A Model for Preference

A MODEL FOR PREFERENCE

D o m i n i q u e P e t i t p i e r r e

I S S C O

U n i v e r s i t y of G e n e v a 54 r o u t e des A c a c i a s C H - 1 2 2 7 Geneva, S w i t z e r l a n d

S t e v e n K r a u w e r L o u i s d e s T o m b e

I n s t i t u u t v o o r A l g e m e n e T a a l w e t e n s c h a p R i j k s u n i v e r s i t e i t U t r e c h t

T r a n s 14

3512 J K Utrecht, The N e t h e r l a n d s

D o u g A r n o l d

C e n t r e for C o g n i t i v e S t u d i e s U n i v e r s i t y of E s s e x Colchester, CO4 3SQ, E n g l a n d

G i o v a n n i B. V a r i l e

DG XIII, B a t i m e n t J e a n M o n n e t C o m m i s s i o n of the E u r o p e a n c o m m u n i t i e s

P.O. Box 1907, L u x e m b o u r g , L u x e m b o u r g

Abstract

In t h i s p a p e r w e a d d r e s s the p r o b l e m of c h o o s i n g t h e b e s t solution(s) from a set of i n t e r p r e t a t i o n s of t h e same o b j e c t (in our c a s e a s e g m e n t of text). A n o t i o n of p r e f e r e n c e is stated, b a s e d on p a i r w i s e c o m p a r i s o n s of c o m p l e t e i n t e r p r e t a t i o n s in o r d e r to o b t a i n a p a r t i a l o r d e r a m o n g the c o m p e t i n g i n t e r p r e t a t i o n s . A n e x p e r i m e n t a l i m p l e m e n t a t i o n is d e s c r i b e d , w h i c h u s e s P r o l o g - l i k e p r e f e r e n c e statements.

1.

Introduction

In t h i s p a p e r we a d d r e s s the p r o b l e m of c h o o s i n g the b e s t solution(s) from a set of i n t e r p r e t a t i o n s of the same t e x t seg- m e n t (For the sake of brevity, t h r o u g h o u t this t e x t w e u s e the t e r m i n t e r p r e t a t i o n , w h e r e in fact w e s h o u l d w r i t e r e p r e s e n t a - tion of an i n t e r p r e t a t i o n ) . A l t h o u g h d e v e l o p e d in the c o n t e x t of a m a c h i n e t r a n s l a t i o n s y s t e m (the E u r o t r a project, A r n o l d 1986, A r n o l d and des T o m b e 1987), we b e l i e v e t h a t our a p p r o a c h is s u i t e d to m a n y o t h e r f i e l d s of c o m p u t a t i o n a l

l i n g u i s t i c s and e v e n o u t s i d e (pattern r e c o g n i t i o n , etc.).

A f t e r a b r i e f o v e r v i e w of the p r o b l e m (section 2), w e s u g g e s t a g e n e r a l m e t h o d to deal w i t h p r e f e r e n c e (section 3) and t h e n d e s c r i b e a p o s s i b l e i m p l e m e n t a t i o n

(section 4). A n a p p e n d i x g i v e s a c t u a l e x a m p l e s of p r e f e r e n c e s t a t e m e n t s .

2.

What is preference?

In t h e c o m p u t a t i o n a l l i n g u i s t i c s literature, the t e r m 'preference' has b e e n u s e d in d i f f e r e n t contexts. W e shall m e n - t i o n a few, s e l e c t i v e l y , (in s e c t i o n 2.1 w h i c h m a y b e skipped) and t h e n s t a t e our

own v i e w (in s e c t i o n 2.2).

2.1.

Various approaches

w h e r e p r e f e r e n c e is p a r t of the p a r t i c u l a r c o m p u t a t i o n b e i n g p e r f o r m e d (Wilks 1973, Fass and W i l k s 1983, P e r e i r a 1985) f r o m the c a s e w h e r e it is a s e p a r a t e process, run a f t e r the r e s u l t s of t h e c o m p u t a t i o n have b e e n o b t a i n e d (Jensen et al 1983, W e i s c h e d e l a n d S o n d h e i m e r 1983).

A f r e q u e n t a p p r o a c h to p r e f e r e n c e is scoring. A n u m e r i c s c o r e is c a l c u l a t e d , i n d e p e n d e n t l y , for e a c h c o m p e t i n g i n t e r p r e t a t i o n a n d is t h e n u s e d to r a n k the i n t e r p r e t a t i o n s . T h e b e s t i n t e r p r e t a - t i o n s are t h e n chosen. T h e s c o r e c a n b e the n u m b e r of c o n s t r a i n t s s a t i s f i e d b y t h e i n t e r p r e t a t i o n (Wilks 1973, Fass & W i l k s 1983), w h e r e t h e s e c o n s t r a i n t s m i g h t be a s s i g n e d r e l a t i v e w e i g h t s b y t h e l i n g u i s t (Robinson 1982, C h a r n i a k 1983, B e n n e t t a n d S l o c u m 1985) or c a l c u l a t e d b y t h e c o m p u t e r (Papegaaij 1986). S u c h t e c h n i q u e s h a v e b e e n u s e d e x t e n s i v e l y for s p e e c h r e c o g n i - t i o n (Paxton 1977, W a l k e r et al 1978) and in the field of e x p e r t s y s t e m s (such as Mycin, B u c h a n a n & S h o r t l i f f e 1984), w h e r e the c a l c u l a t i o n of b o t h s c o r e and r a n k i n g b e c o m e q u i t e c o m p l e x w i t h p r o b a b i l i t i e s and t h r e s h o l d s .

T h e p r o b l e m w i t h s c o r i n g is t h a t it seems q u i t e u n n a t u r a l for a l i n g u i s t to a s s o c i a t e a s c o r e (or w e i g h t or p r o b a b i l - ity) to a p a r t i c u l a r r u l e or p i e c e of d a t a w h e n the k n o w l e d g e b e i n g e n c o d e d is in fact q u a l i t a t i v e . F u r t h e r m o r e , c o m b i n i n g the s c o r e s b a s e d o n d i f f e r e n t t y p e s of r e a s o n i n g to c a l c u l a t e a g l o b a l s c o r e for a r e p r e s e n t a t i o n s e e m s a r a t h e r a r b i t r a r y p r o c e d u r e . S u c h a u n i f o r m metric, e v e n if it c a n m o d e l a c t u a l l i n g u i s t i c k n o w l e d g e , forces t h e g r a m m a r w r i t e r to j u g g l e w i t h n u m b e r s to g e t t h e b e h a v i o u r he wants, thus m a k i n g t h e p r e f e r e n c e p r o c e s s obscure.

A f u r t h e r d i s a d v a n t a g e of this a p p r o a c h is t h a t t h e s c o r e is o f t e n b a s e d on t h e w a y i n t e r p r e t a t i o n s are built, r a t h e r t h a n on the p r o p e r t i e s of t h e i n t e r p r e t a t i o n s t h e m s e l v e s .

P r e f e r e n c e is a l s o m e n t i o n e d in a l i n g u i s t i c c o n t r o v e r s y s t a r t e d by F r a z i e r and F o d o r (1979) w i t h t h e i r p r i n c i p l e s of r i g h t a s s o c i a t i o n and m i n i m a l a t t a c h m e n t (Schubert 1984). T h e r e t h e p r o b l e m is to d i s a m b i g u a t e m a n y r e a d i n g s (or i n t e r p r e t a - tions) of a s e n t e n c e in o r d e r to find the g o o d (preferred) one(s). V a r i o u s c o n t r i b u - t i o n s on t h a t issue h a v e in c o m m o n t h a t b a d i n t e r p r e t a t i o n s a r e a b a n d o n e d b e f o r e b e i n g finished, d u r i n g c o m p u t a t i o n (Shieber 1983, P e r e i r a 1985). A l t h o u g h this m e t h o d s p e e d s up t h e c o m p u t a t i o n , t h e r e is a r i s k t h a t a p o s s i b l i t y w i l l be a b a n d o n e d t o o early, b e f o r e t h e r e l e v a n t i n f o r m a t i o n h a s b e e n found. T h i s is s h o w n by W i l k s et al (1985) w h o c l a i m to h a v e the ideal s o l u t i o n in P r e f e r e n c e S e m a n - tics, w h i c h u s e s as p a r t of its c o m p u t a - tion s c o r i n g and ranking.

2.2.

Our notion of preference

O u r a p p r o a c h , a l t h o u g h s t e m m i n g f r o m e a r l i e r w o r k in t h e E u r o t r a p r o j e c t (McNaught et al 1983, J o h n s o n et al 1985), is, w e b e l i e v e , n e w a n d original.

W e m a k e t h e f o l l o w i n g a s s u m p t i o n s : i the r e l a t i o n ' t r a n s l a t i o n of' b e t w e e n

t e x t s as e s t a b l i s h e d b y a m a c h i n e t r a n s l a t i o n s y s t e m h a s to be one to one

(1-1)?

ii T h e r e is a p r i o r i no formal or l i n g u i s - tic g u a r a n t e e t h a t t h i s w i l l b e the c a s e for t h e r e l a t i o n as a w h o l e or for the t r a n s l a t i o n s t e p s b e t w e e n i n t e r - m e d i a t e l e v e l s of r e p r e s e n t a t i o n . (An a t t e m p t to f o r m a l i z e t h i s c a n be f o u n d in K r a u w e r a n d d e s T o m b e 1984 or in s e c t i o n 4 of J o h n s o n et al 1985).

T h e p r o b l e m w e w a n t to a d d r e s s h e r e is t h e following:

G i v e n t h e fact t h a t one to m a n y (l-n) t r a n s l a t i o n s do occur, h o w do w e e n s u r e t h a t t h e final r e s u l t is still I-1.

T h i s p r o b l e m is n o t r e s t r i c t e d to m a c h i n e t r a n s l a t i o n :

O f t e n a p r o g r a m (for e x a m p l e a p a r s e r or a t e x t g e n e r a t o r ) p r o d u c e s m a n y i n t e r p r e t a - t i o n s of t h e s a m e o b j e c t (usually a t e x t segment) w h e n in t h e ideal c a s e o n l y one is wanted. In t h e f o l l o w i n g w e r e f e r to a 'l-n t r a n s l a t i o n ' for t h i s g e n e r a l p h e n o m e n o n .

W e see t w o t y p e s of s o l u t i o n s to this problem, e a c h of t h e m a p p l i c a b l e to s p e c i f i c c l a s s e s of cases:

i S p u r i o u s r e s u l t s c a n b e e l i m i n a t e d on t h e b a s i s of t h e i r o w n i n d i v i d u a l p r o - p e r t i e s (e.g. w e l l - f o r m e d n e s s , c o m - p l e t e n e s s ) ; for t h i s w e w i l l u s e the t e r m 'filtering'.

ii S p u r i o u s r e s u l t s c a n be e l i m i n a t e d v i a c o m p a r i s o n of c o m p e t i n g r e p r e s e n t a - tions, w h e r e o n l y t h e b e s t one(s) w i l l h a v e t h e r i g h t to survive; for this w e w i l l u s e t h e t e r m 'preference'.

T h e r e are t w o m a i n t y p e s of l-n -ness: i l i n g u i s t i c a l l y m o t i v a t e d (i.e. real

a m b i g u i t y in analysis, or t r u e s y n o n y m y in g e n e r a t i o n ) .

ii a c c i d e n t a l , c a u s e d b y o v e r g e n e r a t i o n of the d e s c r i p t i v e d e v i c e s t h a t d e f i n e t h e r e s u l t i n g (or i n t e r m e d i a t e ) i n t e r p r e t a - tions.

N o t e t h a t o v e r g e n e r a t i o n a n d a m b i g u i t y or s y n o n y m y m a y h i d e c a s e s of u n d e r g e n e r a t i o n

(cf t h e r o b u s t n e s s p r o b l e m ) .

W e d e f i n e t h e a p p l i c a t i o n of p r e f e r e n c e as t h e s e l e c t i o n of t h e b e s t element(s) f r o m a set of c o m p e t i n g i n t e r p r e t a t i o n s of t h e s a m e object.

A c c o r d i n g to t h i s d e f i n i t i o n t h e s c o r - ing a n d r a n k i n g m e c h a n i s m d e s c r i b e d in t h e p r e v i o u s s e c t i o n is a c a s e of p r e f e r e n c e .

In t h e r e s t of t h i s p a p e r w e w i l l d e s c r i b e a p r e f e r e n c e d e v i c e t h a t is d i f - f e r e n t f r o m t h e s c o r i n g a n d r a n k i n g m e c h a n i s m in t h e s e n s e t h a t it is n o t b a s e d on t h e w a y i n t e r p r e t a t i o n s a r e built, b u t r a t h e r on l i n g u i s t i c p r o p e r t i e s Of t h e o b j e c t s t h e m s e l v e s . Its m a i n c h a r a c t e r i s t i c s a r e that:

it a p p l i e s t o c o m p l e t e a n d s o u n d (well formed) i n t e r p r e t a t i o n s only. T h a t is, all t h e o t h e r m o d u l e s of c o n s t r u c t i o n , t r a n s f o r m a t i o n a n d f i l t e r i n g h a v e b e e n a p p l i e d (Ex: p a r s i n g , W h - m o v e m e n t , etc). Thus, for t h e s e m o d u l e s all c o m - p e t i n g r e p r e s e n t a t i o n s are e q u i v a l e n t , a n d all t h e i n f o r m a t i o n n e e d e d for c o m - p a r i n g t h e m h a s b e e n found.

ii it is b a s e d o n p a i r w i s e c o m p a r i s o n b e t w e e n a l t e r n a t i v e (competing) i n t e r p r e t a t i o n s of the s a m e object. T h e p r o b l e m c a n t h e n b e s t a t e d as fol- lows:

H o w do w e m a k e u s e of t h e l i n g u i s t i c k n o w l e d g e in o r d e r to i n s u r e a i-i t r a n s - l a t i o n ?

It is o u r b a s i c b e l i e f t h a t it is i m p o s s i - b l e for t h e l i n g u i s t to k n o w t h e e x a c t n a t u r e of a c l a s s of c o m p e t i n g i n t e r p r e t a - t i o n s in a d v a n c e . T h i s i m p l i e s t h a t he c a n n o t in g e n e r a l f o r m u l a t e o n e s i n g l e rule t h a t p i c k s o u t t h e b e s t one.

3.

The proposed method

3.1.

Basic idea

O u r p r o p o s a l is t h e f o l l o w i n g :

- It s h o u l d be p o s s i b l e to m a k e (linguistic) s t a t e m e n t s of the type: if r e p r e s e n t a t i o n A h a s p r o p e r t y X, a n d B p r o p e r t y Y, t h e n A is to be p r e f e r r e d o v e r B (e.g. 'in law t e x t s d e c l a r a t i v e sen-

t e n c e s are b e t t e r t h a n q u e s t i o n s ' , or ' s e n t e n c e s w i t h a m a i n v e r b are b e t t e r t h a n s e n t e n c e s w i t h o u t one').

- O n t h e b a s i s of a s e t of s u c h s t a t e m e n t s it s h o u l d b e p o s s i b l e to e s t a b l i s h a p a r - tial o r d e r o v e r t h e s e t of c o m p e t i n g r e p r e s e n t a t i o n s .

- A n d in t h a t c a s e t h e n u m b e r of c a n d i - d a t e s c a n b e r e d u c e d by, for example, let- t i n g o n l y t h e m a x i m a l e l e m e n t s survive, or d i s c a r d i n g t h e m i n i m a l ones.

3.2.

Problems with the method

T h e f i r s t (but l e a s t serious) p r o b l e m is t h a t it is n o t c e r t a i n t h a t l i n g u i s t s w i l l a l w a y s b e a b l e to m a k e s u c h s t a t e - m e n t s (we w i l l c a l l t h e m ' p r e f e r e n c e s t a t e m e n t s ' ) o v e r p a i r s of r e p r e s e n t a - tions. E x p e r i m e n t a t i o n is n e c e s s a r y .

T h e s e c o n d o n e is m o r e s e r i o u s : it w o u l d b e h i g h l y u n r e a l i s t i c to e x p e c t t h a t t h e r e s u l t of a p p l y i n g of t h e p r e f e r e n c e s t a t e m e n t s w i l l b e a l i n e a r order, in f a c t t h e r e is n o t e v e n a g u a r a n t e e t h a t t h e o r d e r w i l l be p a r t i a l . In g e n e r a l t h e o u t - c o m e w i l l b e a d i r e c t e d graph. T h e r e a r e t h r e e w a y s of t a c k l i n g t h i s p r o b l e m :

T h e l i n g u i s t s h o u l d t r y to m a k e t h e set of p r e f e r e n c e s t a t e m e n t s h o m o g e n e o u s a n d c o n s t r a i n e d , a n d s h o u l d h a v e c o n - t r o l o v e r t h e w a y in w h i c h t h e y a r e applied, so t h a t he c a n a v o i d c o n t r a d - i c t o r y s t a t e m e n t s .

ii O n e t r i e s to m a k e a formal d e v i c e t h a t c h e c k s w h e t h e r c o n t r a d i c t i o n s c a n Occur.

iii O n e t r i e s t o c o m p a r e p a i r s of c o m p e t i - t o r s in a s p e c i f i c o r d e r s u c h t h a t it c a n b e g u a r a n t e e d t h a t t h e r e s u l t is a l w a y s a p a r t i a l order.

A t t h e m o m e n t (iii) is t h e m o s t feasible, (ii) t h e m o s t a m b i t i o u s , a n d (i) t h e m o s t d e s i r a b l e s o l u t i o n . C u r r e n t l y w e e n v i s a g e a c o m b i n a t i o n of (i) a n d (iii).

T h e t h i r d p r o b l e m is t h a t of t h e m a x i - mal e l e m e n t s . I d e a l l y t h e r e w o u l d b e j u s t one m a x i m a l element, i.e. t h e p r e f e r r e d r e p r e s e n t a t i o n . T h i s c a n n o t b e g u a r a n t e e d t o be true.

T h e p r o b l e m s s k e t c h e d h e r e are b y no m e a n s t r i v i a l . T h a t is w h y w e w a n t to e x p e r i m e n t w i t h a f i r s t i m p l e m e n t a t i o n of t h i s m e t h o d , t o i d e n t i f y t h e v a r i o u s r e l e v a n t p a r a m e t e r s in t h e s p e c i f i c c o n - t e x t of E u r o t r a .

4.

The proposed implementation

be a d a p t e d for a w i d e r a n g e of a p p l i c a - tions. W e g i v e in t h e a p p e n d i x some com- m e n t e d e x a m p l e s s p e c i f i c to o u r p a r t i c u l a r context.

4.1.

Preference rules

P r e f e r e n c e s t a t e m e n t s are e x p r e s s e d b y the u s e r in t h e f o r m of r u l e s ( p r e f e r e n c e rules). T h e r e a r e t h r e e t y p e s of p r e f e r - ence rules: s i m p l e rules, D r e d e f i n e d r u l e s and c o m p o s i t e rules. A p r e f e r e n c e r u l e a p p l i e d to t w o r e p r e s e n t a t i o n s of i n t e r p r e t a t i o n t r i e s to d e c i d e w h i c h one is b e t t e r t h a n the o t h e r ( p r e f e r r e d to t h e other). It is n o t g u a r a n t e e d t h a t a r u l e can a l w a y s t a k e a decision.

A s i m p l e p r e f e r e n c e r u l e is of t h e f o r m p = (Patternl > Pattern2)

The n a m e of the r u l e is p, a n d P a t t e r n l and P a t t e r n 2 are c u r r e n t p a t t e r n s . W h e n g i v e n t w o a r g u m e n t s (two r e p r e s e n t a t i o n s or subparts) A a n d B (written p(A,B)) the s y s t e m w i l l t r y to m a t c h P a t t e r n l w i t h A and P a t t e r n 2 w i t h B. If t h i s s u c c e e d s t h e n A is b e t t e r t h a n B (or A is p r e f e r r e d to B or A>B). If it fails t h e n the s y s t e m w i l l try to m a t c h A w i t h P a t t e r n 2 a n d B w i t h Patternl. If t h i s s u c c e e d s t h e n B is b e t t e r t h a n A.

P r e d e f i n e d r u l e s are p r o v i d e d for t h e c a s e s w h e r e s i m p l e r u l e s c a n n o t e x p r e s s some u s e f u l b a s i c p r e f e r e n c e s t a t e m e n t . For example, in o u r a c t u a l i m p l e m e n t a t i o n (cf a p p e n d i x ) , t w o D r e d e f i n e d r u l e s say t h a t a t r e e s t r u c t u r e w i t h f e w e r (more) b r a n c h e s t h a n t h e o t h e r is to b e p r e f e r r e d to one w i t h m o r e (fewer) b r a n c h e s . T h i s c a n n o t be e x p r e s s e d w i t h t h e p a r t i c u l a r l a n g u a g e for p a t t e r n s .

A c o m p o s i t e p r e f e r e n c e r u l e is of form

p = ( P a t t e r n l , P a t t e r n 2 )

= >

(pl($V,$W),

p2 ($X, $Y),

.-.)

the

I d e n t i f i e r s p, pl, p2, ... are r u l e names, P a t t e r n l a n d P a t t e r n 2 a r e a c t u a l p a t t e r n s , and SV, $W, $X, $Y, ... are v a r i a b l e iden- tifiers, t h a t s h o u l d a l s o o c c u r in P a t - t e r n l ($V,$X) a n d P a t t e r n 2 ($W,$Y) w h e r e t h e y i d e n t i f y s u b - p a r t s of t h e i n t e r p r e t a - tions. W h e n g i v e n t w o a r g u m e n t s A and B, the s y s t e m t r i e s to m a t c h A w i t h P a t t e r n l and B w i t h Pattern2. If t h i s succeeds, the v a r i a b l e s SV,$X,.. o c c u r r i n g in P a t t e r n l and S W , $ Y .... o c c u r r i n g in P a t t e r n 2 are i n s t a n t i a t e d to s u b - p a r t s of A a n d B r e s p e c t i v e l y . T h e n t h e s y s t e m t r i e s e a c h p r e f e r e n c e r u l e of t h e list, w i t h the i n s t a n t i a t e d a r g u m e n t s , till one rule can decide. In t h i s c a s e t h e r e l a t i o n s h i p h o l d i n g b e t w e e n A a n d B is the s a m e as t h a t h o l d i n g b e t w e e n t h e s u b - p a r t of A a n d the s u b - p a r t of B. If no r u l e of t h e l i s t

can d e c i d e t h e n p r e f e r e n c e is not decided. If the i n i t i a l m a t c h d o e s n ' t succeed, t h e n an a t t e m p t w i l l be m a d e to m a t c h A w i t h P a t t e r n 2 a n d B w i t h Patternl. If t h i s s u c c e e d s t h e s y s t e m t r i e s t h e r u l e s of t h e list in t h e same w a y as above. C o m p o s i t e p r e f e r e n c e r u l e s a l l o w r e c u r s i o n .

T h i s f o r m a l i s m is v e r y m u c h i n s p i r e d b y the p r o g r a m m i n g l a n g u a g e Prolog: a p r e f e r - ence r u l e is a n a l o g o u s to a t h r e e a r g u m e n t p r e d i c a t e (two i n t e r p r e t a t i o n s a n d t h e r e s u l t i n g r e l a t i o n s h i p ) , a s i m p l e r u l e to an a s s e r t i o n , a n d a c o m p o s i t e r u l e to a c l a u s e w i t h s u b - g o a l s .

4.2.

General algorithm

I n i t i a l l y , all c o m p e t i n g o b j e c t s are in t h e s e t of n o n o r d e r e d o b j e c t s N a n d t h e set of o r d e r e d o b j e c t s O is empty. Then, the f o l l o w i n g is r e p e a t e d u n t i l N is empty: an o b j e c t is r e m o v e d f r o m N a n d is c o m p a r e d to e a c h o b j e c t of O (if any), t h e n it is a d d e d to O.

T h i s a l g o r i t h m d o e s n o t e n s u r e t h a t t h e r e s u l t i n g d i r e c t e d g r a p h of p r e f e r e n c e r e l a t i o n s h i p s a m o n g t h e c o m p e t i n g o b j e c t s has no cycle. Anyway, m a x i m a l (minimal) e l e m e n t s can be d e f i n e d in t h e f o l l o w i n g way:

A n o b j e c t E is a m a x i m a l (minimal) ele- m e n t if n o c o m p e t i n g o b j e c t is b e t t e r

(worse) t h a n E.

T h u s an o b j e c t in a c y c l e of t h e g r a p h c a n n o t b e m a x i m a l (minimal).

To g i v e t h e u s e r c o n t r o l of h o w r u l e s are t r i e d on t h e c o m p e t i n g objects, o n l y one d i s t i n g u i s h e d r u l e is a p p l i e d to e a c h c o m p e t i n g pair. In t h e g e n e r a l c a s e it s h o u l d be a c o m p o s i t e r u l e t h a t just p a s s e s its t w o a r g u m e n t s to t h e r u l e s of the list, t h u s e n s u r i n g t h a t o n l y t h e s e r u l e s are t r i e d a n d in t h a t order.

T h e p a t t e r n m a t c h i n g m e c h a n i s m of c o m - p o s i t e r u l e s is q u i t e p o w e r f u l . (see a l s o t h e a p p e n d i x ) : It a l l o w s some p r e f e r e n c e s rule to b e a p p l i e d o n l y to s e l e c t e d o b j e c t s ( s a t i s f y i n g a p r e c o n d i t i o n ) . It also a l l o w s (recursive) e x p l o r a t i o n of s u b - p a r t s of r e p r e s e n t a t i o n s (a d e r i v a t i o n t r e e for e x a m p l e ) , in p a r a l l e l o r not. F i n a l l y it e n a b l e s t h e u s e r to g i v e p r i o r - ity to s o m e p r e f e r e n c e r u l e s o v e r some others.

4.3.

Problems with the implementation

A l t h o u g h w e d e c i d e d t h a t t h i s m o d e l is g o o d e n o u g h for p r e l i m i n a r y e x p e r i m e n t a - tion, c e r t a i n p r o b l e m s are a l r e a d y apparent:

some r u l e c a n be a p p l i e d to a p a i r of a r g u m e n t s in b o t h o r d e r s (if p(A,B) and p(B,A) a r e b o t h p o s s i b l e ) . In p a r t i c u l a r a p r e f e r e n c e d e c i s i o n s h o u l d n o t b e t a k e n b e t w e e n i d e n t i c a l objects.

- I n f i n i t e r e c u r s ! o n c a n o c c u r w i t h c t m p o - site p r e f e r e n c e rules.

- M a x i m a l (minimal) e l e m e n t s m a y n o t e x i s t in t h e r e s u l t i n g g r a p h of p r e f e r e n c e r e l a - t i o n s h i p s (for e x a m p l e if all e l e m e n t s are in a cycle).

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

C u r r e n t l y it is t h e u s e r ' s r e s p o n s i b i l - ity to a v o i d t h e s e p r o b l e m s b y w r i t i n g " s e n s i b l e " rules. In t h e n e x t s e c t i o n w e s k e t c h s o m e p o s s i b l e s o l u t i o n s t h a t are c o n s i d e r e d for a f u t u r e i m p l e m e n t a t i o n .

5.

Future directions

T h e i m p l e m e n t a t i o n of t h i s p r e f e r e n c e m o d e l h a s b e e n w r i t t e n in Prolog. T o f a c i l i t a t e e x p e r i m e n t a t i o n , a m e c h a n i s m is p r o v i d e d for t r a c i n g t h e p r e f e r e n c e r u l e s a p p l i c a t i o n to o b s e r v e t h e i r b e h a v i o u r .

T h e m o d e l d e s c r i b e d a b o v e is v e r y f l e x - ible. W e a r e c u r r e n t l y s t u d y i n g t h e i m p l e - m e n t a t i o n of v a r i a n t s of t h e b a s i c c o m - p a r i s o n a l g o r i t h m :

W e are i n v e s t i g a t i n g a l g o r i t h m s t h a t would:

- r e d u c e t h e n u m b e r o f c o m p a r i s o n s , b y a i m i n g at e x t r a c t i n g o n l y t h e m a x i m a l (minimal) e l e m e n t s , w i t h o u t t r y i n g to o r d e r all e l e m e n t s .

- c a l c u l a t e t h e t r a n s i t i v e c l o s u r e of t h e d i r e c t e d graph, a n d t h e n r e m o v e all c o n - t r a d i c t o r y r e l a t i o n s h i p s , t h e r e b y r e m o v i n g all cycles. T h i s a m o u n t s to s a y i n g t h a t t w o i n t e r p r e t a t i o n s a r e n o t c o m p a r a b l e if t h e i r c o m p a r i s o n l e a d s to c o n t r a d i c t o r y d e c i s i o n s .

- c o m p a r e t h e c o m p e t i n g i n t e r p r e t a t i o n s stepwise, t h a t is all c o m p a r i s o n s a r e p e r - f o r m e d w i t h t h e f i r s t r u l e in a list, t h e n o n l y t h e p a i r s for w h i c h t h e r e is no d e c i - sion y e t a r e c o m p a r e d w i t h t h e s e c o n d rule, a n d so on.

ACKNOWLEDGEMENTS

W e w o u l d l i k e to t h a n k Paul Bennett, M a g h i King, G e r t j a n V a n Noord, M i k e R o s n e r and S u s a n W a r w i c k for t h e i r f r u i t f u l c o m - m e n t s and t h e i r support.

APPENDIX

In t h e c u r r e n t f r a m e w o r k of E U R O T R A (Arnold a n d d e s T o m b e 1987), r e p r e s e n t a - t i o n of i n t e r p r e t a t i o n s are d e r i v a t i o n trees, c o n t a i n i n g at e a c h n o d e a set of a t t r i b u t e - v a l u e pairs. H e r e is a v e r y s k e t c h y and i n t u i t i v e d e s c r i p t i o n of t h e

s y n t a x u s e d in t h e p a t t e r n s :

- T h e i d e n t i f i e r s s, np, v p etc. a r e v a l u e s of t h e d i s t i n g u i s h e d a t t r i b u t e of t h e n o d e (in t h e s e examples, t h e s y n t a c t i c c a t e g o r y ) .

- C u r l y b r a c k e t s d e l i m i t a set of c o n d i - t i o n s t o b e s a t i s f i e d b y a node. F o r e x a m p l e ( s , f = d e c l a r a t i v e } i n d i c a t e t h e r e q u i r e d c o n d i t i o n s on t h e n o d e for t h e d i s t i n g u i s h e d a t t r i b u t e ( s h o u l d h a v e v a l u e s) a n d for an f a t t r i b u t e (should h a v e v a l u e d e c l a r a t i v e ) .

- SA, SB, etc. a r e v a r i a b l e i d e n t i f i e r s . - s . [ n p , v p ] i n d i c a t e s a t r e e w i t h r o o t s

a n d t w o d a u g h t e r s n p a n d vp.

- ? o r (?) i n d i c a t e s an u n s p e c i f i e d node. - * i n d i c a t e s a l i s t of u n s p e c i f i e d

nodes.

- S A i P a t t e r n i n d i c a t e s t h a t t h e v a r i a b l e $A is i n s t a n t i a t e d to t h e s u b - t r e e t h a t m a t c h e s P a t t e r n

- $ m o r e b r a n c h e s (and $ 1 e s s _ b r a n c h e s ) is a p r e d e f i n e d p r e f e r e n c e r u l e t h a t p r e f e r t h e a r g u m e n t t h a t h a s m o r e

(less) b r a n c h e s t h a n t h e other.

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

Example

1

p0 = ( $ A ! ( ? ) , $ B ! ( ? ) => (pI($A,$B),

p 2 ( $ A , $ B ) ) , pl = ( ( s , f = d e c l a r a t i v e )

> { s , f = i n t e r r o g a t i v e } ) , p2 = ( s . [ n p , v , $ A ] s , * ] ,

s . [ n p , v , $ B ! s , * ] ) => (pI($A,$B),

p 2 ( $ A , $ B ) )

T h i s set of p r e f e r e n c e r u l e s w i l l explore, in p a r a l l e l , t w o trees, f r o m t o p to bottom, a l w a y s t a k i n g t h e 's' branch, and p r e f e r t h e t r e e in w h i c h it finds a d e c l a r a t i v e s e n t e n c e ( o p p o s e d to an i n t e r r o g a t i v e ) . I f o n e i n v e r t s t h e o r d e r of pl a n d p2 in the d i s t i n g u i s h e d c o m p o s i t e r u l e p 0 t h e t r e e s w o u l d b e e x p l o r e d f r o m b o t t o m to top.

R u l e p0 j u s t p a s s e s its a r g u m e n t s to pl or

p2~

R u l e pl p r e f e r s a d e c l a r a t i v e s o v e r an i n t e r r o g a t i v e s.

R u l e p2 i d e n t i f i e s t h e e m b e d d e d s in e a c h a r g u m e n t a n d p a s s e s t h e m to pl or p2.

Example 2

p0 = ( s . [ n p , v p . [ * , $ A ! ( ? ) ] ] , s . [ n p , v p . [ * , $ B ! ( ? ) ] ] ) => (pI($A,$B),

p2 = (np.[*,$A!np] , $B!pp) => (pl($A,$B),

p 2 ( $ A , $ B ) , p 3 ( $ A , $ B ) ) ,

p3 = (np.[*,$A!(?)], n p . [ * , $ B ! ( ? ) ] ) => (pI($A,$B),

p 2 ( $ A , $ B ) , p 3 ( $ A , $ B ) ) .

G i v e n two sentences, this set of r u l e s will p r e f e r the one t h a t has the p p a t t a c h e d d e e p e r in t h e s t r u c t u r e t h a n the o t h e r (right a t t a c h m e n t ) . T h i s e x a m p l e is r e s t r i c t e d to e x p l o r e o n l y e m b e d d e d nps. For b o t h arguments, rule p0 i d e n t i f i e s the last d a u g h t e r s of the v p of a s e n t e n c e s, and p a s s e s t h e m to p r e f e r e n c e rules pl or p2 or p3.

R u l e pl will p r e f e r a p p a t t a c h e d u n d e r an np to a pp (which w a s a t t a c h e d h i g h e r in the structure).

Rule p2 will b e t r i e d o n l y if pl was not applicable. It is t h e r e for the case the pp is i m b e d d e d d e e p e r in the np.

Rule p3 is s i m i l a r to rule p0, e x c e p t t h a t it t a k e s the last d a u g h t e r s of a np. It is t r i e d o n l y if pl and p2 are not a p p l i c a - ble.

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