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8/3/2019 Language Syntax
http://slidepdf.com/reader/full/language-syntax 1/6
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
8/3/2019 Language Syntax
http://slidepdf.com/reader/full/language-syntax 2/6
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
8/3/2019 Language Syntax
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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
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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 •
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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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I l l C h o m s k y , N . S yn t a c t i c S t ru c t u res . M o u t o n P u b l i s h e r s , T h e t I a g u e ,
Ne t he r l a nds , 1957 .
[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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