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ANAPHORA AND LOGICAL FORM: ON FORMAL MEANING REPRESENTATIONS FOR NATURAL LANGUAGE

Bolt

B o n n i e Nash-Webber B e r a n e k and Newman C a m b r i d g e MA 02138

Inc.

Raymond R e i t e r D e p a r t m e n t o f Computer S c i e n c e U n i v e r s i t y o f B r i t i s h Columbia V a n c o u v e r , B . C . , Canada Abstract We a r g u e , on favor of repre sentations We t hen adop f unct ion" for repre sentation, ident i f y i n g th of anaphoric c sugge s t s prope r t i e s of a th facil itate ante possi ble re appro p r i a t e such pro with t o de possi ble r i c h c l a s s of a

invoking general world knowledge. The separate issue of choosing the most a p p r o p r i a t e antecedent from t h i s set w i l l , in general, require plausible reasoning b a s e d on s u c h g e n e r a l w o r l d k n o w l e d g e . We a r e a l s o aware of instances where such knowledge is required even to propose possible antecedents. Nevertheless," In this p a p e r , our c o n c e r n i s t o e x p l o r e the implications of a purely syntactic appfoach as well as to ascertain i t s limitations. It turns out that a surprisingly r i c h class of anaphora, both p r o n o u n s and e l l i p s e s , i s a m e n a b l e t o s u c h an approach, provided that an appropriately structured logical MRL i s used. W e s h a l l f i n d t h a t t h e use o f such an MRL l e a d s t o p a r t i c u l a r l y s i m p l e r u l e s for i d e n t i f y i n g possible antecedents, and that the structure of the MRL can be exploited computationally to preclude c e r t a i n i n a p p r o p r i a t e ones. We s h a l l also find that this task of identifying p o s s i b l e r e f e r e n t s i s i n t i m a t e l y bound up with an ability to form •PPLopriate descriptions of them, an3" tfiat these cfescrlptlons are, in turn, intimately related to logical form. I I .

1.

to provide a computational approach to certain problems i n anaphora i n natural language;

2.

to argue in favor of formal meaning representation languages (MRLs) f o r natural language.

Why L o g i c a l

Meaning

Representations?

Although there i s u n i v e r s a l agreement within the AI community that natural language understanding systems must provide some underlying meaning representation onto which surface s t r i n g s are mapped, the nature of this representation remains a contentious issue. One a s p e c t o f t h i s d e b a t e has to do w i t h the form t h a t t h i s r e p r e s e n t a t i o n should take.' There appear to be two points of view: logical forms [e.g., S a n d e w a l l , 1 9 7 1 ; Woods, e t a l , 1972] and structured networks [e.g., W i l k s , 1975; Schank, 1975; Simmons, 1 9 7 3 ] ,

These two o b j e c t i v e s a r e n o t independent. It appears t h a t the s o l u t i o n s to c e r t a i n problems in anaphora are best formulated with respect to an appropriately structured logical MRL, so that the structural entities o u t o f w h i c h such a n MRL is composed suggest possible a n t e c e d e n t s f o r anaphor r e s o l u t i o n . More specifically, we have set ourselves the following problem: what form should a meaning representation assume in order to facilitate the identification of possible antecedents of anaphorlc expressions, and ~what computational mechanisms does t h i s task require? Moreover, we have chosen to investigate t h i s problem of i d e n t i f y i n g a set of possible antecedents without Natural

formal Despite this lack of any d i s t i n c t i o n between n e t w o r k s and logical forms, there is a widespread bias w i t h i n t h e A I c o m m u n i t y a g a i n s t l o g i c a l MRLs for natural language. [See for example, C h a r n i a k and Wilks, 1976]. We suspect

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that there are two i m p l i c i t assumptions underlying t h i s a n t i - f o r m a l p o i n t of view: 1. t h a t the c h o i c e o f a logical form necessarily implies a commitment to a corresponding proof t h e o r y as o n e ' s s o l e c o m p u t a t i o n mechanism; 2. t h a t logical forms must have their "natural" representation at the implementation level, e.g., that ( x ) ( E y ) . Px,y & Qx,y must be represented by the S-expression ( ( X ) ( E Y)(AND (P X Y)(Q X Y ) ) ) . N e i t h e r o f these assumptions i s j u s t i f i e d . We have a l r e a d y observed t h a t networks can be best viewed as implementation l e v e l r e p r e s e n t a t i o n s f o r l o g i c a l f o r m s , and as we shall show in S e c t i o n I V . , the c o m p u t a t i o n s t h a t we propose for anaphor r e s o l u t i o n w i t h i n a l o g i c a l MRL are in no way based on any k i n d of p r o o f t h e o r y . I f i t i s the case then that logical forms and networks are one and the same, why p r e f e r one over the o t h e r ? We f a v o r l o g i c a l form o n the f o l l o w i n g g r o u n d s : A.

Semantics

By virtue of i t s being a formal l a n g u a g e , a l o g i c a l form i n h e r i t s a w e l l cfefmea semantics, namely, i t s Tarskian semantics. This i s not the case for network r e p r e s e n t a t i o n s p r e s e n t e d _in vacuo (i.e., without a t r a n s l a t i o n mechanism mapping the network to a l o g i c ) . As Woods [1975] p o i n t s out, networks often fall short of t h i s requirement. B.

Computation

The high level conceptual representatio n of meaning p r o v i d e d by logical form s encourages th e f o r m u l a t i o n o f a p p r o p r i a t e p r o c e s s i n g a l g o r i t h m s at an e q u a l l y h i g h c o n c e p t u a l l e v e l , independent of how these l o g i c a l forms ar e r e p r e s e n t e d at the im p l e m e n t a t i o n This 1e v e l . provides f o r p e r s p i c u o u s de s c r i p t i o n s o f algorithms, the without spec i f y i n g irrelevant, CONS cell le v e l , pointer chasing deta i l s required by network representatio ns. The exampl es of S e c t i o n I V i l l u s t r a t e the such ease w i t h which r u l e s can be f o r m u l a t e d , as w e l l a s t h e i r conceptual cl a r i t y .

There are two issues here: representational perspicuity and r e p r e s e n t a t i o n a l adequacy. The first is l a r g e l y a s u b j e c t i v e m a t t e r . We b e l i e v e l o g i c a l forms to be more r e a d a b l e and comprehensible than their corresponding network f o r m s , e s p e c i a l l y when the usual Natural

network primitives are considerably augmented i n o r d e r t o c o r r e c t l y represent logical connectives and q u a n t i f i e r s and t h e i r scopes [Schubert, 1975; Hendrix, 1975] . i ssue The se cond r e p r e sent a t i o n a l largely adequacy - i s f a r more i m p o r t a n t , d e a l i n g wi t h the a b i l i t y of a g i v e n MKL t o express t h e meani ng of s u r f a c e s t r i n g s . A related of cToseTy i s s ue is th at r e p r e s e n t a t i o n a l c l o s u r e . Can one t e l l , from the g i v e n s p e c ! " F i c a t i o n of an MRL, what can and wh at ca nnot be ex pressed Bee ause any l o g i c a l MRL has within it? d e f i ned s yntax a nd a w e l l b o t h a wel 1 d e f i n e d se m a n t i c s i t ne c e s s a r i i y e x h i b i t s a h i g h deg ree o f c l o s u r e . T h i s i s not the case f o r n etwork r e p r e s e n t a t i o n s pr esented jj2 v a c u o , p r e c i s e l y b ecause t hey have no Many o f semantics, the net work based meaning re p r e s e n t a t i o n s i n c u r r ent n a t u r a l systems language 19 75; W i l k s , [Sch ank, 1975; Norm an and Rumelh a r t , 19 75] suffer from t h i s def ec t , a f a c t t h at m akes i t diffic ult extremely their to ass ess content. It is inst ructive i n con n e c t i o n w i t h the above d i s c u s s i o n t o note these that v e r y same i s s u e s were ho t l y de bated w i t h i n the data base managemen t comm u n i t y d u r i n g the e a r l y 1970 s. There t o o , the b a s i c c h o i c e wa s bet ween a ne twor k view o f data [CODASYL, 1971 ] or and a 1o g i c a l so-called £el.a t i q n a ^ , view Codd , 1970] . Moreover, the a rguments advanc ed i n f a v o r of the re l a t i o n a l view were i n many ways i s o m o r p h i c t o t hose we h ave ma de f a vor i n g logical f orm f or meanin g repr esenta t i o n s . At l e a s t w i t h i n the d a t a base comm u n i t y , the logical view cu r r e n t l y pre v a i l s , primarily i t s high beca use cone e p t u a l level s o - c a l l ed p r o v i des "data independen c e , " i . e . , the on e 's v iew o f im piemen t a t i o n data i s inde pendent of details. III.

On A p p r o p r i a t e L o g i c a l MRLs

I n t h e p r e v i o us s e c t i o n , we ar gued on fairly g e n e r a l grounds i n f a v o r o f f o r m a l for meaning represe n t a t i o n languag es n a t u r a l language Of c o u r s e , not j u s t any logical MRL wi 11 d o . At the ver y l e a s t , any such f o r m a l language mu s t prov i d e for quantification logical and the usual connectives, b ut these even under requirements t here broad rema i n s a spectrum of logical possib le representations, There a re a t 1e a s t two dimensions t o t h i s spectrum c o r r e sponding to represent a t i o n a l and level r e p r e s e n t a t i o n a l s t. r uc t ur e . wiTn' r e s p e c t to level, r e p F e s e n t a t l o ns in current systems range surfacy" from ve r y [Simmons, 197 0] "deep", to very ones [ Wilks, primitive-based 1975;

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Schank, 1975]. Wilks, i n Computational Semantics [Charniak and W i l k s , l 9 7 6 ; 1761 provides a good d i s c u s s i o n of these issues. In t h i s p a p e r , we use as illustration an MRL t h a t keeps v e r y c l o s e to t h e s u r f a c e syntax and l e x i c o n . We do so because t h e c o m p u t a t i o n a l t a s k t h a t we have taken as a " f o r c i n g f u n c t i o n " f o r an adequate representation, namely, identifying possible antecedents for anaphor r e s o l u t i o n , s e e m s not to r e q u i r e a deep l e v e l and is moreover f a c i l i t a t e d by a " s u r f a c y " one, at l e a s t f o r a broad and i n t e r e s t i n g c l a s s o f phenomena. Our f o c u s in d i s c u s s i n g l o g i c a l MRLs is on t h e i r r e p r e s e n t a t i o n a l s t r u c t u r e . We have found t h a t the need to provide appropriate antecedents for anaphor resolution suggests certain structural c o n s t r a i n t s on p o s s i b l e MRLs which g r e a t l y facilitate this process. In this c o n n e c t i o n , we emphasize t h a t we are not here proposing a f u l l y developed l o g i c a l MRL. To do so would r e q u i r e , at the v e r y l e a s t , adequate r e p r e s e n t a t i o n s f o r t e n s e , modality, mass t e r m s , events, etc. i s s u e s which we have so f a r c o m p l e t e l y ignored. The MRL used in t h i s paper is merely a v e h i c l e for displaying certain f o r m a l s t r u c t u r a l p r o p e r t i e s which we have found necessary f o r the i d e n t i f i c a t i o n o f antecedents. Our b e l i e f i s t h a t any f u l l y articulated logical MRL w i l l have to p r o v i d e these s t r u c t u r a l u n i t s i f i t i s t o deal effectively with anaphora. Accordingly, one way of viewing our p r o p o s a l is as a s e t of design c o n s t r a i n t s on the s t r u c t u r e of p o s s i b l e l o g i c a l MRLs for n a t u r a l language. The remainder of this section d e a l s w i t h these s t r u c t u r a l properties. A

*

Lambda-expressions

For a f o r m a l MRL to be adequate f o r the resolution of verb phrase ellipsis, it must provide for constructions equivalent to l a m b d a - e x p r e s s i o n s . ( T h i s has a l s o been observed b y several linguists recently, i n c l u d i n g Sag [1976] and W i l l i a m s [ 1 9 7 7 ] . ) For example, the sentence p a i r La. John l o v e s Mary. 2. So does B i l l . requires, as the antecedent of the e l l i p s e d verb phrase, the formal c o n s t r u c t M x ) [Love x , Mary] corresponding to "loving Mary", whence the resolved sentence l b . becomes B i l l , >s(x) [Love x , Mary] which s i m p l i f i e s t o Love B i l l , Mary Natural

(Note that our preferred notation for applying a lambda-expression to an argument is to f o l l o w the argument by the lambda e x p r e s s i o n , c o r r e s p o n d i n g to normal subject-predicate word order i n E n g l i s h . ) B. Separation of Descr i g t i ^ o n a l A s s e r t i o n ' a l I n f o r m a t i o n :'~Types

and

Since the antecedents of many anaphoric expressions are d e s c r i p t i o n s , an adequate f o r m a l i s m must be so o r g a n i z e d t h a t these descriptions stand out c l e a r l y . For example, c o n s i d e r the p a i r of sentences 2a. Some c o t t o n T - s h i r t s are e x p e n s i v e , b. but not the one Mary gave J o h n . In a "flat" predicate calculus MRL (ignoring the d i s t i n c t i o n between "some" p l u r a l and "some" s i n g u l a r ) , sentence 2a. might be r e p r e s e n t e d by (Ex) . Cotton x & T - s h i r t x & Expensive x Now i n t u i t i v e l y , the antecedent of "one" i n sentence 2b. i s something l i k e "cotton T-shirt", but from the flat predicate c a l c u l u s r e p r e s e n t a t i o n , t h e r e is no more reason to suppose t h a t Cotton and T - s h i r t form a p o s s i b l e antecedent than Cotton and Expensive, or T - s h i r t and Expensive, or any one o r a l l t h r e e . That i s , t h e r e i s no structural indication that Cotton T-shirt is a r e f e r e n c e a b l e u n i t . We b e l i e v e such a n i n d i c a t i o n i s necessary i n any formalism adequate for anaphor resolution. Using the s t r u c t u r e of a t.yped l o g i c , p r e d i c a t e s t h a t c o n s t r a i n the range of a quantified v a r i a b l e - i . e . , types - ( l i k e T-shirt here) can be structurally distinguished from p r e d i c a t e s t h a t a s s e r t things (as "Expensive" does here). Moreover, using the lambda o p e r a t o r , the n o t i o n of type can be extended from s i m p l e o n e - p l a c e p r e d i c a t e s to more complex ones to yield all and o n l y the a l l o w a b l e referenceable e n t i t i e s . For example, we can r e p r e s e n t "T-shirt" as T - s h i r t "cotton T - s h i r t " as X ( u : T - s h i r t ) [ C o t t o n u] " T - s h i r t t h a t Mary gave F r e d " as > , ( u : T - s h i r t ) [Gave Mary, F r e d , u] (The first is merely a shorthand for > , ( u : T - s h i r t ) [True] .) N o t i c e t h a t we are postulating a representation for "cotton T - s h i r t " that is more highly structured than a s i m p l e c o n j u n c t i o n of C o t t o n and T-shirt, i.e. ( T - s h i r t x & C o t t o n x) . Specifically, w e are s e p a r a t i n g t h a t p a r t of the noun phrase d e n o t i n g the p r i m a r y

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manipulations of s t r u c t u r e d MRL;

class to which an e n t i t y belongs ( u s u a l l y t h e head n o u n ) f r o m t h o s e parts denoting restrictions on that c l a s s (conveyed by a d j e c t i v e s and r e l a t i v e c l a u s e s ) . This provides yet another structural p r o p e r t y t h a t a l o g i c a l MRL s h o u l d p o s s e s s in order t o f a c i l i t a t e the i d e n t i f i c a t i o n of antecedents for anaphor resolution. Consider 3.

Mary and

bought a t i e - d y e d c o t t o n T - s h i r t Fred bought an e m b r o i d e r e d o n e .

Whether intuitively "one" refers to "cotton T-shirt" or "tie-dyed cotton T-shirt" or merely "T-shirt", it must refer at l e a s t t o " T - s h i r t " , the primary c l a s s d e n o t e d b y t h e noun phrase. There is no way (pronominally) in E n g l i s h to refer to a restriction without also referring to the primary c l a s s . This is o u r m a i n r e a s o n f o r k e e p i n g them distinct i n o u r l o g i c a l MRL. Another consequence o f t h i s s e p a r a t i o n of descriptional from assertional information is that it avoids problems t h a t Woods [ 1 9 7 5 ] d i s c u s s e s with respect to adequate representations for r e l a t i v e clauses. First, sentences like "A dog t h a t had r a b i e s b i t a man" and " A dog t h a t bit a man had rabies" can be a s s i g n e d d i s t i n c t r e p r e s e n t a t i o n s , f o r example (Ex: X(u:Dog) . Bit x, (Ex: MurDog) . Have x,

[Have u , R a b i e s l ) ( E y : M a n ) y [ (Ey:Man) . B i t u, y] ) Rabies

More i m p o r t a n t l y , p r o c e s s i n g r u l e s s u c h a s those proposed in S e c t i o n IV, can treat t h e s e two r e p r e s e n t a t i o n s d i f f e r e n t l y . As Woods point out, conventional semantic networks f a i l t o represent the d i s t i n c t i o n between these two sentences. From the perspective of t h e a b o v e d i s c u s s i o n , one reason for t h i s is c l e a r : a conventional network is a representation, at the implementation level, of a "flat" predicate logic. IV

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Examples

In this section, we present several fragments of discourse, each containing anaphoric expressions pronouns and/or ellipses. Recall that we are not concerned here w i t h the kinds of e x t e r n a l k n o w l e d g e n e e d e d t o c h o o s e among possible antecedents for an anaphoric e x p r e s s i o n . What w e a r e concerned with is insuring that 1.

i n cases where t h e a n t e c e d e n t of an anaphoric expression is not e x p l i c i t l y p r e s e n t , i t can often be derived through purely syntactic Natural

2.

an

appropriately

t h e p r o p e r t i e s we have p r o p o s e d f o r a logical MRL make s u c h m a n i p u l a t i o n s s i m p l e t o e x p r e s s and a p p l y .

our approach to Since d e v e l o p ing form, we have anaphora and 1o g i c a l one discovered that i t is compatible with major l i n e of thought in t r a n s f o r m a t i o n a l linguistics today (For a survey of current ideas on anaphora i n l i n g u i s t i c s and p s y c h o l o g y , s e e [ N a s h - W e b b e r , 1977].) That line of thought i s i l l u s t r a t e d both by Chomsky's recent remark that the "general p r i n c i p les of anaphora apply to logical forms rather than to surface structures directly" [ C h o m s k y , 1 9 7 5 : 241 f t . 3 1 ] , a s w e l l a s by r e c e n t r e s e a r c h on logical t h e o r i e s of verb phrase d e l e t i o n and g a p p i n g [ S a g , 1 9 7 6 ; W i l l i a m s , 1 9 7 7 ] . set W i t h o u r ex a m p l e s , w e g i v e a s m a l l yield the of man i p u l a t i on r ules whic h needed a n t e c e d e n t s . We make n o c l a i m s f o r rules; there t h e com p l e t e n e s s of these obvious ly rem a i n s a g r e a t de a l o f w o r k t o (see . S e c t i o n be done a l o n g thes e lines VI) . b e l i eve, We do howe v e r , t h a t t h e example s i n d i e a t e t h e u t i l i t y of our b a s i c a p p r o a c h , and t h a t t h i s a p p r o a c h provides a pr o m i s i n g for further di rection researc h. A.

Implicit

Sets

Our f i r s t e x a m p l e i l l u s t r a t e s one way of deriving a set as a candidate antecedent for "they". Consider the sentences 4a. b. The

Mary g a v e e a c h boy a T - s h i r t , She b o u g h t tjiem a t F i l e n e ' s .

f i r s t may b e 4c.

represented

as

(Vx:Boy)(Ey:T-shirt) . Gave M a r y , x , y

(For simplicity, we w i l l ignore the f a c t t h a t "each boy" is probably anaphoric, referring to e a c h boy i n some p r e v i o u s l y m e n t i o n e d s e t o r one i m p l i c i t l y d e f i n e d b y context, and treat it rather as a u n i v e r s a l l y q u a n t i f i e d noun p h r a s e . ) are c o n s i d e r i n g each Notice that we since we want to sentence i n d i v i d u a l l y that is assign it a repr e s e n t a t i o n c o r r e c t , b u t w h i c h d o es n o t depend on what may f o l l o w . The r e s u I t w i T l often be a reading that is in some sense n o n c o m m i t t a l : i t w i l l be vague but true. If subsequently we l e a r n more a b o u t t h e situation, we wi l l refine this reflect our new representation to knowledge s t a t e .

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The second sentence we initially with its anaphoric o v e r t l y marked, t h a t i s ,

represent elements

4 d . Bought SHE^ THEY , F i l e n e ' s (We s u b s c r i p t the pronoun symbols merely to keep s e v e r a l i n s t a n c e s of the same one d i s t i n c t , as would be the case in "They thanked her f o r t h e m " . ) Next, we i d e n t i f y possible referents for the anaphoric terms. Since Mary is the o n l y female a r o u n d , we t r i v i a l l y a s s i g n her as the referent of SHE. Regarding candidate antecedents for THEY, , we p o s t u l a t e two ways of d e r i v i n g p o s s i b l e s e t s from sentences l i k e 4a. 1. Form the set d e s c r i p t i o n of any type restricting a universally quantified variable. (toe r e p r e s e n t the set d e s c r i p t i o n of type C by { x | C x } . ) 2. Let to be a (prior) formula not containing the anaphoric element THEY, nor any n e g a t i o n in the main clause. ( I n the c u r r e n t example, 4c. plays the r o l e of W.) Suppose to has an e x i s t e n t i a l l y quantified variable y that lies within the scope of a universally quantified variable. Form the set d e s c r i p t i o n of the set of y ' s s a t i s f y i n g W. T h i s is a straightforward procedure, i n v o l v i n g the t y p e of y r e s t r i c t e d by an e x p r e s s i o n d e r i v i n g from W. Details are given in [Nash-Webber, forthcoming], but the example should suggest i t s b a s i c o u t l i n e . Thus, sentence 4a. y i e l d s {x|Boy x ) , the set o f b o y s , v i a the f i r s t p r o c e d u r e , and { v | T - s h i r t v & (Ew:Boy) . Gave Mary,w,v} via the second one, i.e. the set o f T - s h i r t s , f o r each of which t h e r e is some boy to whom Mary gave i t . Substituting each of these sets in turn for THEY^, yields 4e. Bought Mary, {x|Boy x } , F i l e n e ' s f. Bought Mary, ( v | T - s h i r t v & (Ew:Boy) . Gave M a r y , w , v } , F i l e n e ' s That is, e i t h e r Mary bought a l l the boys a t F i l e n e ' s o r she bought there all the T-shirts she gave out. Real w o r l d knowledge would now be needed to choose the more p l a u s i b l e r e a d i n g . Notice that in English the pronoun "they", as w e l l as many p l u r a l noun phrases, are ambiguous between a c o l l e c t i v e r e a d i n g ( " a l l t o g e t h e r " ) and a distributive one ( " t a k e n one at a t i m e " ) . Sometimes, a l e x i c a l item w i l l indicate that a plural should be understood d i s t r i b u t i v e l y , a s " e a c h " does i n "Mary's suitcases were each weighed at the Natural

airport". Sometimes, semantic s e l e c t i o n a l r e s t r i c t i o n s can be used to choose between the two. For example, " p i l e " requires a collective interpretation of i t s object: "She p i l e d them i n t o a heap" doesn't mean "for each one, she p i l e d i t i n t o a h e a p " . But o f t e n , o n l y unknown aspects of the situation can furnish the appropriate information. For example, if we l e a r n t h a t " M a r y ' s s u i t c a s e s were weighed at the airport", we cannot say f o r c e r t a i n whether each one was weighed there s e p a r a t e l y o r j u s t the whole l o t t o g e t h e r . In l i n e then w i t h the p o l i c y d e s c r i b e d above of always o p t i n g for a vague but true interpretation, rather than making unsubstantiated choices, we w i l l i n t e r p r e t plurals non-distributively, unless or u n t i l a d d i t i o n a l i n f o r m a t i o n would l e a d u s to an a l t e r n a t e d e c i s i o n . B.

T

ype Antecedents

Our next example i l l u s t r a t e s the identification of descriptions as c a n d i d a t e antecedents f o r anaphoric " o n e " . 5a. Mary gave each boy a green T - s h i r t , b. She gave Sue a red one. t o e i n t e r p r e t sentence 5a. l i k e 4a. above, except f o r the a d d i t i o n a l m o d i f i e r " g r e e n " on T - s h i r t . (tfx:Boy) (Ey: X ( u : T - s h i r t ) [Green u]) . Gave Mary, x, y Sentence 5b. can be r e p r e s e n t e d as (Ez: A(u:P?) [Red u ] )

initially

. Gave SHE 1 Sue,z

That is, there is something o f unknown type P? t h a t should be d e r i v a b l e from context, which we know e x p l i c i t l y is r e d , which some known female SHE, gave Sue. Our task is now to i d e n t i f y possible antecedents f o r SHE, and P?. There are s i m p l e s y n t a c t i c c r i t e r i a f o r r e j e c t i n g Sue as an antecedent for SHE,. So again by d e f a u l t , t h e r e being no o t h e r females a r o u n d , we a s s i g n Mary as the r e f e r e n t f o r SHE,. As for P?, i t s p o s s i b l e antecedents include a l l "recently" mentioned types, independent o f the p a r t i c u l a r q u a n t i f i e r s . ("Recent" seems to mean here the c u r r e n t s e n t e n c e , the p r e v i o u s one, and perhaps the one b e f o r e t h a t . It does not seem to be a f f e c t e d by task s t r u c t u r e [Deutsch, 1975] or s t o r y s t r u c t u r e , or any of the o t h e r f a c t o r s t h a t seem to change the set of available antecedents for definite pronouns, "he", " i t " , e t c . )

Languare-7: Nash-Webber 125

The t y p e s e x p l i c i t l y g i v e n in example 5 are: M u : T - s h i r t ) [Green u] , T-shirt and Boy. Notice t h a t when one type is constructed out of other types via the lambda o p e r a t o r , we i n c l u d e them a l l as possible candidate antecedents. Prescribing e x a c t l y what criteria one would use t o i d e n t i f y t h e most plausible antecedent for P?, or in what way one would a p p l y them, i s n o t w i t h i n the scope of t h i s paper. But they would i n c l u d e the semantic c r i t e r i o n t h a t one be a b l e to p r e d i c a t e Red of an e n t i t y of type P? T h i s would e l i m i n a t e ) v ( u : T - s h i r t ) (Green u] through a p p l i c a t i o n of a "clashing c o l o r " a x i o m : i f something i s g r e e n , it is not red. (Notice that if sentence 5b. had been " F r e d , she gave a l a r g e o n e . " there would be no reason to e l i m i n a t e t h i s d e s c r i p t i o n as a p l a u s i b l e a n t e c e d e n t . ) Under r h e t o r i c a l c r i t e r i a , we would expect parallelism to argue for plausibility. That i s , i f two s u c c e s s i v e sentences are structurally similar ( " p a r a l l e l " ) and i n t h e l a t t e r , a n a p h o r i c "one" h e l p s t o fill role R ( h e r e , the o b j e c t ) , then i t has a very p l a u s i b l e antecedent in the noun phrase filling role R in the p r e v i o u s sentence ( h e r e , the p r e v i o u s o b j e c t "a green T-shirt"). But our p o i n t here i s not t o s p e c i f y procedures for choosing among c a n d i d a t e a n t e c e d e n t s ; it is rather to show how a s u i t a b l e l o g i c a l framework p r o v i d e s in a s t r a i g h t f o r w a r d way a l l and o n l y the a p p r o p r i a t e p o s s i b i l i t i e s . c

*

P r e d i c a t e Antecedents 1•

Simple Ve£b Phrase D e l e t i o n

The next few examples i l l u s t r a t e some problems i n v o l v i n g verb phrase ellipsis, which are handled r a t h e r n e a t l y w i t h i n our framework. 6 a . Mary gave Sue a T - s h i r t , b . Jane d i d t o o . The representation sentence 6 a . i s (Ex:T-shirt)

that

we

assign

to

John h i t a l i n g u i s t Fred d i d t o o . as opposed to John was h i t by a l i n g u i s t . Fred was t o o . *Fred"~~dTd t o o . T h i s example i s s i m p l e i n t h a t t h e r e i s only one such one-place predicate abstractable off a subject: X(r)[(Ex:T-shirt)

. Gave r, Sue, x]

that is, giving Sue S u b s t i t u t i n g f o r P? y i e l d s Jane, X ( r ) I ( E x : T - s h i r t ) which

is equivalent

a

T-shirt.

. Gave r , S u e , x J

to

( E x : T - s h i r t ) . Gave J a n e , Sue Note t h a t this representation commit us to b o t h g i r l s h a v i n g the same T - s h i r t , nor need different. The description of one i s

x does not g i v e n Sue they be the f i r s t

flz: T - s h i r t z & Gave Mary, Sue,

z

"a T - s h i r t t h a t Mary gave S u e " , where ^ indicates the i n d e f i n i t e operator. (z might be c a l l e d in English "the T-shirt which Mary gave Sue" if no o t h e r T - s h i r t i n t h e d i s c o u r s e meets t h i s description.) The second T - s h i r t is d e s c r i b a b l e as V\w: T - s h i r t w & Gave J a n e , Sue w

. Gave Mary, Sue, x

Sentence 6 b . , we i n t e r p r e t as p r e d i c a t i n g something (P?) of Jane t h a t had p r e v i o u s l y been p r e d i c a t e d of someone e l s e : P? Jane To i d e n t i f y possible antecedents for P?, we f i n d t h e o n e - p l a c e p r e d i c a t e s that either are g i v e n e x p l i c i t l y o r can b e d e r i v e d v i a lambda a b s t r a c t i o n o n the subject p o s i t i o n . (Again, one p r o b a b l y need o n l y search f o r such predicates in the current sentence if i t has s e v e r a l c l a u s e s or in t h e one or two sentences Natural

i m m e d i a t e l y p r e c e d i n g i t , a s the h a l f - l i f e of predicate antecedents, like that of t y p e a n t e c e d e n t s , seems to be v e r y short. Note that we are v i e w i n g t h e first argument place of a predicate as corresponding to surface subject p o s i t i o n . Though this requires a different representation for active and passive sentences, we see the need f o r t h i s on other grounds, for example, their difference with respect to simple verb phrase d e l e t i o n :

" a T - s h i r t t h a t Jane gave S u e " . It is important to be able to d e r i v e such d e s c r i p t i o n s , s i n c e t h e e n t i t i e s they d e s c r i b e may serve as a n t e c e d e n t s f o r later a n a p h o r i c e x p r e s s i o n s , f o r example, 6 c . N e i t h e r o f them f i t h e r . where "them" r e f e r s t o t h e i m p l i c i t s e t o f T - s h i r t s g i v e n t o Sue, who is also the most p l a u s i b l e a n t e c e d e n t o f " h e r " .

L a n * u a * e - 7 : Nash-Webber 126

2

*

sloppy

identity

Our ne x t ex ample illustrates a phenomenon t h a t h as been called the "sloppy iden t i t y problem" [Ross, 1967] . I t i n v o l v e s account i n g f o r the appearance of an addi t i o n a l reading f o r sentences c o n t a i n i n g d e l e t e d verb phr ases. That i s , while sente nee 7a seems unambiguous, sentence 7b migh t mean e i t h e r t h a t Fred beats G a r t h ' s w i f e or t h a t he beats h i s own. How do we ace ount f o r t h i s ? 7a. Garth beats h i s w i f e , b. Fred does t o o . We a s s i g n 7a. an i n i t i a l r e p r e s e n t a t i o n in which its anaphoric term i s o v e r t l y marked. 7 c . Beat G a r t h ,

'S(Wife)HE1

(where 'S is d e f i n e d to be a f u n c t i o n t h a t takes a unary p r e d i c a t e l i k e W i f e , S c h o o l , etc., and returns a function like "wife-of", "school-of", etc. 'S(Wife), f o r example, is a f u n c t i o n that takes a man as i t s argument and r e t u r n s h i s w i f e : 'S(Wife)John is John's w i f e . Having a function like ' S e l i m i n a t e s the need t o p o s t u l a t e a separate "Y-of" function for every unary p r e d i c a t e Y.) With no o t h e r male a r o u n d , we can a s s i g n HE, t o Garth b y d e f a u l t , t h a t i s , 7 d . Beat G a r t h ,

'S(Wife)Garth

We a s s i g n sentence 7b. the

representation

7 e . P? Fred Now, w h i l e t h e r e are no e x p l i c i t o n e - p l a c e predicates around to serve as an antecedent f o r P?, t h e r e are two ways in which to a b s t r a c t one from 7 d . (i) >(r)[Beat r, ( i i ) y ( r ) [Beat r ,

>(r)[Beat r, y(r)[Beat r,

(While we have not done so h e r e , it is actually i m p o r t a n t t o d i s t i n g u i s h whether an argument p l a c e was o r i g i n a l l y f i l l e d by an a n a p h o r i c e x p r e s s i o n or by a f u l l noun phrase. Observe t h a t i f sentence 7a. had read " G a r t h b e a t s G a r t h ' s w i f e " , which would be r e p r e s e n t e d s i m p l y as 7 d . , the

from

3a. John h i t a c o p . b. L i k e w i s e , a CIA a g e n t . The f i r s t sentence may be r e p r e s e n t e d as 8c.

(Ex.-Cop)

. H i t John, x

and the second one as (Ey:CIA-agent)

8d.

. Q? y

where G? stands f o r an anaphoric p r e d i c a t e like P?, but one whose argument f i l l s a non-subject r o l e . To r e s o l v e 6>?, we must i d e n t i f y the one-place predicates that can be abstracted from n o n - s u b j e c t positions. From 8 c . , we g e t > ( r ) [ H i t John,

r]

substituted for $? in 8 d . , y i e l d s . y,

>,(r)[Hit John,

r]

or more s i m p l y , (Ey:CIA-agent) that i s ,

That i s , e i t h e r Fred beats G a r t h ' s w i f e o r he beats h i s own.

Predicates

The p o i n t of the next ex ample is to illustrate abstracting one-place p r e d i c a t e s from p o s i t i o n s o t h er than the surface subject. In English , "1ikewise", "too", "similarly", etc. , followed o p t i o n a l l y by a p r e p o s i t i o n and then by a noun phrase i n d i c a t e t h a t the r o l e filled by the new noun phrase in a p r e v i o u s l y mentioned p r e d i c a t e is a n o n - s u b j e c t one. (As i l l u s t r a t e d earlier, a noun phrase f o l l o w e d by an a u x i l i a r y requ i r e s t h a t the noun phrase f i l l s the s u b j e c t r o l e of a previous predicate.)

(Ey:CIA-agent)

'S(Wife)Garth] 'S(Wife)r]

Natural

3' Abstracting Non-Subject P o s i t i o n

which,

'S(Wife)Garth] 'S(Wife)r]

The f i r s t represents beating Garth's wife and t h e second, beating one's own. Substituting f o r P?, we get the two p l a u s i b l e readings Fred, Fred,

f o l l o w i n g s e n t e n c e , "Fred does t o o " , c o u l d o n l y mean t h a t Fred beats G a r t h ' s w i f e . Thus in an a c t u a l i m p l e m e n t a t i o n , we would have to i n d i c a t e "he = G a r t h " , r a t h e r than simply replacing "he" with "Garth", in order t o d e r i v e a l l and o n l y the correct lambda a b s t r a c t i o n s . )

. H i t John, y

" L i k e w i s e , John h i t a CIA a g e n t . "

It might appear t h a t one c o u l d r e s o l v e " l i k e w i s e " - e l l i p s e s a t the level of the surface s t r i n g a l o n e , but t h i s i s not the case. Consider the f o l l o w i n g example: 9a. John gave S a l l y her p r e s e n t , b. Likewise, Fred. Obviously, while s u b s t i t u t i n g "Fred" for "Sally" i n the s u r f a c e s t r i n g would y i e l d an i n t e r p r e t a b l e s e n t e n c e , "John gave Fred

Langua g e - 7 : Nash-Webber 127

her p r e s e n t " , t h i s i s n o t the only, nor the most p l a u s i b l e r e a d i n g o f the e l l i p s i s in 9b.

That i s , f o r e v e r y man f o r whom there is some donkey t h a t he owns, he b e a t s i t . Now w h i l e t h e r e is nothing explicit to serve a s the antecedent f o r " i t " , i t t u r n s out t h a t " i t " can a l s o r e f e r e n c e a c e r t a i n kind of functional entity which a r i s e s from e x i s t e n t i a l s .

We r e p r e s e n t 9 a . as 9 c . Gave J o h n , S a l l y ,

'S (Present) SHE.

which we i n t e r p r e t as 9 d . Gave J o h n , S a l l y ,

'S(Present)Sally

she being the only female Sentence 9 b . , we r e p r e s e n t as 9e.

We p o s t u l a t e the following rule identifying a p o s s i b l e antecedent f o r

around.

1 . Find a t y p e r e s t r i c t i o n which c o n t a i n s an existentially quantified variable y not w i t h i n the scope of e i t h e r a universal q u a n t i f i e r or negation.

Fred

To r e s o l v e ( , we i d e n t i f y the o n e - p l a c e p r e d i c a t e s t h a t may be a b s t r a c t e d from non-subject p o s i t i o n s . From 9 d . , we g e t

s u b s t i t u t i n g for c l a r i t y , we g e t

and

flattening

2 . Determine t h e d e s c r i p t i o n o f y with respect to t h i s type r e s t r i c t i o n : any e n t i t y which s a t i s f i e s t h i s d e s c r i p t i o n is a possible antecedent for IT. (Again, we o m i t the s p e c i f i c a t i o n of the rule for determining y's description, a l t h o u g h one should be c l e a r from t h e example.)

for

For i . , t h e r e i s one such type r e s t r i c t i o n - [(Ey:Donkey) . Own u , y ] . The d e s c r i p t i o n o f the e x i s t e n t i a l l y q u a n t i f i e d y i s

-Gave J o h n , F r e d , ' S ( P r e s e n t ) S a l l y " L i k e w i s e , John gave Fred S a l l y ' s present."

ii .

-Gave J o h n , F r e d , ' S ( P r e s e n t ) F r e d " L i k e w i s e , John gave Fred F r e d ' s present."

That i s , i t i s a f u n c t i o n w h i c h , given a u, r e t u r n s a donkey t h a t u owns if u owns a donkey. For a g i v e n x t h e n ,

-Gave J o h n , S a l l y , Fred " L i k e w i s e , John gave S a l l y F r e d . "

Donkey

Again, the p r e f e r r e d i n t e r p r e t a t i o n would be chosen by u s i n g w o r l d knowledge. C.

Own

is a donkey that into i. yields

"Donkeys"

x

owns,

Substituting

iii .

As our f i n a l example of how an appropriate logical representation of a sentence can y i e l d antecedents necessary f o r anaphor r e s o l u t i o n , we w i l l c o n s i d e r a particularly bothersome class of s e n t e n c e s , i l l u s t r a t e d by example 1 0 .

N o t i c e t h a t t h i s r u l e i s independent o f how the type c o n t a i n i n g the e x i s t e n t i a l has been q u a n t i f i e d . Thus, in 1 1 . Some man who owns a donkey b e a t s i t . 1 2 . Which man who owns a donkey b e a t s T t ?

10. Every man who owns a donkey beats i t .

the antecedent of "it" is the donkey obtained by applying function ( i i ) to the q u a n t i f i e d v a r i a b l e associated w i t h "man".

in identifying the The problem lies I t i s not " a donkey", antecedent o f " i t " . The sentence do es n o t mean t h a t every man but who owns a donk ey b e a t s a donkey, rather that he b e a t s any donkey t h a t he there is •no way of owns. Moreover , existential quantifier construing the "it" a s s o c i a t e d w i t h " a donkey" such t h a t How does the falls within i ts scope. "it" emerge from c o r r e c t antecede n t f o r our framework? We first interpretation

for IT.

assign

sentence Natural

10

v

•

Discussion

The examples of Section IV were designed t o i l l u s t r a t e t h e f e a s i b i l i t y of deriving possible antecedents for anaphoric expressions d i r e c t l y from a n appropriately structured logical representation. Notice t h a t basic to t h i s r e p r e s e n t a t i o n is an adequate indication of the scope of logical operators -

the

Langua 128

Nash-Webber

q u a n t i f i e r s , conjunction and negation f o r o t h e r w i s e , we c o u l d not d e a l c o r r e c t l y w i t h a n t e c e d e n t s a r i s i n g from e x i s t e n t i a l s (e.g., t h e examples i n S e c t i o n s IV.A and IV.D). A l s o b a s i c i s the r e c o g n i t i o n and c o r r e c t attachment of m o d i f i e r s - r e l a t i v e c l a u s e s , p r e p o s i t i o n a l p h r a s e s , prenominal modifiers, e t c . - necessary f o r c o r r e c t l y handling "one" anaphora (e.g., Section IV.B). Taken t o g e t h e r , these impose the r e q u i r e m e n t of a p r e - p r o c e s s o r f o r mapping surface strings onto logical forms a t least as p o w e r f u l as t h a t of the LUNAR system [Woods e t a l , 1972]. It follows t h a t much of the burden of antecedent i d e n t i f i c a t i o n is actually being placed upon t h i s pre-processor, g i v e n the need f o r an a p p r o p r i a t e l o g i c a l form b e f o r e our approach can be a p p l i e d . It should a l s o be c l e a r t h a t what we are describing in this paper is e s s e n t i a l l y a competence model f o r anaphor resolution. In ~ Its crudest i m p l e m e n t a t i o n , one would f i r s t generate a s e t of p o s s i b l e a n t e c e d e n t s , and then t e s t each of these by p l a u s i b l e reasoning using g e n e r a l w o r l d knowledge. Of c o u r s e , we are n o t s e r i o u s l y proposing such a g e n e r a t e and t e s t implementation. There are a v a r i e t y of h e u r i s t i c s t h a t can be invoked to a i d the c h o i c e of a most p r o b a b l e antecedent and any performance model must make use of such knowledge. ( H e u r i s t i c s f o r a s s i g n i n g antecedents have been proposed t h r o u g h o u t the linguistics, psychology and AI literatures. See [Nash-Webber, 1977] f o r a d i s c u s s i o n of many of them.) Nevertheless, even a performance model must have the a b i l i t y to determine the space of possible alternatives from which such h e u r i s t i c s are to make t h e i r c h o i c e . Since some of these a l t e r n a t i v e s may not be p r e s e n t e x p l i c i t l y , i t i s here t h a t the approach o f t h i s paper becomes r e l e v a n t . VI,

Further

Problems

As t h i s paper i s n e c e s s a r i l y b r i e f , w e do n o t have the space to d i s c u s s at l e n g t h such i n t e r e s t i n g i s s u e s a s the e f f e c t s o f n e g a t i on or v a r i o u s opaque c o n t e x t s on the a n t e c e d e n t s evoked. These are k i rid s of [Nash-Webber, forthcoming]. d i s c u s sed in We wi 1 1 , however, mention one such i s s u e — t h e problem o f e x i s t e n t i a l noun phrases i n neg a t i v e c o n t e x t s . The scope of negation is inherently ambiguous, and as with quantifiers, different scope interpretations yield different antecedents. Moreover, some i n t e r p r e t a t i o n s may y i e l d no antecedent at all. For example, we know t h a t in a positive context, a n e x i s t e n t i a l noun phrase w i l l always result in an e n t i t y which can be d e s c r i b e d in terms of t h a t Natural

context. So, if John m a r r i e d a Swedish girl, "she" can r e f e r t o the Swedish g i r l t h a t John m a r r i e d . However, in a n e g a t i v e c o n t e x t , "she" may r e f e r t o o t h e r e n t i t i e s depending on how the scope of n e g a t i o n is interpreted. Negated Vejrb 13a. John d i d n ' t marry a Swedish g i r l , b. He l i v e d w i t h he_£ f o r t h r e e y e a r s . "she" = the Swedish g i r l John was involved with Negated Modi f i e £ 14a. John d i d n ' t marry a Swedish b. She was from Denmark.

girl,

"she" = the g i r l John m a r r i e d Negated Main Desc£ijDtor 15a. John d i d n ' t marry a Swedish g i r l , b. She was at l e a s t 15 years HTs s e n i o r . "she" = the Swedish female John married Negated

Proposition

16a. John d i d n ' t c a t c h a t r o u t , b . *He ate i t f o r d i n n e r . A g a i n , we would want to post u l a t e a for neutral initial r e p r e s e n t a t i on but n e g a t i o n , one t h a t might be vag ue, would n e v e r t h e l e s s be t r u e . Only when we to were r e q u i r e d to e.g., i n o rder r e s o l v e an anaphoric e x p r e s s i o n - would we then a t t e m p t to ma ke a commitmen t t o the scope of n e g a t i o n , (Note t h a t a b e l i e f context poses much the same pr oblem as the negation, i . e . t h a t of determin ing scope of b e l i e f . Fo r example, in 17a. John t h o u g h t he m a r r i e d a Swedish girl, b. but she was r e a l l y from Denmark. as in Example 14 above, " s h e " is the g i r l t h a t John m a r r i e d . Here a g a i n , i t i s o n l y the m o d i f i e r "Swedish" that should be taken a s f a l l i n g w i t h i n the scope o f belief.) As we mentioned e a r l i e r , b e f o r e one can f i x on a p a r t i c u l a r MRL, one must p r o v i d e for mass concepts; for tense; for q u a n t i f i e r s other than universals and e x i s t e n t i a l s ; for f a c t s , events, states or acts; and for generics, among o t h e r things, as the following examples illustrate.

L a n * u a * e - 7 : Nash-Webber 129

18a. When John s p i l l s beer, b. his dog l i c k s i j : up. " i t " = the b i t of beer 19.

that John s p i l l s

John drinks beer because i.t tastes good .

" i t " = beer 20a. Many l i n g u i s t s smoke, although b * t n e v know r t c a u s e s c a n c e r . "they" "it" 21a. b.

b.

smoke

=

linguists

A b e a g l e s m i l e d at me y e s t e r d a y , They a r e v e r y f r i e n d l y d o g s .

"they" 23a.

t h e l i n g u i s t s who smoking

Few l i n g u i s t s s m o k e , s i n c e t h e y know i t c a u s e s c a n c e r .

"they" 22a. b.

= =

=

the

generic

class

John dunked M a r y ' s inkwell. r t made h e r c r y .

of

braids

beagles in

"it"

=

24a.

John dunked M a r y ' s b r a i d s i n inkwell. He d i d n ' t regret doing i t .

b. "it"

=

b.

Acknowledcjem e n t s

the

the event of John's dunking Mary's b r a i d s in the i n k w e l l the

This research was supported by the National Institute of Education under Grant MS-NIE-C-400-76-0116 and by the N a t i o n a l R e s e a r c h C o u n c i l o f Canada under Grant A-7642. The a u t h o r s w i s h t o t h a n k D r . A l a n M a c k w o r t h and D r . William Woods f o r r e a d i n g and s u g g e s t i n g i m p r o v e m e n t s t o e a r l i e r d r a f t s of t h i s paper. References

the act of dunking Mary's braids in the i n k w e l l

F i n a l l y , a l t h o u g h w e have i n d i c a t e d t h e need for p l a u s i b l e inference for choosing an a p p r o p r i a t e c a n d i d a t e from a set of possible antecedents (e.g., Section IV.B.), it is also the case that such inferencing may be needed to derive Possible antecdents. That is, not all possible antecedents are structurally derivable. 25a.

N o t i c e t h a t our t r e a t m e n t o f a l l o f t h e examples of Section IV has a d e c i d e d l y s y n t a c t i c c h a r a c t e r : d e s c r i p t i o n s of those e n t i t i e s proposed as p o s s i b l e antecedents are either explicitly present in some f o r m u l a o f t h e MRL, o r c a n b e d e r i v e d f r o m such a formula by appropriate local operations on i t s s t r u c t u r e , independent of the availability of general world knowledge. While there a r e cases where w o r l d knowledge i s r e q u i r e d even t o d e r i v e possible antecedents for pronouns, we believe we have shown that the vast majority can be derived by purely syntactic considerations and that world k n o w l e d g e i s used ( p e r h a p s heuristically) to select from among these. The determination of possible antecedents based on such purely syntactic considerations and the formulation of design constraints o n MRLs t o f a c i l i t a t e t h i s process best describe the objectives of t h i s paper.

Y e s t e r d a y I saw a c o u p l e i n t h e park. H e was w e a r i n g s h o r t s and she had on a d a s h i k i .

C l e a r l y , w h a t i s r e q u i r e d i s some s o r t of general knowledge of the f o r m : "A couple u s u a l l y c o n s i s t s o f two individuals, one m a l e and one f e m a l e . " A l t h o u g h we c a n see no a priori reasons why a f o r ma l approach could not a c c o m m o d a t e t h e use o f p l a u s i b l e r e a s o n i n g i n the d e r i v a t ion of p o s s i b l e a n t e c e d e n t s , we h a v e c h o s e n n o t t o e x p l o r e t h e s e i s s u e s in t h i s paper, R a t h e r , our intention in this work i s t o f i r s t d e t e r m i n e j u s t how far an e s s e n t i al l y s y n t a c t i c approach can be p u s h e d . Natural

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££ocessinc|, Amlter&am. Power of Artificial

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Mash-Wehher