An Application of Inside out Functional Uncertainty to Anaphora Resolution

69

An Application o f

Inside-out Functional Uncertainty

to Anaphora Resolution

K je t il S tra n d U n iv e r s it y o f O s l o D e p a r tm e n t o f L in g u is t ic s P o s t b o k s 1 1 0 2 B L I N D E R N

0 3 1 7 O S L O N O R W A Y

e - m a i l: k je t i l . s t r a n d @ i l f .u i o . n o

Abstract

F o r s o m e t im e n o w , it h a s b e e n k n o w n th a t in u n i f i c a t i o n g r a m m a r s w e c a n u s e

fu n ction al uncertainty t o m o d e l c e r t a i n l i n g u i s t i c

p h e n o m e n a ( K a p l a n a n d Z a e n e n 1 9 8 9 ) . D a l r y m p l e e t a l. ( 1 9 9 0 ) in t r o d u c e d th e n o t io n o f inside-out functional uncertainty, a n d s h o w e d h o w th is c o n c e p t c o u l d a c c o u n t f o r th e d e s c r i p t i o n o f s y n t a c t i c c o n s t r a in t s o n a n a p h o r i c b i n d i n g . S o fa r , h o w e v e r , n o m e t h o d f o r c o m p u t i n g i n s i d e - o u t f u n c t i o n a l u n c e r t a i n t y e q u a t i o n s h a s b e e n d e s c r i b e d in th e lite r a tu r e . T h i s p a p e r p r e s e n t s a n a l g o r i t h m a n d a P r o l o g i m p l e m e n t a t io n f o r th e c o m p u t a t i o n o f a s u b s e t o f e q u a t i o n s i n v o l v i n g in s id e - o u t f u n c t io n a l u n c e r ta in ty . T o illu s tra te th e d e ta ils , th e m e t h o d is a p p l i e d t o r e s o l u t i o n o f t h e N o r w e g i a n l o n g - d i s t a n c e r e f l e x i v e [ s e g ] . P r o l o g is w e l l s u ite d t o m o d e l th e i n s i d e - o u t f u n c t io n a l u n c e r t a in t y in q u e s t i o n , a lt h o u g h it is n o t a f u n c t io n a l p r o g r a m m i n g la n g u a g e . T h e m a in r e a s o n s f o r th is a re th e u s e o f l o g i c a l v a r ia b le s , th e i n h e r e n t s e a r c h i n g b e h a v i o r o f t h e P r o l o g m a c h i n e , a n d t h e b a c k t r a c k in g t o a lte r n a tiv e c o n t in u a t io n s w h i le f a ilin g .

1

Inside-out functional uncertainty

u t t e r a n c e . I f w e p r e s e n t th e f u n c t i o n a l s tr u c tu r e a s a d i r e c t e d g r a p h , it is p o s s i b l e t o r e a c h a ll th e r e le v a n t s y n t a c t ic in f o r m a t io n f o r e a c h p h r a s e in th e u t t e r a n c e v i a th e e d g e s la b e ll e d w it h th e s e g r a m m a t ic a l f u n c t io n s . F o c u s i n g o n l y o n th e f u n c t io n a l i n f o r m a t i o n , a r e p r e s e n t a t io n o f th e s e n t e n c e ( 1 ) w i ll y i e l d a g r a p h lik e that in f ig u r e 1.

(

1)

H a n s i h å p e t at J o n j v i l l e b e S y lv i^ f o r s ø k e å få O la i til å te n k e p å s e g ? .

Hansi hoped that Jonj would ask Sylvia

to try to make Olai think o f himself/herself?

s e g .

F ig . 1: A g r a p h f o r th e s e n t e n c e in ( 1 ) .

In L F G , it is c o n v e n i e n t t o le t th e a r g u m e n t s in th e f u n c t io n a l e q u a t io n s d e n o t e a s e t o f p a t h s o v e r g r a m m a t i c a l f u n c t i o n s . S u c h a s e t c a n b e d e s c r i b e d b y a r e g u l a r e x p r e s s i o n w i t h t h e g r a m m a t i c a l f u n c t i o n s as a lp h a b e t . F u n c t io n a l u n c e r t a in t y h a s b e e n u s e d t o a c c o u n t f o r l o n g d is t a n c e d e p e n d e n c i e s ( K a p l a n a n d Z a e n e n 1 9 8 9 ) , q u a n t if ie r s c o p e ( H a l v o r s e n a n d K a p l a n 1 9 8 8 ) a n d m o d e l l i n g o f s y n t a c t ic c o n s t r a in t s o n a n a p h o r ic b in d in g ( D a l r y m p l e e t a l. 1 9 9 0 , D a lr y m p le 1 9 9 3 ) . In th e la tte r t w o c a s e s , th e n o t io n o f

inside-out functional uncertainty is u s e d . G i v e n a f u n c t io n a l d e s c r i p t io n

o f a s e n t e n c e , w e c a n d r a w a p ic t u r e o f th e b in d in g r e la tio n as in f ig u r e 2 .

Path into binding domain

(pre_path)

Path into

antecedent

(path_in)

Path into

anaphor

(path_out)

F ig . 2 : T h e u n c e r ta in ty p o in t in th e f u n c t io n a l g r a p h

T h e u n c e r t a in t y p o in t in th e g r a p h c a n v a r y f o r th e s a m e a n a p h o r . T h i s d e p e n d s o n th e s y n t a c t ic c o n s t r a in t s o n th e b in d in g d o m a i n . In f ig u r e 1 w e w i l l h a v e m o r e th a n o n e o f t h e s e p o in t s . I f th e p a t h _ o u t is d e s c r i b e d b y a r e g u la r e x p r e s s i o n lik e X C O M P + : ( A D J ) : O B J I O B J 2 I O B L e * , a n d th e to t a l p a t h f r o m th e g l o b a l f - s t r u c t u r e a n d i n t o th e a n a p h o r is C O M P : X C O M P : X C O M P : X C O M P : O B L t h , w e w i l l h a v e t h r e e p o s s i b l e u n c e r t a in t y p o in t s in th is g r a p h . T h e n o t i o n o f f u n c t io n a l u n c e r t a in t y is d u e t o th is v a r i a t io n , a n d th e n o t i o n " i n s i d e - o u t " is d u e t o th e f a c t th a t th e u n c e r ta in ty is r o o t e d at th e f-s tr u c tu r e o f th e a n a p h o r .

2 Descriptions containing

uncertainty equations

D a l r y m p l e e t a l. ( 1 9 9 0 ) p r o p o s e a n e q u a t i o n l i k e ( 2 ) t o m o d e l th e a n a p h o r ic r e la t io n s h ip b e t w e e n a n t e c e d e n t a n d a n a p h o r :

(2)

< a >

( (P a t h O u t T A ) P a th in )

< CT >

T

a

< a > r e p r e s e n t th e m a p p in g b e t w e e n s y n t a x a n d s e m a n t i c s , Ta th e f -

s tr u c tu r e o f th e a n a p h o r , ( P a t h O u t

T

A ) p i c k s o u t th e s e t o f f -s t r u c t u r e s th at c o n t a in th e a n a p h o r a n d in w h i c h th e a n t e c e d e n t m u s t b e l o c a t e d , a n d P a th in c h a r a c t e r i z e s th e s e t o f p o s s i b l e p a t h s i n t o th e a n t e c e d e n t f r o m t h e s e d o m a i n s . T h e e q u a t i o n s h o u l d b e r e a d a s f o l l o w s : T h e r e s h o u l d e x i s t a n f - s tru c tu re b f r o m w h i c h th e r e is a p a th in th e s e t o f s tr in g s P a th O u t l e a d in g t o

Ta , a n d f r o m w h i c h a n a n t e c e d e n t f-s t r u c t u r e

ant is r e a c h a b l e v ia a p a th in

th e s e t o f s tr in g s P a t h in , a n d

ant a n d

T

A s h o u l d m a p t o th e s a m e s e m a n t ic

p r o j e c t i o n . T h e e q u a t i o n c o u l d v e r y w e l l b e s a t i s f i a b le in m o r e th a n o n e w a y , d e p e n d i n g o n th e c h o i c e o f p a th s f r o m th e s e ts P a th O u t a n d P a th in , r e s p e c t i v e l y . B u t th e c o n t r ib u t i o n o f ( 2 ) t o th e g l o b a l f u n c t io n a l d e s c r ip t io n , is th at w e s t ic k t o o n e o f th e s e w a y s in th e f in a l re p r e s e n ta tio n .

In th is p a p e r , I e x p r e s s th e a n a p h o r ic r e la t io n s h ip t h r o u g h u n if ic a t io n o f t h e A G R fe a t u r e s in th e f -s t r u c t u r e . T h e s e A G R f e a t u r e s p r o j e c t f r o m th e l e x i c a l e n t r ie s o f n o m i n a l h e a d s , a n d c o n s i s t in tu rn o f th e i n d e x , g e n d e r , n u m b e r a n d p e r s o n fe a tu r e s .

N o r w e g i a n h a s a r i c h i n v e n t o r y o f r e f l e x i v e s . T h e y c o m p r i s e 1 ) [ s e g s e l v ] , w h i c h h a s t o b e b o u n d t o a s u b j e c t i v e n o u n p h r a s e in th e m in im a l n u c l e u s ( [ + s b ] , [ + n c l ] , in th e L F G t e r m i n o l o g y ( S e l l s 1 9 8 5 ) ) ; 2 ) [ s e g ] , w h i c h h a s t o b e b o u n d t o a s u b j e c t i v e n o u n p h r a s e o u t s i d e th e m in im a l n u c l e u s , b u t i n s i d e th e m in im a l f in it e t e n s e d d o m a i n ( [ + s b ] , [ - n c l ] ) ; a n d 3 ) [ h a m s e l v ] , [h e n n e s e l v ] , [ d e n s e lv ] a n d [ d e t s e l v ] , w h i c h h a v e t o b e b o u n d in th e m i n i m a l c o m p l e t e n u c l e u s , b u t at th e s a m e t im e d i s j o i n t f r o m th e s u b j e c t i v e p h r a s e in th is d o m a i n ( [ - s b ] , [ + n c l ] ) 2 . I f th e P a th O u t f o r [ s e g ] is s t a t e d a s ( G F - C O M P ) + : O B J I O B J 2 I O B L 0 3 , a n d th e P a t h in a s S U B J I P O S S , th e e q u a t i o n in ( 2 ) m a y b e e x p r e s s e d in th e f o l l o w i n g w a y w h e n a p p lie d t o [ s e g ] ;

( 3 ) ( ( ( G F - C O M P ) + : O B J I O B J 2 I O B L e :t ) S U B J I P O S S :A G R ) = ( T : A G R )

B o t h t o m a k e ( 3 ) m o r e r e a d a b l e a n d t o f o r e s e e s o m e o f t h e i m p l e m e n t a t io n a l m a t t e r s , I d i v i d e ( 3 ) i n t o a c o n j u c t i o n o f e q u a t i o n s . T o a c h i e v e t h is , w e i n t r o d u c e e x is t e n t ia l q u a n t if i e d v a r ia b le s r a n g in g o v e r f - s tr u c tu r e s . T h e e q u a t io n in ( 3 ) w i l l th u s b e t r a n s p o s e d t o th e th r e e e q u a t io n s in ( 4 ) , w h e r e

b a n d

ant a re e x is t e n t ia lly b o u n d f-s tr u c tu r e v a r ia b le s .

( 4 )

b : ( G F -

C O M P ) + : O B J I O B J 2 I O B L g =

T

b : S U B J I P O S S

=

ant

a n t: A G R

=

T

: A G R

T h e r e s o l u t i o n p r o c e s s a m o u n t s t o in s t a n t ia t in g th e i n d e x v a lu e o f th e a n a p h o r ( o r o f s h a r in g th e v a r i a b le i n d e x w it h th e a n t e c e d e n t ) . R e f l e x i v e s a re a ls o o f t e n u n d e r s p e c if ie d r e g a r d in g th e o t h e r m o r p h o s y n t a c t ic fe a tu r e s in t h e A G R f e a t u r e ( e . g . , [ s e g ] is u n d e r s p e c i f i e d w i t h r e s p e c t t o s y n t a c t i c g e n d e r a n d n u m b e r ) . U n i f i c a t i o n o f th e A G R f e a t u r e s w i l l th u s , u n d e r n o r m a l c i r c u m s t a n c e s , a d d i n f o r m a t i o n t o th e l in g u i s t i c d e s c r i p t i o n o f th e a n a p h o r ic p h r a s e , in a d d it io n t o th e in d e x fe a tu r e .

^ T h is a n a lysis o f the N o rw e g ia n an ap hors has been q u e stio n e d , e .g ., b y L ød ru p (1 9 8 5 ). In this p a per I w ill stick to the an alysis g iv en by S ells (1 9 8 5 ). T h e parts o f this

analysis relevant fo r the im plem entation d escrib ed here, is a lso supported b y H ellan (1 9 8 8 ) and D a lrym p le (1 9 9 3 ).

U n d e r th e l e x ic a l e n tr y f o r [ s e g ] is a ls o in s e r te d th e c o n s t r a in t in (5)'*:

( 5 )

( ant :G F *

=

T

)

T h e " n o n c o n t a i n m e n t c o n d i t i o n " in ( 5 ) s a y s th a t n o p a th ( i n c l u d i n g th e n u ll p a th , i . e . , i d e n t i t y ) e x i s t s b e t w e e n th e a n t e c e d e n t a n d th e a n a p h o r f - s t r u c t u r e s . T h i s e n s u r e s th e f ir s t r e q u ir e m e n t o f f-co m m a n d : " F o r a n y

o c c u r r e n c e s o f th e f u n c t i o n s a , P , in a n f -s t r u c t u r e F , a

f-com m an d s p i f

a n d o n l y i f a d o e s n o t c o n t a i n P a n d e v e r y f -s t r u c t u r e o f F th a t c o n t a i n s a

c o n t a i n s P " ( B r e s n a n 1 9 8 2 ; 3 3 4 ) . T h e P a th in in th e s e c o n d l in e o f ( 4 ) is th e d is ju n c t i o n S U B J I P O S S , w h i c h m e a n s th at th is p a th h a s le n g t h o n e . T h i s e n s u r e s th e o t h e r r e q u ir e m e n t o f f - c o m m a n d ( D a l r y m p l e 1 9 9 3 ; 1 5 6 ).

T h e p r o b l e m w it h ( 5 ) is th a t it i n v o l v e s

universal q u a n t i f i c a t i o n o v e r

p a th s in th e s e t o f s t r in g s G F * . T h i s is th e e f f e c t o f n e g a t in g a n e q u a t i o n i n v o l v i n g f u n c t i o n a l u n c e r t a in t y ( D a l r y m p l e 1 9 9 3 ; 1 2 3 ) . S u c h e q u a t i o n s o n l y m a k e s e n s e i f r e la t e d t o c o m p l e t e d f - s t r u c t u r e s , w h e r e t h e y w i l l b e e v a lu a t e d a s tr u e o r n o t. T h i s is a c c o u n t e d f o r in L F G b y tr e a tin g n e g a t io n n o n c o n s t r u c t i v e l y ( K a p l a n a n d B r e s n a n 1 9 8 2 ; 2 1 0 , D a l r y m p l e 1 9 9 3 ; 1 2 3 ). T h e la s t e q u a t i o n is th u s o n l y

co n stra in in g ,

i . e . , it w i l l b e c h e c k e d f o r s a t is fa c t io n in a c o m p l e t e a n d c o h e r e n t f-s tr u c tu re .

T h e e q u a t io n s in ( 4 ) a n d ( 5 ) h a v e t o b e fu r th e r e l a b o r a t e d t o a c c o u n t f o r a ll th e s y n t a c t ic c o n s t r a in t s o n a n a p h o r ic b i n d i n g .T h e [ + s b ] a n a p h o r s m u s t b e b o u n d in s id e th e m in im a l t e n s e d d o m a in . T h i s m e a n s th at n o in t e r v e n in g f -s t r u c t u r e in th e P a t h O u t s h o u l d c o n t a i n th e f e a t u r e T E N S E . T h i s c a n b e e x p r e s s e d in th e f o l l o w i n g w a y 5;

(6)

[

in t: G F +

=

T

b : G F +

=

int

in t-T E N S E

_]

T h e [ - n c l ] f e a t u r e s ta t e s th a t a ll n o n - r e f l e x i v e a r g u m e n t s i n s i d e th e m i n im a l n u c l e u s s h o u l d b e d i s j o i n t f r o m th e a n a p h o r in q u e s t i o n . A s ( 7 ) s h o w s , it is p e r f e c t l y p o s s i b l e f o r th e [ - n c l ] a n a p h o r [ s e g ] t o c o r e f e r w i t h a

reflexive a r g u m e n t in s id e th e m in im a l n u c le u s :

^ T h e con strain ts in ( 5 ) and ( 6 ) are assu m ed to b e e x p re s s e d as c o n ju n c t s to the existential quantified constraints in (4 ), s o the variables a n t and b w ill b e p rop erly b ou n d .

^ D a lrym p le (1 9 9 3 ; 136) uses the fo llo w in g notation to ex p ress the constrain t in (6 ):

( (D o m a in P a t h G F t ) A n t e c e d e n t P a t h )o = t g ( - > T E N S E )

(7 )

M a r t in i b a o s s s n a k k e til s e g j o m [ s e g s e lv ] i /s e g j.

Martini asked us to talk to himi about himself

T h e m i n i m a l n u c l e u s is th e m i n im a l f - s t r u c t u r e c o n t a i n i n g b o t h th e a n a p h o r a n d a fe a tu r e P R E D , th at is , n o in t e r v e n in g f-s t r u c t u r e b e t w e e n th is f - s t r u c t u r e a n d th e a n a p h o r s h o u l d c o n t a i n P R E D . In th is d o m a i n a ll th e n o n - r e f l e x i v e c o - a r g u m e n t i n g f - s t r u c t u r e s s h o u l d h a v e a n i n d e x d i s jo i n t f r o m th e i n d e x o f th e a n a p h o r . T h i s s o - c a l l e d

co-argum ent disjointness

condition c a n b e s ta ted w ith th e h e lp o f a c o n s tr a in t lik e that in ( 6 ) .

The inside-out algorithm

K a p l a n a n d M a x w e l l ( 1 9 8 8 ) s h o w e d th a t th e v e r i f i c a t i o n p r o b l e m f o r e q u a t i o n s c o n t a i n i n g o u t s id e - i n f u n c t io n a l u n c e r t a in t y w a s tr iv ia l, w h i le th e s a t i s f i a b i l i t y p r o b l e m w a s d e c i d a b l e in th e a c y c l i c c a s e . W h e t h e r th e s e r e s u lt s h o l d a l s o f o r e q u a t i o n s i n v o l v i n g i n s i d e - o u t u n c e r t a i n t y , is n o t o b v i o u s . I m a g i n e , f o r in s t a n c e , th e c a s e w h e r e a n e q u a t i o n e n a b le s u s t o b u i l d e v e r m o r e c o m p r e h e n s i v e f-s t r u c t u r e s b y a d d in g A D J o n o u r w a y o u t. T h i s c a n c e l s th e p r o p e r t y o f

rootedness w h i c h is u s u a lly p r e s u p p o s e d f o r

l in g u i s t i c d e s c r ip t io n s .

In th e a p p l i c a t i o n c o n s i d e r e d in th is p a p e r , h o w e v e r , th is p r o b l e m n e e d n o t a r i s e . T h i s w i l l b e e v i d e n t b y a c l o s e r i n s p e c t i o n o f th e e q u a t i o n s c o m p r i s i n g i n s i d e - o u t f u n c t io n a l u n c e r t a in t y , a n d in p a r t ic u la r th e fir s t t w o e q u a t i o n s in

(4).

N o n e o f t h e s e e q u a t i o n s c o u l d b e

d efin in g ,

u s in g th e L E G t e r m i n o l o g y , in th at th e y a l l o w in f o r m a t io n t o b e a d d e d in a m o n o t o n i c w a y d u r i n g c o n s t r u c t i o n t im e . T h e a n t e c e d e n t

ant f o r a n in t r a s e n te n tia l

a n a p h o r a lw a y s h a s t o b e r e a l iz e d b y o t h e r m e a n s in th e g l o b a l f -s t r u c t u r e , e it h e r a s a n e l e m e n t s u b c a t e g o r i z e d f o r b y a n e x i s t in g P R E D , o r o t h e r w is e r e a liz e d in te r m s o f a p r o je c t i o n f r o m th e c -s tr u c tu r e . T h is is a ls o th e c a s e f o r th e f - s t r u c t u r e r e p r e s e n t in g th e b i n d i n g d o m a i n

b, a n d f o r a ll g r a m m a t ic a l

f u n c t io n s in P a th O u t a n d P a th in . O n l y th e th ir d e q u a t io n in

(4),

u n if y i n g th e A G R f e a t u r e s , a d d s i n f o r m a t i o n , in th a t th e a n a p h o r is a t t a c h e d w it h its a n t e c e d e n t b y s h a r in g o f i n d e x v a lu e s . T h u s o n l y th e la tte r e q u a t i o n is d e f i n i n g in th e L E G s e n s e . T h e c o n s e q u e n c e o f th is a r g u m e n t, is that w e c a n tr e a t t h e i n s i d e - o u t u n c e r t a i n t ie s w i t h r e s p e c t t o th e f in a l c o h e r e n t a n d c o m p l e t e f - s t r u c t u r e f o r th e s e n t e n c e a s a w h o l e . E o r th is a p p li c a t i o n w e o n l y h a v e t o c o n s i d e r t h e g r a m m a t i c a l f u n c t i o n s in t h e f in a l g l o b a l r e p r e s e n t a t io n as c a n d id a t e s f o r p o s s i b l e s te p s in th e u n c e r ta in ty p a th s.

T h e a l g o r i t h m is c a l l e d l O , a s it is b a s e d u p o n a t r u e , " i n s i d e - o u t " r e c u r s iv e tr a v e r s a l o f a f in it e g r a p h . In p u t t o th e a lg o r it h m a re th e g l o b a l f - s t r u c t u r e E S , th e f -s t r u c t u r e f o r th e a n a p h o r ic e l e m e n t ana a n d th e r e g u la r e x p r e s s i o n

r e g _ e x p

d e s c r i b i n g th e P a t h O u t f r o m

ana t o th e p o s s i b l e

b i n d i n g d o m a i n s . W e s ta rt b y a s s i g n i n g F S t o th e v a r i a b l e p a r a m e t e r

f s t r u c . T h e n w e t r a v e r s e in t o a n a , o n e s te p ig f ) at th e t im e . A t e a c h s te p

g f w e in s ta n tia te th e c o r r e s p o n d i n g p a r t o f p a t h b y c o n c a t e n a t i n g g f in f r o n t o f th e v a r i a b l e p a t h r e s t . O n e a c h c o r r e s p o n d i n g s t e p d u r i n g w it h d r a w a l w e c h e c k f o r a m a t c h b e t w e e n r e g j e x p a n d p a t h , a n d tr y t o r e s o l v e th e a n a p h o r i f w e h a v e a m a t c h . O u t p u t is e it h e r s u c c e s s , w it h th e A G R fe a tu r e o f an a u n if ie d w it h th e a n t e c e d e n t , o r fa ilu r e .

A b o v e , w e s ta te d th a t r e g j e x p in th e [ s e g ] c a s e c o u l d b e d e s c r i b e d b y th e r e g u la r e x p r e s s i o n ( G F - C O M P ) '* ' : O B J I O B J 2 I O B L g . O n l y f - s t r u c t u r e s at th is " d i s t a n c e " f r o m a n a s h o u l d b e t a k e n i n t o a c c o u n t as p o s s i b l e b in d in g d o m a i n s . I f s o m e s u f f i x o f p a th s a t is fie s th is d e s c r i p t io n at a ll, w e w i l l b e in o n e o f t h r e e s it u a t io n s o n o u r w a y o u t o f th e g r a p h , sta rtin g f r o m an a at th e in n e r m o s t le v e l:

1 ) W e h a v e n o t r e a c h e d th e v a r ia b le p o in t in th e g r a p h w h e r e p a th m a t c h e s r e g j e x p . In th is c a s e p a th s h o u l d b e a s u f f i x o f

r e g j e x p . ( e .g ., p a t h

= O B L t h ) .

2 ) W e h a v e a s it u a t io n w h e r e p a th m a t c h e s r e g j e x p .

ie .g ., p a th = X C O M P : X C O M P : O B L t h ) .

3 ) W e h a v e p a s s e d th e v a r ia b le p o in t w h e r e p a th m a t c h e s r e g j e x p .

{ t .g .,p a t h = C O M P : X C O M P : X C O M P : X C O M P : O B L t h ) .

T h e s e th re e s itu a tio n s c a n b e illu s tr a te d as in f ig u r e 3 :

3. Pre_path

2. Matching

1. Not yet matching

FS

A N A

F ig . 3 : T h e th re e p o s s i b l e s itu a tio n s

T h e m a t c h in g p r o c e s s c a n b e d o n e o n e a c h l e v e l w h i le w it h d r a w in g in th e r e c u r s i o n . T o k e e p t r a c k o f w h i c h o f th e t h r e e s it u a t io n s w e a r e in , w e i n t r o d u c e t w o f l a g s : m a t c h ? a n d r e s o l v e d ? . T h e s e f l a g s c a n b e in o n e o f t w o s ta te s:

true

o r

false.

I n it ia lly , a n d in s it u a t io n 1 a b o v e , t h e y a r e b o t h

N o w w e a re in a p o s i t i o n t o d e s c r i b e th e a lg o r it h m :

l O 1. [ W e h a v e r e a c h e d th e a n a p h o r ]

I f f s t r u c is i d e n t ic a l w it h a n a , te r m in a te w it h p a th s e t t o th e e m p t y p ath .

l O 2 . [ S e a r c h a s te p fu r th e r d o w n in th e f-s tr u c tu r e ]

F o l l o w a g r a m m a t ic a l f u n c t i o n g f f r o m f s t r u c . C a ll th e f - s tr u c tu r e w h i c h g /" p i c k s o u t f o r te m p . S e t p a th t o th e c o n c a t e n a t i o n o f g f a n d th e v a r ia b le p a t h _ r e s t a n d c a l l l O r e c u r s i v e l y w it h te m p a n d p a t h _ r e s t , a n d th e o t h e r p a r a m e te r s u n c h a n g e d . L e t u s a s s u m e that w e s e e k d e p th fir s t. I f f s t r u c c o n t a i n s n o g r a m m a t ic a l f u n c t io n , c o n t i n u e in th e la st p o s s i b l e a lte r n a tiv e c o n t in u a t io n . E v e n tu a lly w e w i l l r e a c h th e a n a p h o r an a .

O n e a c h le v e l o n th e w a y b a c k in th e r e c u r s io n w e d o th e f o l l o w i n g :

a ) I f r e s o l v e d ? is

true,

t e r m in a t e w it h s u c c e s s . b ) M a k e a r e s o lu t io n try i f

1)

th e f l a g r e s o l v e d ? is

false

a n d

2 ) w e a re in a le g a l b in d in g d o m a in (th e re is a m a t c h b e t w e e n p a th a n d r e g j e x p , a n d

m a t c h ? is s e t t o

true)

I f th e r e s o l u t i o n s u c c e e d s , s e t r e s o l v e d ? t o

true.

In a n y c a s e , te r m in a te w it h s u c c e s s ( i f r e s o lu t io n fa ils o n th is l e v e l , w e s h o u ld a n y w a y try o n a h ig h e r l e v e l) .

c ) I f m a t c h ? is

true,

a n d w e d o n 't h a v e a m a t c h b e t w e e n p a th a n d r e g j e x p , t e r m in a te w it h f a ilu r e ( w e a re in s itu a tio n 3 a b o v e , a n d h a v e n o t s u c c e e d e d in r e s o lu t io n o f th e a n a p h o r in s id e th e le g a l b in d in g d o m a i n ) .

d ) O t h e r w is e , i f p a th is a s u f f i x o f r e g j e x p , te r m in a te w it h s u c c e s s .

( B o t h r e s o l v e d ? a n d m a t c h ? a re

false.

T h i s m e a n s th at w e h a v e n o t y e t r e a c h e d a le g a l b in d in g d o m a i n o n o u r w a y o u t )

e ) O t h e r w is e , te r m in a te w it h fa ilu r e . ( N o s u f f ix o f th is p a th b e t w e e n F S a n d a n a w i l l e v e r s a tis fy

o r n o t . O n c e in s t a n t ia t e d t o

true,

a f l a g w i l l k e e p th is v a lu e in th e a c tu a l e n v ir o n m e n t .

5

The Prolog code

T h e p r o g r a m c o n s i s t s o f t w o p r e d i c a t e s : i n s i d e _ o u t / 6 a n d c h e c k / 6 . I n s i d e _ o u t /6 h a s t w o e n tr ie s , w h i le c h e c k / 6 h a s th re e e n trie s . T h e a rg u m e n ts in b o t h c a s e s c o m e in th is o r d e r : fs tr u c , a n a ,p a th , r e g _ e x p , m a tc h ?,

r e s o l v e d ? .

in sid e _ o u t(A n a , A n a , [], R e g E x p , M atch , R e s o l v e d ) !.

in sid e _ o u t(F S , A n a , [G F I Path], R e g E x p , M atch , R e s o lv e d )

fo llo w (F S , G F , T e m p ),

in sid e _ o u t(T e m p , A n a , Path, R e g E x p , M atch , R e s o lv e d ),

ch e c k (F S , A n a , [G F I Path], R e g E x p , M atch , R e s o lv e d ).

T h e f l a g s ( a n d th e r e s o l u t i o n o f th e a n a p h o r ) a re h a n d le d i n s i d e th e c h e c k / 6 g o a l . I f R e s o l v e d is s e t t o

true

o n a n e a r lie r l e v e l , w e c o n t i n u e to w it h d r a w :

c h e c k (_ , _ , _ , _ , _ , R e s o l v e d ) n o n v a r ( R e s o l v e d ) , !.

W e a r e in s it u a t io n 2 : W e h a v e a m a t c h b e t w e e n P a th a n d R e g E x p . W e s e t M a t c h t o

true,

a n d try t o r e s o l v e th e a n a p h o r . I f r e s o l u t io n s u c c e e d s o n th is l e v e l . R e s o l v e d is s e t t o

true,

o t h e r w i s e it r e m a in s a v a r ia b le . In a n y c a s e , th e g o a l w i l l s u c c e e d , s o w e c a n c o n t in u e t o w it h d r a w :

c h e c k (F S , A n a , Path, R e g E x p , M atch , R e s o lv e d )

m atch(Path, R e g E x p ),

M atch = true,

re so lv e (F S , A n a, Path, R e s o lv e d ).

W e a re in s itu a tio n 1: B o t h R e s o l v e d a n d M a t c h a re v a r ia b le s , a n d w e d o n o t h a v e a m a t c h y e t . T h e P a th s o f a r is a s u f f i x o f o n e o f th e d e s c r i b e d p a th s in R e g E x p . T h e c h e c k / 6 g o a l s u c c e e d s , a n d w e c o n t in u e t o w it h d r a w :

c h e c k (_ , _ , Path, R e g E x p , M atch , _ )

vaifM atch ),

su ffix(P a th , R e g E x p ).

th e c o n t i n u a t i o n in s id e e n t r y 2 , w h e r e R e s o l v e d r e m a in s a v a r ia b le . O n th e s u c c e s s i v e l e v e ls , e n try 2 w i l l b e e v o k e d a s l o n g as w e h a v e a m a tc h .

I f w e r e a c h s it u a t io n 3 w i t h o u t a n y r e s o l u t i o n ( M a t c h is

tr u e ,

a n d R e s o l v e d is s t ill a v a r i a b l e ) c h e c k / 6 f a i ls o n th is l e v e l , a n d d u e t o t h is , i n s i d e _ o u t /6 fa ils o n th e s a m e l e v e l.

I f w e r e a c h a s itu a tio n w h e r e b o t h R e s o l v e d a n d M a t c h a re s till v a r ia b le s , a n d P a th n e it h e r m a t c h e s R e g E x p n o r a s u f f i x o f R e g E x p , c h e c k / 6 f a i ls im m e d ia te ly .

T o g i v e a f l a v o r o f th e a p p r o a c h t a k e n , I i n c l u d e a n e x a m p l e o f th e r e s o l v e /4 g o a l in th e [ s e g ] c a s e :

resolv e(F S , A n a , _ , R e s o lv e d )

(fo llo w (F S , su bj. A n t); fo llo w (F S , p o s s. A n t)),

n ot(contain ed(A n a, A n t)),

A n t : agr = = A n a : agr.

R e s o lv e d = true.

re s o lv e (_ , _ , _ , _ ).

T h e f - c o m m a n d r e s tr ic tio n is g u a r a n te e d b y th e fir s t t w o lin e s : In lin e o n e w e f o l l o w a p a th o f le n g t h o n e

(subj

o r

poss)

t o i d e n t i f y th e f - s t r u c t u r e o f th e a n t e c e d e n t ( A n t ) , a n d in l in e t w o th e g o a l fa ils i f A n a is c o n t a i n e d in ( o r id e n t i c a l t o ) A n t . R e s o l u t i o n a m o u n t s t o u n i f i c a t i o n o f th e A G R fe a t u r e s , a n d i f a ll th e s e g o a l s s u c c e e d . R e s o l v e d is s e t t o

true.

I f a n y o f th e g o a l s f a ils , th e s e c o n d e n t r y f o r r e s o l v e / 4 s u c c e e d s , a n d th e R e s o l v e f la g r e m a in s a P r o l o g v a r ia b le .

6

Conclusion

7

Acknowledgements

I a m g r a t e f u l t o M a r y D a l r y m p l e f o r s t im u la t in g d i s c u s s io n s a n d h e lp f u l c o m m e n t s o n a n e a r l ie r v e r s i o n o f th is p a p e r . I w o u l d p a r t ic u la r ly l ik e t o th a n k J a n T o r e L ø n n i n g f o r e x t e n s i v e a n d v e r y h e l p f u l d i s c u s s i o n o f th e i s s u e s p r e s e n t e d h e r e . I o f c o u r s e ta k e r e s p o n s i b i l i t y f o r a ll f l a w s in th e r e a s o n in g , e r r o r s o r c o n f u s i o n s in th e p a p e r .

8

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Control and Complementation. In J o a n B r e s n a n ( E d .) :

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Long-distance Dependencies,

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K r o c h , A . ( E d s . ) : A lt e r n a t iv e C o n c e p t i o n s o f P h r a s e S tr u c tu r e . C h i c a g o U n i v e r s i t y P r e s s , ( p p . 1 7 - 4 2 ) .

L ø d r u p , H e l g e 1 9 8 5 :

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a n d seg

selv). In S k r if t s e r ie N o . 2 1 , U n iv e r s it y o f B e r g e n .