Paper presented at the 6th Amsterdam Colloquium, December 1986. Appeared in the proceedings (Groenendijk et al. eds., pp. 331-353, 1987). Slightly extended version appeared under the same ti t le in R. Bartsch, J. van Benthem, and P. van Emde Boas, eds., Semantics ond Contextual Expressiotr, pp. 295-318, Dordrecht, Foris, 1989. B O U N D V A R I A B L E S I N S Y N T A X ( I n s T H E R E A N Y ? ) A n n a S z a b o l c s i R e s e a r c h I n s t l t u t e f o r L l n g u i s t i c s H u n g a r i a n A c a d e n y o f S c i e n c e s H 1 2 5 O B u d a p e s t , P . O . B o x 1 9 Cument theories of granrmar handle both extraction and anaphorization by lntroducing variables lnto slmtactic representatl.ons. Combinatory categor ia l grammarr e l lmlnates var lables comesponding to gaps. Uslng the combinator U, the paper extends this approach to anaphors, whlch appear to act as overt bound varlables o . O U T L I N E MOst Current theories Of grammar handle t 'extract iontt as wel l aS "anaphor ic b ind ing ' r by in t roduc ing var iab les in to syn tac t ic representat ions . A rad ica l a l te rna t ive is o f fe red by the theory o f combina tory ca tegor ia l g rammarr one sa l ien t p roper ty o f wh ich is tha t i t e l im inates syn tac t ic var iab les conrespond ing to gaps . The ques t ion ar ises whether such an approach can be extended to anaphors, which act as overt bound variables. The paper proposes a natural syntact ico-semantic treatment for the core cases of binding' and examines i ts in te rac t lon w i th ex t rac t ion and coord ina t ion processes . The paper is organized as fol lows. Sect ion 1 reviews some of the fundamental assumptions concerning the rnot ivat ion and format of combinatory categorial grammar. Sect ion 2 introduces the problern posed by anaphors and presents the essence of i ts solut ion.Sect ion 3 takes up the problem of two-complement verbs, and Sect ion 4 pied p ip ing . Sec t ion 5 conc ludes w i th a b r ie f d iscuss ion o f the s ta tus o f Iocal i ty and Pronouns. 1 . B A C K G R O U N D The Government--Binding (GB) theory works on the assumption that al l grammatical relat ions, including those relevant for the assignment of the taro les , a re to be de f ined in s t r i c t l y loca l te rms. There is a precise analogue of this assumption in var ious versions of categorial and phrase structure grammar (CGIPSG): the restr ict ion of the interp r e t a t i o n o f c o n c a t e n a t i o n t o f u n c t i o n a l a p p t i c a t i o n ( F A ) . T h e common assumption leads to essent ial ly the same problems and associated solut ions in GB and in CG/PSG. To express their equivalence in the pert inent respect, I wi l l refer to al l these theories as FAgrammars. FA-grammars make the prediction that natural language functors are to be adjacent to their arguments. One set of data that may const i tute a glar ing counterexample to this includes sentences informally descr ibable as containing a gap lef t by a lef tward or r ightward extracted const l tuent : ( 1 ) a . b . You think tlrat Marlr likes Bill' tltlO do you think ttrat Mar5r likes I put the cup on the table. I put on the table THE BIGCEST CUP YOU HAVE EVER SEEN. The standard solut ion to this problem goes as fol lows. In accordance wi th the FA-s t ra tegy , the gap is f i t led by a p laceho lder in te rpre ted as a var iable and, in necessary deviat ion from the FA-strateglr ' the extracted const i tuent is af f ixed to the sentence in a syncategorematic fash ion resembl ing the in t roduc t ion o f b ind ing opera tors in Iog ic . In v iew o f what such sentences mean, the procedure seems semant ica l l y cor rec t . Not ice , however , tha t th is so lu t ion makes one expec t tha t the poss ib i l i t i es fo r gaps and ex t rac ted cons t i tuents to occur in na tura l language are the same as those for var ia 'bres and operators in logicalsyn tax . Th is expec ta t ion is no t borne ou t . cons ider the fo l l0w ingparad igmat ic cases o f d ivergence no ted in the l i te ra tu re : ( 2 ) a . F r e e v a r i a b l e s : f x r _ say B i l I . b. Vacuous operators: t :< [a]* lrlhat did Mary see Bill? c . Crossed b ind ing : )x , ty [ f x (w) ]t llhat, do you yonde*noa t-o tafk 3!eul _i 1s _^? d . B i n d i n g o v e r a r b i t r a r y d o m a i n s : A x [ . . . r . . . 1 t z r llho., did you rneet John, who likes_ z ? wnoi Oia you go home without rneetingl_-?- 1 ! T h e o n l y w a y o u t i s t o s u p p r e m e n t t h e g r a m m a r w i t h f i l t e r s , i . e . ,w e l l f o r m e d n e s s c o n d i t i o n s i m p o s e o n t h e i n p u t o r t h e o u t p u tof rules. These may be formurated in term" oi gou"rnment project ions(Kayne 1983) , fea ture perco la t ion convent ions iCazdar e t a l . 19g5) ,or storage mechanisms (Cooper 1gg3) etc. C"rror. ,to al1 is the proper_ty tha t , hav ing the s ta tus o f ax ioms, these f i i te rs can a t bes t s ta tethe facts co*ectry but cannot exprain why the facts are as they are. Ades- -s teedman (1gg2) observe tha t there is an ar te rna t ive wayto approach s t ruc tu res r i ke ( r ) . rn "y u i " r , i " " ' i n " FA_res t r i c t ion andp r o p o s e t o a d d f u n c t i o n a l c o m p o s i t i o n t o t h e a p p a r a t u s o f c a t e g o _rial grammar. This extension ar lows the grammar to assign the samein terpre ta t ion to ex t rac t ion s t ruc tu res w i thout invok ing pracehordervar iab les , syncategoremat ic opera tors , and f i l te rs : ( 3 ) C o m p o s i t i o n : I f cATa l " w i th E . g . : v h o NP f e cAT . lu ana $ e cATo1" then t$ , $ f e in te rp re ta t i on l x [ t ' tS ' x i ] .the do you think that lrlary likes s l v p v p l N p : ' * ' s lne The introduct ion of an argument can now be delayed i f , and onry i f ,the i tems intervening between i t and i ;"- ; r ; ; ; I " " . r , combine with i to r i t s func tor . r ' combina t ion" means appr ica t ion or compos i t ion . Notetha t th is ex tens ion does no t mere ly a r low us to der ive the we l r_fo rmed ex t rac t ion s t ruc tu res o f (1 .1 , l t a fso o i f " "= an exp lanat ion o fthe i l l fo rmedness o f the s t ruc tu res in (2 ) . (ea1 1" f ine bu t no t anS, and the ungrammat ica l i t y o f (zU,c ,d I i r= i i . i fow f ro rn the lack o fp roper match i .ng in the par t i c ipa t ing ca tego. i " " . (S teedman 1987 ac tua l l y imposes d i rec t iona l i t y cons t ra in ts oncompos i t i rcn , some o f wh ich fo110w f rom the ,semant ics , , o f compos i t ionand some o f wh ich amount to empi r i ca l c ra ims about Engr ish . They w i l rb e r e v i e w e d a t t h e e n d o f t h i s s e c t i o n . ) Promis ing as th is l ine o f research seems to be , i t i s immedia-te ly c rear tha t FAC-grammar can on ly handre sentences w i th a one_to_one cor respondence be tween "ex t rac ted , cons t i tuents and rgaps , r . r t i sthere fore char renged by the ex is tence o f so-car led paras i t i c gap sen_ t e n c e s l i k e ( A ) : ( 4 ) t r t u l t i p l e b i n d i n g : l r [ . . . x . . . x . . . 1 llhatrdid you file -' vittrout reading _.? He i3 a m€rn rho., everione vho lqpqv5 -, efids .rp likine --.r Uhat, do you tninl -1 got filed witfrout John readiie .r.? The poss ib i l i t y o f mu l t ip le b ind ing . i s p red ic ted by the var iab le introduct ion strategy in FA-grammars. Note, though, that the restr ict ions on the re la t i ve pos i t ions o f the two gaps , d iscussed by Engdahr (1983) and o thers , ca l l fo r fu r ther f i l te rs in those theor ies . Szabo lcs i (1983) observes tha t (4 ) need no t cons t i tu te an argument against the var iabre-free approach. The. condit ions under wh ich mul t ip le gaps are poss ib le a re suggest ive o f a fu r ther spec i f i c operat ion on functors being at work here. The operat ion introduced in t h a t p a p e r u n d e r t h e n a m e c o n n e c t i o n ( a f t e r x a y n e ) w i r r m a k e t h e cor rec t p red ic t ions : 1 ( 5 ) C o n n e c t i o n : I f t e a O t ( . l U ) l c a n d g e C A T O I . t h e n a O t " l " w i t h t h e i n t e r p r e t a t i o n , \ x f C , x ( $ , x ) ] . E.g.: what you fited vittrout reading N p s l v p v p l N p ( v p l v p ) l N p VPINP by cor rnec t ion S l n e U y c o m p o s i t i o n $ i e r t can be demonstrated that there is a fair ly crose paral leri 'sm between the working of composit ion and connect ion on one har.d, and of the rures and f i l ter ing mechanisms employed in FA-grammars on the other. we are not deal ing with notat ionar. var iants, however. As was pointed out above, the relevant apparatus of FA-grammars is st ipulat ive in nature. The appa.atus of FACC-grammar is rrot . The avai labi l i ty of composit ion and corrnect ion fol lows from the fact that we model led lexicar i tems with funct ion-argument structures -i t i .sjust as naLurar for funct ions to compose anci to connect as i t is to apply ' To put i t that way, FACC-grammar explains why the construct ion of empir ical ly adequate FA-grammars is possibre; but not v ice versa. steedman (r985b) raises the quest ion of what inventory of operat ions composit ion and connect ion are drawn from. He observes that they are i .dent ical to the combirrators B and s of curry--Feys (1958), respect ively, and sug,gests that categorial grammar should in general be based on combirrators. Given that one of the fundamentar results of combinatory logic, as curry puts i t , is that , ,var iables are a logicar ly unnecessary but pract icalry very useful devicerr, the exclusion of placeholder var iables from derivat ions wi l l no longer be a mere expedient but receives coherent mathenrat icar support . More precisely, steedman argues on both gr.ammatical and computat ionar plus parsing grounds that adequate grammars for natur.ar ranguage are to be based on (some ex tens ion o f ) the fo l low ing sys tem: 2 ( 6 ) B = l f g x . f ( g x ) [ c o m p o s i t i o n ] S = )rfgx. fx ( gx ) [connection]l .C = ) fxy.fyx [permutat ion_] r = l x . x f i d e n t i t y ] CI = trxf . fx [rais ing] whi le i t may be a matter of debate whether c is to be used in syn tax , I I I t . I; he argues-t l rat I (as wel l as the constant funct ion creat ing combinator K, Ar[a.f ) is to be excluded because i t would al low unrecoverable de le t ion , so to speak . on the o ther hand, the compos i te combina tor c r has for long been known to be operat ive in grammar. C I , i . e , , t y p e r a i s i n g i s t h e o p e r a t i o n M o n t a g u e ( r c Z a ) u s e a to ensure tha t a l l noun phrases der ,o te genera l i zed quant i f ie rs . But , apar t f ronr the t rea tment o f scope, ra is ing seems necessary to p rov ide the appropr ia te ca tegor ies fo r sub jec ts tha t undergo compos i t ion (c f . the example in (5 ) ) , and fo r ,non-cor .s t i tuen ts ' r tha t undergo ex t ract ion or coord ina t ion . The fo l low ing is c iue to Dowty ( lgs5) , wno develops a p roposa l in S teedman (1985a) : (7) John gave (vP lNPacc ) /NPa"a v P \ ( ( v P l N P ) / N P ) VP The raised categories ar low Mary and a book to compose into the ,noncor rs t i tuent " i la r1 r a book , o f ca tegory Vp\ ( (vp /Np) /Np) . Th is may app ly to the two-con,premeri t verb gave i i rectry, or i t may f i rst conjoirr with Susan a record c. f the same category. F inar ry , 1e t me summar ize the ac tuar opera t ions to be r rsed below on the bas is o f S teedman (1997) . A word about no ta t ion : g iven tha t r do no t have a backwards s rash , ! w i r r be used ins tead. ( 8 ) A p p l i c a t i o n : A / B B t B A l B = A Compos i t ion : A /B B/C = A lC B l C A l B = A l C B / C A ! B = A / C R a i s i n g : A +-sYn A =) Ra is in8r " * : A =) 2 . A N A P H O R I C B I N D I N G - T H E B A S I C I D E A l t le are now in a posit ion to appreciate the problems posed by ref lexives and rec ip roca ls (anaphors) . s tandard theor ies fo r low chomsky (1981) in ass ig r : ing the fo l low ing pr im i t i ve p rope l t ies to anaphors : (9 )a . An anaphor i s a var iab le tha , t q lus t no t remain f ree . b . The b inder must be an argument tha t i s h ie r .a rch ica l ry more prominent thar i the anaphor. c . T h e b i n d e r m u s t b e l o c a l . The f i rs t p roper ty i s remin iscent o f p rcper , ty (2a) no ted fo r gaps . In fac t , Por la rd 's (1984) FA-gnan imar . , fo r ins tance, ass igns the same f fee var iab le in te rpre ta t ion to h imse l f tha t he ass igns to the p laceho lder t for gaps. The cl i f fercnce is that himserf and t are acccmpa,nied by son 'ewhat d i f fe ren t a lgor i thms fo r f ind ing the i r an tecedents and f 'o r ac tua l l y ge t t ing bound by them. Now, thcre are obv ious reasons why we I{a4r a book ( v P l N P ) \ ( ( v P l N P ) / N P v P \ ( V P / N P ) B / ( B ! A ) B ! ( B / A ) S / ( S / A ) ( i n d e x e d a s B ) ( i ndexed as B ) ( i n d e x e d a s B ! ) ( i n d e x e d a s C I ) ( indexed as CI) cannot fol low him anc Likeminded theorists in straightfor-wardly assimi la t ing anaphor .s to gaps le f t by ex t rac t ion . F i rs t , ye d id r ro t use p laceho lder var iab les fo r gaps . In our thecry, the fact that "gafrs" must not remain f ' ree sirnply for lcrred from the fact that the pert inent argumerrt must be suppl ied soorrer cr later i f ue are to get a ful l sentence. Given that "gaps'r are r .ot v isib re , i t was easy to a rgue tha t the on ly l tem whose p lacenrent and in te rpre ta t io r , we need to account fo r . i s the "gap f i l l e r . " . Bu t anaphors are sune ly v is ib le a rguments , and the i r b i .nders a re a lso independent ry necessary arguments. so there is every re€isor i to expcct that we need bound var ' iables for the treatment of anaphors. The problem is, though' that we did r iot merely opt lor a frarner*ork which al lcws us to hand le spec i . f i ca l l y ex t rac t i cn s t ruc tu res w i t l iou t . us ing bound var i ab les in syn tax . we commi t ted ourserves to conrb ina tory log ic , wh ich does r ,o t have bound var iab le i tems a t a l l . I t appe:ars, therefore, that thc treatment of anapl ior bincl ing is kind of a test case l 'or the tenabi l i ty of the general cLaim that natural language grammar is to be based on (the proposed kincj of) combinatory logic. rn what iol l .ows r wi l l exanrine anaphors in this r ight. Rather than trying to prcvide a sophist icated empir icar analys is c f b ind ing fac ts , r w i l l focus on the essent ia l p roper t ies o f anaphors within thc context of thc thcory reviewed in sect ion l . Pend ing the d iscuss ion o f locar i t y , re f lex ives appear to have two uncontroversial . proper-t ies. one, thcy are a kind of noun phrase. Two, they di f fer f rom other members cf the species in their rneani.ng. Both John and himserf car i ser-ve as the object of hi t , for instance. But by combin ing John w i th h i t ue ge t the Vp-mean ing lx [ t r i t . ( j ) (x ) ] , and by combin ing h imser f w i th h i t we ge t the mean ing Ax [ r r i t ' ( x ) (x ) ] . Whi le combinatory logic has no bouncl var iab. les and therefore we car:not ide'nt i fy himserf ui th the f i r .st bound instance of x in lx [ t r i t , (x ) (x ) l , i t does have opera t ions (combina tors ) tha t iden t i f y the argurnents of the fur:ct ion they apply to. one sucl i con,binator is U , t h e d u p l i c a t o r : ( 1 0 ) U = l f x . f x x (11) r f g i s , l y . tz [nyz ] , then ug is Ar lx [ rxx ] (Ay)z [nv" ] ) = l x lnxx ] . Let g be nrul t ip l icat icn, for instance -a two-argument funct ion rhose argunrents can of course be dist inct. Therr t {g wi l l be squaring a one-argument funct ion which need not be 1ooked upon as a pr imit ive but carr be def ined as mult iply ing i ts argunient by i tserf . Now, i t is clear that the contr ibut ion of himself to hi t hirnself is the sanie as the cont r ibu t ion o f u to the mean ing o f ug . Th is en ta i l s (12) : (12j The meanir ' : ,g of himself is the same as the nreaning of U. With this we have a straightforward account of the semantics o f re f lex ives . Note , however , tha t the fac t tha t they are e i k ind o f NP appears to be unaccounted for. The rnult ip l icat ion/squaring analog;r may no t seem revea l ing in th is respec t . A f te r . a r1 , u i s a func t ion over mu l t ip l i ca t ion in squar ing , wh i le h i rnse l f i s the f i rs t a rgument of hi t . But not ice that what u cloes to i ts inpr.r t is to turn i t f rcm a two-p lace func t ion in to a one-p)ace func t ion , wh ich is essent ia r ry the sanre as to provide the f i r .st argrrmer:t . The conceptual gap wi lr be b r l d g t : d b y f u r : c t i o n - . a r g u m e n t s t r u c t u r e r e v e r s a , I , i . e . , r a i s i n g : t I I ( 1 3 ) c I = , l x f . f x ( ra1 Ar[ral ( )y lz[nvr] | = Ay\s [ny"] (a) = \ .Cn^r) Th is t e l l s us s -ha t k i nd o f a noun ph rase a re f l e r i ve i s : no th ing bu t a ra i sed k ind . G ive r : t ha t r a i s i ng i s amp ly mo t i va ted i n t he g rammar , ref lex ives are by no means except ior ia l in th is regar .d. The a:bove reasoning, leacing to the r .ecogni t icn that ref lex ive mus t be ra i sec noun ph rases can a rsc be pu t i n t he f o r l cw ing way . l l may be taken to be a p r im i t i ve comb ina to r . r f i t i s no t , howeve r , one o f i t s d e f i n i t i o n s i s ( 1 5 ) : (1s) u = s(cr) tgAhAx[e*(n*) ] ( , rvAf Fy] 1 = )h,rx[rrxx] That i s , u i s ob ta inec l by app ly ing the connector to the ra iser . rn yet other words, every expression that is interp,retable as u has a raised kind cf category, al thougt: not every expression with a raised kind of category is interpretable as U. Compare: llary s / ( s ! N P ) A r [rm] l,iary ( s ! N P ) l ( ( s l N P ) / N P ) ( s ! N p ) ! ( ( s r w p ) / N p ) ( s t N p ) ! ( ( s r N p ) / r { p ) ) e,\ yvx [e*v] )g]y [gmy] lhAx lhxx] Himself has the standard raised Np category of ( "narrow scope. ) ob-jects. But just as the interpretat icn of everyone cl i f fers from that of l {ary, himself has i ts own interpretat icn, too. The gap with heself o f ca tegory s / (s !Np) i s due to the fac t tha t u i s by de f in i t ion a two-place f 'unct ion, wher:ce i t cannot be the interpretat ion of a onep lace func tor . ( f 0 )a . eve ryone s / ( s ! N P ) )rvx [rx] b. everyone (tZ 7 ever:rone hit S / ( S ! N P ) ( S ! N P ) / N P Afvx I fx ] ry lz [n : . t ' yz ] hesel f s / ( s ! N P ) himsel f Cons ide r . now the de r , i va t i on o f a s imp le examp le : himself ( s ! N P ) ! ( ( s ! N P ) / N P ) Ahlu [nuu-] S ! NP )u [rr i t ,uu]l S vx fn:.t 'rx] Sumrnar iz ing the bas ic idea: h imse l f i s ass igned a lex ica l in ter.pretat ior: which ( i ) is conscnar: t with i t being a stancjard kind of NP, and ( i i ) a l l cws r . rs to der ' i ve thc requ is i te in te rpre ta t ion fo r Everyone hi t himself wit l iout fur. ther tr icks. 3 Pr io r to p rc lceed ing to mo 'e compl .ex cases , le t me br ie f l y commer: ' t on the signi f icancc of the fact th:r t tJ is a lexical and rroE a syntact ic cornbinator. Consider the sentence John turned. I f we could argue corrvincingly that this is synoriymous with John turned himself anc l , morecver ' ' i f th is " t rans format icn" o f t rans i t i ve verbs were fu l$ proc luc t ive , we cou ld use U in syn tax : (18) John turned ( s t n P ) / N P u S!IIF-T Engl ish is certainly not a language with suct, propert ies; whether t terc is a lar iguage l ike that I y i l l leave open. But rhat car: we make o f a l l t h i s ? Szabo lcs i (1986) no tec tha t i f we ' jus t iden t i f ied the se t o f poss ib le syn tac t ic cpera t ions w i t t r thc se t o f poss ib le combina tore , ye would be faced with arn undesirable embarras ce r ichesse. Composite combina to ts can per fc rn indef in i te ly compJex opera t ions in one svocp. I t i s obv ious tha t a t most a very sn ia l l se t o f combina tors a re p lausib le as opera t icns on na tura l l ingu is t i c func tors . Now, i t may no t a t al l be accidental that the conrbir .ators B, S, CI that have bee'n found usefu l in Eng l ish syn tax cons t i tu te a p r i rn i t i ve se t - a se t whose m e m b e r s a r e n o t i n t e r d e f i n a b l e . W e m a y t a k e t h i s t o i n d i c a t e t h a t natural languages restr ict the operrat ions freely avai lable in syntax to n :embers o f such pr im i t i ve se ts - o r , a t leas t , to very m.odes t extens io r rs o f such pr im i t i ve se ts . Compos i te con ib ina tors de f ina t le in te rms o f those pr im i t i ves w i l l on ly be a l lowed i f thcy are embod ied by son ie Iex ica l i tem ; the ca tegor ies anc i , /o r in te rpre ta t ions o f those lexical i tems can thcn be regarded as mere abbreviat ior is for compcsite combinators of the given system. 4 Now, th is res t r i c t ion (wh ich c lear ly has promis ing imp l icat ior is for acquisi t ion as wel l ) may turn out too good to L.e true. Note however that the use of ld out l ined above conforms to i t . U is a composite combinator in the system we er iv isage for Engl ish, and i . t can be argued to be lex ica l . Now, suppose there is in f 'ac t a language in wh ich a1 I t ra r is i t i ve verbs can be used in t rans i t i ve ly w i th a re f lex ive n :ean ing (w i thout rnorpho log ica l ind ica t icn) . In the idea l case we expect this language to be based on a combina' ,or system in whict i l l is a prJ-mit ive -for insiance, B, l l and CI . We predict , ther, , that this lar,guage lras no free parasi t ic gaps because S is not avai lable in i ts syntax. ( f t may have across the boa.rd extrac'c ions since cor:nect ives, whose semant ics i s c lose ly re la tec to S , a rc lex ica l i tems. ) We have thus opened a l ine c f researc t . fo r mathenra t ica l l y coherent paranet r i c v a r i a t i o r : . 3 . T T J O C O M P L E M E N T V E R B S So far we have cnly dealt expl ic i t ly with re: i le; : ives as objects of simple trarnsi t ives. In this sect ion the term "two-ccmplement verb' l wi l l be appl ied indiscr iminately to give, introduce, and talk etc. , that is, to any verb that takes two nor:-subject arguments, whcther those be preposit ional or not. About hinself and i ts brottrers wi l l a lso be t rea ted as syn tac t ica l l y p r in i t i ve un t i l Sec t ion 4 . What does the U-proposa. l imply fol these cases? Let us again begin by sketching the gcneral picture. An expression inter 'preted as I l says, ' I am thc f i rst argument of a furrct ion, and i ts second argument w i l l inescapab ly b ind me ' , Bu t th is on ly s ing les ou t uhat l l cares about. I t is by no means necessary that the funct ior i at issue be an atcmic two-p1ace fur:ct ion, anci her.ce U is not specif ic for ' d i rec t ob jec ts . In p r inc ip le , we t ,ave a l I t t ^e fo l low ing poss ib i l i t i es , w i th g an a tomic th ree-p lace verb : (19) r f l x [ fxx ] ( l y lz tu [gyzu] ) = l x lu [gxxu] l (2C) A f Ix [ fxx ] ( l z lu [gazu] 1 = , \x [gaxx ] ( 2r ) lf tx [fxx] ( rylu [eyau] ) = A x fuxaxl rn ( tg ) u apJ : l ies tc g d i rec t l y , so g 's l s t and 2nd argun ien ts w i l l beider : t i l ' i ed and i t s 3 rd (sub5ect ) a rgument , i s le f t in tac t . We mignthave sa id tha t U app l ied to a two-p lace func t ion whoge va lue is Vp,not s ' rn (20) and (21) e had manageid to conibine with i ts rst and 2ndargr :me ' t , respec t ive ly , be fore U ap l ied to i t . Aga in , U ac tua l l yapJrl ied to two-place funct ions thert contain, but are not ic ient ical tog ' Th is ghows tha t u cap l :u rcs the p .ominer :ce conc i i t ion (9b) on theL. inc ie r qu i te gener .a l i y . Let us n.w gpgrl out what al l t f , is rTr€?rrS and pr.esuppr;ses ingran :mat icar te rms. F i rs t o f a r r , thc ge .erar d iscuss ion re l ied on thetypef ree 'ness o f .co ;b i r .a tc ry Iog ic . rn guc t , te r .ms c r i s 5 "= t r r i i [ i fand u is ;ust ' \ f rx[ fxx], with f any funct icn. our granrmar is typr.rd,however ' , so thc degree o f ra is ing needs to be spec i f . ied . Assumingth' t bcth complements are Nps, and ignorir .g t l re direct icnari ty of ca-tegr - : r i€ i . (as i s in t l i ca te i by the use c . f s t rokes ins tead o f s rashes) ,(19) - (2o l - (2L) can be redor :L as fo i rows. Arg js the i r re levant i ten : : i ' t - . ( r s , ; verb ( z o ' 1 verb re f l ex i ve b inder b inde r l \ r r e f l e x i v e ( s l n e ) l ( t s l N P ) l N P ( ( s l n p ) l N P ) l N P( ( s l N P ) I N P ( ( f s l N P ) l N P ) l N P ) N p NP S I N P arg NP ( ( s l N P )N P ) ( S NP S I N P ne f l ex i ve ( s l w p ) l ( t s l r u p ) l r v p ) arg NP NP S ( 2 f ' 1 v e r t , arg ( s N P ) / / c N P ) N P ) bnd ) t'tPN P ) The f i 'st thing these show is that the or ientat io. of the r .e-f rex ive is dependgnt .on the degree o f ra is ing used to ob ta in i t s syn_tac t ic ca tego.y - Tn (zo ' ) and (21 ' ) tne .e f l i x ives are sub jec t -o r ien-t e d ( r e c a l l a l s o ( I 7 ) ) , w h i l e i n ( 1 9 , ) t h e r . e f l e x i v e i s o b j e c t _ o r i e n _ted, due to i ts higher-o.derra:-sed category. Assuming that the rsta rgument o f a th rce-p lace verb may ra ise e i thc r as in (1g , ) o r as in( 2 f ' ) , t h i s i s j u s t f i n e . This analysis reveals two problematic presupposit ions, howwer: (zz)aThe surface crder of arguments must normalry be the same asthe i r , sen ian t ic o rder " ( thc "sema' t i ca l i y f i r s t , , a rgunrent shcu ld be c loses t to the verL . e tc . ) , and b. I t must be poss ib le to compose thc ( ra ised) secc ,nd argr :me l : twit t r the ver.b. The p'robl€n: posed by (zla) is only tco famiLiar from evenytheory o f b ind ing . r ts most recent fo rnrura t ion is , perhaps , Barss- -Lasn ik 's (198€ ' ) d iscuss ion o f two-ob jcc t verbs o f thc shovtype. Theypoint out that t t 'ere arc several phenc,mena demor:strat ing an asymrrret-r ical r 'e lat ion between two l iPs, al l . of which indicate that the l inea.r.l y f i r s t (da t ive) Np is n :oFts p rominent than the second (accusat ive)NP' (They d iscuss the b ind i 'g p r inc ip les , QNp-pror roun re la t ions , wH-movernent and weak c ross-over , super io r i t y , each . . . o ther , and po la r i ty any. ) Nevertheless, phrase st ructures that do not a l low for d iscon t i nuous cons t i t uen ts w i l l e i t he r make the oppos i t e p red i c t i on o r make no d i s t i nc t i on a t a l l . Now, wh i l e t he rea r i za t i on o f t h i s rnay be a nover ty in GB r i terature, Montagovian l i terature has for long used a wrap operat ion to obta in the sur face order in two-complement verbs o f va r i ous so r t s ( c f . Bach (1979 ) and h i s f o t l owers po r l a rd (1984 ) a n d C h i e r c h i a ( 1 9 8 5 ) , t o n a m e o n l y a f e w . ) Now, whi le i t may be a mat ter of debate whether the theory I p resuppose a l l ows wrap ope ra t i ons , t he pa r t i cu la r ve rs ion deve roped in Ades - -S teedmar i ( 1982 ) and used i n S teedman 's subsequen t wo rk does no t . I n f ac t r even the con f l i c t be tween " su r face o rde r ' r ' and " seman t i c o rde r " i s no t acknow ledged . S teedman es tab l i shes ve rba l ca tego r i es on the bas i s o f neu t ra l su r face o rde r and sees no reason to be l i eve tha t t h e ' r s e m a n t i c o r d e r ' r m a y b e a n y d i f f e r e n t ( p . c . ) . H i s p r o c e d u r e i s adop ted i n Dowty (1985 ) , who adds , ' r t he co r rec t t r ans la t i on o f John shoved Mary B i l l w i l l t he re fo re be showed ' (m) (b ) ( j ) , no t shoyed ' (b ) ( n ) ( j ) " . r f we adop t s teedman 's p roposa r , we have to exc lude comp lemen t or iented anaphors f rom th is t reatment . Of (23a,b) only the ungrammati ca l ve rs ion cou ld be de r i ved : (23)a.* John shoyed hersel f Mar1r . b. John shoved Mary herself. (24) John NP showqd herself s ! N P ) / N P ) / N P ( ( S r N p ) / N P )! ( ( ( S ! N P ) / N P ) / N P ( S ! N P ) / N P r ' \ x ) A y show 'mmy Steedman (p .c . ) suggests tha t th is conc lus ion is ac tua l l y cor rec t . on ly the ex is tence o f sub jec t -o r ien ted ob jec t re f lex ives is universal. A number of languages have no complement-or iented ref lexives a t a l r ; in a number o f o thers , p rdpos i t iona l re f lex ives , whether sub jec t o r complement o r ien ted , a re in fac t s t ressed pronous. These la t te r shourd be t rea ted in some pr inc ipa l l y d i f fe ren t way , and the super f i c ia r ly mis read ing case o f Engr ish (and Hungar ian , fo r tha t mat te r ) i s to be ass imi la ted to the i i s . rn what fol lows r wi l l experiment wi. th an anarysis that includes, rather than excrudes, complement-or iented anaphors. My reason is as fo l lows: ( i ) The c rossl ingu is t i c a rgument i s no t water t igh t . Not every language exhibi ts unbounded dependencies in i ts surface syntax, for instance. Ttr is however does not seem to prevent one fron bel ieving that unbounded dependencies are a natural phenomenon that needs to be accounted fo r in , s3y , Eng l ish . ( i i ) Sub jec t o r ien ta t ion is not an unmarked concept in our theory. The subject is nothing but the last argument of an atomic functor. l r /hi le i t is always possible to seek out the last argument of functors of a given ar i ty, there is no genera l way to re fe r to ras t a rguments in combina tory rog ic . ( i i i ) on the bas is o f a rguments re la ted e i ther to b ind ing in the broad sense or to o ther phenomena, r do ber ieve tha t Eng l ish verbs have aI 'semantic ' r argument order that is di f ferent from the surface order. That i s , I be l ieve in the rea l i t y o f someth ing r i ke a wrap opera t ion . ( i v ) The t rea tment o f ex t rac t ion in two-complement cases makes some s l igh t ry ques t ionabre pred ic t ions in S teedman (1997) , a po in t to be re turned to in Sec t ion 4 . so h is assumpt ions do no t make l i fe so easy in purery syntact ic terms that i t wourd make no sense to trv to modify them. I I ! Mar5r NP In view of these considerat ions I have to choose between adopti n g o r s i m u l a t i n g t h e w r a p o p e r a t i o n . T o r e t a i n t h e c o h e r e n c e of the f ramework , r w i l l op t fo r s imura t ion . rn add i t ion to the s tand a r d r a i s e d c a t e g o r y V P ! ( V P I N P ) , c f . ( 2 5 a . , b ) , o b j e c t s w i l l a l s o b e ass igned the non-s tandard ra ised ca tegory VPl (Vp lNp) , c f . (26) . (25)a. introduce Mary to Bit t [ee or] ( v P l N P ) / P p v p ! ( v p ^ p . ) - . v p ! ( v p l p p ) T D ! V P introduce to BilI [ee o"_l ( V P I N P ) / P P ( V P I N P ) ! ( ( V P I N P ) / P P ) VPlNP The VP! (VP/NP) ca tegory used above is s tandard 1n the sense tha t i t p reserves the d i rec t iona l i t y o f combina t ion , where fore i t i s f ree ly obtainable in syntax and may be input to any of the operat ions that w e p i c k e d f o r E n g l i s h ( c f . ( 8 ) a n d S t e e d m a n ( 1 9 8 7 ) ) . I w i l l a s s u m e t h a t o b j e c t s m a y h a v e t h i s c a t e g o r y i f f t h e y a r e , h e a v y r , i . e . , i f f they are heavier than any complement that comes between them and theverb . (Heav iness in th is sense is a f i l te r app l i cab le to s t r ing tha t are arready assembled: i t wir l throw out rJohn introduced to Birr ne, f o r i n s t a n c e . ) The ca tegory VPl (VPlNp) i s no t s tandard in the same sense. I t i s l i ke the rex icar ly ass igned prepos ing ca tegor ies o f wH-words , S/ (S /NP) and i t s b ro thers . Fur thermore , to avo id d isas t rous e f fec ts i t must be restr icted to being input to B/, the forward mixing versicn of compos i t ion o therw ise no t opera t ive in Eng l ish syn tax : 5 , 6 ( 2 6 ) introduce (vPlNP ) /PP llary to BilI VPl ( VPlNP ( v P l N P ) ! ( ( v P l N P ) / P P ) VP Al though th is wourd su f f i ce fo r the coming d iscuss ion , a few comments are in order here to clar i fy the status of this way of s imu la t ing wrap. The fac t tha t VPl (Vp/Np) i s res t r i c ted to B / con t ra dicts the spir i t of our theory, according to which legi t imate combinators are to apply quite unconstrained in syntax. The onry decent way to accomodate the requisi te restr ict ion is to encode i t in the lexicon. And there is an easy way to do i t . rnstead of vp/(vp/Np) we wir l ass ign the ca tegory (vP! ( (VP/NP) /pp l ) / ( (vp lNp) ! ( (vp lNp) /pp) ) to such objects in the lexicon. r t is easy to see that the lat ter category is o b t a i n e d f r o m t h e f o r m e r b y a p p l y i n g L a m b e k ' s ( 1 9 5 8 ) d i v i s i o n t o i t , in our terms, by apprying composit ion to one argument. Thus B is put in to the lex icon (w i th a spec ia l ma in s lash d i rec t ion) and the re le vant par t o f (26) can be rewr i t ten by us ing app l ica t ion in syn tax : (ZZ1 Mary to Bi l l ( V P / N P ) ! ( ( V P I N P ) / P P )( v p ! ( ( v p l N p ) / p p ) ) / ( ( v p l N p ) ! ( ( v p l N p ) / p p ) ) v P ! ( ( v P l N P ) / P P This i s , o f course , a generar ly app l i cab le method o f s imu la t ing wrap in our g rammar . Never the less , g iven tha t the monst rous ca tegory in (27) wourd nake i t imposs ib le to a r range examples in one r ine , r w i l r re ta in (26) - mark ing B/ as B lex in the res t o f the paper . b . every celebr i t5 l who. . . V P ! ( V P I N P ) VP Idea l l y , the in t roduc t ion o f the , rwrapp ing ca tegory , , fo r ob jec tsshou ld a l row us to s imp l i f y S teedman,s appara t fs : i t shou ld a l low ust o g e t r i d o f B ! , t h e b a c k w a r d s m i x i . , g " o r p o = i i r o ' o p e r a t i o n a s w e r l .unfortunately, i t does not. Apart f rorn the treatment of adjuncts, theexc lus ion o f B ! wou ld on ly a l iow the fo r low ing der iva t ion o f to whomyou introduced Np, for in i tance: Z ( 28 ) to whorn ( s / N P ) / ( ( s / N p ) / P P ) you introduced Np S/NP This may be to le rab le i f Np i . s someth ing l i ke B i l l __ i t i s no t to le r_ab le i f Np is a re f r .ex iue (yo , '=e l f ) , hJwever . t t y p"oposa l fo r re f rex_iv iza t ion impr ies tha t the L i .o " . must be d i rec t ry access ib re to there f lex ive . In a der iva t ion r i ke (2 .81in " -=" i : ; ; ; " " , inescapabty com_bines w i th the verb pr io r to the ob jec t re f l l x ive be ing ab le to cometo the p ic tu re . coord ina t ion aa ia ind ica te tha t th is rea l ry excrudesr e f l e x i v i z a t i o n : - ( 2 9 ) i s g r a m m a t i c a l b u t ( s o t i " n o t . ( r w o n d e r i fth is i s p red ic ted by o the i theor ies . ) (zs1 uary hates vhile Judy admires BilrS/VP VPINP S/V; VPINP NP S/NP (30) r g^ . ' hates, uhile Judy admires herself. The sentence To vhom did you introduce ever , so i t must be der ived inana logy yoursel f? is grammat ica l , how_ t o ( 2 5 a ) : (31) to vhom s/ ( s/PP ) you S / ( S ! N P ) introduced B ! B wi th these observa t ions in rn ind , le t us re tu rn to the phenome:non that serves as the main topic of this ="" i ior, : anaphors that aref i rst arguments of three_place verbs. T h e d i s c u s s i o n o f ( 1 g ' ) t h r o u g h ( 2 t , 1 p r e s u p p o s e d t h a t w e a r edeal ing with the ideal s i tuat ion in wnicn ". , . i . "" order and semanticorder co inc ide . Th is co inc idence may ac tua l ry ob ta in in Eng l ish bu t ,a s w e h a v e s e e n , i t d o e s n o t a l w a y s o b t a i n . b o n s i d e r c o m p r e m e n t _o r i e n t e d a n a p h o r s f i r s t . r n c a s _ e s o f a r g u m e n t o r d e r c o i n c i d e n c ew e m a y f o l l o w ( r s ' ; - s e e ( 3 2 ) - ( 3 3 ) , w h i r " ' o t i " " * i s e w e m a y r e l y o nt h e n e w p o s s i b i l i t y o p e n e d u p i " ( Z o i _ e z j _ l s J e t s a ) : (32) Mary introduced to hinself = U lvP/-P)/PP 'YF/TP everybody who. . .V P ! ( V P I N P I VP ( 3 3 ) w h o s/ ( s/NP ) ttary S/VP introduced to hirnself = ll VP lNP s /vp (yp lNp) /ppnss ( s / N p ) / p p - yourself = U ( S I N P ) l ( ( s ! N p ) / N p ) ( S ! N P ) / P P S / N P B (caveat : The exampres in (32) th rough (se ; 60 no t sound very good. ram informed, however, that this is due to the fact that they are notid iomat ic /p ragmat ica l ry p laus ib le . s im i la r examples invo lv ing rec ip_rocals are much better, €.g., l , lanlr introduced t tre boys to each otheror The boys introduced r.{ar5r to each other. The onry reason why r usere f rex ives is tha t r do no t , r i sh to p ropose an expr ic i t in te rpre ta_t ion fo r rec ip roca ls here . ) C o n s i d e r s u b j e c t _ o r i e n t e d c a s e s n e x t . A s ( 2 1 ) s h o w e d , as imp le r rea t rnent i s poss ib le i f f the i *e levant a rgument ( in ourcase ' the d i rec t ob jec t ) can compose w i th the verb be fore the re f ]ex_ive en ters the p ic tu re . Th is i s poss ib re on the neut ra r o rder , (351,bu t no t i f the d i rec t ob jec t i s p reposed or heavy Np sh i f ted , (36)a n d ( S z 1 t !35) Hary introduced John to herself.(36) fho did lrlar5r introduce to herself?(zz7 ilary introduced to herserf everybody who came into the room. Not ice , though, tha t no t on ly (SO) ar . ,6 1ar , a re a p rob lem. A den iva_t ion in wh ich the d i rec t ob j l c t fo rms a cons t i tuent w i th the verbdoes no t a r row the poss ib i r i t y o f non-cons t i tuent con junc t ion tha ti n v o l v e s r e f l e x i v e s : (38) Ir{ary introduced John to herserf and Birr to himserf. The grammaticar i ty of (3g) indicates that both John to herself andBi r r to h imser f .a le .poss ib le representa t ives o f the ca tegory( s ! N P ) ! ( ( ( s ! N p ) / w p ) / p p ) M o r e o . r e r , t h e c o o r d i n a t i o n i n ( g e ) i s n o tonry ca tegor ia r ry bu t a rso semant icar ry coherent , i .e . , i t has thein terpretat ion, \ f rxF( to x) ( j ) (x) e r ( i " i ia ; t l_h: ' i l := ; f ; ; " ind i_cate tha t the der iva t ion tha t cou ld be used ro r ( -gs) i= . " " i i y r ro tgenera l l y use fu l . r t appears that the only way to account for the possibi l r ty of3rd argument or iented lst argument refrexi .ves is to buitd the skip ofthe i rrelevant argument into the interpretat ion of the refrexive.Th is can be done by us ing the compos i te combina tor B(Bt { )c ins tead o fU as i t s in te rpre ta t ion : g ( ss 1 B(Bw)o = )gtxt z lgzx"f (aa1 Hary lntroduced everyone to hinself = U(VPINP ) /PP VPl ( VPlNP )ru ! ( ( vP lNP) /PP) . vJ ! ( (vP lNP) /PPj vP _ (40 ) John to herse l f = B(Bw)C( s ! N P ) / ( ( s ! N P ) / N P ) ( S ! N P ) / n e 1 1 1( ( s r ! r \ rp ) /NP) /PP l(s !NP) I 1 1 15-1xp;ff i \ ,E;n Blex Blex and Blex are syn tac t ica l l y iden t ica l ; the d i f_ re f lex ives is mere ly due to lex ica l need to pos tuJ_ate re f lex ives in te r_ B i l l to himself ( g ! N P l / ( ( s t N P ) / N P ) ( ( s ! N P ) / N P ) ( s r N p ) / N P ) / P Ps ! N P ) ! ( ( ( s ! N P ) m t F F l The der iva t ions o f the con junc ts fe rence in the or ien ta t ion o f the a m b i g u i t y . I t i s to be no ted tha t the pre ted as e i ther u o r B(BU)c is no t spec i f i c fo r my proposar wh ichd ivorces sur face order f rom semant ic o rder . on s teedman,s ass ignmento f verba l ca tegor ies , sub jec t -o r ien ted d i rec t o i . lec t re f rex ives needto be B(BU) ' i f the verb has t r ro corpr " ; ; ; ; . i i r " " t , th is in te rpre_ta t ion , insp i red by E. Jowsey, was suggested to me by Steedman tod e r i v e ( 4 1 ) h i s w a y : introduceo |grself = B(rllI)C to BiIL( ( s t t rp ) /pp ) /wp ( ( s r r l p ) / ! l ) i i i i J rnp lZpp tZ rup t ; ; ( al ) lrary s / ( s ! N P ) rn o ther words , th is ambigu i ty be tween td and B(Br r )c i s spec i f i c fo r3rd argument o r ien ted ls t a rg i rment re f rex ives , i r respec t ive o f wh ichcomprement is taken to be 1st. The di f fe"ur,"" that category assi .gn_ment to verbs 'makes is tha t s teedman 's ca tegor ies woutd requ i re tha tw e e x p r i c i t r y p r o h i b i t t h e w i n t e r p r e t a t i J r r o r s u c h o b j e c t s ( o re lse we ge t the_ urgrammat ica l pa t te rn i l l us t ra ted in (2a) ) and sub_s t i t u t e B ( B U ) . f o r i t . o n m y c a t e g o r i z a t i o n , L ( s w ) c i s m e r e l y o n ea d d i t i o n a l o p t i o n ; n o c a t l g o r i a r l y j u s t i i i u J i ' t " r p r e t a t i o n n e e d sto be proh ib i ted . (And, as we -h" . r " seen, on ly th is t rea tment a l lowsfor complement o r ien ted re f lex ives a t a I1 . ) i l v , , ca tegor ia l l y jus t i_f ied" r rnean th is . u i s a two-prace func t ion . -There fore any ra isedk ind o f ca tegory tha t can be l toked upon as an-a t reas t two_p lacefunc t ion can be in te rpre ted as l t . On lne o tner hand, B(BW)C is ath ree-p lace func t ion , where fore i t i s on ly " " " i . i "u t " as an in te rpre t_a t ion to ra ised ca tegor ies tha t :1 ?g Looked upon as a t leas t th ree_ : l i ; : " t ; : ; : t ' " " ' ( (s r rvp) /Np) r ( ( (s r rvp) / r ' rp )zp ; t ; : . be in te rpre ted in wi th th is we have covered ar r the re levant cases o f sub jec tand complement o r ien ted anaphors . Note tha t the same procedures w i . l lapp ly i *espec t ive o f wheth l r the verb is f in i te o r in f in i t i va l . Toh i t h imse l f i s in te rpre ted as l * t t i t , * * j " j ; ; ' i ;ne h i ts h imser f .whatever procedure makes sure that the mair ix subject or object"cont ro rs ' r the in f in i t i var , ' sub jec t " w i r r au tomat ica l ) ,y p rov ide theb inder fo r the re f lex ive . Cf . S ieeaman ( f9g5b) . 4 . P I E D P T P I N G up unt i l now preposit ional anaphors have been taken to be syntact ic_a l l y p r im i t i ve . To h i rnse l f was jus_ t assumed to be a lex ica l pp w i ththe in te rpre ta t ion Af rxF( to x ) i * ) j . - ; ; i l " ; " " fu . , io r= : .y no t the f ina lsolut ion' Ref lexivehood-is a p"op""ty to be attr ibuted to bare him_serf , and i t is to be guarant led trrai tne ' . " ' "=rrron that takes i tas €u1 argument preserves this property in i ts value. rn o ther words ' we are dear ing w i th p ied p ip ing . p ied p ip ingis , o f course , no t par t i cu la r to re f rex ives bu t i s a lso opera t ive inWH-express ions and quant i f ie rs . A genera l " "n" . " to handfe i t wassuggested to me by Steedman: the pied piper must know in advance thatthere w i l l be an ex t ra func t ion over i t . (42) r f the s tandard ra ised ca tegory o f Np is in te rpre ted as f ,i t s p i e d p i p e r v e r s i o n i s . i n t e r p r e t e d " " C t S ( n t l g ) .c f . x ! ( x / N p ) a n d ( x r ( x 7 p p 1 ) I ( p p T n p t : - Cons ide r h imse l f and eve rybody as p ied p ipe rs : ( 4 3 ) c ( B ( B U ) B ) = A s l f t x [ r ( e x ) ( x ) ] ( a a 1 c ( B ( B ( l f v x [ r x ] ] ) s ) = r g r h v x [ n ( g x ) ] B(BW)B introduces the extra funct ion g (pe7pp1 into the f i rst argr,rnentand c merely changes the surface order in the result (as we have tarkabout hirnself , rather than tark himserf auout); and simirarry for thequant i f ie r ' Th is g ives us prec ise ly the in te rpre ta t ion assumed above,so the derivat ion-of, say, Mary talks about herself can be spel ledout as fol lows. ( l , tary introduces Bi l l to herself /himself po"!=-no n"*p r o b l e m , s o i t w i l l n o t b e g i v e n . ) (45) Mary talks about N P ( S ! N P ) / P P P P I N P = C ( B ( B w ) B ) Now that we have seen that anaphors may legi tmately be prepos-i t ionar , re t us ask whether b inders may be , ioo . r t seerns they may: (46) Hary talks to everybody about himself. Such examples cons t i tu te a no tor ious prob lem fo r the c ra im tha t thebinder must c-command the anaphor, s ince the pp on top of to every-body is a b ranch ing node. The s tandard GB so lu t ion to th is p rob lem isto assume tha t ta lks to i s reana lyzed as a comprex verb in such-casesand everybody ac ts r i ke a d i rec t ob jec t . The c ia im tha t examples r i ke(a0) may no t re fu te the var id i ty o f the c -command requ i rement i s cor_roborated by the fact that in case the binder is a wH-phrase, thePrepos i t ion must be s t randed: (aZ)a.r To uhom did Marlr talk about himself? b. Uho did Mary. talk to about himself? aro *." ] le probrem of (46) can be approached in the present theory in F i rs t , no t ice tha t what we have so fa r does no t a l l0w theb inder to be pre pos i t iona l in the sense tha t i t fo rms a cons t i tuentw i th the prepos i t ion . The reasons are twoford . on one hand, the re_f lexive interpreted as u or B(Bulc t"r ."s-" i -J"grr"nt of the verb asi ts b inder . r f tha t a rument i s comprex , then t i le whore o f i t w i r r bethe binder. To everybody and, Sdy, brothers of everybody do not dif_fer in this respect. on the other hand, r ,binderhood, ' is not a proper_ty a t a r l , so i t i s cer ta in ry no t someth ing tha t a comprex express ionmay inheri t f rom some part of i t . This is i welcome result . our pro_p o s a r p r e s e r v e s t h e p r o m i n e n c e c o n d i t i o n o n t h e b i n d e r n o t o n l yin the sense that the binder may not be an argument rower in thehierarchy, but also in the sensl that i t , "y rot be part of an argu-ment higher in the hierarchy. Therfore we mlst folrow GB in assumingthat the raised pp about himself takes t" i l ; - ;" ; rather than tarks,as one o f i t s a rguments . The exac t execut ion w i r l be d iscussedshor t l y ' (Hote , by the way, tha t b inderhood cou ld p ied p ipe in jus to n e c a s e : i f w e a s s u m e d t h e p r e p o s i t i o n t o t o b e m e a n i n g r e s s , i . e . ,i f i t were in te rpre ted as r , l x .x . rn th is case to everybody wourd bethe same as everybody. But the contrast in (aZ) shows that this can-not be cor rec t . r f i t were , to uhom cou ld serve as a b inder . ) The o ther way to look a t the prob lem o f (46) i s as fo l lows. herself ( ( s ! N P )! ( ( s ! N P ) / P P ) ) r ( p p l r v p ) ( S ! N P )! ( ( S ! N P ) / p p ) = U The u interpretat ion of refrexives surery preserves the c-command re_qu i rement in i t s en t i re ty . However , what p revents us f rom dev is ing aninterpretat ion for refrexives that at tows the binder to be part of aI 'h igher argument"? l le might let the refrexive know in advance thati t s b i n d e r w i l l b e h i d d e n i n a p p a n d r e t r i e v e i t . E s s e n t i a l ) , y , t h i scourd be ach ieved by in te rpre t ing re f lex ives arso as some (s r igh t ry reordered) vers ion o f the combina tors S or d : ( 4 8 ) S A f g x . f x ( g x ) c f . c o n n e c t i o n ( 4 9 ) I = B ( B S ) B : ) f a b x . f ( a x ) ( u x ) An Sre f rex ive wou ld i t se l f be prepos i t ion less bu t i t s b inder wour .dbe prepos i t iona l , and w i th d , bo th the re f lex ive and the b inder wou ldbe prepos i t iona l . such in te rpre ta t ions wour .d a l row us to "1" . . , ru "n"the second par t o f the c -command requ i rement : the b inder courd be apart of an argument higher in the hierarchy. Th is i s a ser ious probrem because i t ra ises the ques t ion towhat ex ten t th is p roposar deduces , ra ther than merery cap lu res , theempi r i ca l p roper t ies o f b ind ing . G iven tha t our combina tors y ie rd thepower o f the ranbda car -cu lus , we cannot expec t our sys tem to excrudethe w i ldes t b ind ing re ra t ions in p r inc ip le . rn th is s t rong sense the-empi r i ca l p roper t ies o f b ind ing cannot be jus t deduced. we have twoa l te rna t ives here . one is to say tha t i t i s an ad hoc proper ty o fanaphors tha t they have the t r -k ind o f in te rpre ta t ion , ra ther than theS k i n d ' A f t e r a l r , . t h e s e a r e l e x i c a r i n t e r p r e t a t i o n s , a n d n a t u r a rlanguages do no t . have every conce ivabre quant i f ie r in te rpre ta t ion int h e l e x i c o n , e i t h e r . A n o t h e r p o s s i b i l i t y i s t o l o o k f o r a n e m p i r i c a r .b u t i n s o m e s e n s e s t i l l p r i n c i p l e d w a y t o e x c l u d e S r e f l e x i v e s . F o rins tance, i t may be con jec tured tha t the d iv is ion o f labor be tweensyntac t ic combina tors and lex icar combina tors i s even s t r i . c te r thanwas ten ta t i ve ly suggested a t the end o f sec t ion 2 . Narne ly , we mightobserve tha t s i s a combina tor opera t ive in syn tax , wh i re n i s no t .Maybe pr im i t i ve combina tors o f a g iven sys tem are no t merery a r row_ed in , bu t a re a rso res t r i c ted to , syn tax . r w i l r no t pursue th isidea in th is paper . Never theress , i t seems r ike one qu i te reasonab lel ine for further research. g Let us now return to the problem how the complex verb talks toshouLd come about. The easiest way to get the effect would be to re-quire talk and to to compose in an ordinary fashion. Due to the argu-ment o rder we are work ing w i th , however , tn is i s imposs ib le . To can-not compose with talk, regardless whether i t is assigned the normarcategory PPlNp or the extravagant category (vn! (VplpF) ) / t tp: (so) tark ( VPlPpto ) /ppabout to _PPlNP_r ( v p ! ( v p / p p t o ) l /Np-This i s in fac t encourag ing . suppose bro thers o f i s Np/Np e tc . r f tocomposed with talk, brothers of courd arso compose with introduce: (sr1t Mary ui l r introduce brothers of feverybodyl. to himserf . . we must assume, then, tha t there is a rear lex icar i tem ta rkto o f ca tegory (vp /np) /ppabout . on the o ther hand, we w i r l no t assumethe ex is tence o f any lex ica l i tem ta lk about (Vp/Np lZppto . i i " i " "uo f such an i tem wi l l exp la in why (52) i s ungnammat ica l , even though i t is general ly understood that talk can be ei ther (Vp/ppto)/PPabout or (vP lPPabout ) lPPto . ( 52 ) r lrtary talked about everybody to hinrself . I expect that the absence of a lexical talk about has deeper reasons but r w i r l no t inves t iga te the mat te r hene. The absence o f a rex icar introduce brothers of seems quite natural . A t th is po in t i t seems necessary to re tu rn to a syn tac t ic aspec t o f the verbar a rgument o rders r assume, in con junc t ion w i th the assumpt ion o f lex ica l ta lk to . S teedman (1987) i s ab le to p red ic t a I I the fo l low ing da ta cor rec t ly : 10 (5S)a.* l fho did you entrust to the heavy responsibi l i f i of . . .? (Sa1.. lJhat do you wonder who to talk to about? b. llho do you wonder yhat to talk about to? c.r lfhat do you wonder who to talk about to? d.r llho do you wonder yhat to talk to about? Prov id ing tha t verba l ca tegor ies re f lec t the neut ra l sur face order o l the i r a rguments , (53a) as we l l as (54c ,d) a re s t r i c t l y excruded. Now, us ing the converse orders r am assuming, the ta lk da ta o f (5a) w i l l s t i l l b e p r e d i c t e d c o r r e c t l y ( t h e p r o o f i s l e f t t o t h e r e a d e r ) . H o w e v e r r ( 5 3 a ) w i l l a l s o p r e d i c t e d t o b e g r a m m a t i c a l r (55) vho you entrusted to the heavy.. . ( S / N P ) / ( ( S / N P ) / N P ) S / V P ( V P l N P ) / P P P P l N P N P (VP /NP) /NP 333 S/NP ) /NP S/NP q This may sound ( 5ga ) improves d i s a s t r o u s . N e v e r t h e l e s s , a s I . S a g ( p . c . ) p o i n t s o u t , s igni f icant ly i f we use to the bpother of: (5e)U.? Uho did you entrust to the brother sf the heawy.. .? whatever the account o f the cont ras t be tween (53a) and (53b) shou ld be, this possibi l i ty of improvement suggests that the pattern common to these two sentences should not be excluded in the strongest sense. Therefore, in this respect entrust as (vpl t ' lp)/pp seems just i f ied. Not ice , however , another p red ic t ion my proposar makes. G iven the fac t that r have tark to, not only talk, as a lexicar i tem, (s4d) also has a reg i t imate der iva t ion : ta lk to i s (vp /Np) /ppabout . There fore , \ {e expec t tha t (54d) can be improved exac t ly l i ke (53a) can, bu t we do not expec t the same fo r (5ac) , in the absence o f rex icar ta rk about : (54)e.** t lhat, do you wonder uho, to talk about pictures of, toa? f.? Uho, do you uonder vhat, to talk to the brother of, abouta? My in fo rmants repor t tha t the pred ic ted e f fec t i s in fac t very s t rong. (Note , by the way, tha t the cont ras t in (54e, f ) shows tha t improvement has no th ing to do w i th per fo rmance fac to rs re la ted to rength . ) A f te r th is excursus , Ie t me po in t ou t tha t even i f to and bro thers o f a re unab le to compose w i th the verb in sentences l i ke (46) and (51) , there are var ious undes i rab le poss ib i l i t i es fo r compos i t i cn . (56)a.r l lary belreves that John roves herself . b. llho does l{ary believe that John loves? (sz1r. t ' rary talks about brothers of herserf . b. llho does Hary talk about brothers of? o f these, (56a) may ar ise i f the func tor herse l f app l ies to i s ber i -eves that John loves, and (57a) may ar ise i f the pp/Np herself usesin p ied p ip ing is about b ro thers o f . wh i re th is ra t te r pa t te rn i s infact grammaticar with picture-nouns, those obviousry do not repres€ntthe genera l case. 5 . L O C A L I T Y A N D P R O N O U N S Three proper t ies o f anaphors were l i s ted in (9 ) : the necess i ty fo rthere to be a b inder , the prominence cond i t ion on the b inder , and therocar i ty cond i t ion on the b inder . r have argued tha t the r r in te rpre_ta t ion essent ia l l y cap tures the f i rs t two o i these and can, -a t thesame t ime, be handred in the same sys tem tha t takes care o f ex t rac_t i o n a n d c o o r d i n a t i o n e t c v q ^ s v r s L Turn ing to l0ca l i t y now, i t i s to be observed tha t l0car i t ycannot appear as a na tura l cond i . t ion in a sys tem tha t inc r ,udes com_pos i t ion and s imi la r "unboundedness opera t ions , , . r f the t rea tment o fanaphor b ind ing is . to be par t o f th is sys tem, we must resor t to b ru tefo rce to capture the roca l i t y cond i t ion . The bru te fo rce method is ,bas ica l ry , to requ i re tha t u app ly to func tors tha t a re lex ica l ins o m e s e n s e . w i thout go ing in to de ta i l s w i th the prec ise de f in i t ion o f rex_ica l i t y , le t us ask how sad one shou ld be about th is . rs the loca l i t ycond i t ion par t and parce l to the no t ion anaphor , where by , ,anaphor , ,we mean an i tem tha t must be bound Uy a c_c tmmand ing argument ( i .e . ,wh ich is in te rpre ted as U)? The existence of long-distance anaphors has for 10ng beenwel l -known. Most rong-d is t " r , " " r r , .phors necessar i ry res ide w i th in Npsand are exc lus ivery sub jec t -o r ien ted e tc . , tha t i s , appear to have arather pecul iar restr ict ion. A very interest ing case from Modern Greekis repor ted by ra t r idou ( rggo) , however , Greek has two anaphors inthe w-sense, of which ton eafton tou is to be bound rocarry, and tonidhio can be bound, as she puts i t in GB terms, outside i ts governingcategory . The da ta ra t r idou presents ind ica te tha t th is ra t te r rong_d is tance anaphor does no t exh ib i t the pecu l ia r res t r i c t ions ment ionedabove. For example : (58) O Yanis' ipe ston costaoti i lrraria aghapa ton idhio.1 sa id to tha t loves h imse l f i / j / *k Th is seems to ind ica te tha t locar i t y can in genera l be d ivorced f romthe core not ion of anaphor in the u-sense, cJntrary to what currenttheor ies suggest . The rocar i ty cond i t ion ( rex icar i t y requ i rement ) mayin fac t be a b ru te fo rce dev i le emproyed by na turar ranguage to fac i_l i ta te p rocess ing . c lear ly , i t i s very use fur fo r the hearer i f b ind_ing ambigu i t ies a re reduced by hav ing d i f fe ren t fo rms fo r u ; bu t therem a y b e n o t h i n g m o r e t o i t . w h i r e m y p r o p o s a l ( a s i t s t a n d s , a t r e a s t )i s unrevear ing w i th respec t to what rocar i ty cond i t ions d i f fe ren tlanguages may impose on the i r anaphors , i t may be taken to be revea l_ ing in the sense that i t predicts locari ty to be a more or Less ad hocmatter. And, besides exot ic data r ike (5g), acgris i t ion studies seernto suggest that even i l the Engl ish kid" thinXs so. There is another phenomenon that this proposar makes a predict ion fo r , namely , bound versus unbound pronouns. wh i re anaphors ( re f rex ives and rec ip rocars ) must be bound,pronouns may or may not be. one important discovery has been that i ti s eas ie r to charac ter ize the cond i t ions under wh ich pronouns cannotbe bound than the cond i t ions under wh ich they can. Th is d iscovery i sb u i l t i n t o t h e B i n d i n g p r i n c i p r e s o f G B . " * L 1 r a s o t h e r t h e o r i e s .Compare the clauses for anaphors and pronouns: (59)a . An anaphor must be bound (= co indexed w i th a c_commanding argument) in i ts governing category. b. A pronoun must be free in i ts governing category. c . A re fe ren t ia l express ion must be f ree . Arthough factually correct, this formulation has something funny abouti t . I f I contemplate about the meaning of himself ( tnat is, aUtutwhat dist inguishes i t f rom other t tps), the fact that himself must bebound wi lr certainly come to my mind. r f r contemplate about him,however , my f i rs t thought w i r r cer ta in ry no t be , ,wer r , h im is ani tem tha t cannot be bound to sorne th ing too c rose to i t ' . rn o therw o r d s , t h e n e g a t i v e c h a r a c t e r i z a t i o n g i v e n f o r p r o n o u n s i s i n t u i t _ive ly on a very d i f fe ren t leve l than the pos i t i ve charac ter iza t ion given for anaphors. what does combinatory rogic have to say here? As was pointed out above, i t has no bound var iab le i tems. r t does have f ree var i_ abres. But those are l ike any name: they start out f ree and remain free. This does not prevent them from coreferr ing with another name,though: the same thing may happen to have more than one way to namei t , so to speak . And there are combina tors l i ke u , o f course , wh ichg ive the same e f fec t as var iabre b ind ing in usuar theor ies . The morar of this story seems to be the forrowing. The i temsknown as pronouns are mult iply ambiguous. we must dist inguish boundpronouns and free pronouns in the f i rst place. Bound p"-r ,our," """members o f the c rass o f anaphors . As a very f i rs t approx imat ion , they can be assigned a u kind of interpretat lon (and tne ant i_locar_ i ty condit ion can be captured by making them obr. igatory pied pipers). Free pronouns on the o ther hand are essent ia l ry de ic t i c and, g iv en the assumptions above' are inf ini tely many wlys arnuiguous. ( tn comparison with the usual formrrrat ion, we r"y ="y that i le[r""" j i "not one variable to which inf ini tely many di i ferent varues can be ass igned bu t ra ther i t represents in f in i te ly many d i f fe ren t var iab_Ies , each hav ing i t s va lue f i xed once fo r . f f . ) on the grammat icar s ide , the imp l ica t ions o f th is theory a rein l ine w i th Re inhar t ' s (Lgg3) . I t i s common to t rea t ins tances o f' r b i n d i n g b y a n a m e r r a n d " b i n d i n g b y a ( p o s s i b l e ) q u a n t i f i e r , r i n t h esame way. Reinhart separates true binding from mere coreference, ob-serv ing tha t the prominence cond i t ions in the fo rmer case are much st r i c te r . Th is i s what my proposar captures . r t seems, there fore , that both the meri ts and the drawbacks of the present proposar forpronoun b ind ing are essent ia l l y the same as hers . S t r i c t l im i ta t ion on space fo r tunate ly p revents me f rom d iscuss ing them in de ta i l , however . 1 l A C K N O U L E D G E I , I E N T Th is p roposa l f o r anapho rs deve rops an i dea ske tched i n szabo l cs i ( 1 9 8 5 , 1 9 8 6 ) . r n d i s c u s s i n g h o w t o i n c o r p o r a t e i t . i n t o a j o i n t p a p e r ( i n p rog ress ) , I r ece i ved many va luab le commen ts f r om Mark S teedman , a s i s i n d i c a t e d i n t h e t e x t . N O T E S 1 c o n n e c t i o n i s r e n a m e d " s u b s t i t u t i o n " i . n s t e e d m a n ( 1 9 g 5 b , 1 . 9 g 7 ) . ? T h e s e d e f i n i t i o n s a r e q u o t e d f n o m c u r r y - F e y s ( 1 g 5 g , 1 5 2 1 5 3 ) , so r f o l l ow the i r no ta t i on . Reca r l t ha t t he i r r og i c i s t ype f ree . 3 A rn im von s techow has k ind l y po in ted ou t t o me tha t my p roposa l i s a n t i c i p a t e d i n Q u i n e ( 1 9 6 0 ) , a d o p t e d i n h i s ( 1 9 7 9 ) . f a m ' a u i y ashamed o f t h i s gap i n my ph i l osoph i ca l educa t i on . 4 one compos i t e comb ina to r t ha t i s appa ren t l y ope ra t i ve i n Eng r i sh i s BBB (gene ra l i zed compos i t i on ) . Fo r i ns tance , ( 54a ,b ) and ( 5s j ce r . r no t be de r i ved w i thou t i t . 5 M ichae l I ' t oo r tga t po in t s ou t t o me tha t Vp / (Vp lNp ) needs to be res t r i c ted to s impLe B / i n f ac t . Gene ra l i zed compos i t i on , i n con_ j u n c t i o n w i t h t h e p i e d p i p e r c a t e g o r i e s o f S e c t i o n 4 , w o u l d d e r i v e the s t r i ng t o l i a r y B i l l i n te rp re ted as rMary t o B i r r , . The a r te rna t_ i ve p roposed be row avo ids t h i s unwan ted consequence as we1 l . I am gra te fu l t o h im fo r .d i scuss ion abou t t h i s i ssue . 6 In GB terms we might say that two_complement verbs real two comp lemenb bu t a smar l c l ause can be ob ta ined v ia A -ba r t i on . Th i s seems l i ke hav ing the cake and ea t i ng i t , t oo . 7 B ! m igh t be expe l l ed f r om syn tax by ass ign ing a spec ia r d i v i ded ca tego ry t o eve ry ra i sed ca tego ry i n t he Lex i con . wh i re i t may be ul t imate ly usefu l to f ree syntax f rom any k ind of d isharmonic compos i t i on , no te t ha t t he b ig emp i r i ca l d i f f e rence be tween B / and B ! i n Eng l i sh i s t ha t t he l a t t e r appea rs t o be qu i t e gene ra r l y ava i l ab le . I The reader may check tha t B(Bn)c g ives the same e f fec t C 'd the verb , app l ied i t to the ob jec t , and used U fo r the The use o f s impre c wou ld no t in generar sorve our p robrems and wou ld no t a l low the der iva t ion o f (SA) e i ther . 9 r t might be tempting to use s to interpret pronouns not str ictry c-commanded by their binders. At least a simple adopt ion of this idea wou ld have undes i rab le e f fec ts , however 10 Th is i s no t l i te ra l l y t rue bu t , as fa r as verba l ca tegor i .za t ion is concerned, h is g rammar wou ld indeed der i .ve those resur ts . 11 Another se t o f da ta tha t I cannot d iscuss here tha t they are per t inent to the top ic o f th is paper ed anaphors , c f . Barss (199 ) : ( i ) uhich pict t 'es of himselt iT5 oo"= John. think Bi l l . r ikes? ( i i ) Uh ich s to r ies o f h imse l f i l r j d id John. publ ish without 8 i11 . s ign ing? These are no t too d i f f i cu l t to hand le , however , g iven some ex tens ion o f the proposa l in the tex t . I y have adj uncas i f we ref lexire. , t hough , desp i te the fac t inc ludes ex t rac t R E F E R E I I C E S Ades, A . and I t l . J . s teednran (1982) , on the order o f words . L ingu is t i cs and Philosophy 4. Bach, E. ( f979), Control in Montague Grammar. Linguist ic Inquiry 1O. B a r s s , A . ( 1 9 8 4 ) , C h a i n B i n d i n g . M a n u s c r i p t , M I T . Barss , A . and H. Lasn ik ( rga6) , A Note on Anaphora and Doub le ob jec ts . Linguistic Inquiry 17. C h i e r c h i a , G . ( 1 9 8 5 ) , A s p e c t s o f a C a t e g o r i a l T h e o r y o f B i n d i n g . I n O e h r l e e t a I . ( l n p r e s s ) . Chomsky, N. (1981), Lectures on Government and Binding. Foris. Cooper, R. (1983), Quant i f icat ion and Syntact ic Theory. Reidel. cur ry , H .B. and R. Feys (1958) , cornb ina tory Log ic r . Nor th -Hor rand. Dowty ' D-R. (1985) , Type Ra is ing , Func t ionar compos i t ion , and Non- ' Const i tuent Con junc t ion . In Oehr1e e t a I . ( in p ress) . Engdahr, E. (1983), Parasi t ic Gaps. Linguist ics and phirosophy 4. Gazdar, G. et al . (1985), General ized phrase structure Grannmar. B lackwel l . ra t r idou , S . (1986) , An Anaphor Not Bound in r ts Govern ing-ca tegory . Linguistic Inquiry 17. Kayne, R. (1983) , Connectedness . L ingu is t i c Inqu i ry 14 . Lambek, J . (1958) , The Mathemat ics o f sen tence St ruc ture . Amer ican I{athenatical llonthly 65. Montague, R. (1974) , Formal ph i losophy. ya le Up. oehr le , R . e t a r . , eds . ( in p ress) , ca tegor ia l Gramrnars and Naturar Language Structures. Reidel. Porlard, c. (1984), General ized phrase structure Gramrnars, Head Grasunars and Natural Languages. PhD thesis, Stanford University. Qu ine , l l l . v .o . ( rg0o) , var iabres Expra inec t Away. p roceec l ings o f the American Philosophical Society 1O4. Reinhart , T. (1983), Anaphora and Semantic Interpretat ion. Croom H e l m . von s techow, A . ( rgzg) , Deutsche wor ts te l lung . rn Me iser and pam, eds., Linear order and Generat ive Ttreory. John Benjamins. Steedman, M.J . (1985a) , Dependency and coord ina t ion in the Grammar of Dutch and English. Language 60. s teedman, M.J . ( rggsu) , cornb ina tors and ca tegor ia r Grammars . rn O e h r l e e t a I . ( i n p r e s s ) . s teedman, M.J . (1987) , combina tory Grammars and paras i t i c Gaps. Nat ural Language and Linguistic Ttreory (to appear). s teedman, M. -J . and A. szabo lcs i ( in p rogress) , Aga ins t Empty ca tegor ies [Working t i t le]J. szabo lcs i , A . (1983) , EcP in ca tegor ia l Grammar . Manuscr ip t , MaxP lanckIns t i tu t f i i r psycho l ingu is t i k . szabo lcs i , A . (1985) , combina tors and the pro jec t ion pr inc ip re . paeer to the conference on categorial Grammars and Natural Langr:qge Structures. Tucson. s z a b o l c s i , A . 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