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F O R M A L S P E C I F I C A T I O N O F N A T U R A L L A N G U A G E S Y N T A X

A B S T R A C T

T h e t w o - le v e l g r a m m a r i s in v e s t i g a t e d a s a n o t a t i o n f o r g i v i n g fo r m a l

s p e c i f i c a ti o n o f t h e c o n t e x t - f r e c a n d c o n t e x t - s e n s i t i v e a s p e c t s o f n , ~ t u r a l

l a n g u a g e s y n t a x . I n t h i s p a p e r , a l a r g e cl a s s o f E n g l i s h d e c l a r a t i v e

s e n t e n c e s , i n c l u d i n g p o s t - n o u n - m o d i f i c a t l o n b y r e l a t i v e c l a u s e s , i s

f o r m a li z e d u s i n g a t w o - le v e l g r a m m a r . T h e p r i n c i p a l a d v a n t a g e s o f t w o -

l ev el g r a m m a r a r e : 1 ) i t i s v e r y e ~ s y t o u n d e r s t a n d a n d m a y b e u s e d t o

g i v e a f o r m a l d e s c r i p t i o n u s i n g a s t r u c t u r e d f o r m o f n a t u r a l l a n g u a g e ; 2 ) i t

i s f o r m a l w i t h m a n y w e l l - k n o w n m a t h e m a t i c a l p r o p e r t ie s ; a n d 3 ) i t i s

d i r e c t l y i m p l e m e n t a b l e b y i n t e r p r e t a t i o n . T h e s i g n i f i c a n c e o f t h e l a t t e r f a c t

i s t h a t o n c e w e h a v e w r i t t e n a t w o - l ev e l g r a m m a r f o r n a t u r a l l a n g u a g e

s y n t a x , w e c a n d e r iv e a p a r s e r a u t o m a t i c a l l y w i t h o u t w r i t i n g a n y

a d d i t i o n a l s p e c i a l iz e d c o m p u t e r p r o g r a m s . B e c a u s e o f t h e ea s e w i t h w h i c h

t w o - le v c l g r a m m a r s m a y e x p re s s lo g i c a n d t h e i r T u r i n g c o m p u t a b i l i t y w e

e x p e c t t h a t t h e y w i l l a l s o b c v e r y s n i t a b l e f o r f u t u r e e x t e n s i o n s t o

s e m a n t i c s a n d k n o w l e d g e r e p r e s e n t a t i o n .

1 . I N T R O D U C T I O N

F o r m a l s p e c if i c at i o n s o f n a t u r a l l a n g u a g e s y n t a x s h o u l d s e r v e a s a

s t a n d a r d d e f i n i t i o n f o r t h e s y n t a x o f t h e s u b j e c t l a n g u a g e . T h e

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

u n d e r s t a n d a b l e , a n d u s e f ul t o l a n g u a g e s c h o l a rs , u s e rs , a n d i m p l c m e n t o r s

w h o w i s h t o d e v e l o p a p a r s e r f o r t h e t a n g u a g c t o r u n o n a c o m p u t e r .

F u r t h e r m o r e t h e s p e c i f ic a t io n s h o u l d b e m a t h e m a t i c a l l y r i g o r o u s t o t h e

d e g re e t h a t a n i m p l e m e n t a t i o n o f t h e l a n g u a g e c a n b e a u t o m a t i c a l l y

d e r i v e d f r o m t h e s p e c i f i c a t i o n { 1 0 ] . U n f o r t u n a t e l y m a n y o f t h e s e a i m s a r c

d i f f ic u l t t o a c c o m p l i s h p r i m a r i l y b e c a u s e o f t h e d y n a n r i c a n d i n f o r m a l

n a t u r e o f n a t u r a l l a n g u a g e . F o r m a l s p e c i f i c a t i o n i s s t i l l a w o r t h y g o a l to

t h e d e g re e a l lo w e d b y p r e s e n t k n o w l e d g e a b o u t n a t m ' a l l a n g u a g e a n d i u

t h i s p a p e r w e p r o p o s e a mctalanguage for s p e c if y i n g b o t h s y n t a x a n d

s e m a n t i c s o f n a t u r a l l a n g u a g e t h a t h a s p o t e n t i a l f o r s a t is f y i n g t h es e g o a l s .

T h e m c t a l a n g u a g e w e p r o p o se i s t h e two- l evd grammar [1 6 } (a l s o c a l l e d

W - g r a m m a r s a n d t l gs ) . T w o - l ev e l g r a m m a r s h a v e b e e n u s e d e x te n s iv e l y f o rs p e c if y i n g t h e s y n t a x a n d s e m a n t i c s o f p r o g r a m m i n g l a n g u a g e s [ 2] b u t

t h e i r u se i n s p e c i f y in g n a t u r a l l a n g u a g e w a s f i r s t i n t r o d u c e d b y t h e a u t h o r s

[7 , 8, 9] .

E x i s t i n g f o r m a l s p e c i f ic a t io n m c t h o d s f o r n a t u r a l l a n g u a g e s y n t a x

t a k e m a n y f o r m s . O f t h e s e, s o m e o f t h e m o r e c o m m o n a r e a u g m e n t e d

t r a n s i t i o n n e t w o r k g r a m m a r s [ 1 81 , t r a n s f o r m a t i o n a l g r a m m a r s [ 1] , a n d

g e n e ra l iz e d p h r a s e - s t r u c t u r e g r a m m a r s [ 5] . T h e s e m e t h o d s a n d o t h e r s a r c

a l s o s u r v e y e d i n [ 1 7] . T h e d e g r e e t o w h i c h a n y f o r m a l s p e c i f i c a ti o n m e t h o d

s a t i s f i e s t h e a b o v e s t a t e d g o a l s i s s o m e t i m e s d i f f i c u l t t o e v a l u a t e a n d r e l i e s

o n s u b j e c t i v i t y . T h e a u t h o r s d o n o t i n t e n d t o e v a l u a t e th e s e e x i s t i n g

m e t h o d s w i t h r e s p e c t t o t h e r e q u i r e m e n t s o f f o r m a l s p e c i f i c a ti o n l a n g u a g e s

b u t w i l l i n s t e a d c o n c e n t r a t e o n w h y t w o - l e v e l g r a m m a r s s a t i sf y t h e

n e c es s a ry g o a l s i n a m a t h e m a t i c a l l y r i g o r o u s b u t r e a d a b l e a n d e a s y t o

u n d e r s t a n d w a y . I n t h i s p a p e r , t h e t w o - le v e l g r a m m a r m c t a l a n g u a g e w il l

b e u s e d t o d e f i n e a l a r g e c l a s s i f i c a t i o n o f E n g l i s h d e c l a r a t i v e s e n t e n c e s ,

e x t e n d i n g w o r k d e s c r i b e d i n [ 8 ] a n d [ 9 ] . W e w i l l e m p h a s i z e t h e method ofu s i n g t w o - l e v e l g r a m m a r s f o r t h i s p u r p o s e a n d t h e a d v a n t a g e s g a i n e d

r a t h e r t h a n a n y p a r t i c u l a r c h a r a c t e r is t i c s o f t h e g i v e n g r a m m a r .

2 . T W O - L E V E L G R A M M A R S

A t w o - l e v el g r a m m a r c o n s i s ts o f t w o s e l ) a ra t c g r a m m a r s , t h emstaprodu ctlon rule~ (metarules) a n d t h e hyperrules. T h e m e t a r u l e s a r e

g e n e r a l l y c o n t e x t - f r e e r u l e s w h i c h t a k e t h e f o r m :

M E T A N O T I O N :: h y p c r n o t i o n - 1 ; h y p c r n o t l o n - 2 ; .. . ; h y p e r n o t i o n - n .

w h e r e M E T A N O T I O N i s t il e l e f t- h a n d s i de " n o n t e r m i n a l " s y m b o l o f th e

p r o d u c ti o n a n d h y p e r n o t i o n - 1 , h y p e r n o t l o n - 2 , . . . h y p c r n o t i o n - n a r e t h e n

a l t e r n a t i v e s o f t h e p r o d u c t i o n r i g h t - h a n d s i d e . E a c h h y p c r n o t i o n c o n s i s t s

o f protonotions ( t e r m i n a l s y m b o l s ) a n d o t h e r m e t a n o t i o n s . I n t h e c a se o f

E n g l i sh , t h e t e r m i n a l s y m b o l s o f t h e r e c t a - g r a m m a r a r e E n g l i s h w o r d s.

T h e r e c t a - g r a m m a r i t s e lf is u s e d t o d e f i n c t h e c o n t e x t - f r e e ~ sp c c t s o f

E n g l i s h. E x a m p l e m e t a r u l e s a r c :

S E N T E N C E :: D E T E R M I N E R N O U N V E R B .

D E T E R M I N E R : : a; an; t i l e ; t h e s e ; t h o s e ; t h i s ; t h a t .

U S I N G T W O - L E V E L G R A M M A R

Barrett R . Bryant

D a l e J o h n s o n

B a l a n j a n in a t~ h E d u p u g a n t y

D e p a r t m e n t o f C o m p u t e r a n d I n f o r m a t i o n S c i en c es

T h e U n i v e r s i t y o f A l a b a m a a t B i r m i n g b a m

B i r m i n g h a m , A l a b a m a , U . S . A . 3 5 2 9 4

T h e h y p c r r u l e s a re o f t h e f o r m

h y p c r n o t ] o n ; h y p e r a l t e r n - 1 ; h y p e r ~ l t e r n - 2 ; . .. ; h y p e r a l t e r n - n .

T i le h y p e r a l t e r n a t i v e s s e p a r a t e d b y s e m i c o l o n s a r c d i s t i n c t p r o d u c t i o n

a l t e r n a t i v e s . E a c h o f t h e s e h y p e r a l t c r n a t i v e s m a y b e d i v i d e d i n t o a

s e qu e n ce o f h y p e r n o t i o n s s e p a r a t e d b y c o m m a s . I n a t w o - l e v e l g r a m m a r

d e r i v a t i o n t r e e , t h e r e w i l l b e o n e b r : m c h f o r e a c h c l e m e n t i n t h e s e q u e u c c .

A t w o - le v e l g r a m m a r w i t h e i t h er h y p e r r n l e s h a v i n g m o r e t h a n o n e

h y p e r a l t c r n a t i v e o r t w o d i s t i n c t h y p c r r u l e s h a v i n g t h e s a m e h y p c r n o t i o n

o n t h e p r o d u c t i o n l e f t - h a n d s i d e i s n o n d e t c r m i n i s t i c . [ f c a ch h Y l ) c r ru l e h a s

o n l y o n e h y p e r a l t e r n a t i v e a n d a l l h y p c r n o t i o n s i n p r o d u c t i o n l e f t - h a n d

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

A h y p c r r u l e i s a c t u a l l y a p r o d u c t i o n r u l e " p a t t e r n " s i n c e e a c h

h y p e r r u l e c a n p o s s i b l y r e p r e s e n t a n i n f i n i t e n u m b e r o f p r o d u c t i o n r u l e s i n a

c o n t e x t - f r e e g r a m m a r . T h i s i s b e c a u s e e a c h o c c u r r e n c e o f a m e t a n o t i o n i n

t h e h y p c r r u l c r e p r e s e n t s al l se q u e n c e s o f p r o t o n o t i o n s t h a t c a n b e d e r i v c d

f r o m t h a t m e t a n o t i o n . T h a t i s, a h y p e r r u l e m a y b e v ie w e d a s a se t o f

p r o d u c t i o n r u l e s ( c a l l e d strict production rules) i n w h i c h a l l m e t a n o t i o n s

a r e r e p l a c e d b y t h e p r o t o n o t i o n s t h e y d e r i v e . T h e o n l y r e s t r i c t i o n h e r e i s

t h a t i f t h e r e a r c m o r e t h a n o n e o c c u r r c n c e o f a si n g l e r n e t a n o t i o n , t h e n

e a c h i s r e p l a c e d b y t h e s a m e p r o t o n o t i o n s e q u e n c e i n d e r i v i n g t h e s t r i c t

p r o d u c t i o n r u l e s . T h i s i s c a l l e d conM stent substitution. For e x a m p l e , i n t h e

b y p e r r u l c

w h e r e W O R D i s W O R ] ) : t r u e .

b o t h o c cu r r e n c es o f th e m e t a n o t i o n W O R D r e p r ~ e n t t h e s a m e

p r o t o n o t i o n . T h e s e t o f a l l o w a b l e p r o t o n o t i o n s i n t h i s r u l e i s d e f i n ed b y

t h e m e t a r u l c s f o r W O R D . I f t h es e m e t a r u l e s d e f in e a n i n f in i te n u m b e r o f

p o s s i bl e p r o t o n o t i o n s , t h e n t i l e a b o v e h y p e r r u l e a l s o r e p r e s e n t s a n i n f i n i t e

u u m b c r o f s t r i c t i ) r o d u c t i o n r u l e s . [ t i s t i f f s f e a t u r c o f t w o - l e v e l g r a m m a r s

t h a t a l l o w t b c m t o d e f i n e c o n t e x t - s e n s i t i v e a n d r e c u r s i v c l y e n u m c r a b l e

l a n g u a g e s [1 2 ] .

I f c o n s i s t e n t s u b s t i t u t i o n i s n o t r e q u i r e d ( o r d e s i r e d ) f o r m e t a n o t i o n s

w i t h t h e s a m e r o o t m e t a r u l c s ( a n d n a n m ) , t h e n t h e s e m e t a n o t i o n s m a y b e

d i s t in g u i s h e d b y s u b s c r i p t s . F o r e x a m p l e ,

w h e r e S E N T E N C E 1 a n d S E N T E N C E 2 a r e c o r r ec t ;

w h e r e S E N T E N C E 1 i s c o rr e ,c t , w h e r e S E N T E N C E 2 i s c o r r e c t .

I n th i s h y p c r r u l e , S E N T : E N O E 1 a n d S E N T E N C E ~ . a r e d e f in e d b y t h e

s a m e m e t a r u lc s ( a n d r o o t m c t a n o t i o n S E N T E N C E } b u t n e e d n o t h a v e t h e

s a m e i n s t a n t i a t i o n s .

S o m e h y p c r r u l e s c a l l e d predicates a c t a s c o n d i t i o n s w h ic h m u s t b e

s a t i s f i e d fo r t h e d e r iv a t io n t o b e :~ u c ce s sfu l. A p re d i c a t e b e g in s w i th t h e

w o r d w h e r e o r c o a d i t i o n a n d t h e t e r m i n a l d e r i v a t i o n o f t h e h y p e r r u l e i s

t h e e m p t y s t r i n g i f t h e c o n d i t i o n i s s a t i s f i e d a n d w i l l d e r i v e a " b l i n d a l l e y "

( i. e. n o t d e r i v e a n y t e r m i n a l s t r i n g ) i f t h e c o n d i t i o n i s n o t s a t i sf i e d . I n t ir e

t w o - le v e l g r a m m a r o f E n g l i s h p r e s e n t e d i n t h i s p a p e r , a l l h y p e r r u l e s a r c

p r e d i c a t e s a n d s e r v e t o p e r f o r m c o n t e x t c h e c k s s u c h a s s u b j e c t - v e r b

a g r e e m e n t , o b j e c t ~ v c r b a g r e e m e n t , a n d a n y a d d i t i o n a l r e q u i r e d c o n t e x t

c h e e k s w h i c h c a n n o t b e c o n v e n i e n t l y s p e c i f i e d b y a e o n t e x t - f r c e g r a m m a r

( i . e . t i l e mc ta ru l e s ) .

3 . M E T A R U L E S F O R E N G L I S H

T i l e m e t a r u l c s o f t h e t w o - l e v e l g r a m m a r f o r E n g l i s h d e f in e ti r ec o n t e x t - f r e e a ~ p c c t s o f E n g l i s h s y n t* L x. S o m e l e x i c al i t e m s f r o m E n g l i s h c a n

n o t b e e a s i l y d e f i n e d i n a f o r i n a l w a y ( i . e . u s i n g c o n t e x t - f r e e r u l e s ) . T h e s e

i n c l u d e t i l e n o u n s , v e r b s , a d j e c t i v e s , p r o p e r n a m e s , a n d t i t l e s , g i v e n n a m e s

a n d s u r n a m e s f o r p e o p l e w h i c h a r c l c x i c a l c a t e g o r i e s c o n t a i n i n g a l a r g e

n u m b e r o f e l e m e n t s . T h e f o r m a l s p e c i f i c a ti o n o f th e s e c a t e g o r i e s w o u l d b e

p r o d u c t i o n r u l e s o f t l m f o r m :

N O U N : : a a r d v a r k l a b a c u s ; . .. ; z u c c h l n L

V E R B : : a b a n d o n ; a b a t e ; . . .; z o o m .

A D J E C T I V E : : a b d o m i n a l ; a b h o r r e n t i . . 4 z n h c d .

P R O P E R _ N A M E : : A b e r d e e n ; A b i le n c ; .. .; Z a m b i a .

T I T L E : : A d m i r a l ; A r c h b l s l m p ; . .. ; W a r r a n t O f f ic e r.

F o r s i m p l i c i t y w e c h o o s e t o o m i t m o r e f o r m a l s p e c i f i c a ti o n s o f t h e a b o v e

c a t e g o r i e s. A m o r e c o m p l e t e l i s t o f w o r d s i n t h e s e c a t e g o r i e s m a y b c f o u n d

in [14].

5 2 7



The metarules in our two-level grammar illustrate tile specific subset

of English gra mmar defined in this paper. The subset includes declarative

sentences with the subject noun premed;fled and postmodilled, including

postmodification by relative clauses. The choice of this subset is rather

arbitrary since we have used two-level grammars to define a wide variety

of English sentences (e.g. in [7], more extensive modification is allowed and

also compound sentences). This subset will serve to illustrate the power of

two-level gra mmar s for the purposes of defining English syntax. Because

the notation for metarules follows context-free grammar conventions usingnatural language vocabulary, our recta- gramma r is fairly self-explanatory.

The rules of English syntax that have been incorporated into our grammar

are based on English gr amm ar rules given in [3], [11], [131, and [19].

We now enumera te the metarules used in our two-level grammar of

English. A scntence consists of a noun phrase and a verb phrase. The

noun phrase consists of an optional sentence modifier such as a "viewpoint"

adverbial and a subject sequence. The subject sequence consists of two

main subjects, separated by the coordinator and. The main subjects may

be either a list of nouns premed;fled and postmodified or a proper name

premodificd by a restricter.

1 . SENTE NCE :: NOUN_PH RASE VERB_PItRASE PERIOD.

2 , NOUN_PHRASE ::

SENTENCE_MODIFIER SUBJECT_SEQUENCE.

3 . SENTENCE_MODIFIER :: VIEWPOINT COMMA; EMPTY.

4 , VIEWPOINT :~ artlstlcally; eeonoudeaily; etMcally; financially;

geographically; linguistically; militarily; morally; personally;

politically; psyehologleally; publically; t heoretleally; visually.

5. SUBJECT _SEQUEN CE t:MAIN_SUBJECT; MAIN_SUBJECT and MAIN_SUBJECT.

g. MAIN_ SUBJE CT :.* MODIFIED_N AMED_SUBJ ECT~

PRE_NOUN_MODIFICAT10N NOUN_tIEAD

POST_NOUN_MODIFICATION.

7. MODIFIED_NAME D_SUBJECT ::

RESTRIOTERS NAMED_SUBJECT.

8. NAMED_SUBJE CT ~: PROPER_N AME; GIVEN_NAME~

SURNAME; TITLE SURNAME.

tl . RES TRIO TER S :: chiefly; especially; even; just; largely; mainly;

mostly; primarily; not even; only; EMPTY.

10. NOUN_HEAD :: NOUN; NOUN and NOUN;

NOUNJLIST COMMA_OPTION and NOUN.

11. NO UN_L IST ::

NOUN_LIST COMMA NOUN; NOUN COMMA NOUN.

The verb phrase consists of a predicate sequence and an object

sequence. Tlm predicate sequence consists of an auxiliary seqnence (an

optional auxiliary adverb such as a focusing or maximizing adverb

followed by an activ e or passive auxiliary verb) and the main verb of thesentencc,

12. VERB_PIIRASE ::

PREDICATE_SEQUENCE OBJECT_SEQUENCE.

13. PREDICATE_SEQUENCE :: AUXILIAI?~Y_SEQUENGEVERB.

14. AUX-IL IARY_SEQUENC E t: AUXILIARY ._ADVER B_OPTION ;

AUXILIARY_ADVERB_OPTION

AGTIVE_OR_PAS S IVE~A UXILIARY.

15. AIYXILIARY_ADVERI~_OPTION::AUX]LIARY'~ADVERB; MPTY.

18. AUXILIA RY_ADVE RB ::

FOCUSING_ADVERB; MAXIMIZING._ADVERB.

17. FOCUS ING_A DVER B :: again; also; as we;l; at least; equally;

especially; even; fnrtlmr; in addition; in particular; just; largely;

likewise; mainly; mercly~ mostly; no tably; only; partlcula,'l y!

primarily; principally; purely; purely and slmplyl shnilarly i

simply] specifically.

18. MAXIMIZING_.ADVERB :: absolutelyl al togethe r; completclyl

entirely; fully; in Ml respects; perfectly; qulte; thorough ly;

totally; utterly; very fufiy; very thoroughly.lg. ACTIVE _OR_PASSIVE_AUX ILIARY ~

ACTIVE_AUXILIARY; PASSIVE_AUXILIARY.

20. ACTIVE_AUXILIAR Y :

A1 IXILIARY_. [IAVEAUXILIARY_ADVERB_OP TIC N.

21. PASSIVE_AUXILIARY :

AUXILIARY_BE AUXILIARY_ADVERB_OPTION;

AUXILIARY_J~IAVEAUXILIARY_AD VERB~OPTIO N been.

22. ALVXILIARY_BE :: am~ is; were; was.

23. AUX ILL ~Y_ ItA VE :: have; had; has.

24. AUX ILIARY_V ERB z: AUXILIAR Y_BE; AUXILIA RY_HAV E.

25. AUXILIARY_TRAILER : AUXILIARY_ADVERB_OPTION;

AUXILIARY~aA2)VERB_O PT I O N been .

528

The object sequence of a verb phrase can contain both direct and

indirect objects followed by an optional adverbial such as a maximizing

adverb or a time adverb. Objects can be either a proper name, possibly

modified by the restrieters given above, or a noun expression, possibly

premed;fled and postmodified.

2 6 . OBJECT_SEQUENCE ::

I NDI RECT_OBJECT DI RECT_OBJECT

OB JECT_SEQUENGE_ADVERB;

DIRECT_OBJECT OBJECT_SEQUENCE_ADVERB.27. OBJECT_SEQUENCE ~DV ERB : :

O B JEOT_S EQUENO E~LDVERBIAL; EMPTY.

28. OBJE CT_SEQU ENCE_ADV ERBIAL ::

MAXiMIZING_ADVERB; TIME_ADVERB.

29. TIME_.ADVERB :: again; early; first; last; late; next; now; recently;

simultaneously; slnee; then; today; yesterday.

30. INDIR ECT_ OBJE CT :: OBJEC T.

31. DIRECT_OBJECT :t OBJECT.

32. OBJEC T :: MODIFIED_NAMED _SUBJECT;

PRE_NOUN_MODIFICATION NOUN_HEAD

POST NOUN_MOD1FICATION.

We now turn to the pro-noun-modifiers specified in our grammar. The

modifier is a determiner optionally followed by a list of possessive nouns,

an adjective, a sequence of nouns, another list of possessive nouns and a

denominal noun. Examples of this type of construct include "the

murderer's empty black pistol" and "a very rich man's thick wallet." For

context-sensitive purposes, the determiners are divided into "universal"

determiners which may precede both singular and plural nouns anddeterminers which may only precede singular nouns. Furthermore, a

context-frcc restriction of the pro-noun-modifiers is that thcrc can be at

most one list of possessive nouns in a sequence. For convenienc e we choose

to enforce this condition in the hypcrrules instead of the metarules.

33. PRE_NO UN_MOD IFIOATI ON .' :

DETERMINER PRE_NOUN_MODIFIERS.

34. PRE_NOUN_MOD IFIERS :: EMPTY;

POSSESSM,]_NOUN_LIST AD JEOTIVE_OP TION

NOUN_SEQUENCE POSSESSIVE_NOUN_LIST

I) ENO MINAL_NO UN.

35. D ETER MINER ::

UNIVERSAL_DETERM NER; SINGIJLAR_DETERMINER.

311. UNIVE RSALD ETER MINE R : :

tim; some; any; my; your; his; her; its; our; their.

37. SINGULA R_I)ET ERMINE R :: either i neither; anot her;

NOT_OPTION NEGATABLE_SINGULAR_DETERM[NER.

38. N EGATA BLE_ SINGUL AR_DE TERM INER : a; an; eaeb; every.

39. NOT_OPTION :: not; EMI)TY.40. POSSESSIVE _NOUN_LIST :: EMPTY;

POSSESSIVE_NOUN LIST POSSESSIVE_NOUN.

41. POSSESSIVE_NOUN :: NOUN's; NOU N'.

42. ADJEC TIVE _OPT ION ~: ADJECT IVE; EMPTY.

43. NOUN_SEQUENCE :: NOUN; NOUN and NOUN; EMPTY.

The nouns in the NOUNSEQUENCE denote the physical composition of

items (e.g. "the fisherman's rusted iron hook") and thus act as adjectives

Denominal nouns arc adjectives which denote some quality of the noun

being modified (e.g. "her social life" and "his moral responsibility"). Since

there are a large number of these, we omit their formal specification here.

In our g ramm ar subset we restrict post-noun-modifiers to relative

clauses involving people. Man y othe r forms of post-noun-modificat ion are

ferma l]y specified in [7 ]

44. POST_N OUN_M ODIFIC ATION :: RELATIVE _CLAUSE; EMPTY.

45, RELATIV E_CLAUSE ::

who PREDICATE_SEQUENCE OBJECT_SEQUENCE.

Finally, the punctuation in our gram mar is given below

46. PERIOD :: . .

47. COM MA :t ~ .

48. COMMA OPT ION :: COMMA; EMPTY.

49. EMPTY :: .

4 . HYP ERRUL ES F OR E NGLI S H

The hyperru les of tile two-level gra mm ar for English define the

context-sensitive aspects of English syntax which can not be specified by

the context-free rules ef the recta-gr ammar. Unlike the meta- gramma r, the

hyperrulss do not generate any part of the English sentence. They serve

only to verify the context-sensitive conditions of the grammar. This is

done by using predicates ,~ described earlier. Predicates willderive the

empty string if they are satisfied and will derive nonterminal strings of



u s e le s s s y m b o l s o t b e r w i s e . T h e n o t i m ~ t h a t t i l e h y p e r r u l c s w i l l n o t

g e n e r a t e a n y t e r m i n a l s t r i n g b u t i n s t e a d v e r i f y c o n t e x t - s e n s i t i v e e o n d i t i o n s

o f a t e r m i n a l s t r i n g a l r e a d y g e n e r a t e d b y t h e c o n t e x t - h 'e e m c t a r u l e s i s a

n n i q u e f e a tu r e o f o u r a p p r o a c h t o d e s i g n i n g t w o -l e v el g r a m m a r s ( e . g . in

c o n t r a s t , s e e [2 ]) . T h i s w i l l g r e a t l y s i m p l i f y p a r s i n g t w o - l e v e l g r a m m a r s a s

w e w i l l s e e l a t e r .

W e w i l l d e fi n e t w o t y p e s o f p r e d i c a t e s . T h e f i r s t o f t h e s e w il l b e

p r e c e d e d b y t h e p r o t o n o t i o n c o n d i t i o n a n d w i l l b e g i v e n e x p li c i t ly i n t h e

f o r m a l g r a m m a r . A s w i t h t h e r e c t a - g r a m m a r , h o w e v e r , t h er e w il l b e s o m e

r u l e s w h i c h c a n n o t b c p r e c i s e l y d e f i n e d i n t h e f o r m a l s y s t e m . T h e s e r u l e s

r e l a t e t o q u a l i t i e s o f t h e u n s p e c i f i e d l e x i c a l e l a s s c ~ ( e . g . n o u n s , v m ' b s , e t c .)

a n d w i l l b e d e s i g n a t e d b y t h e p r o t o n o t i o n w h e r e . F o r e x a l n p l c , t h e

h y p e r n o t i o n s w h e r e N O U N i s s i n g u l a r , w h e r e V E R B i s p a s t p a r t l e l p le ,

a n d w h e r e N O U N a n d V E R B a g r e e in p e r s o n a n d n u m b e r c al l n o t b c

p r e c i s el y d e f i n e d e x c e p t b y a v e r y l a r g e n u m b e r o f f o r m a l r u l e s s u c h m s

t h o s e g i v e n b e l o w :

w h e r e a a r d v a r k i s s i n g u l a r : E M P T Y .

w h e r e a b a n d o n e d i s p a s t p a r t i c i p l e I E M P T Y .

w h e r e A d a m a n d e r e a g r ee in p e r so n a n d n u m b e r : E M P T Y .

I n t h e s u b s e q n e n t d i s c u s s i o n o f h y p e r r u l e s w e w i l l u s e th e n o t , a t i o n I t u

t o d e n o t e h y p e r r u l e n u m b e r n . T h e s t a r t h y p c r r u l e ( I l l ) o f t h e tw o - l e v e l

g r a n u n a r i s :

1 , S E N T E N O E : c o n d i t i o n S E N T E N O E i s a w e l l - f o r m e d s e n t e n c e .

T h i s h y p e r r u l e h a s a s i t s s t a r t n o t i o n a n E n g l i s h s e n t e n c e w h i c h i s w e l l-

f o r m e d w i t h r e s p e c t t o t h e c o n t e x t - f r e e r u l e s o r t h e r e c t a - g r a m m a r f o r

m e t a n o t i o n S E N T E N C E . T h e n e x t h y p e r ru l e ( H 2 ) e x p a n d s t h e s e n t en c e

w i t h r e s p e c t to w h a t c o n d i t i o n s m u s t b e s a t is f i e d . T h e f o r m a l i z a t i o n o f

t h e s e i s s e l f - e x p l a n a t o r y .

2 . c o n d i ti o n S E N T E N ( I E _ M O D I F I E R S U B J E C T _ S E Q , U E N O I g

A U X I L I A R Y _ S E Q U E N C E V E R B O B J E C T _ S E Q U E N C E

P E R I O D i s a w e l l - f o r m e d s e n t e n c e :

c o n d i ti o n S U I 1 J E C ' I ~ S E Q U E N C E s h o w s s u b j e c t -p r e d i c a t e

agreelnent witbA U X I L I A R Y _ S E Q U E N O E VERB,

c o n d i t i o n S U B J E O T _ S E Q U E N O E i.~ a w e l l - f o r m e d s u b j e c t ,

c o n d i ti o n O B J E O T _ S E Q U E N ( J E

s h o w s o b j ee t ~ p r c d ic a t e a g r e e m e n t w i t h V E R B ,

c o n d i ti o n A U X I L I A R Y _ S E Q U ] ' ; N O E V E R B

is ~ w e l l - f o r m e d p r e d i e a t e ~

c o n d i ti o n O B J E G T _ S E Q U E N ( J E i s a w c l b h w m e d o b j e c t .

T h e f i r s t c o n d i t i o n i s t h a t t h e s u b j e c t s e q u e n c e m u s t a g r e e w i t h t h e

p r e d i c a t e s s p e c i fi e d b y t h e a u x i l i a r y s e q u e n c e a n d v e r b . I n o n r g r a m m s r ,

a g r e e m e n t m e a n s t h a t t h e s u b j e c t a n d t h e s u b je c t - v e r b m u s t a g r e e i n

p e r s o n a n d ! m m b c r . T h e r e a r e t w o p o s s i b i l i t i e s fo r s n b j e c t - v e r b s : 1 ) t h e

a u x i l i a r y s e q u e n c e i a e m p t y ( I t 3 ) iu w h i c h c ~ s c t h e m a i n v e r b m u s t b e

c o n s i s t e n t w i t h t h e s u b j e c t , a n d 2 ) t h c a u x i l i a r y s c q u c n c c i s u o n - e m p W

( H 4 ) i n w f i i e h c a s e i t i s t h e a u x i l i a r y v e r b w h i c h m u s t b e c o n s i s t e n t w i t .h

t h e s u b j e c t : S u b je c ~. s m a y b e i n o u r o f t h r e e f o r m s : l ) t h e s u b j e c t i s a

p r o p e r n a m e ( I I 5 ) , p o s s i b l y m o d i f i e d b y a r c s t r i c t c r ( c .g . " e v e n M r . S m i t h "

o r " p r im a r i l y M r s . J o n e s " ) , a n d t h e r e f o r e r e q u i r e s ~ s i n g u l a r v e r b ; 2 ) th e

s u b j e c t i s a s i n g l e s u b j e c t ( H 6 - H T ) i n w b i c h c a s e i t n ee d o n l y a g r e e w i ~h

. t h e s u b j e c t - v e r b ; o r 3 ) t h e s u b j e c t m a y b c a c o m p o u n d s u b j e c t c o -

o r d i n a t e d w i t h a n d ( f I S - I I 9 ) , i n w h i c h c a s c i t r e q n i r e s a p l u r a l v e r l ) ( e .g .

" J o h n an d B i l l ar c h e r e . " ) .

3 . c o n d i ti o n S U B J E C T _ S E Q U E N C E

s h o w s su b j e e t - p r ¢ , d i c a t e a g r e e m e n t w i t h V E R B :

c o n d l t l o n S U B J E O T _ _ S I , , ' Q U I ~ N O E a g r e e s il tl p e r s o n a n d n u t t l b e r

w i t h V E R B .

4 . c o n d i ti o n S U B J E C T S F Q t J E N C I ~

s h o w s r o d ) j e e r - p r e d ic a t e a g r e e m e n t

w i t h A U X I I , I A R Y _ _ A 1 ) V E I t I L O P T I O N A U X [ I , I A R Y V E R B

A U X I L I A R Y _ T R A I L E R V E R B :

c o n d l t k m S U B J E ( J T _ S E Q U E N C E a g r e e s i n p e r s o n a n d n u m b e r

w i t h A I J X [ L I A R Y _ V E R B .

5 . c o n d i t i o n M O I ) I F I E D _ N A M E D _ S U B J E O T

a g r e e s i n p e r s o n a n d n u m b e r w l t h V E R B :

w h e r e V E R B i.q s l n g , d a r .

8 . c o n d i t io n P R E _ . N O U N _ M O D I F I C A T I O N N O U N I 1 E A D

P O S T _ N O U N M O D I F I C A T I O N

a g r e e s i n person and n u m b e r w l t h V E R B :

c o n d i ti o n N O U N _ t t E A D

a g r e e s i n pe r s o n a n d n u m b e r w i t h V E R B .

7 . c o n d i ti o n N O U N ' a g r e c s i n p e r s o n a n d n u m b e r w i t h V E R B :

w h e r e N O L V N a n d V E R B a g r e e i n p e r s o n a n d n u m b e r .

8 . c o n d i ti o n N O U N L I S T O O M M A _ O P T I O N a n d N O U N

a g r e e s i n p e r s o n a n d n u m b e r w i t h V E R B :

w l m r e V E R B i s p h l r a l .

9 . c o n d i ti o n M A I N _ . S U B J E C T I a .n d M A I N _ S U B J E C T 2

a g r e e s i n p e r s o n a n d n n m b e r w l t h V E R B :

w h e r e V E R B i s p l u r M .

T o s a t i s f y t i l e s e c o n d c o n d i t i o n t h a t t i le s u b j e c t o f a s e n t e n c e m u s t b c

w e l l - f o r m e d , t h e s u b j e c t m a y f a l l i n t o o n e o f t h e f o l l o w i n g c a t e g m ' i e s : 1) if

t h e s u b j e c t i s a n a m e ( I I 1 0 ), t h e n i t is a l r e a d y w e l l - f o r m e d b y t h e

m e t a r u l e s ; 2 ) i f t h e s u b j e c t i s m o d i f i e d ( t i l l ) , t h e n t h e m o d i f i e r s m u s t b e

c o r r ec t ; a n d 3 ) if th e s u b j e c t i s a c o m p o n n d s u b j e c t ( I 1 1 2 ), t h e n e a c h

c o m p o n e n t o f th e c o m p o u n d s u b j e c t m u s t b e w e l l -f o r m e d a c c o r d i n g t or u l e s 1 a n d 2 .

1 0 . c o n d i t i o n M O D I F I E D _ N A M E D _ S U B J E C T i s a w e l l - f o r m e d s u b j e c t :

E M P T Y .

1 1 . c o n d i t i o n D E T E I { M [ N E I ) ~ P R E _ N O U N _ M O D I F I E R S

N O U N t l E A I ) P O ST __ N O U N _ _ M O D I F I C A T I O N

is a w e l l - f o r m e d s u b j e c t :

c o n d i ti o n D E T E R M I N E R I ' R E _ N O U N _ M O D I F I E R S

N O U N _ t l E A D i s c o r r e c t in p r e m o d i f i c a t l o n ,

c o n d i ti o n D E T E R M I N E R N O U N _ I l E A l )

P O S T _ N O U N _ M O D I F I ( 3 A T IO N

i s c o r r e c t i n p o s t m o d i f i c a t l o n .

1 2 . c o n d i ti o n I M A I N _ _ S U B J E O T 1 t ro d M A I N _ S I J B J E C T 2

i s a w e l l - f o r m e d s u b j e c t :

c o n d i t i o n M A I N _ S U B J E C T I i s a w e l l - f o r m e d s u b j c c t ,

c o n d i t i o n M A I N _ S U B J E ( J T 2 i s a w e l l - r e m i n d s u b j c c t .

C o r r e c t n e s s o f m o d i f i c a t i o n i m p l i e s t h a t a s u b j e c t m u s t b c c o r r e c tl y

l ) r e m o d il i e d a n d p o s t m o d i f i c d . W e f i r s t g i v e t h e h y p e r r u [ e s w h i c h e n f o r c e

c o r r e c t p r e m o d i f i c a t i o n . P r e m o d i f i e a t i m l ( H 1 3 ) r e q u i r e s 1 ) c o r r e c td e t e r m i n e r u s a g e ( i .e . w i t h r e s p e c t t o s i n g u l a r a n d p l u r a l n o u n s ) a n d 2 )

a n y p r c m o d i f y i n g n o u n s m u s t b e s i n g u l a r o r " m a s s " n o u n s ( i .e . n o u n s

w h i c h d e n o t e i t e m c o m p o s i t i o n s u c h a s a lu m in u m , b ra ~ ss , e t c . ) . A s i n g u l a r

d e t e r m i n e r ( e . g . a, an, each, e t c .) r e q u i re s a s i u g u l a r n o u n ( I l l 4 ) b u t a

" u n i v e r s a l " d e t e r m i n e r ( e .g . so m e , t h e , e t c .) m a y b c u s e d w i t h s i n g u l a r o r

p l u r a l n o u n s ( I I 1 5 ). I f t h e r e a r c n o p r e m o d i f y i n g n o u n s , t h e n h y p e r r u l c

I l l 6 w i l l a p p l y . A s in g l e p r e m o d i f y i n g n o u n ( I I 1 7 ) m a y b c e i t h e r s i n g u l a r

o r a m a s s n o u n . N o t e t h a t r n l e I l l 7 i s n o n d e t e r m i n l s t i c i n t h a t t h e r e a r e

t w o h y p e r a l t e r n a t i v c s . T h e c o n d it . io n i s s a t i s f i e d i f e i t h e r o n c o f t h e s e

h y p c r r u l e s i s s a t i s fi e d . I f t h e p r e m o d i f y i n g u o u n s a r e c o - o r d i n a t e d w i t h an d

( 11 18 ), t h e n b o t h n o u n s m u s t b e m a s s n o r m s ( e .g . " t h e w o o d e n a n d i ro n

d o o r " i s c o r r e c t b u t " t h e f o r e s t a n d g a rd e n p a t h " i s n o t ) .

I a . c o n d i t k m D E T E R M [ N I , ; R P O S S I , ] S S I V E _ N O U N . L I S T t

N O U N _ S E Q U E N C E I ~ O S S I ~ S S I V E _ N O U N _ L I S T 2

D E N O M I N A L _ N O U N N O U N H E A D

lu c o r r e c t i n p r e m o d i f i e a t l o n :

c o n d i t i o n D E T E R M I N E R c o r r e c t l y p r e m od i fi e .~ N O U N I I E A D ,

c o n d i ti o n N O U N S E Q U F N ( ~ E are s i n g u l a r o r m a s s I I [ ) I I [ I S .1 4 . c o n d i t i o n S I N ( ] I J I , A I { _ D E T E R M I N ] I ] R c o r r e c tl y p r e m o d i f i e s N O U N :

w h e r e N O U N i:~ s i n g u b t r .

1 5. c o n di t io n U N I V F R S A b _ D E T E R M [ N E R

c o r re c t ly p r e m o d i f i es N ( ) U N J I E A D : E M P T Y .

1 8 . c o n d i t io n E M P T Y a r e s i n g u b w o r m a s s n o u n s = E M P T Y .

1 7 . c o n d l L io n N O U N a r e s i n g u l a r o r m a .q s n o u n s :

w h e r e N O U N i s M n g u l a ¢ ; w l m r e N O U N i s a m a s s n o u n .

1 8 . c o n d i t i o n N O O N I a n d N O U N 2 a r c s i n g u l a r o r m a s s n o u n s :

w h e r e N O U N 1 i s a m a s s n o u n ~ w h e r e N O U N 2 i s a m a s s n o u n .

l l y p e r r u l c s [ I 1 9 - II 2 7 d e f i n e t h e c o n d i t i o n s f o r p o s t m o d i f i c a t i o n . A n y

p o s t m o d i f i c a t k ) n o f t h e s n b j c c t m a s t b c i n t h e f o r m o f a r e l a t i v e c l a u s e

w h i c h b e g i n s w i t h who. T l i i s t y p e o f r e l a t i v e c l a u s e r c q n i r e s ~ t h u m a n n o u n

a n d t h e v e r b o f t h e r e l a t i v e c l au s e n m s t a g r e e w i t h t h e m o d i f i e d n o u n . F o r

c x a m p l c ~ i u " T h e m e n w h o f ix c o m p u t e r s w e r e v e r y h e l p f u l , " t h e n o u n m e n

n l us t bc }1~ b ll ll l~ gn nO U l l s i nc e i t i s m od i f i e d by w ho a n d t h e v e r b f i x m u s t

b e c o m p a t i b l e w i t h m e n . T b i s t y p e o f re l a t i v e c l a u s e m a y b e c o n s i d e re d a s

d e s c r i b i n g t w o s e p a r a t e s e n t e n c e s : " T h e m e n f i x c o m p u t e r s . " a n d " T h e m e n

w e r e v e r y h e l p fu l . " I n t h e h y p c r r n l e s w h l e h v e r i f y t h e s e c o n d i ti o n s , t h e

s u b - s e n t e n c e d e s c r i b e d b y b hc r e l a t i v e c l a u se i s f o r m e d a n d t h e n c h e c k e d

f o r c o r re c t n e s s u s i n g h y p c r r u l e I 1 2 r c c u r s i v e l y .

1 9. c o nd i t io n I ) E T E R M I N E I t N O U N . _ I I E A D

P O S T N O U N _ . M O D I F I C A T I O N

I S c o r r e c t i l l p o s t l n o d i l | l : a t l o l | l

c o n d i ti o n P O S T _ N O U N M O D I F I O A T I O N

c o r r e c t l y p o st , m o d l f i e s D E T E R M I N E I { N O U N _ [ l E A D .

2 0 . c o n d i t i o n E M P T Y c o r r e c t l y p o s t m o d i f i c s

D E T E R M I N E I { N O U N _ I l E A l ) : E M P T Y .

2 1 . c o n d i t i o n R E L A T I V E _ C L A U S E c o r r e c t l y p o s t m o d i f i e s

D E T E R M 1 N E I '~ N O U N . I IE A D :

c o n d i ti o n N O U N _ I l E A l ) i s a h u m a n n o u n ,

e o n d i t h m t h e v e r b o f R E L A T I V I , ;_ C , L A U S E

a g re e ~ w l tl l I ) E T E R M I N E l l N O U N _ I I E A D .

529



22. conditlou N OUN is a human norm t where NOUN is a human noun.

23. condition NOUNI and NOUN2 is a human noun t

wlmre NOUN1 is a hu man noun 9

where NOUN2 is a huma n noun.

24. condition NOUN_LIST COMMA_ OPTION and NOIJN

iS a h L I m a n n o n u 1

condition NO UN_ LIS T in a huma n noun~where NOUN is a human noun.

25. condition NOUN1 COMMA NOUN2 is a human noun :

where NOUN1 ia a human noun 9

where NOUN2 is a huma n noun.

2 { 1 . c o n d i t i o n NOUN_L IST COMMA NOUN is a human noun :

c o n d i t i o n N O U N _ L I S T i s a human noun,

wikere NOUN is a human noun.

27. condition the verb of

who PREDICATE_SEQUENGE OBJECT_SEQUENCE

agrees with DETERMINER NOUN~HEAD :

c o n d i t i o n DETERMINER NOUN_IlEAl)

PREDICATE_SEQUENCE OBJECT_SEQUENCE PERIOD

is a well-formed sentence,

Tile third condition that the English sentences defined by our

gramm ar must satisfy is that the predicate (verb) and objects should agrcc.

The type of verb mast correspoud to the nu mber of objects in the sentence:

if the verb is intransitive, then no objects are allowed except for adverbs

(ti28); if the verb is transiti ve, the n a direct objec t is required (H29); and if

the verb is ditransitive, then both a direct and an indirect object are

required (I130).

28. condition OBJECT_SEQUEN(3E_ADVERB

slmws object"predlcate agreement with VERB :

where VERB is iutransitlve.

29. condition DIRE CT_O RJEC T OBJECT_SE QUENI3E ADVERB

shows object.predlcate agreeme nt with VERB :

where VERB is transitive.

30. condition IND1REC T_ORJE CT DiRE CT_O BJEC T

OB JECT _S E QU EN CIE_A1)VERB

shows object.predlcat e agreement with VERB :

where VERB is dltransltive.

The fourth condition for a well-formed sentence is tha t the auxiliar y

adverbs and m ain verb are in correct gram mati cal sequence, if I,here are no

auxiliary verbs (H31), then tile auxiliary sequence is correct according to

the recta-gr ammar. If auxiliary verbs are present then the verb must be a

past partieiple (II32).

31. condition AUXILIARY_ADVERB _OPTION VERB

is a well-formed predicate : EMPTY.

32. condition ALrXILIAI~Y_ADVEI~,B_OPTION

AC TIVE _OR_ PA S SIVE_,AUX/LIARY VERB

is a well-formed predicate :

where VERB is a past parti ciple.

The fifth and final condition which must be satisfied is fro" the object

of the sentence to be well-formed. A simple object (H33) must satisfy the

same conditions as a subject and hyperrules H10-H12 will apply

recursively. An object sequence (H34) is well-formed if the indirect and

direct objects are well-formed.

33, condition OBJE(3T OBJECT_SEQUENCE_ADVERB

is a well-formed object :

c o n d i t i on O B J E C T i s a well-formed subject.

34. condition INDIRECT_OBJEC IT DIREC T_OB JECT

OBJECT_SEQUEN(3E._ADVERB is a well-formed object :

c o n d i t i o n I N D I R E C V r O B J E ( 3 T i s a well-formed nbject~

c o n d i t i o n D I R E C T _ O B J E C T i s a well-formed object.

It can be seen that the above set of hyperrules is relatively concise and the

conditions being described are readily understandable. We claim that the

other goals of consistency, precision (for our subset of English), and

unambiguity are also achieved. In the next section it will be shown how

this specification may be implemented automatically.

5 . T W O - L E V E L P A R S I N ( I

Our method of natural language specification has two-levcls:

metarules for eontexVfree syntax and hyperrules for context-sensitive

syntax. Similarly our method of parsing a two-level gram mar requires a

parser for metarules and a parser for hyperrules. Since the metarules are

context-free, any of the well-known context-free paining algorithms (e.g.

see [17]) may be used to derive a context-free str ucture of some input

sentence. Context-fre e parsing will elimina te all sentences which do not

satisfy the context-free syntax of the language but is unable to eliminate

530

structures which are correct in the context-free sense but incorrect with

respect to context-sensitive syntax. The hyperrule parser will further reduce

the set of sentences which arc considered to be grammaticall y valid by

analyzing the context-free parse tree for context-sensitive violations.

The "parser" for the hyperrules is actually an interp reter developed by

the authors in [4] which evaluates the hyperrules in much the same way as

a progrannning language interpreter executes programs. The hyperrules

are interpreted sequentially in the order that conditions are enumerated in

the grammar. Interpretation proceeds by expanding the stm't notion and

applying the hyperrules to all of the branches of the hypcrrule derivation

tree until all of the prcdicatcs are evaluated. As interpretat ion proceeds,

each node of the derivation tree (corrcsponding to a hypernotion) is

expanded by matc hing it with a hyperrule lcft-hand sldc. The right-h and

side of the matched hyperrule is then used to create a subtrcc for that

node. Each br anch of tile tree is evalua ted from left to right in a prc~ordcr

traversal. The English sentence is syntactically correct if and only if the

resulting terminal string derived by tbe hypcrrulc tree is the empty string.

The method of writing hyperrules to derive only the einpty string

great ly simplifies th e parsi ng process. Trad iti ona lly (e.g. [2, 10]), ~wo-lcvel

gram mars use tile hyperrules to genera te the termin al s~rings of the

language with the metarules being used only to instantiatc hyperrules. For

example, in our gramma r the metanotion SI°NTENCE is nscd to generate

English sentences which arc tben i n p u t to the hype rrule s for anMysis. In

other two-level grammar styles, however, the components of thc sentence

would also be generated by hypcrrules. The result of hyperrules generating

terminal strings is tha t parsing bccmnes considerably more difficult and is

not accomplished without restrictions being placcd on hypcrrules (e.g. [15]).

Our method of interpre ting hypcrrnles places no restricl, ions, thcrclorc

allowing the tlg to be more gencral. T he differences in writing styles are

cxplored further in I4].

The hyperrule interprctatkm algoritbm is outlined below:

Procedure EvMuute (hypcrnotion)

1. Find tile hyperrule to apply wMch has tim hypernotion as its left.:

hand side. This rule will bc of the form:

hypernoffon : hypernotioa-I, hyperaotfon-2, .. . , hypernoth>u-n.

2. Expand the derivat ion tree with hypernotion tts the root of the

current snbtree ~nd tile branches being hypernvtion-t, hypernolion..2,

, hypernotfon-n.

3. Eval uate (hypernntio n-i) for i ~= 1, 2~ .., n.

To explain how this interpreter works, consider the examplc sentence

"Professor White and the students who attend the university gave Mrs.

White a present today." This sentence is seen to be correct, with respect to

context-free syntax and its structural representation is shown in 1,'ignre 1.

The specific metar ules applied arc numbered . We will now apply the

hyperrules to this sentence to show how the context-sensitive conditions

arc verified. For notational convenience we have italicized the protonotions

which correspond to metanotions in the hyperrules. Since the tree will bc

traversed from left to right we will label the branches (i.e. nodes) using a

nmnber (0-8) to denote the level in the tree and a letter (a-e) to indieaLe

lcf~ to right ordering.

The root of the hyperrulc derivation tree is the sentence itself.

[Iyperrulc HI will be applied to initiate the verification process. This will

be followed by H2 which divides the derivat ion tree into five separate

branches, one for each condition which the sentence must satisfy.

0 • Pro f e s so r W h i t e a n d t h e ~ tu d e n t s w h o a t t e n d t h e u n i v e rs i t y g a v e Mrs .

Wh i t e a p re se n t t o d a y .

1 • condition Pro fe sso r Wh i t e a n d t h e s t u d e n t s w h o a t t e n d t h e u n i v e rs i t y

g a v e Mrs . Wh i t e a p re se n t t o d a y , is a well-formed sentence

2a * condition P r o f e s s o r W h i t e a n d t h e s t u d e n t s w h o a t t e n d t h e u n i v e r s i t y

ghows subject-predicate agreement with gave2b * condition P r o f e s s o r W h i t e a n d t h e s t u d e n t s w h o a t t e n d t h e n n i v e r s i t y is

a well-formed subject

2c • condition a p re se n t t o d a y shows object-predicate agreement with gave

2d * condition gave is a well-formed predicate

2e • condition a p re se n t t o d a y is a well-formed object

To expand branch 2a and cheek the first condition, hyperrule H3 (no

anxiliary verbs) is applied. Since the subject is compound, rule H9 will be

applied, requiring the verb to be plural. The "library" predicate will verify

the plurality of gave .

2a • condition Pro fe sso r Wh i t e a n d t h e s t u d e n t8 w h o a t t e n d t h e u n i v e rs i t y

shows subject-predicate agree ment with gave

3a • condition P r o f e s s o r W h i t e an d t h e s t u d e n t s w h o a t t e n d t h e u n i v e rs i t y

agrees in person and number with gave

4a • where gave is plural

5a •



t l y p e r r u l e H 1 2 w i l l b e a p p l i e d t o e x p a n d b r a n c h 2 b a n d d e c o m p o s e

t h e c o m p o u n d s u b j e c t i n t o i t s c o m p o n e n t s . I I y p e r r u l e s l t l 0 a n d I l l l w i l l

t he n a na l yz e e ac h o f t he t wo r e spe c t i ve sub - sub j e c t s f o r we l l - fm 'm e dne ss .

2b * c ond i t i on Pro f esso r W h i t e a n d t h e s t u d en t s w h o a t t en d t h e u n i vers i t y

i s a we l l - fo rm e d sub j e c t

3b * c ond i t i on P r o f e s s o r W h i t e i s a we l l - fo rm e d sub j e c t4b *

3c * c ond i t i on t h e s t u d en t s w h o a t t en d t h e u n i vers i t y i s a we l l - fo rm e d

s u b j e c t

4e * c ond i t i on t h e s t u d en t s i s c o r r e c t i n p r e m od i f i c a t i on

4 d . c o n d i t i o n t h e s t u d en t s w h o a t t en d t h e u n i vers i t y i s c o r r e c t i n

p o s t m o d i f i e a t i o n

Proc e e d i ng t o c ons t ruc t t he t r c e i l l a l e f t - t o - r i gh t m a n ne r , b r a nc h 4c i s

e xpa nde d ne x t u s i ng hype r ru l e I t 13 . S i nc e f i l e de t e rm i ne r i s un i ve r sa l a nd

~ he re i s no p re m od i fy i n g noun se que nc e , hypc r ru l e s I t 15 a nd H16 c o m pl e t e

t h i s sub t r e e .

4c • c ond i t i on t h e s t u d en t s i s c o r r e c t in p r e m o d i f i e a t i o n

5b * c ond i t i on th e c o r r e c t l y p r e m od i f i e s s t u d en t s6a •

5 c • c o n d i t io n E M P T Y a r e s i n g u l a r o r m a s s n o u n s

6b *

T h e e x p a n s i o n o f b r a n c h 4 d i s o n e o f t h e m o r e i n t e r e s t i n g a s p e c t s o f

t he c on t e x t - s e ns i t i ve a na l y s i s s i nc e i t i nvo l ve s a r e l a t i ve c l a use . T he

a n a l y s i s i s p e rf o r m e d b y h y p e r r u l e s H I 9 , H 2 1 , t i 2 2 a n d H 2 7 . N o t e t h a tru l e I I27 r e a r r a nge s ~ hc r e l a t i ve c l a use i n t o a ne w se n t e nc e a nd r e e m 's i ve l y

c a l l s hype r ru l e H2 t o a na l y z e t he ne w se n t e nc e .

4d o c ond i t i on t h e s t u d en t s w h o a t t en d t h e u n i vers i t y i s c o r r e c t i n

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

5d • c ond i t i on w h o a t t en d t h e n n i vers i t y c o r r e c t l y pos t m od i f i e s t h e s t u d en t s

6c . c ond i t i on s t u d en t s i s a h u m a n n o u n

7a * whe re ,students is a h l l i l l D . n n o u n

8& •

6d • c ond i t i on t he ve rb o f wh o a t t en d t h e n n i vcrs l t y a g re e s wi t h the

s t u d en t s

7b * c ond i t i on t h e s t u d en t s a t t en d t h e u n i vers i t y , i s a we l l - fo rm e d se n t e nc e

I n s t e a d o f e x p a n d i n g b r a n c h 7 b f u r t h e r , w c w i l l r e s m n e m l r e x a m p l e

a t b r a n c h 2 c t o v e r i f y t h e c o n d i t i o n t h a t t h e o r i g in M s e n t en c e m u s t h a v e

ob j e c t -p re d i c a t e a g re e m e n t . S i nc e t he ob j e c t se que nc e c on t a i n s a n i nd i r e c t

ob j e c t , d i r e c t ob j e c t a nd a n a dve rb , hype r ru l e H30 wi l l be Nl p l i e d ne x t a nd

s i nc e t he ve rb gave i s d i t r a n s i t i v e , o b j e c t - p r e d i c a t e a g r e e m e n t w i l l h e

sa t isf ied.

2e * c ond i t i on M rs . W h i t e a p resen t t o d a y s h o w s o b j e c t - p r e d i c a t e

a g r e e m e n t w i t h cave

3d * whe re gave i s d i t r a n s i t i v e

4e •

Re t u rn i ng t o t he t op - l e ve l c ond i t i ons , we ne x t ve r i fy t he we l l -

fo rm c dne ss o f t he ve rb gave. Si nc e t he re a r c no a ux i l i a ry ve rbs , hypc r ru l e

l t31 is sa t i sf ied.

2d • c ond i t i on gave i s a we l l - fo rm e d p re d i c a t e

3e •

T he f i na l c ond i t i on t ha t t he se n t e nc e m us t sa t i s fy i s we l l - fo rm c dn e ss of t he

ob j e c t . S i nc e the ob j e c t i s a se que nc e , r u l e H34 wi l l be a pp l i e d t o b r a nc h 2c

t o de c om pose t i l e ob j e c t se que nc e a nd a na l yz e the i nd i r e c t a nd d i r e c t

ob j e c t s i nd i v i du a l l y by ru l e H33 . Ru l e I t a a c a l l s r u l e s I I10 - I I12 r e cu r s i ve l y .

S i nc e Mrs. Whi te i s a na m e d sub j e c t , hype r ru l e H10 i s sa t i s f i e d fo r t i l e

i nd i r e c t ob j e c t . By a pp l y i ng hypc r ru l e s [ I11 , II13 , HI4 , H16 , I t 19 a nd 1120 ,

t he d i r e c t ob j e c t a p r e s e n t wi l l a l so be ve r i f i e d a s a we l l - fo rm e d ob j e c t . T he

a n a l y s i s i s n o w c o m p l e t e a n d t h e s e n t e n c e h a s b e e n d e t e r m i n e d t o b e

c o r r e c t t h r o u g h t i l e p r o c e s s o f o u r t w o q e v e l g r a m m a r i n t e r p r e t a t i o n

m e t h o d .

6 . C O N C L U S I O N S

W e h a v e s h o w n t h a t t w o - l e v e l g r a m m a r s m a y b e u s e d v e r y e l e g a n t l y

t o g i ve a fo rm a l spe c i f i c a t i on o f Igng l i sh c on t e x t- f l ' e c a nd c on t e x t - se n s i t i ve

s y n t a x . I n a d d i t i o n t o t h e s u b s e t w e h a v e d e f i n e d i n t h i s p a p e r , m a n y

o t he r t ype s o f Nn g l i sh de c l a r a t i v e se n t e nc e s ha ve be e n fo rm Ml y spe c i f i e d

us i ng t wo- l e ve l g r a m m a rs {7 ]. T he re se e m s t o be no obs t a c l e t o u s i ng r i g

spe c i f i c a t i ons fo r a ny t yp e o f na t u ra l l a ng ua ge syn t a c t i c spe c i f i c a t i on .

T i l e p r i n c i p a l a d v a n t a g e s o f t h e t w o - l e v e l g r a m m a r m c t M a n g u a g e a r e :

1 ) it i s v e ry r e a d a b l e a n d m a y b e u s e d t o g i v e a f o r m a l d e s c r i p t io n u s i n g a

s t r u c t u r e d f o r m o f n a t u r a l l a n g u a g e ; 2 ) i t i s f o r m a l w i t h m a n y w e l l - k n o w n

m a t h e m a t i c a l p r o p e r ti e s ; a n d 3 ) i t i s d i re c t l y i m p l c m e n t a b l e b y

i n t e r p r e t at i o n . T h e s i g n i f ic a n c e o f t h e l a t t e r f a c t i s t h a t o n c e w e h a v e

w r i t t e n a t w o - l e v e l g r a m m m ' f o r n a t u r a l l a n g u a g e s y n t a x , w e c a n d e r i v e ap a r s e r a u t o m a t i c a l l y w i t h o u t w r i t i n g a n y a d d i t i o n a l s p e c i al i z ed c o m p u t e r

p r o g r a m s . T h e c o m b i n a t i o n o f r e a d a b i l i t y a n d i m p l e m e n t a b i l i t y i s u n i q u e

i n g r a m m a r t h e o r y f o r n a t u r a l l a n g u a g e s .

T o g i v e a c o m p l e t e s p c c i f ic a t io n o f n a t u r a l l a n g u a g e , s e m a n t i c s a n d

k n o w l e d g e re p r e s e n t a t i o n m u s t b e s p e c i f ie d in a d d i t i o n t o s y n t a x . O u r

f u t u r e g o a l s a re t h e i n v e s t i g a t i o n o f t w o - le v e l g r a m m a r f o r s e m a n t i c

spe c i f i c a ti on . Be c a use o f t he e a se wi t h wt f i c h t wo- l e ve l g r a m m a rs m a y

e xpre ss l og i c [6 ] a nd t he i r T u r i ng c om pu t a b i l i t y [12 ] , we e xpe c t t ha t t l g s

wi l l a l so bc ve ry su i t a b l e fo r t he se goa l s .

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[2] Gl e a ve l a nd , J . C . a nd U z ga l i s , R . C . G r a m m a r s / o r P r o g r a m m i n g

Languages. E l s e v i e r N o r t h - I I o l la n d , N e w Y o r k , 1 97 7 .

[3] Cu l i c ovc r , P . W. S y n t a x . 2 n d e d . A c a d e m i c P r e s s , N e w Y o r k , 1 98 2 .

I4 ] E d u p u g a n t y , B . a n d B r y a n t , B . R . " T w o - L e v e l G r a m m a r s f o r

A u t o m a t i c I n t e r p r e t a t i o n . " P r c c . 1 9 8 5 A C M A n n u a l C o n fe r e nc e ,1985, pp. 417-423.

[5 ] Ga z c l a r , G . a nd Pu l l um , G . K . Gen era l i zed Ph ra se S t ru c t u re

Gra mm a r: A Th eo re t i ca l S yn o p s i s . I n d i a n a U n i v e r s i t y L i n g u i s t i c s

C l u b , I n d i a n a U n i v e r s i t y , B l o o m i n g t o n , I n d . , 1 9 8 2.

[ 6] t l e ss c , W , " A C o r r e s p o n d e n c e I le t w e e n W - G r a m m a r s a n d F o r m a l

S y s t e m s o f L o g ic a n d I t s A p p l i c a t i o n t o F o r m a l L a n g u a g e

De sc r i p t i on ." C o mp u t . L i n g u i s t . C o mp u t . La n g . 1 3 (1979), 19-30.

[7] John son, D. U s in g T w o - L e v d G r a m m a r s t o D e s c r i be t h e S y n t a x o f

English. M . S . T h es i s , D e p a r t m e n t o f C o m p u t e r a n d I n f o r m a t i o n

S c ie nc es , T h e U n i w ; r s i t y o f A l a b a m a a t B i r m i n g h a m , 1 98 4 .

[8 ] J o h n s o n , D . an d B r y a n t , B . R . " U s i n g T w o - L e v e l G r a m m a r s t o

D e s c r i b e t h e S y n t a x o f E n g l i s h . " P a p e r s o n C o m p u t a t i o n a l a n d

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