Gazdar, G., Klein.. Mouton, The Hague.
Trang 1H a r r y Bunt, Jan T h e s i n g h and Ko van der Sloot
C o m p u t a t i o n a l L i n g u i s t i c s Unit
T i l b u r g University, SLE Postbus 90153
5000 LE TILBURG, The N e t h e r l a n d s
A B S T R A C T This paper d i s c u s s e s the c o n s e q u e n c e s
of a l l o w i n g d i s c o n t i n u o u s c o n s t i t u e n t s in
s y n t a c t i c r e p r e s e n t i o n s a n d
p h r a s e - s t r u c t u r e rules, and the r e s u l t i n g
c o m p l i c a t i o n s for a s t a n d a r d parser of
p h r a s e - s t r u c t u r e grammar
It is argued, first, that d i s c o n t i n u o u s
c o n s t i t u e n t s s e e m i n e v i t a b l e in a
p h r a s e - s t r u c t u r e g r a m m a r w h i c h is
a c c e p t a b l e from a s e m a n t i c point of view
It is shown that t r e e - l i k e c o n s t i t u e n t
s t r u c t u r e s with d i s c o n t i n u i t i e s can be
g i v e n a p r e c i s e d e f i n i t i o n w h i c h makes
them just as a c c e p t a b l e for s y n t a c t i c
r e p r e s e n t a t i o n as o r d i n a r y trees However,
the f o r m u l a t i o n of p h r a s e - s t r u c t u r e rules
that g e n e r a t e such s t r u c t u r e s entails
quite i n t r i c a t e problems The n o t i o n s .of
l i n e a r p r e c e d e n c e and a d j a c e n c y are
reexamined, and the c o n c e p t of "n-place
a d j a c e n c y s e q u e n c e " is i n t r o d u c e d
F i n a l l y , t h e r e s u l t i n g f o r m o f
p h r a s e - s t r u c t u r e g r a m m a r , c a l l e d
" D i s c o n t i n u o u s P h r a s e - S t r u c t u r e G r a m m a r "
is shown to be p a r s a b l e by an a l g o r i t h m
for c o n t e x t - f r e e p a r s i n g with r e l a t i v e l y
minor a d a p t a t i o n s The paper d e s c r i b e s the
a d a p t a t i o n s in the chart parser w h i c h was
i m p l e m e n t e d as part of the T E N D U M d i a l o g u e
system
I P h r a s e - s t r u c t u r e
d i s c o n t i n u i t y
g r a m m a r a n d
C o n t e x t - f r e e p h r a s e - s t r u c t u r e g r a m m a r s
( P S G s ) have always been p o p u l a r in
c o m p u t a t i o n a l l i n g u i s t i c s and in the
theory of p r o g r a m m i n g l a n g u a g e s b e c a u s e of
their t e c h n i c a l and c o n c e p t u a l s i m p l i c i t y
a n d t h e i r w e l l - e s t a b l i s h e d e f f i c i e n t
p a r s a b i l i t y (Shell, 1976; Tomita, 1985)
In t h e o r e t i c a l l i n g u i s t i c s , i t was
g e n e r a l l y b e l i e v e d until r e c e n t l y that
natural l a n g u a g e c o m p e t e n c e cannot be
c h a r a c t e r i z e d a d e q u a t e l y by a c o n t e x t - f r e e
grammar, e s p e c i a l l y in view of a g r e e m e n t
p h e n o m e n a and d i s c o n t i n u i t i e s (see e.g
e i g h t i e s Gazdar and others revived an
i d e a , d u e to H a r m a n ( 1 9 6 3 ) , of
f o r m u l a t i n g p h r a s e - s t r u c t u r e rules not in terms of m o n a d i c c a t e g o r y symbols, but in
richer c o n c e p t i o n of PSG it is not at all
o b v i o u s w h e t h e r n a t u r a l l a n g u a g e s can be
d e s c r i b e d by c o n t e x t - f r e e g r a m m a r s (see
e g P u l l u m , 1 9 8 4 ) G e n e r a l i z e d
P h r a s e - S t r u c t u r e G r a m m a r (GPSG; G a z d a r et al., 1985), r e p r e s e n t s a recent a t t e m p t
to p r o v i d e a t h e o r e t i c a l l y a c c e p t a b l e
a c c o u n t of n a t u r a l - l a n g u a g e s y n t a x in the form of a p h r a s e - s t r u c t u r e grammar
Apart from being i m p o r t a n t in its own
r i g h t , p h r a s e - s t r u c t u r e g r a m m a r also plays an i m p o r t a n t part in more c o m p l e x
g r a m m a r f o r m a l i s m s that have been
d e v e l o p e d in l i n g u i s t i c s ; in c l a s s i c a l
T r a n s f o r m a t i o n a l - G e n e r a t i v e G r a m m a r the base c o m p o n e n t was a s s u m e d to be a PSG;
in L e x i c a l - F u n c t i o n a l G r a m m a r a PSG is
s u p p o s e d to g e n e r a t e c - s t r u c t u r e s , and in
F u n c t i o n a l U n i f i c a t i o n G r a m m a r
c o n t e x t - f r e e rules g e n e r a t e the input
s t r u c t u r e s for the u n i f i c a t i o n o p e r a t i o n (Kay, 1979)
P h r a s e - s t r u c t u r e g r a m m a r has one more
a t t r a c t i v e s i d e , a p a r t f r o m its
t e c h n i c a l / c o n c e p t u a l s i m p l i c i t y and its
c o m p u t a t i o n a l e f f i c i e n c y , n a m e l y that it seems to fit the s e m a n t i c r e q u i r e m e n t of
c o m p o s i t i o n a l i t y v e r y w e l l T h e
c o m p o s i t i o n a l i t y p r i n c i p l e is the thesis that the m e a n i n g of a n a t u r a l - l a n g u a g e
e x p r e s s i o n is d e t e r m i n e d by the
c o m b i n a t i o n of (a) the m e a n i n g s of its parts; (b) its s y n t a c t i c s t r u c t u r e This entails, for a g r a m m a r w h i c h a s s o c i a t e s
m e a n i n g s with the e x p r e s s i o n s of the
l a n g u a g e , the r e q u i r e m e n t that the
s y n t a c t i c rules should c h a r a c t e r i z e the
i n t e r n a l s t r u c t u r e of every e x p r e s s i o n in
a " m e a n i n g f u l " way, w h i c h allows the
c o m p u t a t i o n of its meaning In this way,
s e m a n t i c c o n s i d e r a t i o n s can be used to prefer one s y n t a c t i c a n a l y s i s to another PSGs area useful tool for the f o r m u l a t i o n
o f s y n t a c t i c rules that meet this
r e q u i r e m e n t , as p h r a s e - s t r u c t u r e rules by their very n a t u r e p r o v i d e a r e c u r s i v e
d e s c r i p t i o n of the c o n s t i t u e n t s t r u c t u r e
Trang 2(I
(2
(3
(4
(5
(6 Leo is h a r d e r g e g a a n d a n o o i t t e v o r e n
(= Leo has b e e n g o i n g f a s t e r t h a n
e v e r b e f o r e )
(7) Ik h o b e e n a u t o g e k o c h t m e t 5 d e u r e n
(= I h a v e b o u g h t a c a r w i t h 5 d o o r s )
(8) Ik h o o t d a t J a n M a r i e de k i n d e r e n de
h o n d h e e f t h e l p e n l e r e n u i t l a t e n
(= I h e a r t h a t J o h n has h e l p e d M a r y
to t e a c h the k i d s to w a l k the dog)
J o h n t a l k e d , o f c o u r s e , a b o u t
p o l i t i c s
W h i c h c h i l d r e n d i d A n n e e x p e c t to g e t
a p r e s e n t f r o m ?
This w a s a b e t t e r m o v i e t h a n I
e x p e c t e d
W a k e m e u p at s e v e n t h i r t y
~i-il o n e of y o u r c o u s i n s c o m e w h o
m o v e d to D e n m a r k ?
T h e s e e x a m p l e s do n o t r e p r e s e n t a s i n g l e
c l a s s of l i n g u i s t i c p h e n o m e n a , and it is
d o u b t f u l w h e t h e r t h e y s h o u l d a l l be
h a n d l e d by m e a n s of t h e s a m e t e c h n i q u e s
(1o)
S e n t e n c e (I), w h i c h has b e e n d i s c u s s e d
e x t e n s i v e l y in the l i t e r a t u r e , p r e s e n t s a
p r o b l e m f o r a n y a n a l y s i s in t e r m s of
a d j a c e n t c o n s t i t u e n t s , s i n c e t h e
p a r e n t h e t i c a l "of c o u r s e " d i v i d e s the v e r b
p h r a s e " t a l k e d a b o u t p o l i t i c s " i n t o
n o n - a d j a c e n t p a r t s T h i s m e a n s t h a t we a r e
f o r c e d t o e i t h e r c o n s i d e r t h e
p a r e n t h e t i c a l as p a r t of the VP, as Ross
(1973) has s u g g e s t e d , or as a c o n s t i t u e n t
at s e n t e n c e level, as has b e e n s u g g e s t e d
by E m o n d s (1976; 1979) In the l a t t e r
c a s e , t h e s e n t e n c e is a n a l y s e d as
c o n s i s t i n g of the e m b e d d e d s e n t e n c e " J o h n
t a l k e d " , w i t h "of c o u r s e " a n d " a b o u t
p o l i t i c s " as s p e c i f i e r s at s e n t e n c e l e v e l
M c C a w l e y ( 1 9 8 2 ) p r o v i d e s d e t a i l e d
a r g u m e n t s s h o w i n g t h a t b o t h s u g g e s t i o n s
a r e i n a d e q u a t e ( w h i c h s e e m s i n t u i t i v e l y
o b v i o u s , f r o m a s e m a n t i c p o i n t of v i e w ) ,
and s u g g e s t s , i n s t e a d , the s y n t a c t i c
r e p r e s e n t a t i o n (9)
(9)
J o h n t a l k e d
T h i s is of c o u r s e no l o n g e r an
o r d i n a r y t r e e s t r u c t u r e , b u t s h o u l d t h a t
be a r e a s o n to r e j e c t i t ? M c C a w l e y t a k e s the v i e w t h a t we s h o u l d s i m p l y n o t be
a f r a i d of c o n s t i t u e n t s t r u c t u r e s l i k e (9) We w i l l r e t u r n to t h i s s u g g e s t i o n
b e l o w
E x a m p l e (2) r e p r e s e n t s a d i f f e r e n t
c l a s s o f p h e n o m e n a , w h i c h a r e
c o n v e n i e n t l y t h o u g h t o f in t e r m s o f
m o v e m e n t s of p a r t s of p h r a s e s In t h i s
e x a m p l e , the NP " w h i c h c h i l d r e n " c a n be
t h o u g h t of as h a v i n g m o v e d o u t of the PP
" f r o m w h i c h c h i l d r e n " , of w h i c h o n l y t h e
p r e p o s i t i o n has b e e n l e f t b e h i n d In
o r d e r to d e a l w i t h s u c h c a s e s , in G P S G a
s p e c i a l t y p e of s y n t a c t i c c a t e g o r i e s h a v e
b e e n i n t r o d u c e d , c a l l e d " s l a s h
c a t e g o r i e s " For i n s t a n c e , t h e c a t e g o r y
P P / N P is a s s i g n e d to a p r e p o s i t i o n a l
p h r a s e w h i c h " m i s s e s " an NP In the
p r e s e n t e x a m p l e , t h i s c a t e g o r y w o u l d be
a s s i g n e d to " f r o m " T h e a s s u m p t i o n t h a t
an NP is m i s s i n g p r o p a g a t e s to h i g h e r
n o d e s in t h e s y n t a c t i c t r e e w h i c h the
p h r a s e - s t r u c t u r e r u l e s c o n s t r u c t for the
s e n t e n c e , u n t i l it is a c k n o w l e d g e d at t h e
t o p l e v e l D i a g r a m (10) i l l u s t r a t e s t h i s
S
s m a l l e s t m e a n i n g f u l p a r t s H o w e v e r , PSG
h a s o n e p r o p e r t y t h a t l i m i t s its
a p p l i c a b i l i t y in d e s c r i b i n g c o n s t i t u e n t
s t r u c t u r e in n a t u r a l l a n g u a g e , n a m e l y t h a t
p h r a s e - s t r u c t u r e r u l e s a s s u m e the
c o n s t i t u e n t s o f a n e x p r e s s i o n to
c o r r e s p o n d to a d j a c e n t s u b s t r i n g s In
n a t u r a l l a n g u a g e it h a p p e n s q u i t e o f t e n ,
h o w e v e r , t h a t the c o n s t i t u e n t s of an
e x p r e s s i o n are n o t a d j a c e n t The E n g l i s h
a n d D u t c h e x a m p l e s e n t e n c e s ( I )-(8)
i l l u s t r a t e this In ( 2 ) - ( 7 ) we s e e
e x a m p l e s of m a j o r p h r a s e s , m a d e up of
p a r t s that a r e n o t a d j a c e n t ; s o - c a l l e d
d i s c o n t i n u o u s c o n s t i t u e n t s We h a v e
d i s c o n t i n u o u s n o u n p h r a s e s in (5) a n d (7),
a d i s c o n t i n u o u s a d j e c t i v e p h r a s e in (3),
d i s c o n t i n u o u s v e r b p h r a s e s in (1) a n d (4),
and a d i s c o n t i n u o u s a d v e r b p h r a s e in (6)
N P [ + W H ] A U X NP V NP P R E P N P / N P
w h i c h c h i l d r e n d i d Ann et i f t s f r o m 0
If we w a n t to do j u s t i c e to the
i n t u i t i o n t h a t the s e n t e n c e at s u r f a c e
l e v e l c o n t a i n s a c o n s t i t u e n t m a d e up by
" w h i c h c h i l d r e n " and " f r o m " , we w o u l d
h a v e to d r a w a c o n s t i t u e n t d i a g r a m l i k e (11), w h i c h , l i k e (9), is no l o n g e r an
o r d i n a r y t r e e s t r u c t u r e
Trang 3w h i c h c h i l d r e n did nn g e t ifts fr m
The t e c h n i q u e of u s i n g p h r a s e s t h a t
m i s s s o m e c o n s t i t u e n t c a n n o t be u s e d for
at l e a s t s o m e of the e x a m p l e s (3)-(8),
s u c h as (5) and (7) In b o t h t h e s e
s e n t e n c e s the d i s c o n t i n u o u s NP c o n t a i n s a
f u l l - f l e d g e d NP, w h i c h c a n n o t s e n s i b l y be
s a i d to " m i s s " the r e l a t i v e c l a u s e or
p r e p o s i t i o n a l p h r a s e t h a t o c c u r s l a t e r in
the s e n t e n c e
W h a t e v e r t e c h n i q u e s m a y be i n v e n t e d to
d e a l w i t h s u c h cases, it s e e m s o b v i o u s
t h a t a g r a m m a r w h i c h r e c o g n i z e s and
d e s c r i b e s d i s c o n t i n u i t i e s in n a t u r a l
l a n g u a g e s e n t e n c e s is a m o r e s u i t a b l e
b a s i s for s e m a n t i c i n t e r p r e t a t i o n t h a n one
t h a t s q u e e z e s c o n s t i t u e n t s t r u c t u r e s in a
f o r m in w h i c h t h e y c a n n o t be r e p r e s e n t e d
It t h e r e f o r e s e e m s w o r t h i n v e s t i g a t i n g
the v i a b i l i t y of t r e e - l i k e s t r u c t u r e s w i t h
d i s c o n t i n u i t i e s , l i k e (9) a n d (11)
2 T r e e s w i t h d i s c o n t i n u i t i e s
If we w a n t to r e p r e s e n t the s i t u a t i o n
t h a t a p h r a s e P has c o n s t i t u e n t s A and C,
w h i l e t h e r e is an i n t e r v e n i n g p h r a s e B, we
m u s t a l l o w the n o d e c o r r e s p o n d i n g to P to
d o m i n a t e the A and C n o d e s w i t h o u t
d o m i n a t i n g the B, e v e n t h o u g h t h i s n o d e is
l o c a t e d b e t w e e n the A a n d C n o d e s :
O n e c o n s e q u e n c e of a l l o w i n g s u c h
d i s c o n t i n u i t i e s is t h a t our s t r u c t u r e s g e t
c r o s s i n g b r a n c h e s , if we s t i l l w a n t all
n o d e s to be c o n n e c t e d to the top node;
(10) and (11) i l l u s t r a t e this In w h a t
r e s p e c t s e x a c t l y do t h e s e s t r u c t u r e s
d i f f e r f r o m o r d i n a r y t r e e s ? M c C a w l e y
(1982) has t r i e d to a n s w e r t h i s q u e s t i o n ,
s u g g e s t i n g a f o r m a l d e f i n i t i o n for t r e e s
w i t h d i s c o n t i n u i t i e s by a m e n d i n g the
d e f i n i t i o n of a tree
A t r e e is o f t e n d e f i n e d as a set of
e l e m e n t s , c a l l e d " n o d e s " , on w h i c h two
r e l a t i o n s a r e d e f i n e d , i m m e d i a t e d o m i n a n c e
(D) and l i n e a r p r e c e d e n c e (<), w h i c h are
the e f f e c t t h a t a t r e e has e x a c t l y one
r o o t node, w h i c h d o m i n a t e s e v e r y o t h e r
n o d e ( i m m e d i a t e l y or i n d i r e c t l y ) ; t h a t
e v e r y n o d e in a tree has e x a c t l y one
" m o t h e r " node, etc (see e.g Wall, 1972)
G i v e n the r e l a t i o n s of i m m e d i a t e
d o m i n a n c e a n d l i n e a r p r e c e d e n c e ,
d o m i n a n c e is d e f i n e d as the r e f l e x i v e and
t r a n s i t i v e c l o s u r e D' of D, and a d j a c e n c y
as l i n e a r p r e c e d e n c e w i t h o u t i n t e r v e n i n g
n o d e s
A n o d e in a t r e e is c a l l e d t e r m i n a l if
it d o e s n o t d o m i n a t e a n y o t h e r node; the
t e r m i n a l n o d e s in a t r e e a r e t o t a l l y
o r d e r e d b y t h e < r e l a t i o n For
n o n t e r m i n a l n o d e s the p r e c e d e n c e r e l a t i o n
s a t i s f i e s the r e q u i r e m e n t t h a t x < y if and o n l y if e v e r y n o d e d o m i n a t e d by x
p r e c e d e s e v e r y n o d e d o m i n a t e d by y
F o r m a l l y : (13) for a n y t w o n o d e s x and y in the
n o d e set of a tree, x < y if and
o n l y if for all n o d e s u a n d v, if x
d o m i n a t e s u a n d y d o m i n a t e s v, t h e n
u < v
P a r t of the d e f i n i t i o n of a t r e e is
a l s o the s t i p u l a t i o n t h a t a n y t w o n o d e s
e i t h e r d o m i n a t e or p r e c e d e o n e a n o t h e r : (14) for a n y t w o n o d e s x and y in the
n o d e s e t of a tree, e i t h e r x D' y,
or y D' x, or x < y, or y < x
T h i s s t i p u l a t i o n has t h e e f f e c t of
e x c l u d i n g d i s c o n t i n u i t i e s in a tree, for
s u p p o s e a n o d e x w o u l d d o m i n a t e n o d e s y and z w i t h o u t h a v i n g a d o m i n a n c e r e l a t i o n
w i t h n o d e w, w h e r e y < w < z By (14),
e i t h e r x < w or w < x B u t x d o m i n a t e s a
n o d e to the r i g h t of w, so by (13) x d o e s
n o t p r e c e d e w; and w is to the r i g h t of a
n o d e d o m i n a t e d by x, so w d o e s n o t
p r e c e d e x e i t h e r
M c C a w l e y ' s d e f i n i t i o n of t r e e s w i t h
d i s c o n t i n u i t i e s c o m e s d o w n to d r o p p i n g the c o n d i t i o n t h a t a n y t w o n o d e s s h o u l d
e i t h e r d o m i n a t e o n e a n o t h e r or h a v e a
l e f t - r i g h t r e l a t i o n I n s t e a d , he p r o p o s e s the w e a k e r c o n d i t i o n t h a t a n o d e has no
p r e c e d e n c e r e l a t i o n to a n y n o d e t h a t it
d o m i n a t e s : (15) for a n y two n o d e s x and y in the
n o d e s e t of a tree, if x D' y t h e n
n e i t h e r x < y nor y < x
We s h a l l c a l l a n o d e u, s i t u a t e d
b e t w e e n d a u g h t e r s of a n o d e x w i t h o u t
b e i n g d o m i n a t e d by x, i n t e r n a l c o n t e x t of
X
Trang 4d i s c o n t i n u i t i e s is i n a c c u r a t e in s e v e r a l
r e s p e c t s ; h o w e v e r , his g e n e r a l i d e a is
c e r t a i n l y c o r r e c t : t r e e s w i t h
d i s c o n t i n u i t i e s can be d e f i n e d e s s e n t i a l l y
b y r e l a x i n g c o n d i t i o n (14) in the
d e f i n i t i o n of t r e e s
H o w e v e r , t h i s is o n l y the b e g i n n i n g of
w h a t n e e d s to be d o n e The n e x t q u e s t i o n
is h o w d i s c o n t i n u o u s t r e e s c a n be p r o d u c e d
by p h r a s e - s t r u c t u r e r u l e s This q u e s t i o n ,
w h i c h is n o t a d d r e s s e d by M c C a w l e y , is far
f r o m t r i v i a l and t u r n s o u t to h a v e
i n t e r e s t i n g c o n s e q u e n c e s for the n o t i o n of
a d j a c e n c y in d i s c o n t i n u o u s tre
es
3 A d j a c e n c y in p h r a s e - s t r u c t u r e r u l e s f o r
d i s c o n t i n u o u s c o n s t i t u e n t s
A p h r a s e - s t r u c t u r e r u l e r e w r i t e s a
c o n s t i t u e n t i n t o a s e q u e n c e o f p a i r w i s e
a d j a c e n t c o n s t i t u e n t s T h i s m e a n s t h a t we
n e e d a n o t i o n o f adjacency i n
d i s c o n t i n u o u s trees, for w h i c h the o b v i o u s
d e f i n i t i o n , g i v e n the < r e l a t i o n , w o u l d
s e e m to be:
(16) two n o d e s x and y in the n o d e set of
a t r e e a r e a d j a c e n t if and o n l y if x
< y a n d t h e r e is no z s u c h t h a t x <
z < y
We s h a l l w r i t e "x + y" to i n d i c a t e t h a t
x and y a r e a d j a c e n t (or " n e i g h b o u r s " ) A
m o m e n t ' s r e f l e c t i o n s h o w s t h a t t h i s n o t i o n
of a d j a c e n c y u n f o r t u n a t e l y d o e s n o t h e l p
us in f o r m u l a t i n g r u l e s t h a t c o u l d do
a n y t h i n g w i t h i n t e r n a l c o n t e x t
c o n s t i t u e n t s T h e f o l l o w i n g e x a m p l e
i l l u s t r a t e s this S u p p o s e we w a n t to
g e n e r a t e the d i s c o n t i n u o u s t r e e s t r u c t u r e :
/k
W a k e y o u r f r i e n d up
To g e n e r a t e the top node, we n e e d a
r u l e c o m b i n i n g t h e V a n d the NP, like:
(18) VP - - > V + NP
S i n c e the V d o m i n a t e s n o d e s at e i t h e r
s i d e of the NP, h o w e v e r , t h e r e is no
l e f t - r i g h t o r d e r b e t w e e n the NP and V
n o d e s , l e a v e a l o n e a n e i g h b o u r r e l a t i o n
For the s a m e r e a s o n t h e r e w o u l d be no
l e f t - r i g h t r e l a t i o n b e t w e e n o v e r l a p p i n g
d i s c o n t i n u o u s c o n s t i t u e n t s , as in (19)
T h e s e d e f i c i e n c i e s c a n be r e m e d i e d by
r e p l a c i n g c l a u s e (14) in the d e f i n i t i o n of
a t r e e by t h e m o r e g e n e r a l c l a u s e (20)
W a k e the m a n up w h o l i v e s n e x t d o o r (20) A n o n t e r m i n a l n o d e x in a t r e e is
to the l e f t of a n o d e y in t h e t r e e
i f a n d o n l y if x ' s l e f t m o s t
d a u g h t e r is l e f t of y ' s l e f t m o s t
d a u g h t e r ( W e r e f r a i n h e r e f r o m a f o r m a l
d e f i n i t i o n of " l e f t m o s t d a u g h t e r " node,
w h i c h is i n t u i t i v e l y o b v i o u s )
N o t e t h a t ( 2 0 ) is i n d e e d a
g e n e r a l i z a t i o n o f t h e u s u a l n o t i o n o f
p r e c e d e n c e in t r e e s , w h i c h c o u l d a l s o be
d e f i n e d by (20) The r e c u r s i o n in (20)
c o m e s to an end s i n c e the t e r m i n a l n o d e s
a r e r e q u i r e d to be t o t a l l y o r d e r e d
It s h o u l d a l s o be n o t e d t h a t (20) is
n o t c o n s i s t e n t w i t h c l a u s e (14): by (2@),
we do g e t a p r e c e d e n c e r e l a t i o n b e t w e e n a
n o d e and its d a u g h t e r n o d e s ( e x c e p t t h e
l e f t m o s t o n e ) and i n t e r n a l c o n t e x t n o d e s
T h i s is n o t q u i t e u n r e a s o n a b l e In (21), for e x a m p l e , we do w a n t t h a t X < Y, a n d
s i n c e Y < C, t h a t X < C, but n o t t h a t X <
B We t h e r e f o r e a d a p t c l a u s e (14) to the
e f f e c t t h a t a m o t h e r n o d e o n l y p r e c e d e s
i n t e r n a l c o n t e x t n o d e s a n d d a u g h t e r n o d e s
w h i c h h a v e i n t e r n a l c o n t e x t n o d e s to
t h e i r left F o r m a l l y : (22) For a n y n o d e s x a n d z in t h e n o d e
s e t N o f a tree, if x D z and t h e r e
a r e no n o d e s u , v in N s u c h t h a t x D
u, n o t x D v, a n d u < v < z, t h e n
n e i t h e r x < z n o r z < x
W i t h t h e m o d i f i c a t i o n s (16) a n d (22),
w e h a v e a c o n s i s t e n t d e f i n i t i o n o f
" d i s c o n t i n u o u s t r e e s " w h i c h a l l o w s us to
w r i t e p h r a s e - s t r u c t u r e r u l e s c o n t a i n i n g
d i s c o n t i n u o u s c o n s t i t u e n t s as f o l l o w s : (23) X - - > A + B + [Y] + C
w h e r e the s q u a r e b r a c k e t s i n d i c a t e t h a t the NP is n o t d o m i n a t e d by t h e X node, but is o n l y i n t e r n a l c o n t e x t The "+"
s y m b o l r e p r e s e n t s t h e n o t i o n of
a d j a c e n c y , d e f i n e d as b e f o r e b u t n o w on the b a s i s of te r e v i s e d p r e c e d e n c e
r e l a t i o n "<":
Trang 5(24)
a d j a c e n t if and o n l y if x < y and
t h e r e is no n o d e z in the t r e e s u c h
t h a t x < z < y
U p o n c l o s e r i n s p e c t i o n , the n e i g h b o u r
r e l a t i o n d e f i n e d i n t h i s w a y is
u n s a t i s f a c t o r y , h o w e v e r , as the f o l l o w i n g
e x a m p l e i l l u s t r a t e s
S u p p o s e we w a n t to g e n e r a t e the
f o l l o w i n g (part of a) t r e e s t r u c t u r e :
To g e n e r a t e the S node, we w o u l d l i k e
to w r i t e a p h r a s e - s t r u c t u r e r u l e t h a t
r e w r i t e s S i n t o its c o n s t i t u e n t s , l i k e
(26):
(26) S - - > P + Q + E
H o w e v e r , t h i s r u l e w o u l d be of no h e l p
here, s i n c e P, Q and E do n o t f o r m a
s e q u e n c e o f a d j a c e n c y pairs, as Q a n d E
a r e n o t a d j a c e n t a c c o r d i n g to o u r
d e f i n i t i o n R a t h e r , the c o r r e c t r u l e for
g e n e r a t i n g (25) w o u l d be (27):
(27) S - - > P + Q + [C] + [D] + E
This is ugly, a n d e v e n u g l i e r r u l e s a r e
r e q u i r e d in m o r e c o m p l e x t r e e s w i t h
d i s c o n t i n u i t i e s at d i f f e r e n t l e v e l s
M o r e o v e r , t h e r e s e e m s to be s o m e t h i n g
f u n d a m e n t a l l y w r o n g , s i n c e the C and D
n o d e s a r e on the o n e h a n d i n t e r n a l c o n t e x t
for the S node, a c c o r d i n g to r u l e (27),
w h i l e on the o t h e r h a n d t h e y a r e a l s o
d o m i n a t e d by S T h a t is, t h e s e n o d e s a r e
b o t h " r e a l " c o n s t i t u e n t s o f S a n d i n t e r n a l
c o n t e x t of S
To r e m e d y this, we i n t r o d u c e a n e w
c o n c e p t of a d j a c e n c y s e q u e n c e , w h i c h
g e n e r a l i z e s the t r a d i t i o n a l n o t i o n of a
s e q u e n c e o f a d j a c e n c y p a i r s The
d e f i n i t i o n g o e s as f o l l o w s :
(28) A s e q u e n c e (a, b, , n) is an
( n - p l a c e ) a d j a c e n c y s e q u e n c e if and
o n l y if:
(i) e v e r y p a i r ( i , j ) in the
s e q u e n c e is e i t h e r an a d j a c e n c y
p a i r or is c o n n e c t e d by a
s e q u e n c e of a d j a c e n c y p a i r s of
w h i c h a l l m e m b e r s a r e a
c o n s t i t u e n t o f s o m e e l e m e n t in
the s u b s e q u e n c e (a, b, , i);
(ii) the e l e m e n t s in the s e q u e n c ~ do
n o t s h a r e a n y c o n s t i t u e n t s )
t r i p l e (P, Q, E) is an a d j a c e n c y s e q u e n c e
s i n c e (P, Q) is an a d j a c e n c y p a i r and Q and E a r e c o n n e c t e d by the s e q u e n c e of
a d j a c e n c y p a i r s Q - C - D - E , w i t h C and D
c o n s t i t u e n t s of P and Q, r e s p e c t i v e l y
A n o t h e r e x a m p l e of an a d j a c e n c y s e q u e n c e
in (25) is the t r i p l e (P, B, D) The
t r i p l e (P, B, C), on the o t h e r hand, is
n o t an a d j a c e n c y s e q u e n c e , s i n c e P and C
s h a r e the c o n s t i t u e n t C
The u s e o f t h i s n o t i o n o f a d j a c e n c y
s e q u e n c e is n o w t h a t the s e q u e n c e of
c o n s t i t u e n t s , i n t o w h i c h a n o n t e r m i n a l is
r e w r i t t e n by a p h r a s e - s t r u c t u r e rule,
f o r m s an a d j a c e n c y s e q u e n c e in t h i s
s e n s e T h e p h r a s e - s t r u c t u r e g r a m m a r
c o n s i s t i n g of r u l e s of t h i s k i n d we call
D i s c o n t i n u o u s P h r a s e - S t r u c t u r e G r a m m a r or DPSG ~ j
It m a y be w o r t h e m p h a s i z i n g t h a t this
n o t i o n o f p h r a s e - s t r u c t u r e r u l e is a
g e n e r a l i z a t i o n of the u s u a l n o t i o n , s i n c e
an a d j a c e n c y s e q u e n c e as d e f i n e d by (28)
s u b s u m e s the u s u a l n o t i o n of s e q u e n c e of
a d j a c e n c y p a i r s We h a v e a l s o s e e n t h a t
t r e e s w i t h d i s c o n t i n u i t i e s a r e a
g e n e r a l i z a t i o n of the t r a d i t i o n a l t r e e
c o n c e p t T h e r e f o r e , p h r a s e - s t r u c t u r e
r u l e s of the f a m i l i a r s o r t c o i n c i d e w i t h
D P S G r u l e s w i t h o u t d i s c o n t i n u o u s
c o n s t i t u e n t s , and t h e y p r o d u c e the
f a m i l i a r s o r t o f t r e e s w i t h o u t
d i s c o n t i n u i t i e s In o t h e r w o r d s ,
D P S G - r u l e s c a n s i m p l y be a d d e d to a
c l a s s i c a l PSG ( i n c l u d i n g G P S G ,-~' ~ith the
r e s u l t t h a t the g r a m m a r g e n e r a t e s t r e e s
w i t h d i s c o n t i n u i t i e s for s e n t e n c e s w i t h
d i s c o n t i n u o u s c o n s t i t u e n t s , w h i l e d o i n g
e v e r y t h i n g e l s e as b e f o r e
4 DPSG and p a r s i n g
F r o m a p a r s e r ' s p o i n t of view, a
d e f i n i t i o n of a d j a c e n c y as g i v e n in (24)
is n o t s u f f i c i e n t , s i n c e it o n l y a p p l i e s
to n o d e s w i t h i n the c o n t e x t of a tree A
p a r s e r has the job of c o n s t r u c t i n g s u c h a
s e t f r o m a c o l l e c t i o n of s u b s t r u c t u r e s
t h a t m a y or m a y n o t fit t o g e t h e r to f o r m
o n e or m o r e t r e e s for the e n t i r e
s e n t e n c e W h e t h e r a n u m b e r o f s u b t r e e s fit t o g e t h e r is n o t so e a s y if the end
p r o d u c t m a y b e a t r e e w i t h
d i s c o n t i n u i t i e s , s i n c e the a d j a c e n c y
r e l a t i o n d e f i n e d by (20) and (24) a l l o w s
n e i g h b o u r i n g n o d e s to h a v e c o m m o n
d a u g h t e r s T h i s is c l e a r l y u n d e s i r a b l e
We t h e r e f o r e m o d i f y the d e f i n i t i o n (20)
of a d j a c e n c y by a d d i n g the r e q u i r e m e n t
t h a t two s u b s t r u c t u r e s (or t h e i r top
n o d e s ) can o n l y h a v e a p r e c e d e n c e
r e l a t i o n if t h e y do n o t s h a r e a n y
c o n s t i t u e n t s :
Trang 6(29)
s u b s t r u c t u r e s for a p o t e n t i a l t r e e
( p o s s i b l y w i t h d i s c o n t i n u i t i e s ) is
to the l e f t of a n o d e y in the s a m e
q o l l e c t i o n if and o n l y if x's
l e f t m o s t d a u g h t e r is l e f t of y's
l e f t m o s t d a u g h t e r , and t h e r e is no
n o d e z w h i c h is s h a r e d by x and y
If the n o d e s x a n d y in t h i s d e f i n i t i o n
b e l o n g to the s a m e tree, the a d d i t i o n a l
r e q u i r e m e n t t h a t x and y do n o t s h a r e a n y
c o n s t i t u e n t is a u t o m a t i c a l l y s a t i s f i e d ,
d u e to the " s i n g l e m o t h e r " c o n d i t i o n
A p a r s e r for D P S G m e e t s c e r t a i n
c o m p l i c a t i o n s w h i c h do n o t a r i s e in
c o n t e x t - f r e e p a r s i n g To s e e t h e s e
c o m p l i c a t i o n s , w e c o n s i d e r w h a t w o u l d
h a p p e n w h e n a c h a r t p a r s e r f o r
c o n t e x t - f r e e p a r s i n g (see W i n o g r a d , 1983)
is a p p l i e d to DPSG
C o n t e x t - f r e e c h a r t p a r s i n g is a m a t t e r
of f i t t i n g a d j o i n i n g p i e c e s t o g e t h e r in a
c h a r t For e x a m p l e , c o n s i d e r the g r a m m a r :
(30) S - - > VP NP
NP - - > D E T N
VP - - > V
For the i n p u t "V D E T N", a c h a r t p a r s e r
b e g i n s by i n i t i a l i z i n g t h e c h a r t as
f o l l o w s :
(31)
G i v e n the a r c V ( 1 , 2 ) in the c h a r t , we l o o k
up all t h o s e r u l e s w h i c h h a v e a " f r e e " V
as the f i r s t c o n s t i t u e n t T h e s e r u l e s a r e
p l a c e d in a s e p a r a t e list, the " a c t i v e -
r u l e l i s t " We " b i n d " t h e V's in t h e s e
r u l e s to t h e V ( 1 , 2 ) arc, i.e we e s t a b l i s h
l i n k s b e t w e e n them W h e n all c o n s t i t u e n t s
in a r u l e a r e b o u n d , t h e r u l e is a p p l i e d
In t h i s case, t h e V P ( I , 2 ) w i l l be b u i l t
T h i s p r o c e d u r e is r e p e a t e d for t h e n e w VP
n o d e W h e n n o t h i n g m o r e c a n be done, we
m o v e on in the c h a r t The f i n a l r e s u l t in
t h i s e x a m p l e is the c h a r t (32)
(32)
W h e n we use D P S G r u l e s and f o l l o w the s a m e
p r o c e d u r e , we r u n i n t o d i f f i c u l t i e s
C o n s i d e r the e x a m p l e g r a m m a r (33)
NP - - > D E T + N
VP - - > V + [NP] + P A R T For the i n p u t "V D E T N P A R T " the f i r s t
c o n s t i t u e n t t h a t c a n be b u i l t is N P ( 2 , 4 ) ; the s e c o n d is V P ( I , 5 ) The VP w i l l
a c t i v a t e the S rule, but this r u l e w i l l
n o t be a p p l i e d s i n c e the NP d o e s n o t h a v e
a b i n d i n g And e v e n if it did, the r u l e
w o u l d n o t be a p p l i c a b l e as the V P ( I , 5 ) and the N P ( 2 , 4 ) a r e n o t a d j o i n i n g in t h e
t r a d i t i o n a l s e n s e
In the n e x t s e c t i o n we d e s c r i b e t h e
p r o v i s i o n s , a d d e d to a s t a n d a r d c h a r t
p a r s e r in o r d e r to d e a l w i t h t h e s e
d i f f i c u l t i e s
5 A m o d i f i e d c h a r t p a r s e r f o r D P S G 5.1 F i n d i n g all a p p l i c a b l e r u l e s
To m a k e s u r e t h a t the p a r s e r f i n d s a l l
a p p l i c a b l e r u l e s of a DPSG, t h e f o l l o w i n g
a d d i t i o n w a s m a d e to the p a r s i n g
a l g o r i t h m
If a r u l e w i t h i n t e r n a l c o n t e x t is
a p p l i e d , we f i r s t f o l l o w the s t a n d a r d
p r o c e d u r e ; s u b s e q u e n t l y we g o t h r o u g h all
t h o s e r u l e s t h a t a p p e a r on t h e a c t i v e -
r u l e l i s t as the r e s u l t of a p p l y i n g the
s t a n d a r d p r o c e d u r e , g i v i n g b i n d i n g s to
t h o s e f r e e c o n s t i t u e n t s t h a t c o r r e s p o n d
in c a t e g o r y to t h e c o n t e x t - e l e m e n t ( s ) in the r u l e t h a t w a s a p p l i e d
In the c a s e o f (33), t h i s m e a n s t h a t
j u s t b e f o r e a p p l i c a t i o n of t h e VP r u l e ( a f t e r the P A R T h a s b e e n b o u n d ) , we h a v e the a c t i v e - r u l e l i s t (34) ( U n d e r l i n i n g
i n d i c a t e s t h a t a c o n s t i t u e n t is b o u n d ) (34) VP - - > V ÷ [NP] + P A R T
VP - - > [ + [NP] + P A R T
VP - - > ~ + [NT] + P A R T
w
We n o w a p p l y t h e r u l e b u i l d i n g the VP The s t a n d a r d p r o c e d u r e w i l l a d d o n e r u l e
to t h i s list, n a m e l y S - - > VP + NP The
VP is g i v e n a b i n d i n g , so w e o b t a i n t h e
f o l l o w i n g a c t i v e - r u l e list:
(35) S - - > VP + NP
VP - - > 9 + [NP] + P A R T
VP - - > [ ÷ [NP] + P A R T
VP - - > ~ + [N~] + P A R T
S i n c e the V P - b u i l d i n g r u l e c o n t a i n e d
a n i n t e r n a l c o n t e x t e l e m e n t , the
a d d i t i o n a l p r o c e d u r e m e n t i o n e d a b o v e is
n o w a p p l i e d ; a b i n d i n g is g i v e n to the NP
in (a c o p y of) t h e S rule The S a r c is
n o w b u i l t in the c h a r t , w h i c h d o e s n o t
c a u s e a n y n e w r u l e s to be a d d e d to t h e
a c t i v e - r u l e list T h e r e a r e no f r e e S's
Trang 7s h o u l d be g i v e n a b i n d i n g So, we c a n l o o k
for o t h e r r u l e s c o n t a i n i n g a f r e e NP
T h e r e is one s u c h rule, the s e c o n d in
(35), but this o n e w i l l be n e g l e c t e d
b e c a u s e it was a l r e a d y p r e s e n t in the r u l e
list before; s e e (34) N o t e t h a t it is
e s s e n t i a l t h a t this r u l e is n e g l e c t e d , as
t h e r e is a l r e a d y a v e r s i o n of the V P - r u l e
on the a c t i v e - r u l e l i s t c o n t a i n i n g an NP
w i t h t h e s a m e b i n d i n g a s t h e
c o n t e x t - e l e m e n t
It m a y a l s o be n o t e d t h a t we h a v e
c o m b i n e d c o n s t i t u e n t s in t h i s e x a m p l e t h a t
are not a d j o i n i n g in the t r a d i t i o n a l s e n s e
(i.e., in the s e n s e of s u c c e s s i v e v e r t e x
n u m b e r s ) In p a r t i c u l a r , we h a v e a p p l i e d
the r u l e S - - > V P ( I , 5 ) + N P ( 2 , 4 ) In a
c a s e l i k e this, w h e r e the v e r t e x n u m b e r s
i n d i c a t e t h a t the c o n s t i t u e n t s in a r u l e
a r e o v e r l a p p i n g , we m u s t t e s t w h e t h e r
t h e s e c o n s t i t u e n t s f o r m an a d j a c e n c y
s e q u e n c e This t e s t is d e s c r i b e d b e l o w
5.2 The a d j a c e n c y s e q u e n c e t e s t
In o r d e r to m a k e s u r e t h a t o n l y
c o n s i t u e n t s are c o m b i n e d t h a t f o r m an
a d j a c e n c y s e q u e n c e , the p a r s e r k e e p s t r a c k
of d a u g h t e r n o d e s and i n t e r n a l c o n t e x t in
a s o - c a l l e d " c o n s t r u c t i o n list", w h i c h is
a d d e d to e a c h arc in the c h a r t ; i n t e r n a l
c o n t e x t n o d e s a r e m a r k e d as s u c h in t h e s e
l i s t s W h e t h e r two (or m o r e ) n o d e s s h a r e a
c o n s t i t u e n t , in the s e n s e of c o m m o n
d o m i n a t i o n , is e a s i l y d e t e c t e d w i t h the
h e l p of t h e s e l i s t s
B y o r g a n i z i n g t h e s e l i s t s in a
p a r t i c u l a r way, m o r e o v e r , t h e y c a n a l s o be
u s e d to d e t e r m i n e w h e t h e r a s e q u e n c e o f
c o n s t i t u e n t s is an a d j a c e n c y s e q u e n c e in
the s e n s e of d e f i n i t i o n (28) This is
a c h i e v e d by o r d e r i n g the e l e m e n t s in
c o n s t r u c t i o n l i s t s in s u c h a w a y t h a t an
e l e m e n t is a l w a y s e i t h e r d o m i n a t e d by its
p r e d e c e s s o r in the list, or is i n t e r n a l
c o n t e x t of it, or is a r i g h t n e i g h b o u r of
it For i n s t a n c e , in the a b o v e e x a m p l e
(25), P and Q h a v e the c o n s t r u c t i o n l i s t s
(36):
(36) P:(A, [B], C)
Q:(B, [C], D)
The r u l e S - - > P + Q + E is n o w
a p p l i c a b l e , s i n c e the c o n s t r u c t i o n l i s t
for S w o u l d be the r e s u l t of m e r g i n g P's
and Q's l i s t s w i t h t h a t of E, w h i c h is
s i m p l y E:(), w i t h the r e s u l t S:(A, B, C,
D, E) From this list, it can be c o n c l u d e d
t h a t the t r i p l e (P, Q, E) is an a d j a c e n c y
s e q u e n c e , s i n c e (P, Q) is an a d j a c e n c y
p a i r (since P's l e f t m o s t d a u g h t e r , i.e A,
is a d j a c e n t to Q's l e f t m o s t d a u g h t e r , i.e
B, as can be s e e n a l s o in the c o n s t r u c t i o n
c o n s t r u c t i o n l i s t by the a d j a c e n c y p a i r (C, D), w h o s e e l e m e h t s are b o t h d a u g h t e r s
of P
A n e x a m p l e w h e r e the a d j a c e n c y
s e q u e n c e t e s t w o u l d g i v e a n e g a t i v e
r e s u l t , is w h e r e the r u l e Y - - > X + B + E
is c o n s i d e r e d for a c o n s t i t u e n t X w i t h
c o n s t r u c t i o n l i s t X:(A, [B], [C], D) The
r u l e is n o t a p p l i c a b l e , s i n c e the t r i p l e (X, B, E) w o u l d n o t f o r m an a d j a c e n c y
s e q u e n c e a c c o r d i n g to the c o n s t r u c t i o n
l i s t t h a t the n o d e Y w o u l d get, n a m e l y : (37) Y:(A, B, [C], D, E)
The c o n s t i t u e n t s B a n d E a r e s e p a r a t e d
in (37) by the s e q u e n c e ([C], D), w h e r e C
is m a r k e d as i n t e r n a l c o n t e x t ; t h e r e f o r e ,
C is n o t d o m i n a t e d by e i t h e r X or B, and
h e n c e the t e s t c o r r e c t l y f a i l s The c u r r e n t l y i m p l e m e n t e d v e r s i o n of the D P S G p a r s e r is in f a c t b a s e d on a
m o r e r e s t r i c t e d n o t i o n of a d j a c e n c y
s e q u e n c e , w h e r e two c o n s t i t u e n t s are
v i e w e d as s h a r i n g a c o n s t i t u e n t z n o t
o n l y if t h e y b o t h d o m i n a t e z, b u t a l s o if
o n e of t h e m d o m i n a t e s z and the o t h e r has
an i n t e r n a l c o n t e x t n o d e t h a t d o m i n a t e s z (see n o t e I) T h i s m e a n s t h a t s t r u c t u r e s
l i k e (38) are n o t g e n e r a t e d , s i n c e P and
T w o u l d s h a r e n o d e B, and T and R w o u l d
s h a r e n o d e C
(38) T
N o t e t h a t a s t r u c t u r e l i k e (38) w o u l d
be an i l l - f o r m e d tree, s i n c e the n o d e s B
a n d C v i o l a t e t h e s i n g l e - m o t h e r
c o n d i t i o n , a n d the n o d e s Q and R,
m o r e o v e r , a r e n o t c o n n e c t e d to the r o o t
n o d e
To d e a l w i t h t h i s m o r e r e s t r i c t e d
n o t i o n o f a d j a c e n c y s e q u e n c e , the
a d m i n i s t r a t i o n in the c o n s t r u c t i o n l i s t s
is a c t u a l l y s l i g h t l y m o r e c o m p l i c a t e d
t h a n d e s c r i b e d a b o v e
6 C o n c l u s i o n s
O u r f i n d i n g s c o n c e r n i n g the u s e of
d i s c o n t i n u o u s c o n s t i t u e n t s in s y n t a c t i c
r e p r e s e n t a t i o n s , p h r a s e - s t r u c t u r e rule, and p a r s e r s m a y be s u m m a r i z e d as f o l l o w s
I T r e e - 1 i k e s t r u c t u r e s w i t h
d i s c o n t i n u i t i e s c a n be g i v e n a p r e c i s e
d e f i n i t i o n , w h i c h m a k e s t h e m f o r m a l l y
as a c c e p t a b l e for use in s y n t a c t i c
Trang 8tree s t r u c t u r e s
2 D i s c o n t i n u o u s c o n s t i t u e n t s can be
a l l o w e d in p h r a s e - s t r u c t u r e rules
g e n e r a t i n g trees with d i s c o n t i n u i t i e s ,
p r o v i d e d w e g i v e a s u i t a b l e
g e n e r a l i z a t i o n to the n o t i o n of
a d j a c e n c y
3 T r e e s w i t h d i s c o n t i n u i t i e s a r e
g e n e r a l i z a t i o n s of o r d i n a r y tree
s t r u c t u r e s , and p h r a s e - s t r u c t u r e rules
with d i s c o n t i n u o u s c o n s t i t u e n t s are
g e n e r a l i z a t i o n s o f o r d i n a r y
p h r a s e - s t r u c t u r e rules Both c o n c e p t s
c a n b e a d d e d t o o r d i n a r y
p h r a s e - s t r u c t u r e grammars, i n c l u d i n g
G P S G , with the e f f e c t that such
g r a m m a r s g e n e r a t e t r e e s w i t h
d i s c o n t i n u i t i e s for s e n t e n c e s with
d i s c o n t i n u o u s c o n s t i t u e n t s , w h i l e
e v e r y t h i n g else remains the same
4 P h r a s e - s t r u c t u r e r u l e s w i t h
d i s c o n t i n u i t i e s can be h a n d l e d by a
chart p a r s e r for c o n t e x t - f r e e g r a m m a r
b y m a k i n g t w o a d d i t i o n s in the
a d m i n i s t r a t i o n ; one in the a c t i v e - r u l e
l i s t f o r r u l e s c o n t a i n i n g a
d i s c o n t i n u o u s e l e m e n t to make sure that
no parse is o v e r l o o k e d , and one in the
g e n e r a l i z e d a d j a c e n c y r e l a t i o n
NOTES I) In this paper, s h a r i n g a c o n s t i t u e n t
has been taken s i m p l y as c o m m o n d o m i n a t i o n
of that c o n s t i t u e n t An i n t e r e s t i n g issue
is w h e t h e r we s h o u l d take s h a r i n g a
c o n s t i t u e n t to i n c l u d e the f o l l o w i n g
s i t u a t i o n A n o d e x d o m i n a t e s a
c o n s t i t u e n t z, w h i l e a n o t h e r node y is
r e l a t e d to z in such a way that z is
d o m i n a t e d by a n o d e w w h i c h is i n t e r n a l
c o n t e x t for y (And still more c o m p l e x
d e f i n i t i o n s of c o n s t i t u e n t s h a r i n g are
c o n c e i v a b l e w i t h i n the f r a m e w o r k of DPSG.)
D e c i s i o n s on this point turn out to h a v e
f a r - r e a c h i n g c o n s e q u e n c e s f o r the
g e n e r a t i v e c a p a c i t y of DPSG With the
s i m p l e n o t i o n of s h a r i n g used in this
paper, it is e a s i l y p r o v e d that DPSG is
more p o w e r f u l than c o n t e x t - f r e e PSG, w h i l e
f u r t h e r r e s t r i c t i o n s on the p r e c e d e n c e
r e l a t i o n in terms of c o n s t i t u e n t s h a r i n g
may have the e f f e c t of m a k i n g DPSG w e a k l y
e q u i v a l e n t to c o n t e x t - f r e e grammar
2) For a p p l i c a t i o n s of DPSG and a
p r e d e c e s s o r , w h i c h was called " a u g m e n t e d
p h r a s e - c o n s t r u c t i o n g r a m m a r " in
s y n t a c t i c / s e m a n t i c a n a l y s i s and a u t o m a t i c
g e n e r a t i o n of s e n t e n c e s , the r e a d e r is
r e f e r r e d to Bunt (1985; 1987)
A C K N O W L E D G E M E N T S
I would like to thank Masaru Tomita for s t i m u l a t i n g d i s c u s s i o n s about p h r a s e -
s t r u c t u r e g r a m m a r and p a r s i n g in general, and DPSG in p a r t i c u l a r
R E F E R E N C E S
m o d e l - t h e o r e t i c s e m a n t i c s C a m b r i d g e
U n i v e r s i t y Press, Cambridge, England Bunt, H.C (1987) U t t e r a n c e g e n e r a t i o n from s e m a n t i c r e p r e s e n t a t i o n a u g m e n t e d with p r a g m a t i c i n f o r m a t i o n In G K e m p e n ( e d ) N a t u r a l l a n g u a g e g e n e r a t i o n
K l u w e r / N i j h o f f , The Hague
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I n q u i r y 10, 211-243
Gazdar, G., Klein E., Pullum, G.K &
S a g , I A ( 1 9 8 5 ) G e n e r a l i z e d
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