t a n c e s

of

what

t h e y

mean.

A s

soon

as t h e a s s o c i a t i o n

between

an

object word and what

it

means has

been

e s t a b l i s h e d by t h e l e a r n e r ' s h e a r i n g , i f f r e q u e n t l y pronounced i n the p r e s e n c e of t h e o b j e c t , t h e word i s u n d e r s t o o d

(10)

excludes words

that

d e n o t e a b s t r a c t e n t i t i e s ,

w h i c h

a r e not

o b j e c t - l i k e

and

u s u a l l y c a n n o t

have a

" p r e s e n c e . "

I t

a l s o

d e n i e s t h a t

every

s t r u c t u r e

word

i n h e r e n t l y d e n o t e s o n e

o r a f e w

d e f i n i t e

relationships

even

i n i s o l a t i o n .

I f

this

were

not

s o ,

one

could

n o t u n d e r s t a n d what k i n d o f r e l a t i o n s h i p

i t

d e s i g n a t e s

i f

used

i n a c o n t e x t .

Lyans

(1 9 6 9 )

,

q u i t e s e n s i b l y ,

d i s t i n g u i s h e s

between

three

d i f f e r e n t

k i n d s

o f s t r u c t u r a l ,

o r

grammatf c a l meaning.

1 . The

meaning

of

g r a m n a t i c a l

items,

such

as

p r p p o s i t i o n s

and

_{c o n j u n c t i o n s .}

2. The

meaning

of

g r a m m a t i c a l f u n c t i o n s ,

such

as

subject

and o b j e c t , i . e .

s y n t a c t i c a l r e l a t i o n s .

3 The

meaning

a s s o c i a t e d w i t h n o t i o n s

s u c h a s

d e c l a r a t i v e ,

i n t e r r o g a t i v e , i m p e r a t i v e ,

i. e.

s y n t a c t i c a l

types.

Ile

further

r i g h t l y

o b s e r v e s

that

g r a m m a t i c a l

items b e l o n g t o

closed

sets, which

h a v e

a f i x e d , small

membership,

e.g.

p e r s o n a l

pronouns.

L e x i c a l

items, on t h e

other

hand

belong

t o open

sets,

which have

a n

unrestricted,

l a r g e memhership,

e

. g o

nouns

Moreover,

l e x i c a l

items

have

both

_{l e x i c a l}

_{( m a t e r i a l )}

and

(11)

In

our

work, t h e distinction between

structure

words

and

c o n t e n t s

words is _{e s s e n t i a l .} T h i s f a c t

is

c l e a r l ~ seen

in

the

preparation of the d i c t i o n a r y used

for

our

experiments.

SOME; PROBLEhIS OF LEXICAL HELATEDNESS

1. Polysemy and Homonymy

While the problem of meaning is complex in itself, the

difficulty

i n c r e a s e s by

another order of

m a g n i t u d e

if one

h a s to deal w i t h words of many

n~eanings or

different

words w i t h

d i f f e r e n t meanings thak have i d e n t i c a l s p e l l i n g s or

p r o n o u p c i a t i o n s . And t h e

decision

as to whether a

given

case

represents o n e polysemous word or two (or

more)

homonyms

is

far from being w e l l d e f i n e d .

The separation can be based on morphological c r i t e r i a . First of

all,

two g r a p h e m a t i c a l l y i d e n t i c a l word forms w i t h different

meanings

are

regarded

a s

homqraphs and separated i f they display a phonematic d i f f e r e n c e

or

i f they b e l o n g to different word

classes.

They

are

a l s o homographs

even if they

belong to the same word c l a s s but possess different i n f l e c t i o n systems.

otherwise,

they r e p r e s e n t the same

word. More

than one meaning

(12)

appearance. A d i s t i n c t i o n between t h e two

can o n l y

be

made,

if

a t a l l , on the basis of t h e h i s t o r i c a l o r i g i n of the words invo

lved.

Direct, t r a n s f e r r e d and

specialized

s e n s e s of

a

word

can

be l i s t e d a l o n g ope d i m e n s i o n of meaning, dominant and

basic

senses

r e p r e s e n t

certain measures

a l o n g a n o t h e r dimension.

Another concept i s s e m a n t i c d e p l e t i o n ,

i n

which

case t h e word

occurs

i n scores

of

e x p r e s s i o n s . Mere, the

verbal o r

s i t u a t i o n a l

context

-

adds

substantially

t o

the

meaning

of t h e

word i n

question.

With polysemy,

however,

the

c o n t e x t

e l i m i n a t e s those

senses

of

the word that

do

not apply and thereby disambiguates

t h e polysemous word. It i s , therefore, i m p o r t a n t from t h e l e x i c o g r a p h i c a l p o i n t of view

t o

d i s t i n g u i s h between

the

degrees of

interaction between

the c o n t e x t and t h e

meaning

of

i n d i v i d u a l

( a ) i n case o f weak i n £ lu e n c e , w e t a l k a b o u t a u t o s e m a n t i c o r

semantically autonomous

words ;

(b) a s t r o n g i n f l u e n c e performs a d i s a m b i g u a t i o n o f polysemous o r homonymous

words;

( c ) t h e c o n t e x t d e f i n e s t h e 'meaning of synsemantic

or

semantically d e p l e t e d words.

Needless to say t h a t

the

above,

as

i n n u m e r a b l e

other,

(13)

it c o u l d be

noted

that, i n e x c e p t i o n a l

cases,

even

the

inmediate

c o n t e x t c a n n o t r e s o l v e t h e ambiguity4

and

two o r

more

i n t e r p r e t a t i o n s

are

acceptable. T h i s p h e n p e n o n i s the

I t

i s

clear

even

t o the

casual

observer

t h a t t o t a l i n t e r c h a n g e a b i l i t y

in

all contexts,

and identity

in

both c o g n i t i v e and emotive

senses,

of two

lexical

units (words,

i n the

s i m p l e s t case]

are

not possible

i n

g e n e r a l . The s e m a n t i c r e l a t i o n s h i r ;

between

synonymy is based on and measured by a l e v e l o f s i m i l a r i t y .

R a t h e r

than

d i s t i n g u i s h i n g

between

the

"meaning"

and

the

"usage"

of

a

word, one

s h o u l d assume

the

v i e w t h a t t h e

former

i s

t h e sum

t o t a l

of t h e p o s s i b i l i t ! i e s of the l a t t e r . This i s b a s i c a l l y

what

j u s t i f i e s

the

e x i s t e n c e of

any

monolingual (and,

p o s s i b l y , b i l i n g u a l ) d i c t i o n a r y .

The

entries

i n the d i c t i o n a r i e s w e

a r e

c o n c e r n e d

with

are b o t h

words

(the i n t e r p r e t a t i o n

and

d e f i n i t i o n of which units a r e

less

t h a n c l e a r - c u t )

and

m u l t i - w o r d l e x i c a l

units.

The two

are

of the same s t a n d i n g

and

function,

and t h e y w i l l be treated

i d e n t i c a l l y .

(14)

D e f i n i t i o n

is the

_most

fuhdamental

concept

associated

with

d i c t i o n a r i e s .

W

e

s h a l l

be

concerned

w i t h

both

classical

A r i s t o t e l i a n

definitions,

based

on

" c l a s s "

and

"characteristics",

and

o p e r a t i o n a l

d e f i n i t i o n s

which

use sententialw

g e n e r a t i v e

terms.

_{I n}

fact,

it

is

o f t e n d i f f i c u l t

o r

impossible t o

separate

equivalence

o r

paraphrase

ciefinitions

,

on

one

hand, and

t h o s e

t h a t

are process-oriented

r e p r o d u c t i o n s ,

on

t h e

other,

In

general.,

*he

l e x i c a l

meaning

can

be

rendered

by

f o u r

basic

instruments

and

t h e i r

various

combinations

:

( a )

t h e

lexicpgraphic

d e f i n i t i o n

enumerates

t h e

most

important

features

of

t h e

l e x i c a l

u n i t

being

defined,

i n

the

simplest

p o s s i b l e

terms;

(b)

q u a l i f i e d

synonyms provide

a

system

of

semantically

most

words;

( c )

exemplification p u t s

the

d e f i n e d

u n i t

in

f u n c t i o n a l

combination

w i t h

o t h e r

u n i t s ;

(d)

a

g l o s s

is an

explanator

or

descriptive

comnent related

t o the

d i c t i o n a r y e n t r y ;

it

may

also

skate

s i m i l a r i t i e s

t o

(15)

-

15

-

AsPECrS. O F THE SCIENCE OF DICPIONARY

1

.

General,

Concepts

U a o u g h

definitions abound, a

reasonable

d i s t i n c t i o n

seems

t o be

to say t h a t

t h e

semantic description of

i n d i v i d u a l terms,

t h e

inventory

of words i s

the customary

province

of

Lexicoqraphy

whereas le&coloqy

refers

to

the study

o f t h e

lexical

material,

of

the

recurrent

patterns

of

semantic r e l a t i o n s h i p s , and

of

any

formal devices, such

as

phonological

and

granmatical

$ystems,

that generate

t h e

latter.

T o

c o n s t r u c t

a

d i c t i o n a r y

of a

given size,.

one

could

choose

the

entries

on

the

basis

of

t h e i r

frequency

of

occurrence or in

r e l y i n g

on

some

measure

o f * u t i l i t y t h a t

is

vaguely t i e d

to

t h e

semantic

generality of

the candidates. N o

s o l u t i o n

i s

perfect

or

even

uniformly

useful

over

the whole

dictionary.

Even the arrangement of

meanings

of a given entry is moot.

we

talk

about l o g i c a l ,

historical and

empirical

orders.

(The

latter

starts w i t h the

c o m o n

and

current

usage followed by

obsolete, colloquial, provincial,

slang

and technical meanings. )

(16)

about

sane

samponent

of the

e x t r a l i h g u i s

tic

world.

Our

work

derives

i t s

data

base

from

an encyclopedic

d i c t i o n a r y .

It

ehould

be

noted

t h a t the

highly polysemous

nature

of

the

entries

in a

linguistic

dictionary

would

have

constituted

an

addi

t

iona

1 complication in this pilot project,

which

h a s

now

been

avoided

w i t h o u t

affecting

t h e

general

validity

of the

resu

Its.

We

propose

t o

i n t r o d u c e

the

tern

lexicometry

to

designate

the,

d i s c i p l i n e

which i n v e s t i g a t e s and

a n a l y z e s

the

q u a n t i t a t i v e

aspects

o f

dictionaries,

t h e

vocabulary

of

a

language

and

various

s u b s e t s

of

t h e

l a t t e t .

Lexicometry would

count,

weigh and

. .

measure,

and

express

t h e

results in

s t a t i s t i c a l

and

m a t h m a t i c a l

terms.

Many

such studies are

widely

known.

Such

is

t h e

one

reported

by

G U ~

raud

( 1

959

:

The

most

frequent

words

are:

(a)

t h e

shortest,

b

the

o l d e s t ,

( c )

the morphologically

simplest,

(d)

the

semanti-caf

l y

most e x t e n d e d ,

i

.e.

g r e a t e s t

number

of

meanings.

possessing

t h e

As

to

the

measure

of

frequency,

n

the

f i r s t

100

words

cover

608

of

an

averagen t e x t ,

I# 81 t l tl M I( Q

1000

85%

f

(17)

Thus

the

remaining

X

( ? )

thousand words

cover

o n l y

2 . 5 % of

t h e

t e x t . H o w e V e r , from

an

information

theoretic

p o i n t

of

view,

the

first

100 words

comprise

3 0 % of

the

information,

I n n n w I

1000 50%

"

11 H (I II n n

4000 70%

'

Consequently, rare

words konvey

a

great

deal

of

information.

We

could

say

that

a frequent

word

i s

most

u s e f u l

in

the aggregate,

and

a

rare

word

in

a

particular

case.

Other

studies in

glottochronology

mhcern thanselves

with

the

rate

to

any particular

vocabulary has

a l s o

been studied.

Finding

_{r e l a t i o n s}

of the above k i n d

is

not

j u s t

an

academic

exercise

to

s a t i s f y

the

c u r i o s i t y

of

a few l i n g u i s t s , but these

relationships

may

have

various

practical applications.

For example, Maas ( 1 9 7 2 ) asserts that

the

knowledge

of a

f u n c t i o n a l

relation between

the length of a t e x t and the

size

o f t h e

vocabulary

used

i n

it

would

be

d e s i r a b l e

in

order

t o estimate the

e f f o r t

needed f o r

extension

of a

machine d i c t i o n a r y or

i n

comparison of

vocabulary c o n t e n t s

of t e x t s of d i f

ferent

l e n g t h s . In the

l a t t e r

case, one can

s t a n d a r d i z e or

normalize

the t e x t s under i n v e s t i g a t i o n by reducing

them

t o a

common

minimal

length through

computational

methods

and

then compare the

r e s u l t i n g

(18)

L e t V be the number of

e l e m e n t s

(words)

i n

a

text

and

N the

I

-

l e n g t h of the text.

Then

we

surmise,

says Maas, a

f u n c t i o n a l

r e l a t i u r n s h i p t o

exist

between N

-

and V:

-

Muller

(1964)

reported

a

r e l a t i o n

between

V

-

and

d

-

such t h a t

the

r a t i o

of their logarithms

i s c o n s t a n t :

lo N

-3.-

=

a,or

v a

= _{N, or,}

10q-

v

1

if

we s e t

-

=

k,

V = L J ,

k

a

Since

the

vocabulary

of

a

language,

however,

is

supposed to

be restricted, so argues Maas, the e x i s t e n c e of a l i m i t i n g value

is

to be

p o s t u l a t e d :

V,=

lim

f

(N)

N+m

As the derivative

of f

-

at a g i v e n

v a l u e

of N

-

represents t h e

r e l a t i v e

increase

in

V -1

it is to

be s t a t e d that

f' (N)

approaches

0

with

i n c r e a s i n g

-

N,

The

d e r i v a t i v e

of

a f at the p o i n t 1

is

assumed to be 1 because

(19)

Therefore

-

f'

i s a

function

that

decreases

m n o t o n i c a l l y

from

1

to

As

a

consequence

of the above

speculations,

in t h e

expression

V

=

N~

_'

-

k

cannot

be

constant.

s t a t i s t i c a l

investigations of the

dramas

by Corneille

have

resulted

in

the

r e l a t i o n s h i p

1

log

E

=

0 . 0 1 3 7 . ( l o g N)

1/3

~ h u s ,

if

N

I

is

g i v e n ,

k

IC

can be

determined,

and V

-

can

be

c a l c u l a t e d

from

Another

noteworthy concept

i s

that

of

r e p e t i t i o n

factor

:

which

shows

how

of

ten

word has

occurred

in

a t e x t

on

the

averaqe.

The

following

r e l a t i o n s h i p has been determined:

(20)

which

d i s p l a y s

a

very

good

agreement

w i t h

r e a l i t y .

N O

s i n g l e

empirical

law

s e w s

to

e x i s t

between

N

and

V

f o r

I D

a l l

N. -

2 ,

The

Problem

of

Coverase

We

_are

now coming

close

to

the core

subject

matter

of

t h i s

paper.

Mackey

( 1 9 6 5 ) s t a t e s t h a t

he

coverage

or

covering

capacity

of an

item

is

the

number

of

t h i n g s

one

can

say

w i t h

it. It can

be

measured

by

the

number

of

o t h e r

items

which

i t

can

d i s p l a c e .

)I

According

to

him,

words

can

displace

other

words

by

Eour

means:

(1

)

i n c l u s i o n ,

( 2 )

extension,

( 3 )

combination,

and

(4!

d e f i n i t i o n ,

1,

A

word

t h a t

already

-

includes

the

meaning

o f

o t h e r

words

can

be

used

instead of

these

( e . g . , _Ls e a t _-

i n c l u d e s

_{- P}

chair

bench,

s t o o l ,

and

place)

,

-

lLlCI

2 .

Words

the

meanings

of

which

are

easily extended

me'kaphorically

can

be

used to

eliminate others

(e.g.,

(21)

3

.

Certain

simple words

can

displace

others

by combining

e i t h e r together

or

with

simple

word

endings

(em

g.

,

news

+

paper

+

man

= j o u r n a l i s t ;

hand

+

book = manual)

.

4

.

Certain

words

can

be

replaced by simple d e f i n i t i o n

( e r g . , breakfast can be d e f i n e d as morning meal; pony a s

small

h o r s e ) .

As

an

example

of t h e a p p l i c a t i o n of the above

principle,

in

the

derivation

of Basic

English

(by

definition), t h e

language was

f i r s t reduced

to

7500 words, and, by r e d e f i n i t i o n ,

c u t

down

t o 1500. These

were

further

reduced t o t h e e v e n t u a l 850 by a technique of "panoptic" d e f i n i t i o n

(eliminate

each word

on

t h e

grounds

that i t i s

some sort

of modification

of

o t h e r

words,

e .

g.

a m o d i f i c a t i o n

i n

time,

numbe-r,

or

s i z e )

.

Basic English, which was founded

essentially

on

the p r i n c i p l e

of

cove

rage, was

a

conscious

reaction

a g a i n s t

the

o v e r - a p p l i c a t i o n of t h e p r i n c i p l e of frequency

i n

s e l e c t i o n . For

Ogden ( 1 933)

,

it

was n o t the frequency

of

a word

which

makes i t u s e f u l , i t was i t s usefulness

which

makes it f r e q u e n t .

In the

following

p a r t of

this

s e c t i o n ,

we a t t e m p t

t o

present

some of the salierit p o i n t s of

Savard

(1 970).

(22)

n o t s u f f i c i e n t

t o

select words for

a restricted

v o c a b u l a r y for

the

purpose of teaching

a

f o r e i g n language, such as

W e n c h ,

to b e g i n n e r s .

An

objective

_{c r i t e r i o n i s l e x i c a l v a l e n c e .} I t would allow

1

.

to o b t a i n a n o v e l p r i n c i p l e of vocabulary s e l e c t i o n ,

2

.

t o assist the i n v e s t i g a t o r s i n s e t t i n g up a base

vocabulary

f o r

French,

3 . t o p r o v i d e a u s a b l e d e f i n i t i o n ,

combination,

inclusion,

and

extension

vocabulary,

4

a t o

correct

a l l

the already

e x i s t i n g

scales

of French

vocabulary,

5. to provide a

valid working

tool

for the

analysis of

t e a c h i n g material.

The

valence problem is a problem of verbal economy. \that he

calls

v a l e n c e

i s

t h e

fundamental

capability

o f

a

word t o be

substituted

for another

word.

It is

Mackey's coveraqe t h a t he

(23)

L i k e Mackey ( 1 9 6 5 ) , he

maintains

t h a t the s u b s t i t u t i o n of one word

for

another

can

he

made by

v i r t u e

of

four criteria:

( 1 )

d e f i n i t i o n , ( 2 )

i n c l u s i o n ,

( 3 ) combinatiori, ( 4 ) e x t e n s i o n .

~ e f i n i t i o n has already been discussed previously.

Linguists do

n o t

t a l k

specifically

about inclusion; r a t h e r , they d e a l

with

synonymy

or

l e x i c a l p a r a l l e l i s m .

Synonyms

are.

words

that have n e a r l y t h e

same meaning,

e . g .

-

lieu

and e n d r o i t . For Savard, the b a s i c

criterion

t h a t permits t o

establish

a

series of the p o s s i b i l i t y of s u b s t i t u t i n g one term f o r another.

One

of

the

s i m p l e s t

a m n g a l l

t h e procedures

of

vocabulary

e n r i c h m e n t consists

o f

j o i n i n g

two

words

order to make

compound

words.

The p r i n c i p l e

0-f

combination

appears as

another

phenomenon

common

t~ a l l langrlages.

It i s n o t necessary t h a t the

number

of s i m p l e words be

unbounded

because

almost

a l l

verbs have a p o t e n t i a l of undetermined sense, and

so

do the a d j e c t i v e s . A word is said to have more or less extension a c c o r d i n g to w h e a e r i t can "cover" a

more

or

less

great number of f u l l y or p ~ r t i a l l y d i f f e r e n t notions.

Polysemy

is

the exact opposite of synonymy. Polysemy becomes

(24)

homonymy

constitute two

very r i c h

sources

of

l e x i c a l economy.

Togethel:

they

form

Savard'

s

l a s t

criterion

of

lexical

valence--the

semantic extension,

Although

the

valence

i t s e l f

has

rfever been mathematically

measured

and

a l t h o u g h there

exis- n o

s c i e n t i f i c

means

of

showing its existence, it h a s neverthe less,

been proven

that

four formal

proceaures

of

lexical

economy permt

to

replace

certain

words

by

other words, and t h a t

is

what S a v ~ d c a l l s

l e x i c a l valence.

The postulated

existence

hypothesis

of

lexical

v a l e n c e

leads

t o the c a l c u l a t i o n of a global i n d e x of valence f o r e k d r y word.

To

evaluate

t h e

power

measure

the power

of

combination of a lexical

unit,

one

inspects

in

t h e d i c t i o n a r y

all the compound words

joined by a

hyphen,

all

the Gallicisms ( i n English, these would be Anglicisms) and, in g e n e r a l , a l l t h e

word

groups.

W i t h a view of a p p r a i s i n g the power of i n c l u s i o n , one

inspects

me

units

of

the general _{l i s t} in two synonym d i c t i o n a r i e s and takes the h i g h e r

number.

The numbei

of

synonyms

t h a t

possess

a word c o n s t i t u t e s a measure of the nunber

of

words

(25)

To measure the power of s e m a n t i d e x t e n s i o n , o n e i n s p e c t s each

of t h e e l e m e n t s of the general list i n the d i c t i o n a r y and c o u n t s the number of meanings g i v e n by the author t o such a word in t h e

list. T h e number of meanings of a word is c o n s i d e r e d as a m a s u r e of i t s power of s e m a n t i c extension.

The g l o b a l i n d e x of lexical valence is t h e sum of t h e four

n o r m a l i z e d c o u n t s . The two c r i t e d i a h a v i n g t h e h i g h e s t c o r r e l a t i o n are d e f i n i t i o n and c o m b i n a t i o n .

In the beginning of t h e study, it was assumed t h a t thk four

v a r i a b l e s were entirely i n d e p e n d e n t of each o t h e r . The results of a f a c t o ~ a n a l y s i s i n d i c a t e that they are n o t c o m p l e t e l y so. A

factor r o t a t i o n shows, however

,

that t h e variables are

s u f f i c i e n t l y i n d e p e n d e n t t o make it necessary t o retain the four

c r i t e r i a of l e x i c a l valence.

A c o m p a r i s o n of t h e rank of t h e first 40 c o n t e n t words on the valence scale w i t h the same words on t h e f r e q u e n c y l i s t allows t o frame a hypothesis t h a t t h e c o r r e l a t i o n between v a l e n c e and

f r e q u e n c y would be rather weak. A more c o m p l e t e s t u d y would show

w i t h o u t d o u b t t h a t : w e have there two very different s e l e c t i o n

p r h c i p l e s .

I n c o n c l u s i o n , i eSan be stated with c o n f i d e n c e that t h e measure of valence i s n o less v a l i d t h a n that of frequency, distribution

.

and a v a i l a b i l i t y . These _{c o n c e p t s}w i l l eventually lead to more efficient d i c t i o n a r i e s with respect to precision,

(26)

ON LEXICOMETRIC RELATIONSHIPS AMONG

THE

SIZE OF D E F I N I N G SET,

TUE: SIZE OF DEFINED SET AND TILE MAXIMUM LENGTH OF DEFINITIONS

1. Some Measures of Coverage

A d i c t i o n a r y may be considered efficient and

economical

i f i t u s e s a

reasonably

small set of words to d e f i n e 9 r e l a t i v e l y large

set o f entries. W e have, however, a very v a g u e idea a b o u t what

size

v o c a b u l a r y i s n e e d e d t o c o v e r a g i v e n number of d i c t i o n a r y

e n t r i e s . (The r e l a t e d problem of c i ~ c u l a r d e f i n i t i o n s seems t o have t o wait for a camputer s o l u t i ~ n . )

I t i s known, for example, that Basic E n g l i s h , Ogden (1 933)

,

involves a l i s t of 850 E n g l i s h words and 50 i n t e r n a t i o n a l words,

which were e v e n t u a l l y used t o d e f i n e the 20,000 English words of Basic Y n g l i s h D i c t i o n a r y . This gives

_{a r a t i o}

of

the number

of

c o v e r i n g . words t o that of d e f i n e d words of 0.045.

West s t u d i e d t h e problem of what c o n s t i t u t e s a simple definition and e s t a b l i s h e d a minimum defining vocabulary of 1 , 4 90 words. The meaning of sane 18,000 words and 6,OQ'u idioms, i.e.

about 2 4 , 0 0 0 expressions, was e x p l a i n e d exclusively by t h e s e

1,490 words, which were not d e f i n e d themselves. The r e s u l t s were p u b l i s h e d in 1 9 6 1 as The 14ew Method English D i c t i o n a r y bf H o p m

West and J. G. E n d i c o t t . The c o r r e s p o n d i n g size r a t i o here i s 0.062,

(27)

can

define

d s e t of about 20 times mat s i z e , b u t

in

g e n e r a l the

behavior of these variables h a s not been i n v e s t i g a t e d and i s not

known i n

any

d e t a i l .

One of us, in F i n d l e r ( 1 3 7 0 ) , has formulated t h e problem i n de.Ein ; ie terms, T h r e e v a r i a b l e s were considered : ( 1 ) t h e

covered set S of size

% ,

(2) the Coverinq set R o f s i z e

% ,

and

L

-

.I)

L

i

parameter.

Usinq the terminology of i n c r e m e n t ratio for Av

/Av

and s i z e

=;: S

r a t i o f o r vR/vS

,

it was p o s t u l a t e d f o r case (a) that

2

*

t h e i n c r e m e n t r a t i o is, i n q e n e r a l , less than one

,

2

*

t h e i n c r e m e n t ratio, i n g e n e r a l , decreases as

v

i n c r e a s e s

,

S

-

*

f o r l a r g e values of

P,

vR

L

-

a s y m p t o t i c a l l v approaches a l i m i t i n g value as

vS

i n c r e a s e s ,

-

*

t h e i n c r e m e n t ratio will, n e v e r exceed the s i x e ratio.

L

A n e x c e p t i o n t o t h i s rule would occur i n a d i c t i o n a r y

s y s t e m , which does n o t treat liomon~ms a s i n d i v i d u a l entries,

A

(28)

It was f u r t h e r asSumed t h a t f o r B=l

,

the

coverincr set and

the

covered set are of the. same s i z e ,

i

. o .

both the i n c r e m e n t ratio and the s i z e ratio equal

o n e .

We 'must

now

correct this s t a t e m e n t becallse not every word i s d e f i n e d by i t s e l f o n l y . If a new word

is

Lntroduced that already

has

a synonym

in

the covering s e t , i t w i l l be d e f i n e d by that synonym. Then the i n c ' r e m e n t ratio i s 0

a n d t h e s i z e r a t i o become less t h a n 1.

For

tke

s e c o n d c a s e , (b)

,

it is n o s t u l a t e d t h a t

*

v

monotonically

decreases a s I) N

increases,

*

N should he s m a l l t o mlnlmize

p r o c e s s i n g t i m e and output volume. A . compromise on these

mnf l i c t i n g requirements is needed. The u l t i m a t e q u e s t i o n i s :-

g i v e n

"What are t h e optimum

yl

and

-

11 values for

a v

f o r certain

-

A

-

s

computer a p p l i c a t i o n s

on

a machine

with

a

given c o s t

s t r u c t u r e ? "

X t i s reasooable to assume that the behavior of

the

three

v a r i a l e s and t h e r e f o r e the answer to the l a s t q u e s t i o n w i l l l a r q e l y denend on t h e semaptic

index

of t h e elements of the

covered set: and on the lexical v a l e n c e of t h e elements of the