local coherence

8/7/2019 local coherence

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C e n te r in g : A F r a m e w o r k f or M o d e l i n g th e

L o c a l C o h e r e n c e o f D i s c o u r s e

B a r b a r a J . G r o s z *

H a r v a r d U n i v e r s i t y

S c o tt W e i n s t e i n ~

U n i v e r s i t y o f P e n n s y l v a n i a

A r a v i n d K . J o s h i t

U n i v e r s i t y o f P e n n s y l v a n i a

This pa per concerns relationships a m on g focus of attention, choice of referring expression, an d

perceived coherence of ut terances wi th in a discourse segment . I t presents a fram ew ork and ini-

tial theory of centering intended to model the local com ponent of attentional state. The paper

exam ines interactions between local coherence an d ch oice of referring expressions; i t argues tha t

differences in coherence correspond in part to the inference dem ands ma de by different types o f

referring expressions, given a particular attentional state. I t demonstrates that the attentional

state properties modeled by cen tering can account for these differences.

P r e f a c e

O u r o r i g i n a l p a p e r ( G r o s z , J o s hi , a n d W e i n s t e i n 1 98 3) o n c e n t e r i n g c l a i m e d t h a t c e r t a i n

e n t it ie s m e n t i o n e d i n a n u t t e r a n c e w e r e m o r e c e n t r a l t h a n o t h e r s a n d t h a t th is p r o p e r t y

i m p o s e d c o n s t r a in t s o n a s p e a k e r ' s u s e o f d i ff e r e n t t y p e s o f r e fe r r i n g e x p r e s si o n s .

C e n t e r in g w a s p r o p o s e d a s a m o d e l t h a t a c c o u n t e d fo r t hi s p h e n o m e n o n . W e a r g u e d

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

p r o p e r t i e s o f a n u t t e r a n c e a n d c h o i c e o f r e fe r r i n g e x p r e s s io n . S u b s e q u e n t ly , w e r e v i s e d

a n d e x p a n d e d t h e i d e a s p r e s e n t e d t h e re i n . W e d e f i n e d v a r i o u s c e n t e r i n g c o n s tr u c t s

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

d e s c r i b in g t h i s e la b o r a t e d c e n t e r i n g f r a m e w o r k a n d p r e s e n t i n g s o m e i n it ia l t h eo r e t i c a l

c l a i m s h a s b e e n i n w i d e c i r c u l a t io n s i n c e 1 98 6. T h i s d r a f t ( G r o s z , J o s h i, a n d W e i n s t e in

1 98 6) h a s l e d t o a n u m b e r o f p a p e r s b y o t h e r s o n t h is t o p i c a n d h a s b e e n e x t e n s i v e l yc i t ed , b u t h a s n e v e r b e e n p u b l i s h e d . 1

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

f r a m e w o r k a n d t h e o r y p r o p o s e d i n G r o s z , J o sh i, a n d W e i n s te i n ( 19 86 ) s o t h a t a n o f-

f ic ia l v e r s i o n w o u l d b e a r c h i v a l l y a v a il a b le . T h e t a s k o f c o m p l e t i n g a n d r e v i s i n g t h i s

d r a f t b e c a m e m o r e d a u n t i n g a s t im e p a s s e d a n d m o r e a n d m o r e p a p e r s a p p e a r e d o n

c e n t e ri n g . M a n y o f t h e s e p a p e r s p r o p o s e d e x t e n s io n s t o o r re v i s io n s o f t h e t h e o r y

a n d a t t e m p t e d t o a n s w e r q u e s t i o n s p o s e d i n G r o s z , J o sh i, a n d W e i n s t e i n (1 98 6). I t h a s

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

* D ivision of A pplied Sciences, Harva rd University, Cam bridge, MA. E -mail: grosz@ das.harvard.edu.t Com puter an d Information Science, Un iversity of Penn sylvania, Philadelphia, PA. E-mail:

[email protected].:~ Dep artment of Philosoph y, University o f Pen nsylvania, Philadelphia, PA. E-mail:

[email protected] Ea rly drafts o f Grosz, Joshi, and W einstein (1986) were in circulation from 1983. So m e citations to other

work have dates betw een 1983 and 1986. T his wo rk utilized these earlier drafts.

@ 1995 Association for C omputational Linguistics



Co mp utational Linguist ics Volume 21, N um ber 2

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

f r a m e w o r k , a n d t h e o ri g in a l t h e o r e t ic a l c la im s . T h i s p a p e r a t t e m p t s t o m e e t t h a t n e e d .

T o a c c o m p l i s h t h is g o a l, w e h a v e c h o s e n t o r e m o v e d e s c r i p t io n s o f m a n y o p e n r e s e a r c h

q u e s t i o n s p o se d i n Gr o sz , Jo sh i , a n d W e i n s t e i n ( 1 9 8 6 ) a s we l l a s so l u t i o n s t h a t we r e

o n l y p a r t i a l ly d e v e l o p e d . W e h a v e a l s o g r e a tl y s h o r t e n e d t h e d i s c u s s i o n o f c r it e ri a f o r

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

1 . I n t r o d u c t i o n

T h i s p a p e r p r e s e n t s a n i n it ia l a t t e m p t t o d e v e l o p a t h e o r y t h a t r e la t e s f o c u s o f a t te n -

t io n , c h o i c e o f r e f e rr i n g e x p r e s s i o n , a n d p e r c e i v e d c o h e r e n c e o f u t t e r a n c e s w i t h i n a

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

s t r a n d s o f p r e v i o u s r e s ea r c h . I t f it s w i t h i n a l ar g e r e f f o r t t o p r o v i d e a n o v e r a l l t h e o r y

o f d i s c o u r s e s t r u c t u r e a n d m e a n i n g . I n th i s s e c t io n w e d e s c r i b e t h e la r g e r r e s e a r c h

c o n t e x t o f t h is w o r k a n d t h e n b r i e f ly d i s c u s s t h e p r e v i o u s w o r k t h a t l e d t o it.

C e n t e r i n g f it s w i t h i n t h e t h e o r y o f d i s c o u rs e s t r u c tu r e d e v e l o p e d b y G r o s z a n d

S i d n e r ( 19 86 ). G r o s z a n d S i d n e r d i s t i n g u i s h a m o n g t h r e e c o m p o n e n t s o f d i s c o u r s e

s t r u c t u r e : a l i n g u i s t i c s t r u c t u r e , a n i n t e n t i o n a l s t r u c t u r e , a n d a n a t t e n t i o n a l s t a t e . A t

t h e l e v e l o f l in g u i s ti c s t r u c tu r e , d i s c o u r s e s d i v i d e i n t o c o n s t i t u e n t discourse segments;

a n e m b e d d i n g r e la t io n s h ip m a y h o l d b e t w e e n t w o s e g m e n t s . T h e in t en t io n a l s t ru c -

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

r a t io n a l e f o r th e d i s c o u r s e , a n d t h e r el a ti o n s r e p r e s e n t t h e c o n n e c t i o n s a m o n g t h e s e in -

t e n ti o n s . A t t e n t i o n a l s t a t e m o d e l s t h e d i s c o u r s e p a r t i c i p a n t s ' f o c u s o f a t t e n ti o n a t a n y

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

s t r u c t u r e a n d o n p r o p e r t i e s o f th e u t t e r a n c e s i n t h e li n g u is t ic s t r u c tu r e .E a c h d i s c o u r s e s e g m e n t e x h i b i t s b o t h local coherence--i.e., c o h e r e n c e a m o n g t h e

u t t e r a n c e s i n t h a t s e g m e n t - - a n d global coherence--i .e., c o h e r e n c e w i t h o t h e r s e g m e n t s

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

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

s e g m e n t , a n d t h e g l o b a l l e v e l m o d e l s a t t e n ti o n a l s t a te p r o p e r t i e s a t t h e in t e r s e g m e n t a l

l eve l .

G r o s z a n d S i d n e r a r g u e t h a t g l o b a l c o h e r e n c e d e p e n d s o n t h e i n t e n ti o n a l s t r u c t u r e.

T h e y p r o p o s e t h a t e a c h d is c o u r s e h a s a n o v e r a ll c o m m u n i c a t i v e p u r p o s e , t h e d i s c o u r s e

p u r p o s e ( D P ) ; a n d e a c h d i s c o u r s e s e g m e n t h a s a n a s s o c i a t e d i n t e n t i o n , i t s d i s c o u r s e

s e g m e n t p u r p o s e ( D S P) . T h e D P a n d D S P a r e s p e a k e r i n t e n ti o n s ; t h e y a r e c o rr e la t e s a tt h e d i s c o u r s e l e v e l o f t h e in t e n t i o n s G r i c e a r g u e d u n d e r l a y u t t e r a n c e m e a n i n g ( G r ic e

1 96 9) . I f a d i s c o u r se i s m u l t i - p a r t y ( e.g ., a d i a l o g u e ) , t h e n t h e D SP f o r a g i v e n s e g m e n t

i s a n i n t e n t io n o f t h e c o n v e r s a t i o n a l p a r t i c ip a n t w h o i n it ia t es t h a t s e g m e n t . L o c h b a u m

( 1 9 9 4 ) e m p l o y s c o l l a b o r a t i v e p l a n s ( Gr o sz a n d Kr a u s 1 9 9 3 ) t o m o d e l i n t e n t i o n a l s t r u c -

t u r e , a n d i s t h u s a b l e t o in t e g r a t e i n t e n t i o n s o f d i f f e r e n t p a r t ic i p a n t s . Sa t i s f a c ti o n o f t h e

D S P s c o n t r i b u t e s t o t h e s a ti s fa c t io n o f t h e D P. R e l a t i o n s h i p s b e t w e e n D S P s p r o v i d e t h e

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

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

r e l a t io n s h i p s a m o n g i t s D P a n d D S P s . G r o s z a n d S i d n e r m o d e l t h e g l o b a l- l e v e l c o m -

p o n e n t o f th e a t te n t i o n a l s t a t e w i t h a st ac k ; p u s h e s a n d p o p s o f f o c u s s p a c e s o n t h es t a c k d e p e n d o n i n t e n t i o n a l r e l a t i o n s h i p s .

T h i s p a p e r i s c o n c e r n e d w i t h l o c a l c o h e r e n c e a n d i t s r e l a t i o n s h i p t o a t t e n t i o n a l

s t a te a t t h e l o c al le v e l. C e n t e r i n g i s p r o p o s e d a s a m o d e l o f th e l o c a l- le v e l c o m p o n e n t

o f a tt e n t io n a l s ta t e. W e e x a m i n e t h e i n t e r a c ti o n s b e t w e e n l o ca l c o h e r e n c e a n d c h o i c e s

o f r e f e rr i n g e x p r e s s i o n s , a n d a r g u e t h a t d i f f e re n c e s i n c o h e r e n c e c o r r e s p o n d i n p a r t t o

t h e d i f f e re n t d e m a n d s f o r in f e r e n c e m a d e b y d i f f e r en t t y p e s o f r e f e rr i n g e x p r e s s i o n s ,

204



Barb ara J. Gro sz et al. Cen tering

g i v e n a p a r t i c u l a r a t t e n t i o n a l s t a te . W e d e sc r i b e h o w t h e a t t e n t i o n a l s t a t e p r o p e r t i e s

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

T h r e e p i e c e s o f p r e v i o u s r e s e a r c h p r o v i d e t h e b a c k g r o u n d f o r t h is w o r k . G r o s z

( 19 77 ) d e f i n e d t w o l e v e l s o f f o c u s i n g i n d i s c o u r se : g l o b a l a n d i m m e d i a t e . Pa r t i c i p a n t s

w e r e s a i d t o b e g l o b a l l y f o c u s e d o n a s e t o f e n ti ti e s r e l e v a n t t o t h e o v e r a l l d i s c o u r s e .

T h e s e e n t i t i e s m a y e i t h e r h a v e b e e n e x p l i c i t l y i n t r o d u c e d i n t o t h e d i s c o u r s e o r s u f f i -c i e n t l y c l o se l y r e l a t e d t o s u c h e n t i t ie s t o b e c o n s i d e r e d i m p l i c i t l y i n f o c u s ( Gr o sz 1 98 1).

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

r e la t e s t o i d e n t i f y i n g t h e e n t i t y t h a t a n i n d i v i d u a l u t t e r a n c e m o s t c e n t r a l ly c o n c e r n s .

S i d n e r ( 19 79 ) p r o v i d e d a d e t a i le d a n a l y s i s o f i m m e d i a t e f o c u s i n g , i n c l u d i n g a

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

f o r t r a ck i n g i m m e d i a t e f o c u s a n d r u l e s th a t s t at e d h o w t h e im m e d i a t e f o c u s c o u l d b e

u s e d t o id e n t i f y th e r e fe r e n ts o f p r o n o u n s a n d d e m o n s t r a t i v e n o u n p h r a s e s ( e.g ., " t h is

p a r t y , . . . . t h a t p a r t y " ) .

Jo sh i a n d Ku h n ( 1 9 7 9 ) a n d Jo sh i a n d W e i n s t e i n ( 1 9 8 1 ) p r o v i d e d i n i t i a l r e su l t s o n

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

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

a r e p r e s e n t a t io n o f th e m e a n i n g o f t h e d i s c o u r s e o f w h i c h i t w a s a p a rt . T o a v o i d

c o n f u s i o n w i t h p r e v i o u s u s e s o f t h e t e rm " f o c u s " i n l in g u i st ic s , t h e y i n t r o d u c e d t h e

c e n t e r in g t e rm i n o l o g y . T h e ir n o t io n s o f " f o r w a r d - l o o k i n g " a n d " b a c k w a r d - l o o k i n g "

c e n t e r s c o r r e s p o n d a p p r o x i m a t e l y t o S i d n e r ' s p o t e n t i a l fo c i a n d d i s c o u r s e f o c u s.

I n al l o f th i s w o r k , f o c u s i n g , w h e t h e r g l o b a l o r i m m e d i a t e , w a s s e e n t o f u n c t i o n t o

l im i t t h e in f e r e n c e s r e q u i r e d f o r u n d e r s t a n d i n g u t t e r a n c e s i n a d i s c o u r s e . G r o s z a n d

S i d n e r w e r e c o n c e r n e d w i t h t h e i n f e r e n c e s n e e d e d t o i n t e r p r e t a n a p h o r i c e x p r e s s i o n s

o f v a r i o u s so r t s (e .g . p r o n o u n s , d e f i n i t e d e sc r i p t i o n s , e l l ip s i s) . T h e y u s e d f o c u s i n g t oo r d e r c a n d i d a t e s ; a s a r e s u l t t h e n e e d f o r s e a r c h w a s g r e a t l y r e d u c e d a n d t h e u s e

o f i n f e re n c e c o u l d b e r e st r ic t e d t o d e t e r m i n i n g w h e t h e r a p a r t ic u l a r c a n d i d a t e w a s

a p p r o p r i a t e g i v e n t h e e m b e d d i n g u t t e r a n c e i n t e r p r e t a t i o n . J o s h i , K u h n , a n d W e i n s t e i n

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

i n to d i s c o u r s e m e a n i n g . T h e y u s e d c e n t e r i n g t o d e t e r m i n e a n almost m o n a d i c p r e d i c a te

r e p r e s e n t a t i o n o f a n u t t e r a n c e i n d i s c o u r s e ; th e y t h e n u s e d t h is r e p r e s e n t a t i o n t o r e d u c e

t h e c o m p l e x i t y o f i n f e re n c e .

I n th i s p a p e r , we g e n e r a l i z e a n d c l a r if y c e r t a in o f S i d n e r ' s r e su l t s , b u t a d o p t t h e

" c e n t e r in g " t e r m i n o lo g y . W e a l so a b s t ra c t f r o m S i d n e r ' s f o c u s i n g a l g o r i t h m t o s p e c i f y

c o n s t r a i n ts o n t h e c e n t e r in g p r o c e s s . W e c o n s i d e r t h e r e l a ti o n s h i p b e t w e e n c o h e r e n c ea n d i n f e r e n c e l o a d a n d e x a m i n e h o w b o t h i n t e r a c t w i t h a t t e n t i o n a l s t a t e a n d c h o i c e s

i n l i n g u i s t i c e x p r e s s i o n .

T h e r e m a i n d e r o f th i s p a p e r is o r g a n i z e d a s f o ll o w s : i n S e c ti o n 2, w e b r i e f l y d e -

s c ri be th e p h e n o m e n a m o t i v a t i n g t h e d e v e l o p m e n t o f ce n te r in g t h at t h is p a p e r a i m s

t o e x p l a i n . Se c t i o n 3 p r o v i d e s t h e b a s i c d e f i n i t io n s o f c e n t e r s a n d r e l a t e d d e f i n i t i o n s

n e e d e d t o p r e se n t t h e t h e o r e t i c a l c la i m s o f t h e p a p e r . I n Se c t i o n 4 , w e s t a t e t h e m a i n

p r o p e r t i e s o f t h e c e n t e r in g f r a m e w o r k a n d t h e m a j o r c l a im s o f c e n t e r i n g t h e o ry . In

Se c t i o n 5 , w e d i s c u s s s e v e r a l f a c t o r s t h a t a f f e c t c e n t e r i n g c o n s t r a i n t s a n d g o v e r n t h e

c e n t e r i n g r u l e s g i v e n i n Se c t i o n 6 . I n Se c t i o n 7 , we d i s c u s s a p p l i c a t i o n s o f t h e r u l e s

a n d t h e i r a b i l i t y t o e x p l a i n s e v e r a l d i s c o u r s e c o h e r e n c e p h e n o m e n a . I n S e c t i o n 8 , w eb r i e f ly o u t l i n e t h e p r o p e r t i e s o f a n u n d e r l y i n g s e m a n t i c f r a m e w o r k t h a t a re r e q u i r e d

b y c e n t e r i n g . F i n al ly , in Se c t i o n 9 w e c o n c l u d e w i t h a b r i e f c o m p a r i so n o f c e n t e r -

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

Gr o sz , Jo sh i , a n d W e i n s t e i n ( 1 9 8 6 ) . I n p a r t i c u l a r , Se c t i o n 9 p r o v i d e s r e f e r e n c e s t o su b -

s e q u e n t i n v e s t i g a t i o n s o f a d d i t i o n a l f a c to r s th a t c o n t r o l c e n t e r in g a n d e x a m i n a t i o n s o f

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

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Computational Linguistics Volume 21, Number 2

2 . P h e n o m e n a T o B e E x p l a in e d

Discourses are more than mere sequences of utterances. For a sequence of utterances

to be a discourse, it must exhibit coherence. In this paper, we investigate linguistic

and attentional state factors that contribute to coherence among utterances within a

discourse segment. These factors contribute to the difference in coherence between the

following two discourse segments: 2

(1) a. John wen t to his favorite music store to buy a piano.

b. He had frequented the store for man y years.

c. He was excited that he could finally buy a piano.

d. He arrived just as the store was closing for the day.

(2) a. John went to his favorite music store to buy a piano.

b. It was a store John had frequented for many years.

c. He was excited that he could finally buy a piano.

d. It was closing just as John arrived.

Discourse (1) is intuit ively more coherent than Discourse (2). This difference may

be seen to arise from different degrees of continuity in what the discourse is about.Discourse (1) centers around a single individual, describing various actions he took

and his reactions to them. In contrast, Discourse (2) seems to flip back and forth amo ng

several different entities.

More specifically, the initial utterance (a) in each segment could begin a segment

about an individual named 'John' or one about John's favorite music store or one

about the fact that John wants to buy a piano.

Whereas Discourse (1) is clearly about John, Discourse (2) has no single clear

center of attention. Utterance (2b) seems to be about the store. If a reader inferred

that utterance (2a) was about John, then that reader would perceive a change in the

entity which the discourse seems to be about in going from (2a) to (2b); on the otherhand, if the reader took (2a) to be about the store then in going to (2b), there is no

change. In either case, in utterance (2c) John seems to be central, requiring a shift from

utterance (2b), while the store becomes central again in utterance (2d), requiring yet

another shift. This changing of 'aboutness' (in fact, flipping it back and forth) makes

discourse (2) less coherent than discourse (1).

Discourses (1) and (2) convey the same information, but in different ways. They

differ not in content or wha t is said, but in expression or how it is said. The variation in

'aboutness' they exhibit arises from different choices of the wa y in wh ich they express

the same propositional content. The differences can only be explained, however, by

looking beyond the surface form of the utterances in the discourse; different types ofreferring expressions and different syntactic forms make different inference demands

on a hearer or reader. These differences in inference load underlie certain differences

2 T h i s e x a m p l e a n d t h e o t h e r s i n t h i s p a p e r a r e s i n g l e - s p e a k e r t e x t s . H o w e v e r , c e n t e r i n g a l s o a p p l i e s t o

d i a l o g u e a n d m u l t i - p a r t y c o n v e r s a t i o n s . I s s u es o f th e i n t e r a c t io n b e t w e e n t u r n - t a k i n g a n d c h a n g e s i nc e n t e r i n g s t a t u s r e m a i n t o b e i n v e s t i g a t ed .

206



Barb ara J . Gro sz e t a l. Ce nter in g

i n c o h e r e n c e . T h e m o d e l o f l oc a l a t t e n ti o n a l s t at e d e s c r i b e d i n t h is p a p e r p r o v i d e s a

b a s is f o r e x p l a i n i n g t h e s e d i f f e re n c e s .

T h u s , t h e f o c u s o f o u r i n v e s t i g a t io n is o n i n t e ra c t io n s a m o n g c h o i c e o f re f e r r in g

e x p r e s s i o n , a t t e n t i o n a l s t a te , th e i n f e r e n c e s r e q u i r e d t o d e t e r m i n e t h e i n t e r p r e t a t i o n o f

a n u t t e r a n c e i n a d i s c o u r s e s e g m e n t , a n d c o h e r e n c e . P r o n o u n s a n d d e f in i te d e s c r ip t i o n s

a r e n o t e q u i v a l e n t w i t h r e s p e c t t o t h e i r e f fe c t o n c o h e r e n c e . W e c o n j e c t u r e t h a t t h i s iss o b e c a u s e t h e y e n g e n d e r d i f fe r e n t i n f e re n c e s o n t h e p a r t o f a h e a r e r o r r e ad e r . In t h e

m o s t p r o n o u n c e d c a s es , t h e w r o n g c h o i c e w i ll m i s l e a d a h e a r e r a n d f o r ce b a c k t r a c k i n g

t o a c o r r e c t i n t e r p r e t a t i o n . 3 T h e f o l l o w i n g v a r i a t i o n s o f a d i s c o u r s e s e q u e n c e i l lu s t r a te

t h is p r o b l e m a n d p r o v i d e a d d i t i o n a l e v i d e n c e fo r o u r c o n j e c tu r e .

(3 ) a . T e r r y r e a l l y g o o f s s o m e t i m e s .

b . Y e s t e r d a y w a s a b e a u t i f u l d a y a n d h e w a s e x c i te d a b o u t t r y i n g o u t

h i s n e w s a i l b o a t .

c . H e w a n t e d T o n y to j o in h i m o n a sa i li n g e x p e d i t i o n .

d . H e c a l le d h i m a t 6 A M .

e . H e w a s s i c k a n d f u r i o u s a t b e i n g w o k e n u p s o e ar ly .

B y u s i n g a p r o n o u n t o r ef e r t o T o n y i n u t te r a n c e (e ) t h e s p e a k e r m a y c o n f u s e t h e

h e a re r . T h r o u g h u t t e r a n c e ( d) T e r r y h a s b e e n t h e c e n t e r o f a t te n t io n , a n d h e n c e i s t h e

m o s t l i k e ly r e f e r e n t o f " h e " i n u t t e r a n c e (e ). I t i s o n l y w h e n o n e g e t s t o t h e w o r d

" s i c k " t h a t i t i s c l e a r t h a t i t m u s t b e T o n y a n d n o t T e r r y w h o i s s ic k , a n d h e n c e t h a t

t h e p r o n o u n i n u t t e ra n c e (e ) r e fe r s t o T o n y n o t T e rr y. A m u c h m o r e n a t u r a l s e q u e n c er e s u l t s i f " T o n y " is u s e d , a s t h e s e q u e n c e ( 4 a ) - ( 4 e ) il l u s tr a t e s .


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


c . H e w a n t e d T o n y t o j o i n h i m o n a sa i li n g e x p e d i t i o n .

d . H e c a l le d h i m a t 6 A M .

e . T o n y w a s s ic k a n d f u r i o u s a t b e i n g w o k e n u p s o e a rl y.

f. H e t o l d T e r r y t o g e t lo s t a n d h u n g u p .

g . O f c o u rs e , h e h a d n ' t i n t e n d e d t o u p s e t T on y .

I n D i s c o u r s e ( 4 ), u t t e r a n c e s (f ) a n d ( g) e x h i b i t th e s a m e k i n d o f m i s d i r e c t i o n a s d o

u t t e r a n c e s ( 3d ) a n d ( 3e ) i n D i s c o u r s e ( 3). T h e f o c u s h a s s h i f t e d f r o m T e r r y to T o n y in

t h e s h o r t s u b s e g m e n t o f u t t e r a n c e s ( e )- (f ) s o t h a t u s e o f " h e " i n ( g) is c o n f u s i n g . T h i s

c o n f u s i o n is a v o i d e d i n t h e s e q u e n c e o f D i s c o u r s e ( 5).


b . Y e s t e r d ay w a s a b e a u t if u l d a y a n d h e w a s e x c i te d a b o u t t r y i n g o u t


3 We presume utterances are processe d in left-to-right order, and that spe akers make initial assignm entsof referent and mea ning that m ay hav e to be retracted if ma terial com ing later in the sentence conflicts.

2 0 7




c. He wanted Tony to join him on a sailing expedition.

d. He called him at 6 AM.

e. Tony was sick and furious at being woken up so early.

f. He told Terry to get lost and hung up.

g. Of course, Terry hadn 't inten ded to upset Tony.

We conjecture that the form of expression in a discourse substantially affects the re-

source demands made upon a hearer in discourse processing and through this influ-

ences the perceived coherence of the discourse. It is well known from the study of

complexity theory that the manner in which a class of problems is represented can

significantly affect the time or space resources required by any procedure that solves

the problem. Here too we conjecture that the manner, i.e., linguistic form, in which

a discourse represents a particular propositional content can affect the resources re-

quired by any procedure that processes that discourse. We use the phrase inference load

placed upon the hearer to refer to the resources required to extract information from a

discourse because of particular choices of linguistic expression used in the discourse.

We conjecture that one psychological reflex of this inference load is a difference in

perceived coherence among discourses that express the same propositional content

using different linguistic forms.

One of the tasks a hearer must perform in processing a discourse is to identify

the referents of noun phrases in the discourse. It is commonly accepted, and is a hy-

pothesis under which our work on centering proceeds, that a hearer's determination

of noun phrase reference involves some process of inference. Hence a particular claim

of centering theory is that the resource demands of this inference process are affected

by the form of express ion of the noun phrase. In Section 7, we discuss the effect on per-

ceived coherence of the use of pronouns and definite descriptions by relating different

choices to the inferences they require the hearer or reader to make.

3 . B a s ic C e n t e r D e f i n i t i o n s

We use the term centers of an utterance to refer to those entities serving to link that

utterance to other utterances in the discourse segment that contains it. It is an utterance(i.e., the uttering of a sequence of words at a certain point in the discourse) and

not a sentence in isolation that has centers. The same sentence uttered in different

discourse situations may have different centers. Centers are thus discourse constructs.

Furthermore, centers are semantic objects, not words, phrases, or syntactic forms.

Each utterance U in a discourse segment (DS) is assigned a set of forward-looking

centers, Cf(U, DS); each utterance o ther than the segmen t initial utterance is assigned

a single backward-looking center, Cb(U, DS). To simplify nota tion , when the relevant

discourse segment is clear, we will drop the associated DS and use CB(U) and Cf(U).

The backward-looking center of utterance Un+l connects with one of the forward-

looking centers of utterance Un. The connection between the backward -looking centerof utterance Un+ 1 and the forward-looking centers of utterance Un may be of several

types. To describe these types, we need to introduce two new relations, realizes and

directly realizes, that relate centers to linguistic expressions.

We will say that

U directly realizes c

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B a r b a r a J . G r o s z e t a l. C e n te r i n g

i f U i s a n u t t e r a n c e o f s o m e p h r a s e 4 f o r w h i c h c i s t h e s e m a n t i c i n t e r p r e t a t i o n . R e a l i z e s

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

c e r ta i n r e g u l a r i t i e s i n th e u s e o f d e fi n i t e d e s c r i p t i o n s a n d p r o n o u n s .

T h e p r e c i s e d e f i n i t i o n o f

U r e a l i z e s c

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

f r o m o t h e r t r e a t m e n t s o f r e l a te d d i s c o u r s e p h e n o m e n a is t h a t th e r e a l i z a t io n r e l a t io n

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

a n u t t e r a n c e i n g e n e r a l , a n d t h e b a c k w a r d - l o o k i n g c e n t e r sp e ci fi ca l l y , a re d e t e r m i n e d

o n t h e b a s is o f a c o m b i n a t i o n o f p r o p e r t i e s o f t h e u t te r a n c e , t h e d i s c o u r s e s e g m e n t i n

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

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

b a s is f o r c o m p u t i n g t h e r e a l i z a t io n r e la t i o n . F o r e x a m p l e , N P d i r e c t l y r e a li z e s c m a y

h o l d i n c a se s w h e r e N P i s a d e f i n i t e d e s c r i p t i o n a n d c i s i ts d e n o t a t i o n , i ts v a l u e - f r e e

i n t e r p r e t a t i o n ( d i s c u s s e d i n S e c t io n 8 ), o r a n o b j e c t r e l a t e d t o i t b y " s p e a k e r ' s r e f e r e n c e "

( K r i p k e 1 9 77 ). M o r e i m p o r t a n t l y , w h e n N P i s a p r o n o u n , t h e p r i n c ip l e s t h a t d e t e r m i n e

t h e c ' s f o r w h i c h i t i s t h e c a s e t h a t N P d i r e c t l y r e a li z e s c d o n o t d e r i v e e x c l u s i v e ly f r o m

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

t h e s t u d y o f d i s c o u r s e i ts el f. A n i n i t ia l f o r m u l a t i o n o f s o m e s u c h p r i n c i p l e s i s g i v e n

i n S e c t i o n 8 . 6

T h e f o r w a r d - l o o k i n g c e n t e r s o f U n d e p e n d o n l y o n t h e e x p r e s s i o n s t h a t c o n s t i t u t et h a t u t te r a n c e ; t h e y a r e n o t c o n s t r a i n e d b y f e a t u re s o f a n y p r e v i o u s u t t e r a n c e i n t h e

s e g m e n t . T h e e l e m e n t s o f C d U n ) a r e p a r t ia l l y o r d e r e d t o r e f le c t r e la t iv e p r o m i n e n c e

i n U n . I n S e c t i o n 5, w e d i s c u s s a n u m b e r o f f a c t o r s th a t m a y a f fe c t t h e o r d e r i n g o n t h e

e l e m e n t s o f Ct. T h e m o r e h i g h l y r a n k e d a n e l e m e n t o f C d U n ) , t h e m o r e l i k e ly i t i s to

b e Cb(Un+l).T h e m o s t h i g h l y r a n k e d e l e m e n t o f C f ( U ~ ) t h a t is r e a l i z e d i n U n + I is t h e

CB ( U ~ + l ) . B e c a u s e C t ( U ~ ) i s o n l y p a r t i a l l y o r d e r e d , s o m e e l e m e n t s m a y , f r o m C f ( U n )

i n f o r m a t i o n a l o n e , b e e q u a l l y l i k e l y t o b e C B ( U n + l ) . I n s u c h c a s es , a d d i t i o n a l c r i t e r ia a r e

n e e d e d f o r d e c i d i n g w h i c h s i n g le e n t i t y is t h e Cb(Un+l).S o m e r e c e n t p s y c h o l i n g u i s t i c

e v i d e n c e s u g g e s t s t h a t th e s y n t a c t i c ro l e i n U n + I m a y d e t e r m i n e t h i s c ho i c e ( G o r d o n ,

G r o s z , a n d G i l l i o m 1 99 3) .

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

C t a r e r a n k e d i n t h e o r d e r i n w h i c h t h e y a r e l i s te d . 7 I n p a r ti c u l a r , f o r p r e s e n t a t i o n a l

4 U need not be a full clause. We use U here to stress again th at it is the utterance, not the string o fwords.

5 In the original manuscript, w e defined realize in terms of situation semantics (Barwise and P erry 1983)and said the relation held "if either c is an element of the situation described by the utterance U or c isdirectly realized by some subpart of U." We discuss this further in Section 7.

6 In the examples in this paper, w e will be concerned w ith the realization relationship that holdsbetween a center and a singular definite noun phrase; i.e., cases where an NP direc tly realizes a center c.Several extensions to the theory presented here are needed to handle plural, quantified noun phrasesand indefinites. It is also impo rtant to note tha t not all noun phrases in an utterance contribute centersto Cf(U) and not only nou n ph rases do so. More general ly , events and other entit ies tha t are moreoften directly realized by verb phrases can also be centers, whereas negated noun phrases typically dono t contribute centers; the stu dy o f these issues is, however, b eyo nd the scope of this paper.

7 To simplify the presentation in the rem ainde r of this paper, we w ill assume in mos t of the discussionthat there is a total order with strict ordering between any two elements; at those places where thepartial ordering makes a significant difference we will discuss that.

2 0 9




purposes, we will use the following schematic to refer to the centers of utterances in

a sequence:

For Un: Cb(Un) = a, Cf(Un) -- (el, e2, . . . ep ) , a = ek, for some k.

For Un+t: Cb(Unq-1) realizes ern and, for all j, j < m, e} is not real-

ized in Un+l; i.e., em is realized in Un+l, and no higher ranked ej is

realized in U~+I.

Finally, we also define three types of transition relations across pairs of utterances.

.

.

.

CENTER CONTINUATION: Cb(Un+l)= Cb(Un), and this entity is the most

highly ranked element of Cf(Un+l). In this case, Cb(Un+t) is the most

likely candidate for Cb(Un+2)) it continues to be Cb in Un+l, and

continues to be likely to fill that role in Un+2.CENTER RETAINING: Cb(Un+l) ~- Cb(Un), but this entity is not the most

highly ranked element in Cf(Un+l)- In this case, Cb(Un+l) is not the most

likely candidat e for Cb(Un+2); although it is retained as Cb in Un+t, it is

not likely to fill that role in Un+2.

CENTER SHIFTING: Cb (U n+ l) ~ Cb(Un) .

The coherence of a segment is affected by the kinds of centering transitions engen-

dered by a speaker's choices of linguistic realizations in the utterances constituting

the segment. Of particular concern are choices among (1) CONTINUATION of the centerfrom one utterance not only to the next, but also to subsequent utterances; (2) RE-

TENTION of the center from one utterance to the next; (3) SHIFTING the center, if it is

neither retained nor continued,s

4 . C l a i m s o f C e n t e r i n g T h e o r y

The centering framework described above provides the basis for stating a num ber of

specific claims about the relat ionship between discourse coherence, inference load, and

choice of referring expression. Under lying these claims is the most fundam ental claim

of centering theory, that to the extent a discourse adheres to centering constraints, itscoherence will increase and the inference load placed upon the hearer will decrease.

We briefly list several major claims in this section, and elaborate on the evidence or

motivation for each in subsequent sections.

• A u n i q u e Cb: Each Un has exactly one backward-looking center. It might

be tho ugh t that a more general definition woul d allow for multiple

backward-looking centers as well as multiple forward-looking centers.

However, this is not the case, as we show in Section 5.

• Rank ing of Ct: The Cf elements are partially ordered according to anumbe r of factors. Several of the factors posited to affect this ordering

are discussed in Section 5, but the full set of factors remains to be

determined. Ranking of elements in Cf(Un) guides determination of

8 Shifting of the center does not in itself mark a discourse segment boundary. The center may shiftwithin a single segment.

210



Barbara J. Grosz et al. Centering

Cb(Un+l),because Cf(Un) is only partially ordered, additional factors

may constrain the choice.9

• C e n t e r i n g c o n s t r a i n s r e a l i z a t io n p o s s i b i l i t ie s : R u l e 1 , discussed in

Section 6, stipulates one constraint cen tering imposes on realization. We

expect that other such constraints exist.

• P r e f e r e n c e s a m o n g s e q u e n c e s o f c e n t e r t r a n s it i o n s: R u l e 2 , discussed in

Section 6, hypothesizes a preference amon g types of transitions.

• P r i m a c y o f p a r ti a l i n f o r m a t i o n : The information needed to compute a

complete unique interpretation for an utterance may not be available

until subsequent utterances are produced. Thus, as discussed in

Section 8, to support centering, a semantic theory must support the

construction of partial interpretations, in particular for elements of Cf.

• L o c a l i t y o f Cb(Un): The choice of a backward-looking center for anutterance Un is from the set of forward-looking centers of the previous

utterance Un-> In this sense the Cb is strictly local. Cb(Un) cannot be

from Cf(U,_2) or other prior sets of forward-look ing centers. 1°

• C e n t e r i n g i s c o n t r o l l e d b y a c o m b i n a t i o n o f d i s c o u r s e f ac to r s: Center

dete rmination is not solely a syntactic, semantic, or pragmatic process.

5 . F a c t o r s G o v e r n i n g C e n t e r i n g

Before we can examine the linguistic features that contribute to an entity's being the

backward-looking center of an utterance, it is necessary to provide support for the

claim that there is only a single backward-looking center. In the definitions in Section 3,

there is a basic asymmetry between the Cf, which is a set, and the Cb, which is a

singleton. Sequences like those in (6) seem to suggest that there might be multiple

Cb's, analogous to the part ially ordered set of Cf's. A priori there is no reason to think

that either Susan or Betsy alone is the Cb of utterance (6b).

(6) a. Susan gave Betsy a pet hamster.

b. She remi nded her that such hamsters were quite shy.

However, if we consider different subsequent utterances, it becomes clear that Susan

and Betsy do not have an equivalent status in the second utterance. The ranking of

the Cr's matters. The variants (7)-(10) differ only in their choice of realization of Susan

and Betsy, in particular in which is pronominalized and which is in subject position.

(7 ) a. Susan gave Betsy a pet hamster.

b. She reminded her that such hamsters were quite shy.

c. She asked Betsy whe ther she liked the gift.

(8) a. Susan gave Betsy a pet hamster.

9 T h i s p o i n t i s c o n n e c t e d w i t h t h e d i s c u s s i o n o f p a r ti a l o r d e r i n g i n S e c ti o n 3.1 0 I t m a y a p p e a r t h a t C b ( U n ) c o m e s f r o m C f ( U n - 2 ) o r p r i o r s e t s o f fo r w a r d - l o o k i n g c e n t e rs , b u t t h e n i t is

o n l y b e c a u s e i t i s i n C f ( U n - 1 ) a l s o .

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Co m putation al Linguist ics Volume 21, N um be r 2

(9 )

b . S h e r e m i n d e d h e r th a t s u c h h a m s t e r s w e r e q u i t e sh y .

c . B e t sy to l d h e r t h a t sh e r e a l l y li k e d t h e g i ft .

a . S u s a n g a v e B e t s y a p e t h a m s t e r.

b . S h e r e m i n d e d h e r t h a t s u c h h a m s t e r s w e r e q u i te s h y.

c . S u s a n a s k e d h e r w h e t h e r s h e l i k e d t h e g i f t .

( 10 ) a . Su sa n g a v e B e t sy a p e t h a m s t e r .

b . S h e r e m i n d e d h e r t ha t s u c h h a m s t e r s w e r e q u i t e sh y .

c . Sh e t o l d Su sa n t h a t sh e r e a l l y l i k e d t h e g i f t .

I f b o t h S u s a n a n d B e t s y w e r e e q u a l l y l ik e ly b a c k w a r d - l o o k i n g c e n t er s i n t h e s e c o n d

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

p e r h a p s , t h e r e w o u l d b e a p r e f e re n c e f o r v a r i a n t s (7 ) a n d (9 ), w h i c h e x h i b i t c o n t i n u i t y

o f g r a m m a t i c a l s u b j e c t a n d o b j ec t . H o w e v e r , t h is i s n o t t h e c a s e. T h e r e is a m a r k e d

d e c r e a s e i n a c c e p t a b i li t y f r o m v e r s i o n (7 ) t o v e r s i o n (1 0), a n d f o r m a n y p e o p l e v e r s i o n

( 1 0 ) i s c o m p l e t e l y u n a c c e p t a b l e .

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

t h is h a p p e n s t o th e s a m e e x t e n t in a ll f o u r v a ri a n ts . I t a l s o c a n n o t b e a t t r i b u t e d s o l e l y

t o a c h a n g e f r o m g r a m m a t i c a l s u b j e c t t o g r a m m a t i c a l o b j e c t p o s i t i o n , a s v a r i a n t (8 )

i n v o l v e s s u c h a c h a n g e a n d y e t i s b e t t e r t h a n v a r i a n t ( 9 ) , w h i c h d o e s n o t . R a t h e r , i t

m u s t b e t h e c a se t h a t Su sa n i s t h e C B a t u t t e r a n c e ( b) a t e a c h o f t h e v a r i a n t s . V a r i an t s (9 )

a n d (1 0) ca n b e s h o w n t o b e w o r s e t h a n (7 ) a n d (8 ) b e c a u s e t h e y v i o l a te t h e c e n t e r i n g

r u l e s p r e s e n t e d i n t h e n e x t s e c t i o n .

T h i s e x a m p l e s u g g e s t s th a t p r o n o m i n a l i z a t i o n a n d s u b j e c t p o s i t i o n a re p o s s i b l e

l in g u i s ti c m e c h a n i s m s f o r e s ta b l i s h in g a n d c o n t i n u i n g s o m e e n t i t y a s th e CB . I n t h e

s e c o n d u t t e r a n c e o f t h e s e s e q u e n c e s , S u s a n i s r e a l iz e d b y a p r o n o u n i n s u b j e c t p o s i ti o n ;

' sh e ' i s th e C B o f t h i s u t t e r a n c e . U t t e r a n c e ( 7c ) c o n t i n u e s Su sa n a s C b , w h e r e a s u t t e r a n c e

( 8 c ) m e r e l y r e t a i n s h e r . U t t e r a n c e s l i k e ( 8 c ) m a y b e u se d t o p r o v i d e a b a s i s f o r a sh i f t

in Cb .11 H o w e v e r , t hi s l e a v e s o p e n q u e s t i o n s o f t h e i n d e p e n d e n c e o f s y nt a ct ic r o le a n d

p r o n o m i n a l i z a ti o n , a n d t h e p r e d o m i n a n c e o f e it h er , f o r c o n t r o l li n g c e n t e ri n g .

T h e f a c t t h a t b e i n g i n su b j e c t p o s i t i o n c o n t r i b u t e s i n a n d o f i t s e l f t o t h e l i k e l i h o o d

a n e n t i t y w i l l b e t h e h i g h e s t - r a n k e d C f (i.e . l i k e l y to b e t h e n e x t C B ) c a n b e s e e n b y

c o n t r a s t i n g t h e f o l l o w i n g t w o s e q u e n c e s , w h i c h d i f fe r o n l y i n th e i r f in a l u tt e r an c e s :

(11) a . S us an i s a f ine f r ien d.

,b . S h e g i v e s p e o p l e t h e m o s t w o n d e r f u l p r e s e n t s.

c . S h e j u s t g a v e B e t s y a w o n d e r f u l b o t t le o f w i n e .

d . Sh e t o l d h e r it w a s q u i t e r ar e . ( Su sa n t o l d B e t sy )

e . S h e k n o w s a l o t a b o u t w i n e . ( S u sa n k n o w s . . . )

11 T h e e ff ec t of v a r i o u s l i n g u i s t ic c o n s t r u c t i o n s o n c e n t e r m o v e m e n t a n d t h e i n t e r a c t io n s o f c e n t e r i n g

s h i f t s w i t h g l o b a l d i s c o u r s e s t r u c t u r e a r e a c t iv e a r e a s o f r e s e a r ch . S e c t i o n 9 p r o v i d e s r e f e r e n c e s t o s u c h

w o r k .

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Barb a ra J . Gro sz e t a l . Cen te r ing

( 1 2) a . S u s a n is a f i n e f r i e n d .

b . S h e g i v e s p e o p l e th e m o s t w o n d e r f u l p r e s e n t s .

c . S h e j u s t g a v e B e t s y a w o n d e r f u l b o t t le o f w i n e .

d . S h e t o l d h e r it w a s q u i t e r a r e . ( S u s a n t o l d B e t sy )e . W i n e c o l l e c t in g g i v e s h e r e x p e r t i s e t h a t ' s f u n t o s h a r e . ( S u s a n ' s e x -

p e r t i s e )

I n t h e ( c) u t t e r a n c e o f e a c h s e q u e n c e , S u s a n i s t h e C b . E i t h e r S u s a n o r B e t s y m i g h t b e

t h e r e fe r e n t o f t h e s u b je c t p r o n o u n i n t h e f o u r t h u t t e ra n c e ; h o w e v e r , t h e r e a p p e a r s t o

b e a s t r o n g p r e f e r e n c e f o r S u s a n ( i.e ., f o r t h e r e a d i n g " S u s a n t o l d B e t s y " ) . 12 B e c a u s e

t h is p r e f e r e n c e m i g h t b e a t t r i b u t a b l e t o p a ra l l e l i s m , t h e l a s t u t t e r a n c e i n ( 12 ) p r o v i d e s

a c ru c i a l t es t. If t h e C f r a n k i n g d e p e n d e d o n p r o n o m i n a l i z a t i o n a l o n e , t h e f o u r t h

u t t e r a n c e w o u l d a l l o w e i t h e r S u s a n o r B e t sy to b e th e h i g h e s t - r a n k e d C f. P a r a l l e l is m

w o u l d s u g g e s t d i f f er e n t p r e f e r e n c e s f o r t h e C b( 1 2e ) in th e t w o s e q u e n c e s . H o w e v e r ,

t h e p r e f e r r e d r e a d i n g o f t h e p r o n o u n ( r es p e c ti v e ly , " s h e " a n d " h e r " ) i n u t t e r a n c e (e ) o f

b o t h s e q u e n c e s i s S u s a n , w h o i s r e a l i z e d i n th e s u b j e c t p o s i t i o n o f t h e ( d ) u t t e r a n c e s .

T h i s p r e f e r e n c e h o l d s r e g a r d l e s s o f s y n t a c ti c p o s i t i o n i n t h e ( e) u t t e r a n c e s . T h u s , w e

c a n e s t a b l i s h a p r e f e r e n c e f o r s u b j e ct p o s i ti o n . I n o t h e r c i r c u m s t a n c e s , h o w e v e r , a s t h e

e x a m p l e s b e l o w i l l u s tr a te , t h e C b m a y b e r e a l i z e d i n o t h e r g r a m m a t i c a l ro le s .

I n t h e f ir s t c l a u s e o f b o t h u t t e r a n c e s ( 1 3d ) a n d ( 14 d ), t h e d i r e c t o b j e c t i s p r o n o m i -

n a l i z e d ; t h e p r o n o u n " i t" r e fe r s to t h e g r e e n p l a s t i c t u g b o a t . I n (1 3) t a k i n g t h e b o a t t o

b e t h e h i g h e s t r a n k e d C f a n d h e n c e t h e m o s t l i k e ly r e fe r e n t fo r " t h e s il ly t h in g " i n th e

s e c o n d c l a u s e o f u t t e r a n c e ( d) y i e ld s a c o h e r e n t a n d e a s i ly c o m p r e h e n s i b l e d i s c o u r s e . 13I n (1 4), h o w e v e r , p r a g m a t i c i n f o r m a t i o n l e a d s t o a p r e f e r e n c e f o r t h e b e a r, n o t t h e b o a t ,

t o b e t h e r e f e r e n t o f " t h e s i l l y t h i n g " i n t h e l a s t u t t e r a n c e ; t h i s p r e f e r e n c e i s i n c o n f l i c t

w i t h t h e b o a t ' s b e i n g t h e m o s t l i k e ly C b. T h a t ( 13 ) is a m o r e c o h e r e n t d i s c o u r s e t h a n

(1 4) c a n b e e x p l a i n e d o n t h e b a s i s o f th i s d i f fe r e n c e . TM

(1 3) a . H a v e y o u s e e n t h e n e w t o y s th e k i d s g o t t h is w e e k e n d ?

b . S t u f fe d a n i m a l s m u s t r e a l ly b e o u t o f f a s h io n .

c . S u s i e p r e f e r s t h e g r e e n p l a s t i c t u g b o a t t o th e t e d d y b e ar .

d . T o m m y li k e s i t b e t t e r t h a n t h e b e a r to o , b u t o n l y b e c a u s e t h e si ll y

t h i n g i s b i g g e r .

12 Sequences in which a similar pronominalization pattern is used but in which the fourth utteranceimplies report o f a dialogue (e.g., "Sh e thanked her and told her she appreciated that the wine w asquite rare.") may lead to interpretations in which the subject pronoun is taken as referring to Betsy;accentuation of the subject may also be used to achieve this result. The first of these suggests a stronginteraction between dialogue verbs and centering, which is also apparen t in direct-speech dialogueexamples. The relationship between this kind of lexical-semantic influence ove r centering and that ofso-called 'e m pa thy ' verbs, e.g., Kameyam a (1985), Walker, Iida, and Cote (1994), remains to be

determined. T he second would app ear to provide add itional evidence for subject preference incentering, based on results o f Hirschberg an d W ard (1991) showing that accenting served to flippreferences (in their study from either strict-to-sloppy or sloppy-to-strict readings for anaphors in theantecedent clause in VP-ellipsis constructions).

13 For the sake of this argument, assume that children like bigger things more than smaller things. If thisis not the case , then the argument merely flips which variants are mo re acceptable.

14 The discrepancy is even greater if "it" is used in the last utterance clause. However, one mightattribute this to repetition of the use o f "it" and so we ha ve avoided the repeated use of a pronoun. Wealso note that "the silly thing" conv eys additional inform ation--roughly, the sp ea ke r's attitude towardthe bear or tug boat (cf. Section 8).

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Co m putation al Linguist ics Volume 21, N um be r 2

(14) a . H a v e y o u s e e n th e n e w t o y s t h e k id s g o t t hi s w e e k e n d ?

b . S t u f f e d a n i m a l s m u s t r e a ll y b e o u t o f f a s h io n .

c . S u s i e p r e f e r s t h e g r e e n p l a s ti c t u g b o a t t o t h e t e d d y b e a r.

d . T o m m y l ik e s it b e t t e r t h a n t h e b e a r t o o , a l th o u g h t h e s i ll y t h i n g i sb i g g e r .

T h u s , t h e d i s c o u r s e s i n ( 1 1) -( 14 ) s u g g e s t t h a t g r a m m a t i c a l r o le is a m a j o r d e t e r m i n a n t

o f t h e r a n k i n g o n t h e Cf, wi t h SUB JE C T > O B J E C T ( S ) > OTHER. Th e e f fec t o f f ac to r s

s u c h a s w o r d o r d e r ( e s p e c ia l ly f ro n t in g ) , c l a u s a l s u b o r d i n a t i o n , a n d l ex i ca l s em a n t i c s ,

a s we l l a s t h e i n t e r a c t i o n a m o n g t h e se f a c t o r s a r e a r e a s o f a c t i v e i n v e s t i g a t i o n ; Se c t i o n

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

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

g l e C b , t h a t g r a m m a t i c a l r o l e a f f e c t s a n e n t i t y ' s b e i n g m o r e h i g h l y r a n k e d i n C f , a n d

t h at l o w e r - r a n k e d e l e m e n t s o f th e C f c a n n o t b e p r o n o m i n a l i z e d u n l e s s h i g h e r -r a n k e do n e s a r e. K a m e y a m a (1 98 5) w a s t h e f i rs t t o a r g u e t h a t g r a m m a t i c a l r o le , r a t h e r t h a n t h e -

m a t i c r o le , w h i c h S i d n e r u s e d , a f f e c t e d t h e C f r a n k i n g . P s y c h o l i n g u i s t i c r e s e a r c h s i n c e

1 9 8 6 ( H u d s o n - D ' Z m u r a 1 9 8 8 ; G o r d o n , G r o s z , a n d G i l l i o m 1 9 9 3 ) s u p p o r t s t h e c l a i m s

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

f y i n g t h e CB . I t f u r t h e r m o r e s u g g e s t s t h a t n e i t h e r t h e m a t i c r o le n o r s u r f a c e p o s i t i o n i s

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

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

r e l a te d t o t h e e f f ec t o f p r o n o m i n a l i z a t i o n o n d e t e r m i n i n g C b ( U n _ l ) , c ro s s - li n g u is t ic

wo r k ( Ka m e y a m a 1 9 8 5 ; P r i n c e a n d W a l k e r 1 9 9 5 ; W a l k e r , I i d a , a n d C o t e 1 9 9 4 ) a r g u e s

t h a t i t p l a y s su c h a r o l e . Se c t i o n 9 l i s t s s e v e r a l p a p e r s a p p e a r i n g a f t e r Gr o sz , Jo sh i ,

a n d W e i n s t e i n ( 19 86 ) t h a t i n v e s t i g a t e f a c t o r s a f f e c ti n g t h e C f o r d e r i n g .

6 . C o n s t r a i n t s o n C e n t e r M o v e m e n t a n d R e a l iz a t i o n

T h e b a s i c c o n s t r a i n t o n c e n t e r r e a l i z a t i o n i s g i v e n b y R u l e 1 , w h i c h i s s t a t e d i n t e r m s

o f t h e d e f in i t io n s a n d s c h e m a t i c i n S e c ti o n 3.

R u l e 1

I f a n y e l e m e n t o f C f ( U n ) i s r e a l iz e d b y a p r o n o u n i n Unq-1, t h e n t h e Cb(Un+l) mus t b er e a l i z e d b y a p r o n o u n a l s o .

I n p a r t i c u la r , t h i s c o n s t r a i n t s t i p u l a t e s t h a t n o e l e m e n t i n a n u t t e r a n c e c a n b e r e a l i z e d a s

a p r o n o u n u n l e s s t h e b a c k w a r d - l o o k i n g c e n te r o f t h e u t te r a n c e is r ea l iz e d a s a p r o n o u n

a ls o . is R u l e 1 r e p r e s e n t s o n e f u n c t i o n o f p r o n o m i n a l r e fe r e n ce : t h e u s e o f a p r o n o u n t o

r e a li z e t h e CB s i g n a l s t h e h e a r e r t h a t t h e s p e a k e r i s c o n t i n u i n g t o ta l k a b o u t t h e s a m e

t h in g . N o t e t h a t R u l e 1 d o e s n o t p r e c l u d e u s i n g p r o n o u n s f o r o t h e r e n t it ie s s o l o n g a s

t h e C b i s r e a l i z e d w i t h a p r o n o u n . ( T h i s i s i l l u s t r a t e d i n e x a m p l e s 7 - 1 0 i n Se c t i o n 5 . )

P s y c h o l o g i c a l r e s e a r c h ( G o r d o n , G r o s z , a n d G i l l io m 1 9 93 ; H u d s o n - D ' Z m u r a 1 98 8) a n d

c ross - l ingu i s t i c r e sea rch (Di Eugen io 1990 ; Kameyama 1985 , 1986 , 1988 ; Walke r , I i da ,a n d C o t e 1 99 0, 19 94 ) h a v e v a l i d a t e d t h a t t h e C B i s p r e f e r e n t i a l l y r e a l i z e d b y a p r o n o u n

i n E n g li s h a n d b y e q u i v a l e n t f o r m s ( i.e ., z e r o p r o n o u n s ) i n o t h e r la n g u a g e s .

T h e b a s ic c o n s t ra i n t o n c e n t e r m o v e m e n t i s g i v e n b y R u l e 2.

1 5 R u l e 1 i g n o r e s c e r t a i n c o m p l i c a t i o n s t h a t m a y a r i s e i f o n e o f t h e f o r w a r d - l o o k i n g c e n t e r s o f U n + l i sr e a l i z e d b y a d e i c t i c p r o n o u n .

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R u l e 2

Sequences of continuation are preferred over sequences of retaining; and sequences of

retaining are to be preferred over sequences of shifting.

In particular, a pair continuations across Un and across Un+l, represented as

Cont(Un,U~+0 and Cont(Un+t,U~+2) respectively, is preferred over a pair of reten-

tions, Ret(Un,U~+0 and Ret(U,+t,Un+2). The case is analogous for pair of retentionsand a pair of shifts.

Rule 2 reflects our intuition that continuation of the center and the use of retentions

when possible to produce smooth transitions to a new center provides a basis for local

coherence. In a locally coherent discourse segment, shifts are followed by a sequence

of continuat ions characterizing another stretch of locally coherent discourse. Frequent

shifting leads to a lack of local coherence, as was illustrated by the contrast between

Discourse (1) and Discourse (2) in Section 2. Thus, Rule 2 provides a constraint on

speakers, and on natural-language generation systems. They should plan ahead to

minimize the nu mber of shifts. This rule does not have the same direct implementation

for interpretation systems; rather it predicts that certain sequences produce a higher

inference load than others. To empirically test the claim made by Rule 2 requires

examination of differences in inference load of alternative multi-utterance sequences

that differentially realize the same content.

Although several cross-linguistic studies have investiga ted Rule 2 (see Section 9),

there are as yet no psycholinguistic results empirically validating it.

7 . A p p l i c a t i o n s o f t h e R u l e s

The two centering rules along with the partial ordering on the forward-looking centers

described in Section 5 constitute the basic framework of center management. These

rules can explain a range of variations in local coherence.TM

A violation of Rule 1 occurs if a pronoun is not used for the backward-looking

center and some other entity is realized by a pronoun. Such a violation occurs in the

following sequence pres umed to be in a longer segment that is currently centered on

John (cf. also examples (9) and (10) in Section 5):

(15) a. He has been acting quite odd. [ C b = John = referent("he')]

b. He cal led up Mike yesterday. [CB = John = referent("he' )]

c. John wanted to meet him urgently. [CB = John; referent("him') =

Mike]

The violation of Rule 1 leads to the incoherence of the sequence. The only possible

interpretation is that the "John" referred to in (15c) is a second person named "John,"

not the one referred to in the preceding utterances in (15); however, even under this

interpretation the sequence is very odd. The next example illustrates that this effect is

16 These rules and constraints have also been used by others as the basis for pronou n resolutionalgorithms based on centering. The earliest such at tempt (Brennen, Friedman, and Pollard 1987) usedthe uniquenes s and locality of Cb constraints and ranked the Cf by grammatical role; it employed avariant of Rule 2 in whic h the stat ed preferences on t ransitions were restricted to transitions betwe eni n d i v i d u a l p a i r s of utterances (rather than the longer se qu e n c e s in the original formulation) and use d todecide be tween possible interpretations of pronouns. Section 9 provides references to other work oncentering algorithms.

215




independent of the grammatical position of the C b and also demonstrates that Rule 1

operates independ ently of the type of centering transition.

(16) a. John has been acting quite odd.

b. He called up Mike yesterday. [C b = John = referent("he")]

c. Mike was s tud yin g for his driver' s test. [CB = Mike = referent("his')]

d. He was an noyed by John's call.

Without utterance (16c), this sequence, like the sequence in (15), is unacceptable unless

it is possible to consider the introduction of a second person named "John." The

intervening utter ance (c) here provides for a shift in center from John to Mike, making

the full sequence coherent. 17

It is important to notice that Rule 1 constrains the realization of the most highly

ranked element of the Cf(Un) that is real ized in Un+t give n that pronominal i za t ion i s used .

Obviously any entities realized in Un that are not realized in Un+t, including the Cb(Un)

as well as the highest ranked element of CdUn), do not affect the applicability of Rule 1.

Likewise, if no pronouns are used, then Rule 1 is not applicable. Two particular ways

in which such situations may hold have been noticed in previous research. Each leads

to a different type of inference load on the hearer, both of which we believe relate to

Rule 1; however, neither constitutes a violation of Rule 1. The result ing discourses are

coherent, but the determination of local coherence (in the first case) or the detection

of a global shift (in the second case) requires additional inferences.

The first case concerns realization of the Cb by a nonpr onominal expression. Rule 1does not preclude using a proper name or definite description for the Cb if there are

no pronouns in an utterance. However, it appears that such uses are best when the full

definite noun phrases that realize the centers do more than just refer. They convey some

additional information, i.e., lead the hearer or reader to draw additional inferences.

The hearer or reader not only infers that the CB has not changed even though no

pronoun has been used, but also recognizes that the description holds of the old Cb.

Sequences (17) and (18) are typical cases.TM

(17) a. My dog is gett ing quite obstreperous.

b. I took him to the vet the other day.

c. The m angy old beast always hates these visits.

(18) a. I'm reading T h e F re n ch L i e u t e n a n t 's W o m a n .

b. The book, which is Fowles 's best, was a bestseller last year.

The second case concerns the use of a pronoun to realize an entity not in the CdUn);

such uses are strongly constrained. The particular cases that have been identified

involve instances where attention is shifted globally back to a previously centeredent ity (e.g. Grosz [1977], Reichman [1985]). In such cases add itiona l inferences are

1 7 E m p i r i c a l i n v e s t i g a t i o n s o f t h e s e c l a i m s o f G r o s z , J o sh i , a n d W e i n s t e i n ( 19 86 ) s u g g e s t t h e y a r e t o os t r o n g . I n p a r t ic u l a r , th e r e s u l t s o f G o r d o n , G r o s z , a n d G i l l i o m ( 19 93 ) s u g g e s t t h a t ( 1 6 d ) w i t h o u t t h e

i n t e r v e n i n g ( c) u t t e r a n c e i s n o t a s b a d a s ( 15 c).1 8 S e q u e n c e ( 1 7) is a n a d a p t a t i o n o f o n e o f S i d n e r ' s e x a m p l e s ( S i d n e r 1 97 9) .

216



Barb a ra J . Gro sz e t a l . Cen te r ing

r e q u i r ed t o d e t e r m i n e t h a t th e p r o n o u n d o e s n o t r e fe r t o a m e m b e r o f t h e c u r re n t

f o r w a r d - l o o k i n g c e n t e r s a n d t o id e n t i f y t h e c o n t e x t b a c k t o w h i c h a t t e n t i o n i s s h if t i n g .

F u r t h e r i n v e s t i g a t i o n i s re q u i r e d t o d e t e r m i n e t h e l in g u i s ti c c u e s ( e.g ., i n t o n a t i o n o r c u e

p h r a s e s [ G r o s z a n d H i r s c h b e r g 1 99 2]) a n d i n t e n t io n a l i n f o r m a t i o n t h a t ar e r e q u i r e d t o

e n a b l e s u c h s h i ft s w h i l e p r e s e r v i n g c o h e r e n c e , a s w e l l a s t h e e f fe c t o n i n f e r e n c e l o a d .

A t h i r d c o m p l i c a t i o n a r i s e s i n t h e a p p l i c a t i o n o f R u l e 1 i n s e q u e n c e s i n w h i c h t h eC B o f a n u t t e r a n c e i s r e a l i z e d b u t n o t d i r e c t l y r e a l i z e d i n t h a t u t t e r a n c e . T h i s s i t u a t i o n

t y p i c a l l y h o l d s w h e n a n u t t e r a n c e d i r e c t ly r e al i ze s a n e n t i t y im p l i c i t l y f o c u s e d b y a n

e l e m e n t o f t h e C f o f th e p r e v i o u s u t t e r a n c e . F o r i n s ta n c e , i t a r is e s in u t t e r a n c e s c o n -

t a i n in g n o u n p h r a s e s t h a t e x p r e s s f u n c t i o n a l r e l a t i o n s ( e.g ., " t h e d o o r , . . . . t h e o w n e r " )

w h o s e a r g u m e n t s h a v e b e e n d i r e c t ly re a l i z e d in p r e v i o u s u t t e r a n c e s ( e.g ., a h o u s e ) a s

o c c u r s i n t h e s e q u e n c e ,

(19) a . T h e h o u s e a p p e a r e d t o h a v e b e e n b u r g l e d .

b . T h e d o o r w a s a ja r.

c. T h e f u r n i t u r e w a s i n d i s a r r a y .

I n t h is s e g m e n t , t h e h o u s e r e f e r r e d t o i n ( 19 a ) i s a n e l e m e n t o f t h e C f( 1 9a ). T h i s h o u s e i s

t h e C b ( 1 9 b ); it i s r e a l i z e d b u t n o t d i r e c t l y r e a l i z e d i n ( 1 9b ). B e c a u s e t h e h o u s e i s t h e C B,

t h e C f (1 9 b) in c l u d e s i t a s w e l l a s t h e d o o r t h a t i s d i r e c t l y r e a l i z e d i n t h e u t t e r a n c e . T h e

C B (1 9c) is t h u s a g a i n " h o u s e . " W e a s s u m e h e r e t h a t t h e d o o r r a n k s a b o v e t h e h o u s e i n

C f (1 9 b) . F o r e x a m p l e , i f ( 19 b ) i s f o l l o w e d b y a s e n t e n c e w i t h ' it ' i n t h e s u b j e c t p o s i t i o n ,

t h e n ' i t' is m o r e l i k e l y to r e f e r to t h e d o o r J 9 T h i s i s c o n s i s t e n t w i t h t h e r a n k i n g o f th e

d o o r a h e a d o f t h e h o u s e i n C f ( 19 b). H o w e v e r , c o n t i n u i t y o f th e h o u s e a s a p o t e n t i a l

C B f o r ( 19 c) i s r e f l e c t e d in t h e d i s c o u r s e s e g m e n t b e i n g i n t e r p r e t e d t o b e " a b o u t " t h e

h o u s e a n d ( 1 9 c ) b e i n g i n t e r p r e t e d i n t h e s a m e w a y a s ( 1 9 b ) w i t h r e s p e c t t o t h e h o u s e .

I n G r o s z , J o s h i, a n d W e i n s t e i n ( 1 98 6) w e d i d n o t e x p l o r e t h is i s s u e fu r t h e r ; t h e g e n e r a l

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

o p e n . 2°

T h e u s e o f d i f f e re n t t y p e s o f t r a n s i t i o n s f o l l o w i n g t h e r a n k i n g s i n R u l e 2 a re

i l l u s t r a t e d b y t h e d i s c o u r s e b e l o w .

( 2 0 ) a . J o h n h a s b e e n h a v i n g a lo t o f t r o u b l e a r r a n g i n g h i s v a c a t i o n .

b . H e c a n n o t f i n d a n y o n e t o t a k e o v e r h i s r e s p o n s i b i l i ti e s . ( h e = J o h n )

C B = J o h n ; C f = { J o h n }

c . H e c a l le d u p M i k e y e s t e r d a y t o w o r k o u t a p la n . ( h e = J o h n )

C 6 -- J o h n ; C f = { Jo h n , M i k e } ( C O N T I N U E )

d . M i k e h a s a n n o y e d h i m a lo t r e ce n tl y .

C B -- J o h n ; C f = { M i k e , J o h n } ( R E T A I N )

e . H e c a l l ed J o h n a t 5 A M o n F r i d a y l a s t w e e k . ( h e = M i k e )

C b = M i k e ; C f = { M i k e , J o h n } ( S H I F T )

19 However, it can refer to the ho use. For example if (b) were followed by "Otherwise from the outside itappeared quite normal. Inside was a different story." A pronoun could also be used in othergramm atical roles to refer to the doo r. We use subject position as the test, because there is no priorsentential context to bias the interpretation.

20 See Section 9 for some rec ent references related to this issue.

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Co mp utational Linguist ics Volume 21, N um be r 2

U t t e r a n c e ( 2 0 b ) e s t a b l i s h e s J o h n b o t h a s t h e C b a n d a s t h e m o s t h i g h l y r a n k e d C f . I n

u t t e r a n c e (2 0c ) Jo h n c o n t i n u e s a s t h e C B , b u t i n u t t e r a n c e ( 2 0 d ) h e i s o n l y r e t a i n e d ;

M i k e h a s b e c o m e t h e m o s t h i g h l y r a n k e d e l e m e n t o f th e C f. F i na ll y, in u t t e r a n c e ( 20 e)

t h e b a c k w a r d - l o o k i n g c e n t e r s h if ts t o b e i n g M i k e . R u l e 1 i s s a t is f ie d t h r o u g h o u t (2 0).

R u l e 1 d e p e n d s o n l y o n t h e o r d e r in g o f e le m e n t s o f C f, a n d n o t o n t h e n o t i o n s o f

r e t a i n i n g a n d c o n t i n u a t i o n .

8 . R equ is i te Properties o f U nd erly ing Semant ic Theory

D i f f e r e n t s e m a n t i c t h e o r i e s m a k e d i f f e r e n t c o m m i t m e n t s w i t h r e s p e c t t o t h e c o m p l e t e -

n e s s o r d e fi n i te n e s s r e q u i r e d o f a n i n t e rp r e t a ti o n . B e c a u s e t h e i n f o r m a t i o n n e e d e d t o

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

u t t e r a n c e o c c u r s in t h e d i s c o u r s e , t h e w a y s i n w h i c h a t h e o r y t re a t s p a r ti a l i n f o r m a t i o n

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

m e r e l y t h a t u t t e r a n c e s t h e m s e l v e s c o n t a i n o n l y p a r t ia l i n f o r m a t i o n , b u t t h a t it m a y

o n l y b e s u b s e q u e n t t o a n u t t e r a n c e t h a t s u f fi c ie n t i n f o r m a t i o n i s a v a i l a b le f o r c o m p u t -

i n g a u n i q u e i n t e rp r e t a ti o n . N o m a t t e r h o w r i c h a m o d e l o f c o n t e x t o n e h a s , it w i l l n o t

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

e s p e c i a ll y tr u e f o r d e f i n it e n o u n p h r a s e i n t e rp r e t a ti o n . F o r e x a m p l e , s e v e r a l i n t er p r e -

t a ti o n s a r e p o s s i b l e f o r t h e n o u n p h r a s e " t h e V i c e - P r es i d e n t o f t h e U n i t e d S t a te s , " i n

t h e u t t e r a n c e

( 21 ) T h e V i c e - P r e s i d e n t o f t h e Un i t e d S t a t e s i s a l so P r e s i d e n t o f t h e Se n a t e .

O n e i n t e r p r e t a t i o n , n a m e l y t h e i n d i v i d u a l w h o i s c u r r e n t l y V i c e - P r e s i d e n t , p r o v i d e s

t h e a p p r o p r i a t e b a s i s f o r t h e i n t e r p r e t a t i o n o f " h e " i n t h e s u b s e q u e n t u t t e r a n c e g i v e n

in (22):

(2 2) R i g h t n o w , h e is t h e P r e s i d e n t ' s k e y p e r s o n i n n e g o t i a t i o n s w i t h C o n g r e s s .

H o w e v e r , a d i ff e r e n t i n t e rp r e t a t io n , o n e w h i c h r e t a i n s s o m e d e s c r i p t i v e c o n t e n t , p r o -

v i d e s t h e a p p r o p r i a t e b a s i s f o r a n i n t e r p r e t a ti o n o f t h e p r o n o u n " h e " i n t h e s li g h tl y

d i ff e r en t s u b s e q u e n t u t t e ra n c e

(2 3) H i s t o ri c al ly , h e is th e P r e s i d e n t ' s k e y p e r s o n i n n e g o t i a t io n s w i t h C o n g r e s s .

A se m a n t i c t h e o r y t h a t f o r c e s a u n i q u e i n t e r p r e t a t i o n o f u t t e r a n c e ( 21 ) w i l l re q u i r e t h a t

a c o m p u t a t i o n a l t h e o r y o r s y s t e m e i th e r m a n a g e s e v e r a l a l te r n a ti v e s s i m u l t a n e o u s l y

o r p r o v i d e s o m e m e c h a n i s m f o r r e t ra c t in g o n e c h o i c e a n d t r y i n g a n o t h e r l at er . O n t h e

o t h e r h a n d , a t h e o r y t h a t a l lo w s f o r a p a rt i a ll y s p e c i f ie d i n te r p r e t a t io n m u s t p r o v i d e f o r

r e f in i n g t h a t in t e r p r e t a t io n o n t h e b a s is o f s u b s e q u e n t u tt e r a n c e s . A d d i t i o n a l u t t e r a n c e s

m a y p r o v i d e f u r t h e r c o n s t r a in t s o n a n i n te r p r e t a ti o n , a n d s e q u e n c e s o f u t t e r a n c e s

m a y n o t b e c o h e r e n t , i f t h e y d o n o t a l l o w f o r a c o n s i s t e n t c h o i c e o f i n t e r p r e t a t i o n .Fo r e x a m p l e , t h e u t t e r a n c e i n ( 2 4 ) i s p e r f e c t l y f i n e a f t e r ( 2 2 ) , b u t y i e l d s a n i n c o h e r e n t

se qu en ce a f t e r (23). 21

2 1 T h e s e e x a m p l e s w e r e f i rs t w r i t t e n i n 1 98 6 w h e n G e o r g e B u s h w a s V i c e - P r es i d e n t . T h e y r e m a i n u s e f u l

f o r i ll u s t r at i n g t h e o r i g i n a l p o i n t s i f t h e t i m e o f o r i g in a l w r i t i n g i s t a k e n i n t o a c c o u n t . A s w e d i s c u s s

l a t e r , t a k e n a s s p o k e n n o w t h e y i l l u s t r a t e n e w p o i n t s .

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Barb ara J. Gro sz et al. Cen tering

(2 4) A s A m b a s s a d o r t o C h i n a , h e h a n d l e d m a n y t r ic k y n e g o t i a ti o n s , s o h e

d o e s we l l i n t h i s j o b .

T o s u m m a r i z e , g i v e n t h a t o n e p u r p o s e o f d i s c o u r s e i s to i n c re a s e th e i n f o r m a t i o n

s h a r e d b y s p e a k e r a n d h e a re r , i t i s n o t s u r p r i s i n g t h a t i n d i v i d u a l u t t e r a n c e s c o n v e y

o n l y p a r t ia l i n f o r m a t i o n . H o w e v e r , t h e la c k o f c o m p l e t e i n f o r m a t i o n a t t h e t im e o f

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

t e r m i n e d . I n c o n s t r u c ti n g a c o m p u t a t i o n a l m o d e l , w e a r e t h e n l e ft w i t h t h r e e c h oi ce s :

c o m p u t e a l l p o s s i b l e i n t e r p re t a t io n s a n d f il te r o u t p o s s i b il it ie s a s m o r e i n f o r m a t i o n i s

r e c e i v e d ; c h o o s e ( o n s o m e b a s i s ) a m o s t l i k e l y i n t e r p r e t a t i o n a n d p r o v i d e f o r " b a c k -

t r a c k in g " a n d c o m p u t i n g o t h e r s l at er ; c o m p u t e a p a rt ia l i n t e r p re t a ti o n . W e c o n j e c t u r e

t h a t t h is t h i r d c h o i c e is th e a p p r o p r i a t e o n e f o r n o u n p h r a s e i n t er p r e ta t io n .

C e n t e r i n g t h e o r y a n d t h e c e n t e ri n g f r a m e w o r k r e l y o n a c e r ta i n p i c t u r e o f t h e

w a y s i n w h i c h u t t e ra n c e s f u n c t io n t o c o n v e y i n f o rm a t i o n a b o u t t h e w o r l d . O n e r o le

o f a s e m a n t i c t h e o r y i s t o g i v e su b s t a n c e t o su c h a p ic t u r e . A t t h e t i m e G r o sz , Jo sh i ,a n d W e i n s t e i n (1 98 6) wa s w r i t t e n , it s t r u c k u s t h a t s i t u a t i o n s e m a n t i c s ( B a r wi se a n d

P e r r y 1 9 8 3 ) p r o v i d e d a p a r t i c u l a r l y c o n v e n i e n t s e t t i n g i n w h i c h t o f r a m e o u r o w n

t h e o r y o f d i s c o u r s e p h e n o m e n a , t h o u g h o u r a c c o u n t r e li ed o n l y o n g e n e r a l f ea t u re s

o f th i s a p p r o a c h a n d n o t o n d e t a i ls o f th e t h e o r y a s t h e n a r t i c u la t e d . T h e t w o m o s t

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

i n t e r p r e ta t i o n w e w i s h e d t o d e v e l o p w e r e ( 1) t h a t i t a l l o w s f o r t h e p a rt ia l i n t e r p r e t a t io n

o f u t t e r a n c e s a s t h e y o c c u r in d i s c o u r s e , a n d (2 ) t h a t it p r o v i d e s a f r a m e w o r k i n w h i c h

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

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

e x t e n s i o n s a n d r e f i n e m e n t s o f th e t h e o r y t o w h i c h w e r e f e r t h e i n t e r e st e d r e a d e r.T h e o r i g i n a l b o o k ( B a r w i s e a n d P e r r y 1 9 8 3 ) m a y b e c o n s u l t e d f o r a n a c c o u n t o f t h e

d i s t in c t i o n b e t w e e n v a l u e - f r e e a n d v a l u e - l o a d e d i n t e r p r e t a ti o n s u s e d b e l o w .

I n t h e d i s c u s s i o n a n d e x a m p l e s i n p r e v i o u s s e c t i o n s , t h e C b a n d t h e e l e m e n t s

o f C f h a v e a ll b e e n t h e d e n o t a t i o n s o f v a r i o u s n o u n p h r a s e s i n a n u tt e r a n c e . T h e

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

o t h e r sy n t a c t i c c o m p l e x i t i e s ( c f . W e b b e r 1 9 7 8 ) a s we l l a s c a se s i n wh i c h t h e c e n t e r

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

C f o f th e p r e v i o u s u t t e r a n c e (c f. S e ct io n 7 ). A s i n g u l a r d e f i n it e n o u n p h r a s e m a y

c o n t r i b u t e a n u m b e r o f d i ff e r e n t in t e r p r e t a t i o n s t o C f. I n p a r t i c u la r , n o t o n l y t h e v a l u e -

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

Fo r e x a m p l e , i n t h e u t t e r a n c e , " T h e V i c e - P r e s i d e n t o f th e Un i t e d S t a t e s i s a l so

P r e s i d e n t o f th e S e n a t e, " t h e n o u n p h r a s e " t h e V i c e -P r e s id e n t " c o n t r i b u t e s b o t h a

v a l u e - l o a d e d a n d a v a lu e - f r e e i n t e rp r e t a ti o n . T h e v a l u e - f r e e i n t e r p r e ta t i o n i s n e e d e d

i n t h e s e q u e n c e ( 2 5 a - c ) , w h e r e a s t h e v a l u e - l o a d e d i n t e r p r e t a t i o n i s n e e d e d i n ( 2 6 a - c ) .

(25) a.

b .

C,

T h e V i c e - P r e s i d e n t o f t h e U n i t e d S t a t e s is a lso P r e s i d e n t o f th e Se n a t e .

H i s to r ic a ll y , h e is t h e P r e s i d e n t ' s k e y m a n i n n e g o t i a ti o n s w i t h C o n g r e s s .

H e i s r e q u i r e d t o b e 3 5 y e a r s o l d.

(26) a.

b .

C.

T h e V i c e - P r e s i d e n t o f t h e U n i t e d S t a t e s i s a l so P r e s i d e n t o f t h e Se n a t e.

R i g h t n o w , h e ' s t h e p r e s i d e n t ' s k e y p e r s o n i n n e g o t i a t io n s w i t h C o n g r e s s .

A s A m b a s s a d o r t o C h in a , h e h a n d l e d m a n y t ri c ky n e g o ti a ti o n s , s o

h e i s w e l l p r e p a r e d f o r th i s jo b .

219




The Cb(25b) and the Cb(26b) are both directly realized by the anaphoric element "he."

But Cb(25b) is the value-free interpretation of the noun phrase, "the Vice-President" (as

in, "The Vice-President of the United States is the President's key man in negotiations

with Congress"), whereas Cb(26b) is the value-loaded interpretation (as in "the p e r s o n

w h o n o w is Vice-President of the United States"). That this is so is demonstrated by

the fact that (25c) is true in 1994, whereas (26c) is not. Centering accommodates thesedifferences by allowing the noun phrase "the Vice-President of the United States"

potentially to contribute both its value-free interpretation and its value-loading at

the world type to Cf(25a). Cb(25b) is then the value-flee interpretation, and Cb(26b)

is the value-loaded one (at the time of the writing of Grosz, Joshi, and Weinstein

(1986), George Bush, but now [1995] A1 Gore). In each sequence, the (a) utterance

underdetermines what element to add to Cf. This underdetermination may continue

in a subsequent utterance with the pronoun. For example, that would be the case if

the in troductory adverbials were left off the (b) utterances.

We conjecture that the correct approach to take in these cases is to add the value-

free interpretation to Cf and then load it for the interpretation of subsequent utterances

if this is necessary. This conjecture derives from a belief that this app roach will most

effectively limit the inferences required. These loading situations thus constitute a

component of the centering constituent of the discourse situation. It remains an open

question how long to retain these loading situations, although those corresponding to

elements of Cf that are not carried forwa rd (either as the Cb or as Cfs of the subsequent

utterance) can, obviously, be dropped.

It is possible for an utterance to prefer either a value-free (VF) or value-loaded

(VL) interpretation but not force it. For example, the second ut terance in the following

sequence prefers a VF interpretation but allows for the VL interpretation that is neededin the third utterance.

(27) a. A: The Vice-President of the U.S. is also President of the Senate.

b. B: I tho ugh t he played some important role in the House.

c. A: He did, but that was before he was the Vice-President.

In a similar way the second utterance in the following sequence22 prefers the VL

interpretation, but allows for the VF. The third utterance requires the VF interpretation.

(28) a. John thinks tha t the telephone is a nuisance.

b. He curses it every day.

c. He doesn 't realize that it is an invention that changed the world.

In these examples, both value-free and value-loaded interpretations are shown to stem

from the same full definite noun phrase.

There appear to be strong constraints on the kinds of transitions that are allowed,

however. In particular, if a g iven ut terance forces either the VF or the VL interpreta-tion, then only this interpretation is possible in the immedia tely subsequent utterance.

However, if some utterance only prefers one interpretation (in a given context), but

allows the other, then the subsequent utterance m ay pick up on either one.

22 Christine Nakatani provided this example, which is far more compel ling than the one originally in

Grosz, Joshi, and Weinstein (1986).

220




For example, the sequence,

(29) a. The Vice-President of the United States is also President of the Senate.

b. He's the President's key man in negotiations with Congress.

in which "he" may be interpreted either VF, or VL, may be followed by either (30) or

(31):

(30) As Ambass ador to China, he handled ma ny tricky negotiations. (VL)

(31) He is requi red to be at least 35 years old. (VF)

However, if we change (29b) to force the value-loaded inte rpretation, as in (26), then

only the value-loaded interpretation (30) is possible. Similarly, if (29b) is changed to

force the value-free interpretation, as in (25b), then only the value-free interpretation

(31) is possible.

Speaker intentions may also enter into the determination of which entities are in

the Cf. The referential uses of descriptions, of which Donnel lan (1966) gives examples,

demonstrate cases in which the "referential intentions" of the speaker in his use of

the desc ription play a role in dete rmining CB(U). For example, consider the fol lowing

sequence:

(32) a. Her husb and is kind to her.

b. No, he isn't. The man you 're referring to isn't her husband.

(33) a. Her husb and is kind to her.

b. He is kind to her but he isn't her husband .

In these examples, 23 the speaker uses a descript ion to refer to something other

than the semantic denotation of that description, i.e. the unique thing that satisfies

the description (if there is one). There are several alternative explanations of suchexamples, involving various accounts of speaker's intentions, mutual belief, and the

like. A complete d iscussion of these issues is bey ond the scope of this paper.

The importance of these cases resides in showing that Cf(U) may include more

than one entity that is realized by a single NP in U. In this case, the noun phrase

"her husband" contributes two individuals, the husband and the lover, to Cf(32a) and

Cf(33a). This can be seen by observing that both discourses seem equal ly appropria te

and that the backward-looking centers of (32b) and (33b) are respectively the husband

and the lover, which are realized by their anaphoric elements.

These examples introduce a number of research issues concerning the represen-

tation and management of the Cb and Cf discourse entities. The account given here

depends on a semantic theory that permits minimal commitment in interpretations.

The open question is which constraints on centers are introduced at which points

during processing. We must leave this as a topic for future work.

23 These examples are from Kripke (1977, p. 21).

221




9 . R e l a t e d W o r k

This theory can be contrasted with two previous research efforts that spurred this

work: Sidner's (1979) original work on immediate focusing and pronouns, and Joshi

and Weinstein's (1981) subsequent work on centering and inferences.

The centering theory discussed here is quite close to Sidner's original theory, bothin attacking local discourse issues and in the general outline of approach. However,

it differs in several details. In Sidner's theory, each utterance provides an immediate

discourse focus, an actor focus, and a set of potential foci. The discourse and actor

foci may coincide, but need not. Her potential foci are roughly analogous to our Cf.

The Cb for an utterance sometimes coincides with her actor focus and sometimes with

her discourse focus. She distinguishes these two to handle various cases of multiple

pronouns. However, as we have shown, utterances do not have multiple Cbs. Further-

more, utterances can have more t han two pronouns, so merely adding a second kind

of immediate focus is of limited use. The difference between these two theories can

be seen from the following example (from Sidner [1979]):

(34) a. I haven' t seen Jeff for several days.

b. Carl thinks he's study ing for his exams,

c. but I think he went to the Cape with Linda.

On Sidner's account, Carl is the actor focus after (34b) and Jeff is the di scourse focus.

Because the actor focus is preferred as the referent of pronominal expressions, Carl is

the leading candidate for the ent ity referred to byhe

in (34c). It is difficult to rule thiscase out w ithout invoking fairly special domain-specific rules. On our account, Jeff is

the CB at (34b) and there is no problem. The type of example Sidner was concerned

about w ould occur if utterance (34c) were replaced by "He thinks he studies too

much." However, the centering rules would still hold in this case. They provide no

constraints on additional pronouns so long as the highest ranked Cf is realized by a

pronoun. However, the rules are incomplete; in particular, as given they do not specify

which p ronoun in a multi pronoun utterance refers to the Cb. The center manag emen t

rules are based solely on the Cb and the highest ranked member of the Cf. As a result,

while there are cases of multiple pronouns for which the theory makes incomplete

predictions, having both an actor and a discourse focus will not handle these cases ingeneral.

Joshi and Kuhn (1979) and Joshi and Weinstein (1981) presented a prel iminary re-

port on their research regarding the connection between the computati onal complexity

of the inferences required to process a discourse and the coherence of that discourse

as assessed by measures that invoke centering phenomena. However, their basic defi-

nitions conflate the centers of an utterance with the linguistic expressions that realize

those centers. In some of their examples it is unclear whether the shift in center or

the particular expression used to realize the center is responsible for differences in

coherence and inference load. Our present work has clarified these differences while

maintaining Joshi and Weinstein's basic focus on the interaction between inferenceload and center management.

Since Grosz, Joshi, and Weinstein (1986) was first circulated a number of re-

searchers have tested and developed aspects of the theo ry presen ted here. 24 This

2 4 O u r l i s t i n g i n t h i s s e c t i o n i s b a s e d o n t h e b e s t i n f o r m a t i o n a v a i l a b l e t o u s . I t i s q u i t e p o s s i b l e t h a t w e

h a v e m i s s e d s o m e r e fe r en c e s . W e w i ll b e g r a t e f u l i f r e a d e r s c o u l d s e n d u s m i s s i n g r e fe r e n ce s .

222



Barb a ra J . Gro sz e t a l. Ce n te r ing

f o l lo w - o n r e s e a r c h c a n b e r o u g h l y g r o u p e d i n a f e w m a i n a r e a s:

• C r o s s - l in g u i s t ic w o r k o n c e n t e ri n g : 25 ( G e r m a n , H e b r e w , I ta l ia n , J a p a n e s e ,

K o r e a n , a n d T u r k is h ): D i E u g e n i o (1 99 0); H o f f m a n a n d T u r a n (1 99 3);

K a m e y a m a ( 19 85 , 19 86 , 1 98 8) ; R a m b o w ( 19 93 ); W a l k e r , I i d a , a n d C o t e

( 1 99 0 , 1 9 94 ); Y o n g k y o o n ( 19 9 1 ); Z i v a n d G r o s z ( 1 99 4 ).

• C e n t e r i n g a l g o r i t h m s : B a l d w i n (1 99 3); B r e n n a n , F r i e d m a n , a n d P o l la r d

( 1 9 8 7 ) ; K e h l e r ( 1 9 9 3 ) ; W a l k e r ( 1 9 8 9 ) ; W a l k e r , I i d a , a n d C o t e ( 1 9 9 4 ) .

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

B r e n n a n (1 99 5); G o r d o n a n d C h a n ( in p r e s s) ; G o r d o n , G r o s z , a n d G i l l i o m

( 1 9 9 3 ) ; G o r d o n a n d S c e a r c e ( 1 9 9 5 ) ; H u d s o n - D ' Z m u r a ( 1 9 8 8 ) ; H u d s o n ,

T a n e n h a u s , a n d D e l l ( 1 9 8 6 ) ; W a l k e r ( 1 9 8 9 ) .

• C e n t e r i n g a n d l i n g u i s t i c re a l i z a ti o n s : 26 C o t e (1 9 92 , 1 99 3) ; H u r e w i t z a n d

L i n s o n (1 99 3); K a m e y a m a ( 19 93 ); N a k a t a n i (1 99 3); P a s s o n n e a u ( in p r e s s,

1 9 9 1 ) ; P r i n c e ( 1 9 9 4 ) ; P r i n c e a n d W a l k e r ( 1 9 9 5 ) ; S u r i a n d M c C o y ( 1 9 9 3 ) ;

T u r a n ( 1 9 9 5 ) ; W a l k e r ( 1 9 8 9 ) .

• C e n t e r i n g , d i a l o g u e , a n d g l o b a l d i s c o u r s e s t ru c t u r e : B r e n n a n '( 1 9 9 5 ) ;

H u r e w i t z a n d L i n s o n ( 1 9 93 ); R o b e r t s ( 1 99 3) ; S p a r c k J o n e s ( 19 93 ); W a l k e r

( 1 9 9 3 ) ; W a l k e r a n d W h i t t a k e r ( 1 9 9 0 ) .

A c k n o w l e d g m e n t s

W e wan t t o t hank Breck Ba ldwin , Fe l i c i aH u r e w i t z , A n d y K e h le r, K a r en L o c h b a u m ,Chr i s t i ne Naka tan i , E l l en P r ince , and LynW a l k e r f o r th e i r v a l u a b l e c o m m e n t s , w h i c hh e l p e d u s i m p r o v e b o t h t h e c o n te n t a n d t h ep r e s e n t a t i o n o f o u r p a p e r . W e a r e a l s og r a t e f u l t o C a r o l y n E l k e n f o r h e l p i n g u sk e e p t r a c k o f t h e v a r i o u s d r a f t s o f t h is p a p e ra n d f o r p r o v i d i n g v a l u a b l e e d i to r i a l h e lp .

P a r t ia l s u p p o r t f o r t h e f ir s t a u t h o r w a sp rov ided by g ran t s NSF IRI -90 -09018 and

IRI-93-08173; the second author wasp a r ti a ll y s u p p o r t e d b y t h e A R O G r a n tDAAL03-89-0031 and ARPA G ran tN00014-90-J-1863.

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