Bureau ot srapoarui

NBS TECHNICAL NOTE

296

A Grammar for

Component Combination

In Chinese Characters

b. kirk rankin iii, stephanie siegel,

ann McClelland, and james l tan

V*

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NBS TECHNICAL NOTE 296

A Grammar for

Component Combination

In Chinese Characters

B. Kirk Rankin III, Stephanie Siegel,

and Ann McClelland

Center for Computer Sciences and Technology

Institute for Applied Technology

National Bureau of Standards

and James L Tan

George Washington University

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.

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Preface

This note describes and evaluates an attempt to analyze the pictorial structure of Chinese characters. The approach underlying this

analysis is borrowed from the field of linguistics. The collection of

objects under study is the set of all well-formed Chinese characters;

that is, the set of all character-like structures which an informant

accepts as actually occurring or possibly occurring. The set of these

well-formed Chinese characters is considered to be a language. The

corpus on which the grammar is based is Mathews' (3) (see Bibliography,

page 118) minus a handful of entries which are deliberately excluded .1/

The task of analyzing this language is taken to be that of constructing a grammar to account for the pictorial structure of characters by generating objects which correspond to characters. These

1/ More precisely, our corpus consists of hand-written copies of the

characters in Mathews'. See Appendix A for a listing and classification

of the excluded entries.

iii
objects are well-formed at a high (syntactic) level of structure only,

and are properly viewed as requiring further processing by an output

transducer which is yet to be constructed. This transducer will

contain rules for size and shape variation in character sub-parts and

rules for precise spatial placement of character sub-parts.

The grammar 1/ displayed in this note is a mixture of various formalisms which in turn are inspired by formalisms used in the fields of

linguistics and computation. Although it is a mixture, the central

property of the grammar is its capability of imposing a kind of phrase

structure on its output characters.2/

1/ The grammar, GCC-3 (Grammar for Component Combination, number three),

is a refinement and extension of the concepts developed in two previously

constructed grammars: GCC-1, in Rankin, Sillars, and Hsu (5) and GCC-2,

in Rankin (4).

2/ See Chomsky (2), Chapter 4 for a discussion of phrase structure

grammars for natural languages.

iv
Phrase structure grammars are well-suited for describing natural

languages or sub-languages whose sentences show an internal structure

in terms of hierarchical combinations of smaller units (e.g, words or

morphemes) into larger units (e.g., phrases and ultimately sentences).

Phrase structure grammars are also well-suited for describing such

artificial languages as some of the logical calculi and some of the

programming languages.

It is now suggested that modified phrase structure grammars can

well describe languages other than the one-dimensional languages just

mentioned. In particular, modified phrase structure grammars are wellsuited for describing the two-dimensional language of Chinese characters.

The following discussion will be in three parts. First, there is

a section dealing with the description of the various phenomena and

processes in the language of Chinese characters. Second, there is a

section in which the grammar constructed to account for this language

is characterized and discussed. Finally, there is a section dealing with

the evaluation of this grammar in terms of criteria originally proposed

for evaluating grammars for natural languages. v
Contents

PREFACE iii

ABSTRACT

I. THE LANGUAGE 2

II. THE GRAMMAR 16

III. EVALUATION 42

ACKNOWLEDGEMENTS 63

APPENDIX A 64

APPENDIX B ........ 68

APPENDIX C.... 74

APPENDIX D 117

BIBLIOGRAPHY 118

VI
A GRAMMAR FOR COMPONENT COMBINATION

IN CHINESE CHARACTERS

by

B. Kirk Rankin III

Stephanie Siegel

Ann McClelland

Center for Computer Sciences and Technology

National Bureau of Standards

and

James L. Tan

George Washington University

ABSTRACT

A linguistic analysis of one aspect of the

structure of Chinese characters is presented. The

analysis is an extension into two dimensions of a general approach to one-dimensional language study.

Results of the analysis are in the form of a threelevel generative grammar. The first level formalizes

restrictions governing the general complexity of wellformed Chinese characters; the second level formalizes co-occurrence constraints among character components

and the particular spatial arrangement of these com- ponents in classes of characters; the third level

constitutes a procedure for selecting actual components

from a lexicon. Finally an evaluation of the grammar

is presented, in terms of criteria used in evaluating

natural language grammars.

Key-Words

Chinese characters phrase structure grammar

grammar linguistics

generative grammar frame, embedding

component combination two-dimensional languages
I. THE LANGUAGE

A. INTRODUCTORY

This discussion of the language is based on two fundamental notions:

component and frame . Chinese characters may be viewed as occupying a

hypothetical square ;1/ they may also be viewed as being composed of recurring sub-parts - here called components . The segmentation of characters into components segments the square in a variety of ways. These

segmentations of the square are here called frames . Frames can thus be

viewed as abstract representations of classes of characters.

With the notion of component and frame now introduced, the notion

of positioning of components with respect to frames can be discussed.

The following position classes are necessary in a description of

Chinese character component combination: NORTH, SOUTH, WEST, EAST,

BORDER, INTERIOR, and FREE. Thus, the character *"(=] is segmented

as follows: N and is represented by the frame

1/ This is, in fact, a part of the traditional native Chinese view of

Chinese characters.
the component W is a WEST and the component P] is an EAST.

The character &

is segmented as follows:

5c

, and is represented by the frame ; the component V-1-? is a NORTH and

the component Jv is a SOUTH. The character |;fc| is segmented as

follows: , and is represented by the frame ; the

component is a BORDER and the component jfc. is an INTERIOR,

(BORDERS may occupy two, three, or four sides of the square. Other

examples are 2 , , and .) Thus, a frame for any

two-component character consists of two sub-frames of equal area.

The only such frames are •> , and . The

single-component character fM .1 is represented by the frame

and the component \®j *" s a FR^E#

Based on the discussion so far, in particular the notions of

frame and position class, we can represent the above four characters as:

W E for fa for

fr E

and for J+3 , where the symbols in the frame are obvious

abbreviations for the position class names. In fact, the grammar
provides further information for W, E, N, and S in the form of subscripts on these symbols and these will be discussed just below.

There are, to be sure, characters of greater complexity than

those mentioned above. For example, there is the character

whose frame can be viewed as being derived from simple frames by means

of a process of frame -embedding . A 2* is represented by the frame

, which is derived by means of the embedding of in

the EAST part of Note that here embedding results in two

sub-frames of equal area, the sum of their areas being equal to the

area of the sub-frame not embedded in. Frames for other complex characters are derived by means of similar embeddings. 1/

A final word on positioning. Most components occur in many but

not all positions. Only a few occur in only one position. As was

seen above j the component *A\^ is a WEST and an INTERIOR; it is

1/ Actually, any frame except is derived via frame-embedding.

See page 11, ff,
also an EAST, a NORTH, a SOUTH, and a FREE. The component 13 is

a WEST and an EAST, and nothing else. The component 3^ is a BORDER

only.

The broad outline of the phrase structure of Chinese characters

arises out of this classification of components into position classes.

However, if a grammar were constructed to represent this and only this

classification, it would be inadequate because it would generate a

great deal of unacceptable output. Further inspection of the cooccurrence properties of components has prompted us to sub-classify

each position class according to the dimensions of strength and

adjunctiveness .

Before discussing these two co-occurrence properties, we will

have to introduce the concept of "in construction with". Two components

are in construction with each other if they occur in sub-frames of

equal area. For example, in A-fz\ > /£ and fcj are in construction with each other. The frame for ^0 > which is

contains two sub-frames of equal area, one in which /F occurs and
one in which Jr) occurs. A component is in construction with a

complex character sub-part if it occupies a sub-frame whose area is

equal to the sum of the areas of the sub-frames occupied by the components in that complex sub-part. For example, >f£ has the frame

X is in construction with the complex sub-part

. A occupies the shaded sub-frame: whose

area is equal to the sum of the areas of the sub-frames occupied by

4 and 2<v ' name ly» tne shaded sub-frames:

m

2

We are now ready to introduce the concept of strength which was

mentioned just above. A component is strong in a particular position

if it can be in construction with many single components and with many

complex character sub-parts while in that particular position. It is

perhaps the case that many of the strong components in our lexicon are

so limited in terms of the number of components with which they can

occur that they do not fit this definition, under any reasonable interpretation of the term "many" (even though the notion "can be in

construction with" is not intended to be corpus restricted). There
seems, in fact, to be a scale of strength, only the outlines of which

are understood currently. 1/ At the present time we therefore consider

a component to be either strong or not strong with respect to a particular position. For example, ^s is strong in WEST because it can be

in construction with III (in A*H ^» (_, ^n

-'jLj ^ anc^

with many other single components; and with q (in >Jq )> |^l

(in /\\o\ )> and with many other complex character sub-parts. Similarly, f*%\ is a strong SOUTH, ll is a strong EAST, and + + is

a strong NORTH. All BORDERS are strong. INTERIORS (since no INTERIOR

can occur with many BORDERS) and FREES (since strength is a property of

components in construction) are not strong. It is typical that a

component which may occur in several positions is strong in one or more

positions and not strong in others. A good example is (__» • It i- s

strong in SOUTH and not strong in EAST, WEST, and NORTH.

1/ See page 55 for a discussion of this problem. Much more informant

work is needed before this limitation can be corrected.
A property of certain strong components is ad junctivenes s . 1/

A strong component is either an adjunct or it is not regardless of

position. That is, an adjunct is an adjunct wherever it occurs. An

adjunct is a strong component which cannot occur in FREE. Examples of

adjuncts are A and * in WEST, •] and ]5 in EAST,

/i»\ and /!(_, in SOUTH and -^— and V

7 in NORTH. Adjuncts

have the further property that they may never be in construction with

adjuncts. Thus the structure —~~ is not an acceptable character

since both ^n> and —J— are adjuncts. In fact, it was in order

to avoid generating such unacceptable structures that the dimension of

adjunctiveness was established.

1/ Rankin (4) recognized both strong and non-strong adjuncts (p. 32)

Further informant work has prompted us to reassign non-strong adjuncts

either to the class of strong adjuncts or to the class of FREE

components. This solution, incidentally, seems to be not entirely satisfactory.
Since they must be strong components, adjuncts occur only in WEST,

EAST, NORTH, SOUTH, and BORDER. Among the strong components in each of

these position classes, some are adjuncts and some are non-adjuncts.

Based on the discussion so far, we can give the grammar's full

representation of the four sample characters given on pages 2 and 3. For

^"F| , there is

1^.1 , there is

% ; for %J , there is

Ef

#-

, and for {*1 k, there i

N sF • fnr

sf

j —»»«.

re is F

W determines a WEST component which is strong (by subscript s) and

sf

non-adjunctive (by subscript f indicating that the component can occur

in FREE.) E determines any EAST component by lack of subscript, for

any EAST can be in construction with a strong non-adjunctive WEST.

N _ determines a strong (by s) adjunctive (by f ) NORTH. S determines

sf f

a non-adjunctive (by f) strong or non-strong (by lack of s) SOUTH.

(Note how the constraints on the occurrence of strong components and

adjuncts are governed by these subscripts.) B, I, and F are subscriptless in the grammar, B always being strong, I and F being insensitive

to the strength dimension, but both I and F being non-adjunctive.
One of the processes involved in the formation of Chinese characters is that of component repetition. We here recognize four 1/

types of repetition; horizontal continuous, as in Q§ 5 vertical,

as in ^_ j triangular, as in qq j and horizontal discontinuous, as In X X " With the exception of the horizontal discontinuous cases, all 2/ instances of repetition function in the grammar as nonstrong, non-adjuncts in WEST, EAST, NORTH, SOUTH, INTERIOR, and

FREE. The horizontal discontinuous cases function as strong adjuncts

1/ For a treatment of repetition which recognizes the existence of more

than four types and which is non-generative in nature see Rankin (4)

In a generative treatment, such as we are presenting here, we feel

that only these four should be recognized.

2/ There are a few exceptions in this observation. Some structures,

like 4*f and E7Q , could be generated by repetition rules, but are

not, because they are strong components and it is desirable that strong

components be listed in the lexicon as single components, This inclusion of complex structures in the lexicon is one of the limitations

in the current treatment.

10
in BORDER and do not occur in any other class.

These instances of repetition are represented in the grammar as

follows: m as (horizontal continuous), as

(vertical), *~L as (triangular) , and $

%J( as

(horizontal discontinuous).

B. DETAILS

What follows now is a rather more detailed account of some of the

phenomena and processes that have just been introduced.

The process of frame-embedding has been mentioned briefly. In

this detailed treatment, we will use the notions of host-frames,

occupant-frames, and product-frames.

Further, we will highlight the process of frame-embedding by

ignoring all marks which in the grammar may occur in frames or subframes - except for the mark H (for "host"), which is the recursive

element in the grammar that activates the process of frame -embedding,

We will refer to the sub-frame containing H as the "H sub-frame".

We will use the formula:

11
Occupant-frame + Host-frame -» Product-frame

which is read "Embed the occupant -frame in the host-frame to produce

the product-frame". The host-frame always has H in one of its subframes (or in its only sub-frame in H ). This one sub-frame may

be thought of as the hypothetical square or size and shape transformations of it. The occupant frame (always of the form:

• ) may or may not have H in one of its

sub-frames. The product-frame of any embedding will have H in one of

ics sub-frames if the occupant-frame that produced it has an H subframe. The product-frame of the first embedding is always identical to

the occupant-frame of the first embedding.

Sample Single Embeddings:

Occupant-frame + Host-frame -* Product-frame

+ H

+ H

ffl

12
In general, H may occur in any sub-frame except the border subframe, since border is not a possible transformation of the hypothetical

square. (For purposes of this discussion, "border" sub-frames can be

filled by components from both the BORDER position class and the

horizontal discontinuous repetition class.) Thus there are no complex

borders. 1/

If a product-frame contains an H sub-frame, that product-frame is

then redefined as a host-frame. This redefinition is shown in the

following example.

1/ Actually there are some BORDERS which appear to be complex.

Examples are & and l^\ • Complexity in BORDER is extremely rare

and we circumvent the problem by listing such instances as the two

above as single components in the lexicon. Further, all instances of

horizontal discontinuous repetition appear to subdivide the border

sub-frame. However, they do conform to our general definition of

BORDER in that they occupy two sides of the hypothetical square (see

page 3).

13
Sample first embedding followed by second embedding:

Occupant-frame + Host-frame -* Product-frame

1st

embedding:

2nd

embedding:

H

+

+

H

H

(redefH

inition)

/

Note that in the first embedding one of the sub-frames of the

occupant-frame contains H. It is this occurrence of H that both allows

the second embedding to take place and also marks the place where the

second is to take place. If there were no H sub-frame in the occupantframe, no second embedding could take place.

Further, no occupant-frame in the grammar may contain more than

one H sub-frame. This restriction imposes a "blocking" of embedding.

Once an occupant-frame has been embedded in a host-frame in any

embedding, the sub-frame which is equal in area to the H sub-frame is

permanently blocked from embedding. Another way of saying this is that

the grammar does not allow any host-frame to contain more than one H,

In the following sample products the shaded sub-frames are blocked

from embedding:

m.

H

H

W, m i

&

Wk

v/zs, 1I

w

mi

H

14
There are further constraints on the process of frame-embedding.

First, there is an upper limit of four embeddings in the generation of

any character- -giving rise to a maximum of five sub-frames per frame.

Second, there may be only two BORDERS in the generation of a frame for

any character. (With respect to this constraint, cases of horizontal

discontinuous repetition are treated as BORDERS). Finally, there is a

limit of four sub-frames per frame if any sub-frame is occupied by a

case of horizontal continuous, vertical, or triangular repetition. This

is so because these cases of repetition are in a sense multi-componential. In contrast, cases of horizontal discontinuous repetition

function as a single-component BORDERS.

Blocking of embedding is closely related to the functioning of

strong components in the following sense. A strong component must

occur in every blocked sub- frame of a frame. Further, a terminal frame

contains within it two sub-frames of equal area (shaded in the following

examples: H and ) . A strong component must

I I1

occur in at least ©na of these two sub-frames of equal area. It follows

that an output character contains at most one non-strong component.

15
With respect to adjuncts, they may occur wherever any strong

component may occur with one exception. There are no cases of adjuncts

being in construction with adjuncts. So, not both of the sub-frames

of equal area may be occupied by adjuncts. That is, for example, not

both shaded sub-frames in any one of the following frames may be

occupied by adjuncts: It follows

that in any output character there must be at least one non-adjunct.

Finally, not both sub-frames of equal area in any frame may be

occupied by the same component. If it were otherwise, such output

characters as M£j would be ambiguous (or derivable in more than

one way). One derivation of FJH would be an EAST plus a WEST

with pj filling both positions; the other derivation would be the

correct one: that {EluJ is a case of horizontal continuous repetition,

II. THE GRAMMAR

A. INTWDUCTORY

The grammar is set up to generate output characters in three

stages. The grammar also imposes a hierarchical classification on the

16
set of all output characters, and this can best be seen by first

discussing the three stages of the generative process.

Stage one is a string of symbols generated by a finite state

diagram. This string controls the number and type of embeddings in

the output character. 1/ Stage two is a two-dimensional constituent

array (generated via the process of frame embedding) which determines

the two-dimensional phrase structure of the output character and governs

the positioning, strength, and adjunctiveness constraints on the components to be selected. Stage 3 is the output character itself: a frame

filled with components selected (via a lexical look-up procedure)

from the lexicon.

The hierarchical classification is as follows. Any stage 1

string determines a number of constituent arrays and any stage 2 frame

determines a number of output characters. Thus, the set of all strings

1/ The various constraints and phenomena discussed here in terms of

the grammar have already, of course, been discussed in Section I,

to which the reader is now referred.

17
permitted by the finite state diagram ultimately determines the set of

all output characters. The hierarchy referred to can be depicted as

a tree structure, as follows:

String:

Constituent array:

Output character:

State Diagram

The path from KM to ^ to the output character H gives

the derivation of this output character in terms of how the grammar

generates it. The dashed line between nodes in the tree indicates that in general there are many (though finitely many) other

nodes at the same stage dominated by the same node of the previous

stage. 1/

1/ Or in the case of Stage 1, other nodes dominated or generated by

the state diagram.
B . DETAILS

To produce Stage 1 :

Stage 1 is an output string from a finite state diagram, which

consists of a number of states with input and output transitions. One

state is distinguished by having only output transitions, and this is

the initial state. One state is distinguished by having only input

transitions, and this is the final state. Along the transition arrows

there are either one or two output symbols (K, G, H, H', M, M'). 1/

MM'

1/ These symbols are explained on pages 21 and 22,

19
The initial state is entered and a process of random transition

from the initial state to the final state (perhaps through intermediate

states) is begun. At each transition from state to state one output

symbol is produced. If there is only one symbol along the transition

arrow, that symbol is necessarily chosen. If there are two symbols

along the transition arrow, one is chosen at random. The next transition causes a symbol to be produced to the right of the last-produced

symbol, and so on. As the final state is entered, the last (rightmost) symbol is produced, and the process terminates, producing the

string which is Stage 1: x x....x x.l/

1 2

• n-1 n ~

1/ Since n cannot exceed 5, it might seem inappropriate to set up the

general case for this and all the other stages and processes in the

grammar. However, by so doing, we have achieved ease of manipulation

and generality for such future applications as the study of frameembedding as an isolated process.

20
Sample output strings of the form x x . . .x x , generated

1 2 n-1 n

by the state diagram, are: KM* (by taking the topmost path through the

diagram), G (by taking the bottom-most path through the diagram), KHM

and KHHM (by taking two of the middle paths through the diagram)

.

The nature of any string generated by the state diagram determines

the size and complexity of the final output character. For example no

string may exceed length five, and this restriction guarantees that no

output character shall have more than five components.

Each symbol in the string represents a set of frames (see the

correspondence table on pages 23 and 24). The frames of each set have

certain properties in common, related to the embedding process, and to

the border-non-border distinction. Border here includes not only the

position class BORDER but also the discontinuous repetition cases,

which are represented by the same frame configuration as the BORDER

position class and which function in the grammar subject to the same

restrictions.

H V is the one frame which is a host only. That is, it

21
is the initial step with respect to frame embedding.

G= > is the one case of non-embedding. It is neither

a host nor an occupant.

H= ' H E

s H

, and H ' = •

are the sets of frames which function as both hosts and occupants.

They are the intermediate steps with respect to frame embedding. They

are distinct sets in that H is non-border and H' is border.

M=

'"st E

fi

, and M'= «

are the sets of frames which function as occupants only. They are the

terminal steps with respect to frame embedding. They are distinct in

that M is non-border and M' is border.

Finally, the state diagram (by distinguishing H from H' and M

from M' and by prohibiting certain transitions) guarantees that no

output string may contain more than two instances of "symbol -prime".

Thus it guarantees that no output character may contain more than two

borders.

22
To produce Stage 2:

And now, before discussing the process that generates Stage 2,

we will display the output symbol -to-frame correspondence table referred

to above. Each output symbol of the state diagram corresponds to a set

of frames. These output symbols appear as column headings. The filled

frames are listed underneath.

Table of Correspondences Between Output Symbols from Stage 1 and Frames:

K H H« M M«

H F H E

s

B

H W -

sf

E

f tf

W

s H

D

sf

E

s

D

H

W

sf

E

S

s

Ns N sF

H s

f

N

sf

S

s

23
H H' M M'

sf

There are two steps in the process that generates a Stage 2

constituent array from Stage 1 string. First, a sequence of frames

is created. Second, if there is more than one frame in the sequence,

these frames are compiled into a constituent array.

First, each symbol in any string of Stage 1 corresponds to a

column in the table of correspondences. To obtain the sequence of

frames, select at random one frame from each column indicated by the

Stage 1 string. Thus a sequence of frames is created: E . . .E . The

frames of the sequence E,...E consist of sub-frames which contain

either or both of two types of marks: (1) the mark H (for Host) which

sets up the process of frame embedding and (2) the marks called con- 24
stituents which will later be used in the process of component selection. At this stage in the process, since we are concerned with frameembedding, only the frame configurations and the mark H will be relevant

to our discussion.

Second, when there is more than one frame in the sequence, the

process of frame- embedding is initiated so as to compile the sequence

of frames into a constituent array.

To produce the constituent array, apply the frame- embedding formula:

Occupant-frame + Host-frame -» Product-frame

to the sequence of frames:

E E„ .... E 1 ^ n ^ 5 12 n

The frame-embedding process may be viewed as a recursive process

initiated by E which is the hypothetical square, or host-frame of

the first embedding. Hence we will set E.. = H.. ; H.. for the first

host-frame. The subsequence E E is the set of oc cup ant -frames

which are called upon during the embedding process, one occupant-frame

necessary for each embedding. Note that where there is only one frame

2.5
in the sequence, it is not possible to define either host or occupant

frames.

Embed occupant-frame E in host-frame H to obtain productframe H2. Redefine H2 as the host-frame of the second embedding. Embed

E in H_ to obtain product-frame H_. Continuing in this way, embed

occupant-frame E. in host-frame H._, to obtain frame H-, etc., until

E is embedded in ILi to obtain the final product-frame H , which is

defined to be the constituent array.

A distinction should be made between H and H. » i = l> 2, ..., n.

H^ is a well-formed frame with an H in one sub-frame. H is a mark

which indicates the precise location of embedding. H, = E, is the

hypothetical square with an H inside, h • Size and shape trans-

______ formations of this hypothetical square are created automatically as

we go through the recursive process. In other words, the sub-frame

containing an H, of a product-frame H., is considered to be the transformed hypothetical square.

H, which is present in one sub-frame of each E- except E and each

26
H- except R (constituent array), acts as the indicator of the subframe in which the next embedding is to occur. In this way H is the

activator of the frame- embedding process. When an H fails to appear in

a product-frame after an embedding has taken place, that product-frame

cannot be redefined as a host-frame, and the process stops. That final

product-frame where H fails to appear is, of course, H , the constituent

array.

This discussion of the recursive process of embedding occupantframe is host-frame to produce product-frame and redefining productframe of the previous embedding as host-frame and embedding again, until

the constituent array (Hj.) is obtained may be expressed in compact form

as the following sequence of formulas where + is the embedding operation:

E

2 + Hx

-• H2

E„ + H _ H

3 .2 .3

E, + H^^

1 <: n < 5

HE + H - H

n n-1 n

27
For each occupant-frame + host-frame embedding a product-frame is

produced. This product-frame is then the host-frame of the next

formula in the sequence. The recursive nature of the embedding process

is evidenced by the generation of a sequence of formulas in which there

is a successive production of product-frames and redefinition as hostframes. The sequence ends with the production of the final productframe H , the constituent array.

An example of the generation of a constituent array from an output

string is now given:

28
String KHM

Sequence of frames

Constituent array

Hi

Host frame of

1st embedding

1 2 3

H W

s H

N

sf

S

s (Occupant frames)

Product frame of

1st embedding

(redefined host frame)

/

W

s N sf

Ss

H,

Product frame of

2nd embedding

29
The string KHM gives the sequence of frames E , E„, E-, and

these frames then enter into the embedding process:

Occupant-frame + Host-frame -* Product-frame

E

i + H

i-1 -

H

i

The process is repeated in this case until Eg is embedded in H2 to

produce H~, the constituent array.

To produce Stage 3 :

We will now describe the process which generates an output character from a Stage 2 constituent array. The process selects a component

in the lexicon for each constituent which occurs in the constituent

array of Stage 2. The constituents are handled in order according to

the size of the sub-frames that they occupy - from largest to smallest.

For constituent arrays having two sub-frames of equal size a diagonal

order, from top-left to bottom right is followed. 1/ Specifically, the

1/ Actually, this corresponds to the traditional stroke order. A person

trained in traditional calligraphy writes most Chinese characters starting at top-left of the hypothetical square, and finishing at bottom-right.

30
"north" sub-frame precedes the "south" sub-frame; "west" precedes "east"}

and "border" precedes "interior."

These constituents are of the form £ , where £ is a symbol cor- a

responding to one of the position classes, or to one of the repetition

classes, and a Is a subscript which gives information on strength and

adjunct iveness. The combination of £a's allowed guarantees that each

output character has at least one non-adjunct, and at most one non-strong

component (see pages 15 and 16).

For instance, for the Stage 2 constituent array Wa , the

S

constituents are (in order) W . N~, and S. In the case of W_, we have

S SE O

2 as W and a, is the single subscript s. For N

f we have E as N and a. is

the double subscript sf . Finally, S is an example of E with a. as the

null subscript.

Next it will be necessary to describe the lexicon, an essential

tool used in the creation of stage 3.

31
The lexicon is a table with components 1/ down the side for each

row, symbols across the top for column headings, and tallies at certain

row-column intersection points signifying that the components may occur

in the positions signified by column headings W, E, N, S, B, I, or F, 2/

or may undergo the repetition processes signified by V, C, T or D. 3/

1/ Each of the components has a unique number associated with it. These

numbers are not a part of the formal apparatus of the grammar. We are

including them for the purpose of making lexical look-up easier for those

readers familiar with Chinese characters. The component numbers are of

the following form: S.T„N, where S is the number of strokes in the

component (S*l-19), T=l-8 characterizes the types of the last stroke

(last in the sense of traditional stroke order) of the component: 1 for

horizontal, 2 for vertical, 3 for dot, 4 forV-like, 5 for S -like, 6

for / -like, 7 for hooked, and 8 for multi-directional. N is the number

of the component in the sub- list.

2/ These column headings are abbreviations of the position classes

discussed in Section I. W*WEST, E=EAST, N=NORTH, S=SOUTH, B=BORDER,

I=INTERIOR, and F=FREE.

3/ These column headings are abbreviations of the repetition processes discussed in Section I. V=Vertical repetition, C=horizontal

Continuous repetition, T=Triangular repetition, and D=horizontal

Discontinuous repetition.

32
Sample Lexicon:

(The superscripts on some of the tallies are to be ignored. Their

significance will be explained on page 74.)

3.2.11 4

3.3.3

4.4.4 1

6.3.13 k

6.8.3

/u.

7.1.5

7.3.3 1

WEN V C T D

In general, the lexicon will be used in the following way. For

any constituent T. • we examine the column specified by Z, where £ is

a

any one of the eleven column headings, to determine the set of rows

which have tallies corresponding to the subscript a»

If a is f or includes either f or f (such as in S., or N f

),

we must further determine the subset of these rows which also have

tallies in column F. Note that the column F hag two functions. First,

it is one of the columns denoted by E. Second (as In this part of the

33
discussion), it is a column to be searched for adjunctiveness information in conjunction with the search in column £.

The following chart summarizes the types of subscripts which

may occur in each constituent mark, and the types of tallies which

match the subscripts.

34
Subscripts*

Tallies

by a

activated

Lnt

1 .

Column E Column F Explanation

8, », X The null subscript specifies

a row which has any tally in

the S column.

8 8 The s subscript specifies a row which has an s tally in

E.

f 8, B X The f subscript specifies a

row which has both an x tally in column F, and either

an s tally or an F tally in

column E.

BE s~ X The Sf subscript specifies

a row which has both an s" tally in column E, and an x tally in column F.

sf 8 X The sf subscript specifies

a row which has both an s tally in column E, and an x tally in column F.

sF 8 x" The sf subscript specifies a row which has both an s tally

in column E, and no x tally

in column F.

* Note that ST does not occur. See page 8 footnote.

35
For each of the first two cases (0 and s) a set of rows is

determined by searching column S. For each of the last four cases

(f, sf , sf, and sf) a set of rows is determined by searching column £,

and further, a subset of this set is determined by searching column F.

At this point, a single row is randomly selected from the set or subset

thus determined, and the component (if the symbol of the constituent

is W, E, N, S, B, I, F) or repetition of the component (if the symbol

of the constituent is V, C, T, or D) on that row replaces the constituent

being processed. This restriction prevents the class of ambiguous

derivations mentioned on page 16.

The lexical search procedure can be summarized in the following

way:

Constituent array

Constituents Ta

Column Headings

Lexical search

Components c

SCI

tallies tallies

Ta

El F

tallies

c

- Output character

36
An example of the generation of an output character from a

constituent array is now given.

The stage 2 constituent array, wW

8

, is processed to

generate an output character in the following fashion.

First, the constituents are ordered according to the decreasing

size of the sub-frames that they fill. Since there are two terminal

sub-frames of equal size, the order of these last two is determined by

the diagonal line procedure.

Then, the sets or subsets of rows which have tallies corresponding to each constituent are determined. In other words, column W will

be searched for the set of rows which have tallies corresponding to subscript s. Column N will be searched for the set of rows which have

tallies corresponding to subscript s", and further, we determine the

subset of this set of rows having x tallies in column F. Finally

column S will be searched for the set of rows which have tallies

corresponding to subscript s. To illustrate what is taking place at

this point, the tallies corresponding to W will be circled once in

s

37
the sample lexicon, the tallies corresponding to N- will be circled

sf

twice, and the tallies corresponding to S will be circled three times,

3.2.11

3.3.3

4.4.4

6.3.13

6.8.3

7.1.5

7.3.3

H

t

X

*

A-*

WENSBIFVCTD

©

©

Then one of the rows in each set or subset is picked at random,

with the constraint that the row selected for N- may not be the same

sf '

as the row selected for S , since they are in construction with each

other. Again, one, two and three circles will be used to illustrate

38
the tallies corresponding to the sets or subsets of tallies.

3.2.11

3.3.3

4.4.4

6.3.13

6.8.3

7.1.5

7.3.3

'A t

X

*

fc

a

WENSBIFVCTD

Finally, the component which occurs on the row of the tally

just selected replaces 2 . a.

39
This example can also be represented in the following way:

Constituent array ww

s s 8

Constituents W. V

Column headings

Lexical search

Components

N

a

f k *.

Output character

f

1

X

40
Sample Derivation from Total Grammar;

String K H H M

Constituent array W s

C

S

S

Output character

1 a

41
III. EVALUATION

A. GENERAL REMARKS

How are grammars for component combination to be evaluated? There

are two criteria which are used here: completeness and tightness .

These criteria are well-known in the literature of natural language

study. Tightness and completeness taken together in fact constitute

the transformationists' "minimal requirements" on natural language

grammars - that they should generate all and only the grammatical

sentences of the languages under study. 1/

There are, of course, other conditions that might be put on a

successful grammar of component combination - conditions having to do

with simplicity, with the choice of a grammar model, with relative

correctness of structural descriptions assigned by the grammar to

output objects, with integratability of the grammar with other

grammatical processes necessary in the total description of Chinese

1/ See, for example, Bach (1), page 5

42
characters, with possible applicability of the grammar or grammar model

to other two-dimensional languages, and so on. In this note, however,

we will be concerned only with completeness and tightness.

GCC-3 constitutes an attempt to construct a simple grammar which

is balanced between completeness and tightness. It seems to be nearly

as simple as possible in terms of the size of the lexicon of components

and the number and complexity of grammar rules. It is neither 100 per

cent tight nor 100 per cent complete, but it would seem that any adjustment to make it tighter would result in less simplicity and/or

completeness, and that any adjustment to make it more complete would

also result in less simplicity and/or tightness.

1. Completeness

A complete grammar for the language of Chinese characters is one

which generates all of the well-formed characters in the language.

This is an extremely difficult condition to satisfy, if only because

it is so difficult to determine in many cases exactly what is and what

43
is not in the language. 1/ The problem here is probably no worse than

the problem in natural language study of deciding for border-line

strings whether or not they are grammatical sentences of the language

under study.

A less demanding condition is that a successful grammar generate

all the well-formed characters in some target corpus.

Such a grammar will be called "corpus-complete", and a grammar

that is complete with respect to the language will be called "languagecomplete." Only corpus -completeness will be used in evaluating GCC-3.

The grammar might then be tested against other corpora for corpuscompleteness. In this way, the language- complete grammar would be

approximated by the grammar which is corpus -complete for several

corpora, but it would never be known whether the grammar actually

attains language-completeness.

1/ Decisions on what is and what is not in the language are currently

based on judgments given by the informant.

44
2. Tightness

A tight grammar for the language of Chinese characters is one which

generates only well-formed Chinese characters. Tight grammars are easy

to come by. A trivial example would be a "grammar" which lists some

small number of actually-occurring characters.

In a way analogous to the completeness situation, we may speak of

corpus-tightness and language-tightness. If a GCC is language-tight,

then it generates only those characters in the target corpus. It

turns out that any serious GCC, i.e., one which attempts to reveal

the internal structure of the characters (and does not simply list

characters), is almost bound not to be corpus-tight. This is an

empirical observation, and an analogous observation probably holds for

any serious attempt at grammar construction for natural language corpora.

Only language-tightness is used in this evaluation.

Lack of completeness implies insufficient output, or under-generation. Lack of tightness implies too much output, or over-generation.

We have discussed over-generat ion of output characters so far, but

45
there is another type of over-generation, and that is the over-generation of derivations per character.

An output object from any grammar is said to be ambiguous if the

grammar can generate it in more than one way, i.e. , provides more than

one derivation of it. The problem of whether or not there are ambiguous

characters, or what would be meant by "ambiguous character" have by no

means been solved. However, it seems that every character in the

language is uniquely segmentable into components by the informant, and

therefore our current position is that there are no ambiguous characters

in the language of Chinese characters. Consequently, a grammar that

generates any character is more than one way "over-generates".

B. EVALUATION OF GCC-3

1. Completeness

GCC-3 appears capable of accounting for 94% of the acceptable

46
characters in Mathews*. 1/ The characters that GCC-3 cannot account

for fall into seven known small classes. 2/ The grammar could be

adjusted so as to account for these classes, but only with a great loss

in tightness and/or simplicity.

First, there are those characters which contain more than five

components. Since the state diagram in the grammars sets a maximum of

five components per character, such characters cannot be accounted for.

Examples are: Jjjf ( ^ , +-f- , E) > J

~l > A ' and

L_ ) and

^ (+•/", jt » /V » .±- 'A, » and

/n\ ).

1/ To arrive at an indication of how complete GCC-3 is, we conducted

the following test. We selected (via a random number table) 200

characters from Mathews'. We then attempted to generate each character

from GCC-3. We found that GCC-3 could generate 188 of the 200—some

in more than one way. (See the discussion of ambiguity on pages 56-62),

2/ With the exclusion of possible clerical errors.

47
Second, there are those characters which are (or which contain subparts which are) complex in both NORTH and SOUTH (represented by the

frame

H

H

H H

or in both EAST and WEST (represented by the frame

Examples of

) . Examples of H

H

are: in construction

, -r/Li with ^*- ) and P£ ( j£j in construction with

^

).

G=7

H H are 4

Xfc C !+- in construction with t

and m < _H_ in construction with o,o )

f°3 £

Third, there are those characters which contain weak components

in strong positions: either a weak component in construction with a

weak component or a weak component in construction with a complex

character sub-part. Examples of characters having a weak component in

construction with a weak component are: £3 , where £ 3 and

tti are in construction but both weak, and ^E , where ^t

and )il are in construction but are both weak. Examples of characters in which there is a weak component in construction with a complex

character sub-part are: ipjj?. > where 7 is weak, but in construction with fi> » and mjtj , where ~fc is weak but in construction

48
with

Fourth, there are those characters which contain more than two

BORDERS. Since the state diagram prohibits any output character

from having more than two BORDERS, such characters cannot be accounted

for by the grammar. Examples are J7=g , which contain the three

BORDERS X^_ , F3

, and "1 , and 3ki , in which there ai

the three BORDERS i , *~1

, and j

Fifth, there are those characters in which there is a BORDER in

construction with a non-FREE component. Since in the grammar, the

set of INTERIORS (those components which are in construction with

BORDERS) form a proper subset of the set of FREES, BORDER plus nonFREE structures cannot be accounted for by the grammar. The only

known examples are x *T , in which the INTERIOR - (in construction with BORDER / ) is an adjunct, and ^57 , in which

the INTERIOR / (in construction with BORDER W ) is an

adjunct.

Sixth, there are those characters which contain the form «.

.

49
(This form is not to be confused with , a component in the

lexicon, and for structural reasons cannot be considered simply a

shortened variant of .) There are doubts as to whether this

form should be considered a component. If it were, it would seriously

affect the tightness of the grammar. Therefore, all that can be said

is that there are characters which contain it and cannot be accounted

for by the grammar because the grammar does not list it as a component.

Examples are ~/j\ > where — is between /V and ^ ,

and i*L » where — is between *"^* and ./V.

Seventh, there are a few characters, which if segmented into

components, would yield extremely irregular frames. 1/ Examples are:

{i]\'/]\ f whose frame would be something like , and

1/ These constitute a type of component superimposition. Component

superimposition is discussed in Rankin (4). However, the type of

superimposition discussed there does not include these characters.

50
pjkl , whose frame would be something like Since the

only frames in the frammar are , and

or results of combining these, characters segmentable into

frames like those above are not accountable for by the grammar.

There are two final observations. First, some characters which

cannot be accounted for by the grammar fall into more than one of the

classes discussed above. Second, some characters which appear to fall

into one of the above classes are actually accounted for by the grammar.

This is so, because there is always the option of listing as a single

component those complex sub-parts which give trouble. For example,

the complex sub-part y is listed as a component, even though it

might fall into class seven above, and the complex sub-part /JQ

is listed as a component even though it might be segmented into yl

plus \Z7 > which segmentation would cause characters containing

JjQ to fall into class three above. Generally, decisions on segmentation are motivated by three considerations: (1) a structure is

segmented into two components if the two components either must not

51
touch or need not touch; (2) a structure is segmented into two components if the segmentation generally corresponds to one of the three

recognized frame types: • , and ; (3) a

structure is segmented into two components if each sub-structure can

occur in different environments. 1/

2. Tightness

A. Over-generation of output characters

Rather than sampling random output with a view to assigning a

tightness percentage, we feel it is more to the point ot sub-classify

the unacceptable output on linguistic grounds. The reason is that

potentially there exist infinitely many grammars equivalent to GCC-3 in

the sense that they all generate the same language, all having different

tightness percentages associated with them. For example, we could construct a GCC-4 from GCC-3 by substituting the following set of trans1/ For a previous and more detailed discussion of segmentation, see

Rankin (4) , chapter 4.

52
itions for the bottom-most transition which produces the single

symbol G.

Then there would be added to GCC-3 rules by which Gl would

ultimately determine the subclass of the current FREE class which

contain, e.g., fewer than five strokes: G2, G3 , and G4 would respectively determine subclasses containing 5-to-10 strokes, ll-to-15

strokes, and more than 15 strokes. GCG-4 would generate precisely the

same language as that generated by GCC-3, but random output from GCC-4

would contain a higher percentage of acceptable characters than random

output from GCC-3. This is so because GCC-4 has a higher probability

of generating single- component characters, and all of these are by

definition acceptable.

There are three classes of unacceptable output. The first class

of unacceptable output contains characters of excessive size. Here,

53
there are three sub-classes. First there is a sub-class which contains

characters of excessive overall size. Examples are (1) 1/ and (2).

The problem with these output characters is that the frame for each has

the maximum number of sub-frames, and each sub-frame is occupied by a

component which is itself very large. Second, there is a sub-class

containing characters which are excessively horizontal. Examples are

(3) and (4). The problem here is that the frames for these characters

are of the maximum horizontality allowed by the grammar, and the subframes are filled with "very horizontal" components. Then, there is a

corresponding excessively vertical sub-class. Examples are (5) and (6),

The frames for these characters are of the maximum vertical ity allowed

by the grammar, and the sub-frames are filled with "very vertical"

components

.

1/ This output character and the following five (where there are

numbers in parentheses) are found in Appendix D.

54
The second class of unacceptable output contains characters in

which there are co-occurrence problems. That is, it is not the case

that, say, every WEST can occur with every EAST (even given the strength

and adjunctiveness constraints), and so on for other pairs of classes.

The one pair of classes which gives rise to the greatest number of cooccurrence problems is the BORDER-INTERIOR pair, but there are cooccurrence problems for every pair. Examples are yf 4r > "-^ » an<^

?!, , in which ft and J-^ » </— and — , and

^T and , respectively s imply should not co-occur.

Finally, there is a class of unacceptable output characters which

contains certain components in strong positions, these components

being only moderately strong. There seems, in fact, to be a scale of

strength, Among WESTS, for example, the scale ranges from, say /

(very strong) through -^r- (moderately strong) to Jfi. (weak).

Currently in the grammar, the class of strong components includes very

strong and moderately strong components. This blurring of the scale of

strength gives rise to such unacceptable output characters as jrc}f

55
, where ^y and _¥- are only moderately strong

( -jrr and J\_, being weak).

B. Over-generation of Derivations

There are three types of ambiguous characters. Actually, ambiguity

is not apparent at the output character level, but only at the posttransducer level. This is because our current output characters contain

parts of their deriviations - their frames. For example, at the output

character level, the following are distinct: tIA and

f tf

However, at the post-transducer level both would be realized as m •

which is for that reason ambiguous. In this treatment, we will have to

discuss ambiguity as if we already had the output transducer referred

to on page iv and we will use the term "character" to mean "posttransducer character."

First, some characters which are (or contain) horizontal arrays

of three or more components are ambiguous with respect to the grouping

of components. For example, 'fie/r has two derivations, one of which

imposes a '[• plus ffln" grouping, the other of which imposes a

56
• Lfflf plus fr grouping. Then some of the characters which are

(or contain) vertical arrays of three or more components are ambiguous, — Jo"

The sub-part o of the character 'fl. has two derivations, one

"J

of which imposes a "q" plus -4— grouping, the other of which

imposes a plus jr. grouping.

This type of ambiguity is introduced in the first step of the

process that generates Stage 2, that is, in the selection of frames

from the table of correspondence. It is possible for two distinct

sequences of frames (which are generated by the same output string)

ultimately to determine the same character. This is shown in the

following two derivations of TEjI • In these, and the derivations

to follow, the single arrow -» is used for "directly determine" and

the double arrow =£ for "ultimately determine".

57
Two derivations of ' *J3

KHM KHM

'

H W

s H

sf

E H H E

s s f Ef

V V

W -li£ E E

f

E

s V V

w

Output

Transducer

k

Output

Trans ducer.

m m

58
Second, there are those characters which are themselves (or

which contain components which are) further segmentable into components,

For example, «• is listed in the lexicon as a single component -

because of its frequency of occurrence (specifically, it is a strong

EAST). It is also the case that r» can be generated by the grammar

as /!_, in construction with ^^

This type of ambiguity is introduced at Stage 1, where it is

possible for two distinct output strings from the state diagram ultimately to determine the same character.

59
KM

N7f

Output """"N Transducer J

/L

Output

Transducer

60
Finally, some characters are (or contain sub-parts which are)

anal yz able in more than one way-but into the same frame . An example

is -5f- which is analyzable as either

J>/ or N/

a- ft

. So

«./ •Jf- in isolation is ambiguous, and any character which contains

j£_ as a sub-part is ambiguous.

This type of ambiguity is introduced (as in the first type discussed here) in the frame selection process. However, unlike the first

type, these characters have identical frames at the output character

level

.

61
Two derivations of

-J^-

KM

V

KM

v

N,f Nsf

Sf

\

tHOutput

Transducer

v/

*t

Output

Transducer

?1-

62
)

ACKNOWLEDGEMENTS

The research summarized in this note was supported by Rome Air

Development Center under RADC contract number (30-602 ) -66-4042. We

are grateful for this support.

We wish to thank the following people for reading earlier versions

of this note and for making valuable suggestions: Dr. Stephen J.

Tauber, Mr. H. H, Ku, and Mr. David Rosenblatt of the National Bureau

of Standards; Mr. W. C. Watt of Technical Operations Research; and

Professor E. I. Burkart of American University.

Finally, we are indebted to Delores Allnutt of the National Bureau

of Standards for typing the final version.

63
APPENDIX A

Classes of Mathews' entries which are deliberately excluded from the

corpus (Mathews* sometimes lists several semantical ly related entries

under one number. The number in parentheses indicates which of these

entries is referred to .

)

The following classification of excluded Mathews' entries arises

out of a first approximation to a filtering process aimed at excluding

entries which are not totally well-formed. We selected these particular

ones in the following way. First, Mathews' lists all of these characters as secondary or tertiary variants. Second, the informant considers most of them to be less than acceptable. . Third, they do not

fit well into the current grammatical framework. This is by no means

a definitive listing or classification.

64
1. "Radicals" which are cited in Mathews' as separate entries

but which do not occur in isolation in everyday usage. 1/

240 (3) &

1282 (2) 1_

1373 (2) K>7

2735 (3) 1 xx

2989 (2) t

3037 (2)

I5

3097 (2) \

3153 (2) A

4737 (2) %

5570 (2)

1439 (2

1650 (2

2735 (2

5788 (3

5838 (2

5922 (2

6124 (2

6739 (3

7666 (2

<«

/

'J + •/-

1/ A comparable example in English lexicography is the listing of bound

morphemes (e.g., the prefix "pre-"), which do not occur as free words.

Many Chinese dictionaries do not even list these radicals as lexical

entries.

65
2. Printed forms whose hand-written variants are acceptable. 1/

297 (2) g 5283 (3)

^

2309 (3) jT) 5788 (2) -jr

3. Abbreviations whose unabbreviated forms are acceptable:

560 (2) J*L 3366 (3) yjv.

921 (2)

^ 3617 (2)

-J£]

1082 (2) ^y 3953 (2)

^

1205 (2) |g 6534 (2) £

2222 (2)

^

7030 (2) 7J

2753 (2) iQ_ 7615 (2)

^

1/ This list includes only those printed forms for which Mathews*

lists acceptable hand-written variants. In other cases, Mathews' lists

printed forms only (without their hand-written variants). We account

for these by copying into our lexicon only their hand-written variants.

For example, we list in our lexicon ? for the Mathews' entry - ,

J for X , iL for *|- , and

^

for -^-

66
4. Pictorially bizarre variants of acceptab

3883 (3

3953 (3

3992 (2

4083 (2

4464 (2

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67
APPENDIX B

1. Variation Processes and List

Component variation has been extensively studied, but a final

statement on this phenomenon is not ready for presentation. What

follows is a statement of four general processes and a list of rather

more ad hoc variations. Component variation belongs properly in the

rules of the output transducer, which has not been constructed, and

is presented here mostly as an aid to human generation of output characters.

Further, some of the general variation processes may not be

precisely stated here, and there are indications that some of the

instances of ad hoc variation should be grouped together into general

processes.

Variation Process 1^, ( BORDER)

For certain components whose base forms 1/ have or [^

1/ A base form is that form of a component which can occur in isolation,

those which belong to FREE.

68
in their "eastern" portions, this process causes the BORDER variant

to assume a shape wherein becomes and becomes

I

( . Examples: 2.5.7: f\^ - j] , , 12.8.1: *± - ^g_

Variation Process 2_, (WEST )

For certain components which have in their "south central"

portions, this process causes the WEST variant to assume a shape wherein becomes / . Examples: 4.1.7: ir -> i^ , and

8.1.3: >6- - >£

Variation Process 3_, (WEST)

For certain components which contain ^£ or a ^J< -like

structure, this process causes the WEST variant to assume a shape

wherein ^-^ becomes v . Examples: 4.4.21: rf\. -> 5F >

and 7.4.6: j£ _+ Jj?

Variation Process 4, ( BORDER)

For certain components which have V or V in their "southeastern" portions, this process causes the BORDER variant to assume a

shape wherein \ or \ become \^_ . Examples: 5.4.5: u\

69
/v - A- ' and 5 - 4 - 8: tK - ^

5. Ad hoc variations

Number Base Form Position Variant Form

2.1.2

2.2.3

2.4.2

2.4.4

2.5.3

2.8.14

3.1.4

3.1.6

3.1.13

3.2.2

3.2.3

3.2.7

3.2.8

3.3.1

+ B r

X. N X

/v N,S /v

A I (sometimes) A

7b B 71)

f- W 1

a B a

-^- sometimes

^

+ B f

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4- I (sometimes) f

i^- S #

t B -t

70
Number Base Form

3.4.1

3.5.8 f

4.1.6 j=\

4.1.18 £}

4.2.9 -41

4.2.16 -i4.3.11 ^

4.4.4 AT

4.4.16

4.4.21

4.5.9

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4.7.5

4.8.10

9

z

Position Variant Form

N (sometimes) A.

N (sometimes) 4*

S n

sometimes Q

E t

N,S 4-

B -x

N A_

S X

B *-_

S <<-

S (sometimes) *

B J

B '}

B fB

71
Number Base Form Position Variant Form

5.2.4 w

B

$

P

5.3.10 /I B n

5.4.13 %. W %

5.4.19 7v N

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5.8.6 ;iti B ^ L

6.1.5 "£ s •£•

6.1.18

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6.3.2

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6.7.1

8.2.7

8.3.6

4

b *r

w J[

-fw f6.3.13 £ W £

*|y

8.1.6 m N *H

72
Number Base Form Position Variant Form

9.3.3

9.4.4

11.3.1

11.8.1

12.3.2

t

bt.

13.3.1 M

N

W

B

N

yK

^

N

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13.7.2

14.1.1

£3

/I

B £3

71

73
APPENDIX C

The Lexicon

The lexicon is described on pages 34 through 39. There is, however, one extra-grammatical type of information included in the lexicon

which must now be explained. There are superscripts (1-5) on some of

the tallies, 1/ the significance of these superscripts is that the

component on the row of this tally, when it occurs in the position

class specified by the column heading of the tally, undergoes a shape

variation. Superscripts 1-4 refer to variation processes 1-4 described in Appendix B; superscript 5 refers to the ad-hoc list of

variants in Appendix B. The ad-hoc list follows the order of appearance of components in the lexicon.

1/ In two cases the component itself is superscripted. There are

cases where there is more or less free variation among the component

variants.

74
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8.3.4

8.3.5

8.3.6

8.3.7

8.3.8

8.3.9

8.3*10

8.3.11

8.3.12

8.4.1

8.4.2

8.4.3

£3

*

t

$

|\

£

JiL

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£

/iv

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-5

s

-5

5

X X

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a

104
WENSBIFVCTD

8.4.4 £

8.4.5 *

8.4.6 *

8.4.7 t

8.4.8 %

8.4.9

8.4.10 *.

8.4.11

8.4.12 k

8.7.1 A

8.7.2

>

8.7.3

8.7.4 A

8.8.1 ft

8.8.2 5fb

8.8.3 n

105
9.1.1

9.1.2

9.1.3

9.1.4

9.1.5

9.1.6

9.1.7

9.1.8

9.1.9

9.1.10

9.2.1

9.2.2

9.2.3

9.2.4

9.2.5

9.3.1

9.3.2

8l

&

OOQ

CM

%

ffi

m

it

H

h

4iU

WE NS BI FVCTD

-2

s

106
9.3.3 i w E N S B I F

V

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D i 8

-58 X

X

9.3.4

a 8 X

9.3.5 M, I 1 X

X

X

9.3.6 s X

X

9.3.7

9.3.8

9.4.1

A S S8 8 s XXX

XXX &

H.

9.4.2 £ S 8 X

9.4.3

9.4.4

9.4.5

Q 5 s 8S 88 4X

X

XX

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X

9.4.6

9.7.1

9.8.1

9.8.2 * s8 8SS S8 I3 XX

XXX

^nfc &^

10.1.1 * S 8 8 X

107
WENSBIFVCTD

10.1.2

10.1.3

10.2.1

10.2.2

10.2.3

10.2.4

10.2.5

10.3.1

10.3.2

10.3.3

10.3.4

10.3.5

10.3.6

10.3.7

t

&

Jo.

5l

a

IT

ti

I

10.3.8

10.3.9

10.4.1 it

108
WEN B I V C T D

10.4.2

Jk

10.5.1 u

10.7.1 M

10.7.2 n

10.7.3 f

10.8.1

fit,

10.8.2

11.1.1

[IT)

11.1.2 &

11.1.3 k

11.1.4 t

11.1.5 k

11.1.6

V

m

11.1.7 m

11.1.8 i

11.1.9 t

109
11.2.1 #

11.3.1

11.3.2 h

11.3.3

11.3.4 \

11.3.6

11.4.1

11.4.2

11.5.1 At.'X2L

11.8.1 'tots

12.1.1 S3

12.1.2 an

12.2.1

*+

12.3.1 i » «\

WENSBIFVCTD

11.3.5 ft

x

12.3.2 SA -5s 110
W E N S B I V C T D

12.3.3

12.3.4

12.3.5

12.3.6

12.3.7

12.3.8

12.4.1

12.8.1

at

&%

tf%

i • «

\

7La

13.1.1

13.1.2

13.1.3

13.1.4

13.1.5

j£7

-£-

£?

ife. 13

/.v

13.2.1 ^

13.3.1 £M

13.3.2

111
w ENSBIFVCTD

13.7.1

13.7.2

13.8.1

13.8.2

m

8

i

s

s

I

s

I

I

s

s

s

8

I

s

8

I

S

I

8

S

s

s

8

8

S

S

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x

5

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X

X

X

X

X

X

X

X

X

X

X

X

X

X

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$j

14.1.1

14.2.1

14.3.1

Alt 1

1 if*

14.3.2

irx'

14.3.3

^

14.3.4

14.4.1

11;

at

li)

14.4.2 m.

15.2.1

15.4.1

15.7.1

H

^a

112
15.7.2

WEN V C T D

16.1.1

16.1.2

16.3.1

16.4.1

51? a la

Si

iSi

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17.2.1

17.3.1

17.3.2

aao

5\

17.3.3

18.8.1

19.8.1

titi

113
We now present a listing of components that occur in only one

position.

WEST only:

2.2.5 13.3.18

+

2.6.2 / 3.5.4

*

3.1.5 t 3.5.5 *

3.2.10 i3.5.9 i

3.2.11 \

3.6.1 *

3.3.12 C- 3.6.2

EAST only:

.5.12 ^fe

4.6.1

5.3.16 ^

6.3.1

7.5.2

2.5.5 V 3.7.3 \—:

4.7.3

114

2 7.3 i|

NORTH only :

2.1.1 /- 2.7.2 i—? 4.1.9 Jt£

2.1.3 .3- 2.8.9 ^7 4.2.14 +^

2.1.4 -1- 3.1.11 y^v 4.3.19 5"?

2.3.3 7 3.3.9 Z; 4.5.6 <0

K
4.7.4 *±-, 7.7.1 Jk, 10.7.1

^

5.4.23 /K. 8.7.1 jg^ 11.1.7 {ffl

6.3.20 A/: 8.7.3

%xx, 13.7.1 ^^

6.4.8 /^ 8.7.4 ^L, 15.7.1 ffi?

6.7.2

^

9.7.1

^^

SOUTH only :

3.8.14 ;iu 4.3.18 ni\ 6.4.12 *

BORDER only:

1.8.3 L 3.3.16 f 5.6.1

1.8.4 1 3.4.4 JL. 6.3.8 n

2.2.4 u 3.5.7

1 r 6.5.4 r

2.5.4 /3.8.10 h 6.8.7 A

2.5.6 r 4.1.17 Q 7.5.3 /

2.8.7 c 4.4.18 i_ 7.8.2 *

3.1.14 / 4.5.10 > 8.3.12 *s

3.2.12 r 4.8.7

^

12.1.12

a o

o a

115
FREE only ;

1.7.1

J

3.2.9 Y 5.1.24 £b

3.4.5 1 5.3.13

V

3.6.3 15.8.7 m,

3.7.2 t 6.1.13 n

4.1.1 E? 6.2.8 %

4.1.20 # 6.3.11 1

4.2.12 ft 6.3.12

4.4.19

^

6.3.14

4.8.8

7.3.10

jf>

8.3.11 IL

8.4.3 7K

8.8.2

~$f10.3.4

11.1.4

11.5.1

14.2.1

16.3.1

4thL ft

mi

-^ 6.7.3 ^ 17.3.2 Ml

116
APPENDIX D

£3K&W&

^

3

>tfc>

***

A1A

1M.

W

117
BIBLIOGRAPHY

1. Bach, E., An Introduction to Transformational Grammars , New York:

Holt, Rinahart and Winston, 1964.

2. Chomsky, N., Syntactic Structure , The Hague: Mouton and Company,

1957.

3. Mathews, R.H. , A Chinese-English Dictionary , Cambridge, Massachusetts* Harvard University Press, 1960.

4. Rankin, B.K. Ill, "A Linguistic Study of the Formation of Chinese

Characters," University of Pennsylvania Dissertation, 1965.

5. Rankin, B„K. Ill, Sillars, W.A., and Hsu, R.W», "On the Pictorial

Structure of Chinese Characters", National Bureau of Standards,

Technical Note 254, Washington, 1965.

118 »U.S. GOVERNMENT PRINTING OFFICE: 1966 —251-022/53

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