On Context Dependence In Modal Constructions

O n C o nt ext D ep endence III Modal Constructions Anette Frank and H ans K amp Rank Xerox Research Centre and University of Stuttgart new rep r es e n t at i o n format for dy n am i c discourse in D RT , where contextual dyn am i cs is modeled i n terms of up d ate conditions. This new representation format is motivated by the study of context depen­ dence in modal constructions, i n particular by serious problems b esetting ear­ lier approaches to modality and modal subordination in D RT . We present an alternative D RT an alys i s that provides a unified ana l ys i s of relative modality and modal subordination, and which accounts for a wi der range of data as regards m odal subordination relative to negation and g r ad e d modal context.s. Thi s paper investigates a 1. Introduction One of the d i s t ing u ish i n g featu res of D RT i s its focus on re p r e sentat i o n al aspects of meaning . A nother important characteristic of the theory is the in­ sight that the m ean i n g of sentences cannot be determined by truth conditional semanti cs proper. A pervasive feature of natural language semant. i cs i s that. it is essentially depe n d ent on ( m aterial introduced within ) t h e previous discourse context ; DRT and FCS were t. he first sema. n tic theories that made this specific kind o f context dependence formally precise ( Kam p ( 1 9 8 1 ) , IIei m ( 1 982) ) . To account for anaphoric binding i n donkey sentcnces ( l a) , D RT and FSC a.ss i gn the conditional a ' dynamic' an alys i s which i s ' i n ternal' i nasmnch as it concerns the relation between t h e antecedent a n d t h e scope. It i s ' e x t er­ nally static' in t h a t the dynam i cally ' aug m e nte d ' contexts of the antecedent and cons e q ue nt are ' i n v i s i b l e from the ou tsi d e ' , i .e. , from the vantage point of the conditional as a whole. This accounts for the fact that the i n d efi nit e in t h e antecedent of the first sentence of ( l a ) can serve as antecedent for t he pronomin al i n i t s scop e , b u t not for t h e p ronoun i n t h e :;ecoIl d senten c e . , (1) a . I f a farmer owns b. If a farmer owns a a donkey, h e beats it. # H e doesn't l i k e it. donkey, he beats it. It might kick back . S i n ce Roberts ( l 989) i t is wel l-known that there are exceptions to this rule. In Roberts' account the con d itional i s a nal y z e d as externally static but. internally d y n a m i c to accou nt for ( l a) , while i n 'moda.1 subordination ' contexts ( l b ) a special a cco m m oda tion device may a pp l y, to make material t h at is e m b e d d ed within the antecedent or scope of the con ditiona.! accessible for anaphori c b i n d ­ i ng . Geurts( 1 09.5) pro p ose s a presl1ppositional accoun t. of modal su b ordinati o n that i s more restrictive than Ro berts ' a.c commodation an alysis. © 1 99 7 by A nette Fra n k a n d H a n s Kamp Aaron Lawson (eo), SALT VII, 1 5 1 - 1 68 , Ithac a , NY: Corn e l l U n i versity. ANETTE FRANK AND HANS KAMP 1 52 Both Roberts ' and Geurts ' DRT analyses are reconstructions of Kratz e r's ( 1 978, 1 99 1 ) analysis of relative and graded modality. However, t heir D RS rep­ resentations do not distinguish between, e.g. , deontic and epist e mic modality, nor between indicative and counterfact u al conditionals. Geurts ' analysis does not account for modal subordination relati ve to a negated context , and does not appropriately render the context dependence of modal sentences that are to be interpreted as being relative to the preceding factual discourse. We propose a new representatio n format for dynamic discourse i n D RT , which allows u s to state a unified analysis of relative modalit y and modal sub­ ordination that reconstructs Kratzer's notion of context dependent or relative modality at the DRS level, and thus accounts for the p r oble m s j ust ment i o n ed. 2. Cont ext dep endence in modal constructions There i s a broad consensus nowadays that modal verbs, much like frequency adverbials , are best analyzed in terms of generalized quantification . This view not only leads to a n atural analysis of graded modals ( p robably, unlikely) , but ­ more important ly-it captures the inherent context dependence of modal con­ structions: as e.g. pointed out recently by von Fintel ( 1 995 ) , gen eralized quan­ tifiers can be taken to involve a variable of an appropriate type, which gets inte r preted in context and thus determines-in conj unction w i t h the restric­ tive clause- the quantificational domain. For modal operators this vie w was anti ci pated by K ratzer ( 1 978) , who characterized modal operators as bei ng rel­ ative to, or conte x t u ally dependent o n , different kinds of i n t ensional c o n text s . 2. 1 Relative and graded modality The i m p act of K ratzer 's analysis of relative m odality is that modal expres­ e.g. must in ( 2 ) , are not semanticall y ambiguous between different read­ i ngs traditio n a l l y classified as epi.stemie, deontic or circumstantial, but that there is a n e u t ral modal operator that is conte x t ua lly dependent on d i ffer­ ent k inds of i nten s ional background c o n t e x t s-e p istemic (2<1) , deontic ( 2 b ) and circumstanti al (2c)-that constitute its modal base ( Kratzer{l 99 1 : 639/640 ) ) . sion s , (2) a. ( In view of the available evidence, ) Jockl must be the mur dere r . b . ( In vie w of what the law p rovid e s , ) Jockl must go to j ai l . c. ( In view of t h e present state o f his nose etc . , ) Jockl must slleeze. Kratzer( 1 9 8 1 ) extends this analysis to the concept of gra ded m odality, i . a. in order to account for deon t i c and counterfactual modalit y ( 3) , where the modal operator i s analyzed as dou bly rela tive: Graded modality i nvolv e s a second b ackg r ou n d context , t h e o l'de ring s o u rce o( w ) , wh i ch i n duces a partial order :::;o ( w) on the set of worlds determi ned by the modal base f ( w ) . For the deontic ON CONTEXT DEPENDENCE IN MODAL CONSTRUCTIONS conditional ( 3a) , the modal operator is relative to a circumstantial modal b ase and a deontic ordering source, while the counterfactual ( 3b) is analyzed relative to an empty modal base and a totally realistic ordering source. ( 3) a. If M ax buys a car, he must pay taxes . b . If Max had bought a car, he would have paid taxes . As is brought out by ( 4 ) , modal subordination is to be viewed as a special in­ stance of the more general phenomenon of relative modality: in ( 4a ) the modal base is not given by linguistic means, and t herefore must be accommodated; in (4b) t he modally subordinated sentence is interpreted relative to the context set up by the scope argument of the first , modalized sentence ( which in turn is to be i nterpreted as r·e/ative to some accommodated backgroun d context ) . (4) 2. 2. a. ( Cleo i s nominated for t h e first race . ) Cleo might win the first race. b. Suppose C leo were nominated for the first race. She would certainly win ( i t ) . DRT accounts of m odal subordi n a t i o n K ratzer's analysis of relative and graded modality is wel l suited to cope with anaphoric binding and presupposi tion projection out of modal contexts, and this is the m ai n reason why i t was ' reconstructed' i n various t heories of modal­ ity in the framework of D RT , as e.g. Roberts ( 1 989 ) and Geurts(l !J95 ) . Now , while both Roberts' and Geurts' theories are built on Kratzer's analysis of relative and graded modality, we argue t h at they do not treat modal s ubordi­ nation as a special instance of relative modality. Roberts ' accommodation account. Following K ratzer's analysi s , modal operators are interpreted relative to a modal base and an ordering source, which denote sets of propositions, but are not defined in the D RS language and therefore are not represented in the D RS . The impact of Roberts' theory is to allow for a ccommodation of ( sub ) DRSs in order to account for modal subordination: in (5) the modal base of the necessity operator is further re­ stricted by accommodation of the scope D RS of the previous modal structure into the restri ctor DRS o f t he second, 'subordi nated ' modal construction . ( 5) A t h i ef I might break i nto the house. He would take the silver. I 0 thief( x ) break- into- the-hollse ( x ) x thief( x ) break-i nto- t h c- h O ll s e ( x) x 0 y y=x take-si l vcr(y) 1 53 ANETIE FRANK AND HANS KAMP 1 54 A general problem of the accommodation account i s that it i s too unrestricted ( see Geurts( 1 995) ) . Moreover, the analysis doesn't distinguish between epis­ temic (5) and deonti c modality ( 6 ) : (6a) is assigned a D RS that is structurally i dentical to ( 5 ) , and similarly (3a-b) are assigned identical DRSs ( modulo tense ) . The semanti c distinction between epistemic and deonti c modality is only available at the level of the verification conditions . This is unsatisfactory in particular in cases like (6b) , where the deonti c context is introduced by linguistic means: the context dependent interpretation of the deontic senten ce cannot , then, be represented in the DRS . Thus, Roberts ' th eory is a hybrid t heory: rel ative modality is only captured in terms of verification conditions, while modal subordination, a special i nstance of relati ve modality, is accounted for, by the accommodation mechanism, at the level of the DRS. (6) a. A fireman may break into t h e house. He must rescue t h e child. b. A ccording to German tax law , Max must pay taxes for his car. Geurts ' presuppositionaljanaphoric account. Geurt s ' theory is also built on Kratzer's analysis , while focussing on the p henomenon of presupposition pro­ j ection. It diverges from Roberts ' account in that a modal is taken to presup­ pose its domai n , thereby t aming the powerful device of accommodation. The D RS language is enriched by propositional referents p, q, which denote sets of world-function pairs. Such referents can build terms p+ f{, "the indexed propo­ sition denoted by p incremented w i t h the information in f{" ( Geurts( 1 995:8 1 ) ) . Modal operators are represented as relations between propositional terms p and q ( see ( 7 ) ) , and are assigned the meaning i n ( 8 ) , where the ordering source a is a set of propositions and a, a' sets of world-fu n ct ion pairs. Modal subor­ dination is analyzed in terms of a ( vari ant of) the theory of presupposition as anaphora ( van der Sandt ( 1 992) ) : the presupposi tional domain q of a subordi ­ n ated modal i s bound to a referent p established b y t h e restrictor or scope of a preceding modal sentence. It is easily seen that a presuppositional t heory of modality-in conj unction with accessibility constraints for ( p resuppositional ) binding-is more restricted than Roberts' accommodation account. (7) p q q' q = (8) I �lief(x) break-in(x) I I I A thief m i ght break i n . H e would take t h e sil ver. Geurts( 1 995:86/87) p + p O q q' = q + take-silver(x) q 0 q' Let a be some gi ven ordering source. Then: Geurts ( 1 995 :90) Iw { D ) = { {a, a') : VS E a , 3t E a , t :::;o (w) 05 & Vt' E a , if t' :::;o (w) t then {'EO" } Iw( O) = { ( a , a' ) : 305 E a , Vs ' E a, if 05 ' :::;o (w) s then 05' E O" } But t he theory suffers from two main problems . First , as in Roberts ' analysis the ordering source i s not represented in the D R S , bllt only figures i n the verification cond i tion ( 8 ) . The epistemic vs . deonti c sentences ( 3a-b ) are thus 155 ON CONTEXT DEPENDENCE IN MODAL CONSTRUCTIONS assigned i dentical DRSs. It i s also not possi ble to represent the presupposi­ tionall anaphorically dependent meaning of deontic sentences that are to be interpreted as being relative to a deonti c antecedent context that is overtly introduced by the preceding discourse (6b ) . Another problem ( acknowledged by Geurts) i s that the analysis doesn't account for modal subordination relati ve to negation contexts (9). Since there i s no proposi tional referent available that could b i n d the pres u p p o s e d modal b ase of the counterfactual , the pronomi nal anaphor cannot be resolved. 1 I don't (9) h ave a m icrowave oven. I wouldn't k n ow what to do it. with This problem is of a more general nature: the analysis cannot account for relative modality wrt. the factual antecedent context , as illustrated by ( 1 0 ) . While the presuppositional modal base i s clearly dependent o n the context i n­ troduced by t h e first sentence, there i s no propositional referent that i dentifies this context . The modal base of the conditional can on ly be accommodated . ( 10) There are t w o people i n t h e room. If o n e o f them leaves t h e room , t here will s t i l l be one person in the room . x p q r peopJe(Y) Y p 3. = ? q IY I = P + I� = room (x) 2 E Y I in(Y ,x ) leave( y ,x} r = q + I� E Y in(z,x) I q 0 r A DRSs and the represent atio n of contextual dynamics Fran k ( 1 99 6 ) pursues an analysis of modality and m o d al subordination that follows the spirit of Kratzer 's theory of relative modali ty, whi le di verging from her analysis of deonti c and counterfactual modali ty as involving graded m odal­ ity. As i n Geurts' an alysis we make use of cont ext referents G, H , denoting sets of world-function pairs, and which can build 'annotated ' or updat e conditions G : : F + [{ ' . The notion of relative modality i s rendered in terms of an a n aphoric c on t e x t referent X' that fi gures i n t h e domain argument of a general i zed modal quantifier. The logical form of modal operators i s as i n ( 1 1 ) . Rel ati ve modal­ i ty a n d i t s speci al instance of modal s u b ord i n a t io n are captured in terms of anaphol'ic b i n ding of t h e modal operator's ( possi bly complex ) modal base X ' . 2 (11) But X' G H X' = ? G : : x' + evident ly, 0 bei ng Q H :: G + very s i m i l ar � to Geurts' D RS will not contain l i ke ( 1 0 ) e i t he r : app roach , this anaphoric a n a l y s i s does n ' t solve t h e ab ove m e n t i o n e d p roblem for exam p l es a n y c o n t e x t referen t t h a t rep resents t h e p i ece the of d i s- ANETTE FRAN K AND HANS KAMP 1 56 course introduced by the first sentence. The conditional cannot , t herefore, be analyzed as anaphorically dependent on the preceding factual discourse con­ text i n terms of anaphoric binding of its modal base XI . .'J. l . From re la t i o n a l s e m a ntics for DRSs t o upda t e conditions D RT's main insight is that the meaning of a sentence is essent i ally co n t ext dependent, that each sentence must be interpreted re lat i v e to its preceding con­ text, or "as an addi tion to, or ' update' of, the context i n which i t i s used" ( van Eij ck&K amp ( 1 997: 1 7 9) ) . Following this dynamic perspective, the mean i n g of a sentence i s to be captured i n terms of context change conditions rather than i n terms of truth conditions proper. To make this view formally precise van Eij ck& K amp( 1 997) define a relational , or dynamic semanti cs for DRSs, 3 where the meaning of a ( parti al ) DRS D is stated as a relation between i nput and output. assignments s and Sl from i n di viduals of U into M : . [D]�. But not only does this relational semantics account for the dynamic meaning of sentences i n discourse. B y extension of the D RS language with the sequen cing operator ' i ' D RSs now explicitly rep resent t.he dynamics o f d i scourse : ., [ D i D I ] � iff th ere is an s" with ., [D] � a n d s,, [ D I ] � ( see van Eij ck&Kam p ( 1 997) ) . Yet , the dynam i c aspect of meaning that i s thus built i n to t h e semanti cs and represe n t ation of D RT is still of no help for the problem we enco unt ered for ( 1 0 ) : the states s , S l t h at record the assignments of referents i ntroduced in t h e preceding 'inpu t ' context are not in the object language, and therefore can not serve as representational objects to provide a context-type antecedent for the anaphoric modal base of the modal operator. But i t i s obv i o u s h ow t h e dynamic view on the s e m a ntics of D RSs can b e imported into t he DRS syn­ t ax , so as to yield an explicit representation of this contextual depe n d e n ce of sen t e n ce meaning. Modulo the i n t ensional fram e work , there is a direct corrc­ spondence between the relational semantics of DRSs and update conditions on context referents ( 1 2) , where context referents denote sets of worl d -fun c ti o n pairs ( see below for ful l definition ) : an u p d at e condition G : : F + f{ 1 charactcr­ i zes the 'update' of an ' i n p u t ' con t e x t (referent) F with a DRS f{1 , to yield the 'output ' context ( referent ) G, where e(G) denot e s the set of sta t e s ( w l , g) for which there is a state (WI, ! ) E e ( F ) s . t h . (WI, !) a n d (wl , y) constitute correct i nput and output states i n the relational meaning of 1"":/: ( w l,j) [ K/] ( wl,g ) . ( 1 2) 3. 2. (w, e ) pM G : : F + f{ 1 i ff e ( G ) = { ( WI , g) : ( � ( Wl , !) E e( F ) ) ( w l , j ) [ f{I ] ( WI , g ) } Rep res e n t a t i o n of contextual dynamics in DRT Instead of u s i n g upda t e condi tiolls G :: F + f{1 for 'subordinate' con text s only, w e now extend t h e u se o f these conditions to expl ici t ly rep resent t h e d y - ON CONTEXT DEPENDENCE IN MODAL CONSTRUCTIONS namics of a discourse within the D RS that is to represent its dynamic meaning. We will first outline the main i dea by going through the critical examples, and then , in 3 . 4 . , i ntroduce the semantic formalism in much more detail . Let us first consider how the problemati c example ( 1 0) works out within this new representation format . In ( 13) t h e first sentence, 51 , i s represented as context dependent upon an antecedent context referent F in terms of the update condition G : : F + Kr , where KJ corresponds to the D RS t hat. is to be constructed for 51 . The second sentence, 52 , is in turn characterized as context dependent on the antecedent context established b y t he first. sentence, represented b y the referent G, in terms of the update condition H : : G + K2 , with K2 the represent at ion to be constructed [or 52 . Once t he accessi bility conditions for anaphoric binding are i n place ( se e 3 . 4. ) , i t will fall out t hat the context referent G t hat represents t h e content conveyed b y the first senten ce is accessible for the anaphoric referent X' , the modal base of the condi t i onal w i t h i n K2 , and t hat-v i a this anaphoric depen dency-t h e an ap h o ri c expres­ sions th em and the room find accessible referents, defined i n the universes of If, and Ko . Unbounded presuppositions are accommodated i nto the ' highes t ' pos­ sible DRS, accessible from the context the presupposition projects from, here the D RS Ko that is interpreted relative to the empty context A t he disco u rse s t arts o u t with: e ( A ) { (w' , '\ ) : w' E IV} , '\ the empty [unction . ( 13) Th e r e are two p eople in t h e ro o m . I f one o f t h em leaves t h e room , t h ere will still be one person in the room . = + A F G H F :: A �oom(r) Y I G : : F + people ( Y ) H :: G An s. S. A + H ' H " X' X' = If' : : G X' + I Y 1 = 2 the_room er) y yEY leave(y,r ) � H" : HI + in( Y ,r) z z I E Y in(z ,r) unified a n a lysis of relative modality a nd modal subordination an aly s i s along these lines i m med i ately accounts for modal subordination in ( 1 4) : the first co n d i tional is r e pre s e n ted as being nlative to t h e ( empty or accommoda.t ed ) factual co n tex t F , e n a b l i n g a n a phor i c or presuppositional binding into the ' main context ' , while the second conditional i s rclalivf' l o t h e modal context established b y t h e first conditional i n terms o f an ap hori c refer­ ence to the referent G" that ' a nnotates ( : : )' its scope DRS. A ccessi bility m u s t be defined so as to l i cense bindi n g of X" to Gil , and-vi a this condition­ bi nding of anaphoric expressions within th e DR Ss annotated by H ' or H " to material that is defined within the D RSs annotated b y G' and G" ( see 3 .4 . ) . as 1 57 1 58 ( 14) ANETTE FRANK AND HANS KAMP If a t hief breaks into the house, h e will take the silver. If i n addition he finds the safe , he will try to open it A F G H house(y) F :: A + y w v G :: F + G " X' X' = F G ' : : X' + H' H" H :: G + X" X" = G " H' : : X" + silver(w) x G' thief(x) the_house(y) 1 1 <> breaLi n ( x , y ) tksafe( v) fi n d ( x , v ) <> safe(v) I G " .. . . G, ' H" : : II' + + I 1a 1 tksi l ver ( w ) , ke ( x , w ) t try-open ( x , v ) I It is easy to see that this analysis caracterizes T'e/ative modality an d m odal subordination as a unified phenomenon : in both cases the anaphori c mod al base is bound to an accessi ble context referent introd uced by the preced ing discourse. As we argued for (4), the difference between the two types of context depen dent modality is captured by the fact that in the fi rst instance ( 1 3 ) the antecedent referent denotes a 'factual' (nonmoda.l ) contex t , whereas i n the modal subordinat ion instance of ( 1 4 ) the anteceden t referent denotes a modal contex t , i n trod u ced by the preceding conditional . The analysis also accounts for modal subordi nation relat ive to n egated contexts ( 9 ) , which was n ot captured by Geurts' analysis: ( I S) I didn't b u y A F G I F :: A + G :: F + I :: G + H i � a microwave oven . I wouldn't know what to I speaker(i) .. II . . I' I" X ' X' = H I F + x . I' : : x' + ffilcrowave-oven(x) buy(i,x) D <> I" : : I' + � 'J . . .. I I' I do w i t h at-to+ knOw-wh do-with(i , x) it. 1 In 3 . 4 . we define n egati o n to t ake s cope over an u p d ate condition. The coun­ terfactual in ( 1 5 ) can then be re p res e n te d a s anapho ric to the referent Il , w h i ch denotes a co unterfactual co n te x t where Max bought a microwave oven . The an a l y s i s of d eont i c modals differs from Kratzer's gra ded modality.'l The m o d al base of the deont i c modal is complex: it is anaphoric to a con­ text F + D, F a factual cont e x t , D a context referent r e pr e se n ting a deontic context , which i s introduced by linguistic means a s in ( 1 6 ) , or else must. be ac­ commodated as Qbligation (D} . The distinction b e t wee n d eo ntic a n d ep i s t emic modality i s now explicitly represented , in te r m s of a context referent D that i n virtue of bei n g an a r g u ment of a deontic predi cate qualifies as d eo nti c . ON CONTEXT DEPENDENCE IN MODAL CONSTRUCTIONS ( 16) A F G F :: A + G :: F + 3. 4 . I A ccording to German tax law , Harry must pay taxes. Dh 6 German-tax-law(D) D G ' G" X' X' = F + D G ' : : x' + harry(h) emy G " : : G' + I pay-taxes(h) I Verification, wellfo u ndedn ess and accessibility We briefly present a semantics for the representations mot i vated above. In ( 2 1 ) ( which is based upon a simpler language 5 ) an update condition G : : F + [{' i n ( 2 1 e ) not only defines a proper context change potentia.! for K' , but also constrains [{' to hold true relative to the eval uation state (w, e) . Two aspects requ i re more detailed d iscussion: the evaluation of [{' relat i ve t.o e-< G U f in ( 2 1 e-g) and the normalcy restriction * for modal quantifiers ( 2 1 g ) . The normalcy selection function * ( w , G) , to be defined i n t he model , denotes the set of worlds where everything holds t ru e which is n o rm ally the case, relative t o w, in the context G ( d. Morrcau ( 1 99 2 ) ) . I n ( 2 1 g ) this normalcy selection function constrains the set of states in t h e quantificational dOImli n , which allows u s to cope with conditional variahility o r nonmonotonicity ( sec Frank ( 1 996 ) ) , and , moreover, to account for modal subordination relati ve to modal constructions hosting the quantifier no (see 4 . 2 . ) . I n update conditions G : : F + [{ ' ( 2 1 e) the D RS K ' must b e intcrp rctcd rel ative to a com plex function e -< G U f ( defined by ( 20 ) ) . T h i s is n e ces s a ry , e . g . , i n order to allow for accessibility of context referents defined in Un from within a DRS K ' , where G : : F + f{' E Conn . Th i s situation is found, e.g. i n ( 1 3 ) , and is represented by the schematic D RS ( 1 7) . S ince F i s free i n f{ 1 , the function 9 that i s to verify [{' s h o u l d be defined for F and shou l d assign i t t h e value that i s fixed by e. Since F E dom ( e ) , i t seems straightforward to evaluate [{' i n ( 2 1 e) relati ve to a state e U f. But t. his leads to t he problem of n o n -wellfo 1l ndedn ess: in ( 1 7) , G E dom ( e ) , in p ar t i c u l ar, G denotes a set of pairs ( W' , g) . If [{ ' is evaluated relat.ive to a state (Wi, e U f), G will be in the d o m ai n of e U f, and G will thus be in the dom ai n of every 9 in pairs (w' , g) E e ( G ) : That is, e(G) would give t h e standard set-theoretic notion of a function belongi n g to its own t r an s i t i ve closure and thus violate t h e Axiom of Fou ndation . In other words, (w, e ) does not verify f{. f{ is logical l y false. ( 1 7) G: F+� F G To guarantee wel lfoun dcdncsH we ri en n e, i n ( 1 8) , a rel ation < on context ref­ erents which records the embcdding s t r u c t u r e of context referents relat i ve to 1 59 ANETIE FRANK AND HANS KAMP 1 60 el U e2 where e l : Uindre!_K -+ U w E W Uw,M , e2 : an embedding function e, e Ucr e!_ K -+ �( W x G) as i n ( 2 1 ) . The set of context referents X i s defined as a partially ordered system (X, < ) , which i s constrained to be wellfounded ( 1 9 ) . B u t note that even with ( 1 9 ) we still cannot assign a meaning to DRSs l i ke ( 1 7 ) : i f K' is evaluated relative to e U f , 9 will be undefined, since G being i n its domai n immedi ately violates wellfoundedness as defined by ( 1 9 ) and ( 1 8 ) . = ( 1 8) ( 19) F < e G i s the smallest relation bet.ween context referen t s F, G E X relative to an embedding function e s . t h . V (w' , g ) E e 2 ( G ) : FE dom (g2 ) or V( w' , g ) E e2(G) : :l X E dom (g2 ) : F < g X . � X and (X, < ) wel/founded. A function e dom( e2) = el U e 2 for A D RSs is wel/founded i ff In ( 2 1 ) wellfoundedness is t herefore ensured 'on the fly' , by defining K' i n up­ date conditions G : : F + K ' to be evaluated relative to states (w' , c-<G U J) , w i th e-<G defined i n ( 2 0 ) . Intuitively, dom e e -< G ) i s a subset of dom ( e ) which contains only those context referents X that are ' smaller' , i n terms of the relation < c ( 1 8 ) , t h an G, and which will thus not cause 9 to be non-wellfounded. ( 20) Let e e -< o = = (21 ) el U e2 be a wellfounded embed d i ng function for A D RS s , th e n U e�, where e; = e2 r { X E dom ( e2 ) : X 1= G & G </ e X } . Let J( be a DRS ( UK Uindr e!-K U Ucr e f -K , C o n K ) , w i t h ConK a set of conditions of the form referred to in ( a-i ) , j\.tf an intensional model ( see Kamp&Reyle ( 1 996 ) ) and e a wellfounded embedding function c = el U e2 w h e r e e l : Uin dre! _K -+ U wE W Uw,M and e 2 : Ucref_K -+ �( W x G ) ( G a set of embedding functions ) and e ( A ) = W x { A } , A the em p ty function . * is a normalcy selection function , defined in t he model, which yields , for a world w and a context ( a set of world-function p ai r s ) G t he set of worlds * ( w , G ) where E v e rything holds t r u e which is n o rm a lly l h e case, relative to w, in th e co n text G ( cf . Morreau ( 1 992 ) ) . (w , e) PM K i ff :I f : e �uJ( f & v,· E C on K : ( w , J) PM ,. [ [{D (w.J) = { ( w , g) : f � UJ( 9 & V, E Con K : ( w , g) P M , } . ( w.J ) [ K D (w ,g) iff f � uJ( 9 & V, E ConK : ( w , g) P M , . a . - d . atomi c D R S conditions ( sec K am p & Reyle ( HJ93, 1 996) ) c. ( w , e) PM G : : F + [(' iff e ( G) { (w' , y) : :I ( w', J) E e ( F ) s . t h . ( w ' , e -<ouj) [J( 'D (w',g) } & :I (w , g ) E e ( G) . f. (w, e) PM -, G : : F + [{' i ff e ( G ) { (w', g) : :I ( w ' , J) E c ( F ) s . t.h . ( w ' , e -<o ud K 'D (w',g) } & -, :I ( w , y) E e ( G ) . g . (w , e ) P1H G : : X' + K ' M H : : G + [{" iff e ( G) { ( w' , g) : :I ( w' , x') Yc ( X ' ) s . t h . (w' ,e-<oux,} [ [{'] (w',g} } & e ( H ) = { ( w', h ) : :I (w' , g ) E e ( G ) s . t. h . ( w ',e-< H U9} [J("] (w',h) } & ( A , B ) E Quan tM ( Q ) , where Cl = = = = 161 ON CONTEXT DEPENDENCE IN MODAL CONSTRUCTIONS = { ( w' , g ) : ( w' , g) E e ( G ) & w' E * ( w , { (w", g' ) : 3 (w" , x') E e (X' ) sth. (wU,e-<aUx') [ K '] (wu,g} } ) } & B = { ( w' , g) : (w' , g) E e ( G ) & w' E * ( w , { (w" , g') : 3 ( w" , x') E e ( X' ) s th . (wU , e -< G ux,} [ K'] (wu,g} } ) & 't:/( w' , g) : ( w' , g) E e ( G ) & w' E * ( w , { (w", g') : 3 ( w" , x') E e( X ') s.t h . (wU, e -< G ux,} [ K '] (wu,g} } ) -+ 3 (w' , h ) E e ( EJ ) } . h . (w, e) PM G = F + D iff e ( G) = { (w', g) : 3 ( w', J) E e ( F ) 3 ( w' , d) E e( D ) sth. (w' , g) = (w', fUd) } I. (w , e) P M G ' � G iff 't:/(w', g) E e( G) 3 ( w' , g') E e ( G' ) s .th . g' � g.6 A Kamp & Reyle( 1 993) define accessibility in terms of a relation of DRS-subordi­ nation 2: , which larg ely corresponds to the hierarchical st.ructure of D RSs . For our new DRS representation language, implicitly defined by ( 2 1 ) , this relation is extended by the clauses i n (22 ) . (23) defines a special subord i n at i on relati on « between context referents t hat m irrors the semantic relat i o n < in ( 1 8 ) . T h i s relati o n further constrains t h e accessibility of context r e fe ren ts for anaphori c b i ndin g (24 ) : a context. referent X m ay not be bound to any referent Y that is ' l arger' than X , for such bi n d i ngs wou l d be in vi olation of wellfoundedness . (22) ( 2:3 ) ( 24 ) . For Ko a D R S , « i s t h e s m all est relation to satisfy conditions ( a-d ) : i f G : : F + K ' E C onK] l Ko 2: [(1 , t hen F « G and 't:/Z E UK ' : Z « G ; b. if G = F + D E C onKl l [(0 2: [(1 , then F « G a n d n « G; c. if G ' � G E ConK" [(0 2: [(1 , t hen G ' « G ; d . i f F « G a n d G « H t h e n F « II . a. A d i s c o u r s e referent y E [h.;, i s accessible, w i t h i n a D RS for a discourse referent ;T occurring i n a D RS [(" iff K ' 2: K" an d if :1:, y c o nt ext referent.s, t hen x 1:. y . K , J{ 2: [{ ' , Mo dal subordinat i o n-what you can and cannot d o 4. 4 For Ko a D RS , 2: i s the s m a l le s t relation satisfying conditions ( a-d ) : a. i f G : : F + K " E ConK 2 & F : : X + K ' E ConKl , Ko 2: KJ , Ko 2: Kz t.hen K' 2: K" and Kl 2: K' and K2 2: K " ; b . if G : : F + [{" 0 H : : G + [{III E ConK" where Ko 2: K1 , then [{" 2: K ill , K l 2: K " an d Kl 2: /( 111 ; c. if � G : : F + K" E Con/';l l w h e r e Ko 2: /(1 , t. hen KJ 2: K" ; ' d. K 2: K' , and i f /(' 2: /(" an d K" 2: K ill then K ' 2: K 'II . 1. Nega t i o n Our analysis accounts for modal su bord i nat i on relati ve to negat.ion cOlltex t s ( 1 .5 ) , where the modal b ase of the subj unctive modal i s anaphoric t o the all- ANETTE FRANK AND HANS KAMP 1 62 notating referent H of the negated update condition. According to ( 2 1 £) II denotes a set of collntf1jactual states (w', h ) , where w' of. w. And from (22)­ (24 ) i t follows that t h e referent x is accessible from the scope D R S of t he subordin ated modal The analysis also rules out cases like ( 25 ) : the second sentence i s nonmodal, and therefore cannot induce modal subordi nation i n terms of anaphoric binding to a context referen t . Since the context referent G ' that is introduced by negation i s not accessible as an i nput referent for the update condition of the second sentence, the pronoun it cannot be bOllnd .7 ( 2 .5 ) Clarissa doesn't own a bike. # S he loves it. I n order to rule out subordination of indicative cond itionals relative to negation contexts ( 26 ) , we adopt a pragmatic constraint on senten ce mood, following Stalnaker( 1 976 ) : the denotation of the context referent 0' that annotat.es the restrictor of an indica t i v e conditional must contai n a state t h at is tied to the evaluation world. This accounts for ( 9/ 1 5 ) vs. (26 ) : since the negated antecedent context is coull t e lj"actual (sec ( 2 l f) ) , indicati ve mood is ruled out . (26) Fred d i d n ' t buy a microwave oven. # He might use i t . 4 - :2. Graded m odality vVe also account for graded modal forces ( 29 ) , where for probably,. unlikely, etc. we assum e a probability measure p.8 I n (27) the condition al q u ant ifies over (sufficiently normal ) worlds/states where Max goes to China, an d i s ver­ i fied if those worlds where he buys books in China are assigned a. sufficiently high relative probability. S ubordination of the second sentence to t h e scope of the graded conditional const rains its universal quantification to range over worlds where Max buys books i n C hina, but now with res t r i ct i on to what i s normally the case i n su.ch a si tuation. The cond ition is veri fled i ff all states that pertain to such norm al wor l d s can be extended to satisfy the scope argument . In the structura.l l y similar (28) t he modal quantifier is assigned the meaning of n o , which con strains the scope argument B of q to be t he em pty set : under normal circumstances ?vl ax will not buy books if he goes China. If t he deno­ tation of G' an d Gil w e re defined i n terms of the sets A, H of the relat.ional quanti fier, we could not refer to Gil to establish a modal subordination read i n g : Gil would denote t h e empty set . Yet , according t o (21g) Gil denotes t he fu l l ( context dependent ) i ntension o f the scope D RS , such t h a.t by anaphoric rd­ erence to Gil in (28) the second modal u n i versally quantifies over t hose rather abnormal worlds where M ax buys books in Chi na- again with relat i v i zation to worlds where things evolve as i s n o r m al for such a ( quite abnormal) s i t u ation . (27) If M a x goes to C h i n a , he p robably buys books. Mary will adrn i n� t hem . 1 63 ON CONTEXT DEPENDENCE IN MODAL CONSTRUCTIONS (28) If I go to China , in n o case will I buy . books. I wouldn 't r ead them . A F G H F :: A + G :: F + I C x' + 1 speaker(i) G' G il X' X' F G' : : = go-to(i,c) I I0 �:' :�x9,"+ D <> H' H" X" H :: G + china( c) Iz G il : : G ' + books ( Z ) buy ( i , Z ) H" : : H' + I� +1 T : : II' read ( i , Z ) II I Our pragmati c con s traint OIl s e n ten c e mood�indicative modals arc relative to a context that contains a state that i s tied to the evaluation world- is in accordance with ( 29a- c , f) , but not with (29d -e) . 9 While unlikely and there 's a sligh t chance presumably both denote the q uan ti fi e r unlikely, to be as s i gn ed a low relative p r obability, the restrictions on se n t e n c e mood differ: (29i) is a possible con t inuation for ( 29d) but not for (2ge ) , w h i le (29ii ) i s fi n e wit h ( 2ge) . (29) If M ax goes to China, he ( necessarily) will buy a book . If Max goes to China, he p robably will buy a book . If M ax goes t o C h i n a , he might buy a book . If Max goes to C h i n a , th e re '05 a slight chance that he'll buy a book . i . H e will have a h ard time reading i t . e . If Max goes to C h i n a , it 's unlikely thal he will b u y a book . f. M ax goes to China, in Tl O case w i l l he buy a book . i . # He will have a hard time reading i t . i i . H e would hav e a h a r d t i me reading i t . a. b. c. d. For i n d i ca tive moda.ls we assume the selection funct i on * to b e cen tered : th e evalua t io n wo r ld fi gures within t he set of accessible nor'mal worl d s w h er e Max goe s to China. But with unlikely the s u bset of those worlds w h e re h e in addi tion buys books may or may not contai n the evaluation world . \Ve s u gg est that the con t r ast in (29) is to be ca. p tured in terms of a ( p r a g mat i c) restriction: for a slight chance the s c op e arg u m e n t lJ in t h e den otation of unlikely must contain the evaluation world , while i t Illay not for u n l ik el y . T h eSf� r es t r i c tion s are i n accordance with the m o n o t o n i c it y properties of these qua.n tifiers . 1 0 Fol­ l owing our p r agmati c conditions on se n ten ce mood, anaphoric reference to the s c o p e a rg ument Gil of unlikely is t hen only licit for ( 29i i ) , while for a slight chance m o d al subord i n ation is p o s s i b le with indicat i ve mood ( 29i) . 1 1 ­ -1 . 3. Alodal subordination vs. accommodation We have shown t h at the anaphoric an a l y s is of modal s u bo r d i n a t io n copes with a wi de variet y of data. Yet. , i t is not llllc ontrover s i al that the a nap h o ri c approach is the right way to go ( s e e e.g. Rohert.s( 1 99.5 ) ) . ANETTE FRANK AND HANS KAMP 1 64 Let us first mention one i mmediate problem of the anaphoric approach , which, however, can be resolved quite straightforwardly. ( 3 0 ) is semantically equivalent to (28 ) , but structurally distinct . In (30) the context referent that represents the negated context is embedded within the conditional 's scope and not accessible for the subsequent modal , to induce modal subord i n ation. ( 30 ) If Max goes t o China, he will not buy books. He would not read them . O n e could take this as a weakness of the anaphoric/presuppositional approach to modal subordination , and argue i nstead that the 'inherent' force of s u bj unc­ t i ve mood is to refer to ( and accommodate) th e other case, computed as the complement ( set ) of some accessible context (see Corblill ( l994 ) ) . But besides the wellformed subordination cases (:30) and (9/ 1 5 ) this predicts ( 3 1 a) to m ean that Fred would have been unhappy if he hadn 't got a letter! (3 1 b) shows t h at ( an aphoric) reference to the oth er ca s e is only possi ble for otherwise. Instea d , we propose to analyze ( 30) a s structurally equi valent to ( 28 ) , given the equiv­ alence of 'y'. and . 3 . This can be defended in view of the syntax- semantics i n terface, since the ( implicit) modal quantifier and sentential n egation are both located within the functional proj ection of sentence struct ure. (31) Fred got a letter today. a. # He would have been unhappy. b. Otherwise he wou l d h ave been unha,ppy. Robert s ( l 995) explicitly argues against the a,n aphori c approach. One of her central examples i s ( :� 2 ) , which an anaphoric analysis i s unable to h andle. Yet , (:32) does not strike u s as a parti cularly coherent di scourse. 1 2 I t requi res some additional inferencing, namely acco mmodation of the missing i n formation that the leprechaun A ndy could meet i s one of those w h o have a pot of gold (or a flying carpet in ( i ) of fn . 1 2) . But this accom modated i n formation doesn't correspond to the presupposed modal b ase o f the con d i tional i n (:32c ) . 1 3 ( 32) a. If Andy m et a leprechaun, he'd be delighted , Robert s ( 1 9 9 5 , 6 74 ) Lepn�chauns sometimes have a pot of gol d . c. If Andy was rea.lly lucky t h e lepr [.] m ight l e t h i m have some of i t . b. \"/e m ake a clear distinction b e t wee n the anaphorie arwlysi.s of m odal subordi­ nation, w h i ch m ay i nvol ve a.ccommodation of t. he presupposed modal base i f no appropriate antecedent referent is foun d , and acco mmodation o f otherwise presupposed ma.terial , w h i ch m ay cont ri bute to en abling anaphor i c binding, but must be triggered by presuppositional clements (e.g. really luck y i n (32) ) , or, as Robert s ( 1 99 5 ) poi nts out , specific contextual licensing con ditions. This distinct ion i s i l lustrated by ( :3:3 a b ) ( from Corblin ( l 9�H ) ) . Speakers uniformly affirmed that-without the bracketed material--( :3 :3 h) requires some further interpretation effort , as opposed to (:3:3 a) , which comes down to ' adding ' , o r aceommodaLing the i nformation that i s carried b y t h e bracketed o t h e rwis e. 1 65 ON CONTEXT DEPENDENCE IN MODAL CONSTRUCTIONS (33) a. Mary didn't give the name of the witness . ( Jf she had done sol Othe rwise) They would have k i l led h i m . l F G H ·· F .. m Yx z mary{m) gangsters { Y) G' G : : F + -, G' : : F + H :: G + H' HI! X' X' C G ' I witness{x) I give(m,z ,Y) I D6 name(z, x) I I H I ! : : H ' + kill( Y ,x) I b . Mary gave the name of the w I t n e ss . ( If she hadn't don e sol Oth erwise) Thev- would have k i lle d h e r . 1 H' ::- X' + F G H F :: m Yx z m a ry{m) J gangsters{Y) G :: F + give( m , z ,Y) H :: G + X' H' H I ! X' C G H ' ::- X' + 1 witness{x) -, give(m , z, Y) name{z,3:) I6 I H I ! : : H' + I kill(Y , m ) 1 Kasper ( 1 992) g i v es an a n aly s i s of s i m p le s u b j u n c t i v e senten ces as i nvol v i ng i m p l icit ly restricted counterfactual con d i t ionals , w h i ch presuppose, i n the im­ plicit antecedent c l a u s e , "the preconditions for the p o s s i b i l i t y of the conse­ quent to be t r ue" . In ( 33a ) , t h i s presupposition i s s at i sfied by modal subordi­ nation or anapho ric binding of t he modal bas e to the c on t e x t ( r e fe r e n t ) G' , defined by n egat i o n i n t he first sentence. No a c c o m m o dat i o n i s i n o r d e r . I n ( 33b ) , by contrast-without realization of o t h e rwis e-t he D R S d oe s not con­ tain any app r op r i a t e context referent that could i n stantiate the mod al b a s e of t h e i m p l i c i t l y r e s t r i c t e d c o n di t i on a l , a n d at t he s am e t i me sat i s fy t h i s s p e ­ c i fi c p re s u p po s i t i o n . C h oos i n g the factual antecedent context G as modal base of the co unt e r fa ct u a l , t h e " p r e co n d i t io n s for the consequent to become t r ue " m u s t t herefore be accommodated into the re st r i c t o r D RS : the most straightfor­ ward condi tion that com es to mi n d , here, is t h at M a r y didn't gi ve the w i t n e s s ' name. It i s t h i s a d d i t i o n a l accommodation ' effo r t ' that w e believe makes ( 3 3 b ) s l i g h t l y ' harder ' to process as c o m p a r e d to ( 33a ) . In su m , t h e n , we consi der examples like ( 3 1 a ) , (32) an d ( 3 3 b ) to b e d i st i n c t from m odal subordination pmper, w hi c h we concei ve of as a sp e c i a l i n ­ s t a n ce of 1'eiative modality, a n d w h i ch w e analyzed i n t e r m s of anapho ric bind­ ing/accommoda tion of the modal 's a n aphoric modal base X ' . The ex a m p l e s t h at at first s ig h t seem to be p ro b l e mat i c for t h i s ' synt act i cally con d i t ioned ' a n a pho r i c ap p r o a c h were sh ow n to i n vol ve accommodation, i n p a r t i c u l a r , ac­ c o m m o d a t i on of fu rt her m a t e r i al , distinct from t h e ana p hori c modal base . S i n ce, as Roberts ( 1 99 5 ) points o u t , a ccommodation i s to be licensed pragm a.t i ­ cally, t h e ease or d i ffi c u l ty o f processi n g e x am p le s like ( 3 1 a ) , ( 3 2 ) , o r ( 3 3 b ) w i l l 1 66 ANEITE FRANK AND HANS KAMP be heavily dependent on the parti cul ar contextual setup, or the ' will i ngn e ss ' of the int e r p r e t er to do accommodation more or less gratuitously. We consider i t as a pro of the anaphoric approach that i t captures this distinction . 5. Conclusion We have given a unified analysis of relative modality and modal subordina­ tion, based on a new D RT representation form at t hat explicitly represents the contextual dynamics of discourse. The analys is accounts for a wider r ange of data than pre v ious DRT ap p roa ches: in p ar ticular , it i mproves over Roberts' and Geurts ' reconstructions of Kratzer 's th e ory of m o d alit y i n that all relevant contextual parameters of modal constructions are rep resen t e d at the l e v e l of the D RS . We have shown how to solve the problem of we llfoundedncss t. h at was i m p orted by use of our new r e presen t ation format , and form ulated syn­ tacti c constraints on anaphoric binding, which also preserve w e llfoundedness . The analysis ch aracterizes modal subordination as an an ap ho r i c p h e nomenon , a special instance of relative modality. We argue that examples t h at seem problematic for the anaphoric ap proach to modal subordi nation can be solve d , if we clearly distinguish between modal subordination proper, wh i ch is res t ri ct ed in terms of syntacti c conditions on anaphoric binding, and acco m m o­ dation, w h i c h is dep e nd e nt on cont.extual and pragmat i c li c e n sing conditions. ­ Endnotes • The ackn o w l e dgements of this paper address in the first p lace, and somewhat u nusually, one of its authors , Haris K amp , and Ede Zimmermann. The paper r e p o r ts on results of a dissertation who benefitted greatly [rom the support and i nsight of these t wo teachers. We also would l i ke to thank the fol low­ ing people for valuable comments , questions and discussio n : N i cholas A sher , M i r i am Butt , T i m Fernando, .Josef van Genabit h , Daniel H ardt , Rodger K i b­ ble , Peter Krause, A r t h u r M erin , Uwe Reylc, Robert van Rooy, Daniel Rossi , A ntj e Ro fi de u tsch e r, M ichael Sch i ehlen, Ben Shaer, and Carl Vogel . 1 G eurts resorts to a notion of co ntextual suppletion in order to solve this problem . See Fran k ( 1 996) for criticism. 2 A complex modal base i s used for the analysis of deontic modality ( see 3 . 3 . ) . 3 S e e also K am p & Re y l e ( 1 9 9 6 ) , K amp ( 1 996 ) . Their d efi n i t i o n of relat ional se­ mantics follows the spi rit of Heim ( 1 9S2) and Groenendij k&Stokhof( 1 9 9 1 ) . 4 See Frank ( 1 996) for mo t iva t i on and co m prehensive an alysi s . T h e DRS give n i n ( 1 6 ) i s overly simpli stic: i t doesn't account for a possibly con fl i c t i ng factual antecedent context , and i gnores problems of ' t rivially' true deontic sentence s . 5 (21) i s based on the simpler lan gu age DRLi' , defi n e d in ( i ) an d ( ii ) . Here and in ( 2 1 ) we assume K amp&Reyle 's ( 1 993 , 1 996) syntax and ve rifi c a t ion con­ ditions for atomic DRS conditions. The verifi cation of update conditions ( i i . e ) ON CONTEXT DEPENDENCE IN MODAL CONSTRUCTIONS only defines the co n t e x t cha n ge poten t i al for J{ I re l a t i v e to F. Nothing fo l l ows from ( i i .e ) as to the truth of II I relative to (w, e ) . A ssertion of truth is defined by the truth predicate ( i .f ) , applied t o a cont e x t referent G. The predicate is verified by ( w , e ) iff t here is a s t ate (wl , g ) E e ( G ) with WI = w . I n stead of a s i mple assertive D RS III we thus construct a complex structure, con s i s t ing of an update condition G : = F + /(1 together with the truth predicate v G . Yet , w e refrain from using a speci a l tr u t h predicate i n the re p resen tation language. Instead we chose the more constrained language that is i m p l i ci t l y defined by ( 2 1 ) , where assertion of truth is b u i lt i n to the verification condition of updates . f. v G g. -, v G h. G Q H. (i) e. G : = F + /(1 (ii) e. ( w , e) FM G : = F + [{I iff e ( G ) = { (wl , g) : 3 (wl , f ) E e ( F ) s . t h . (w', e -<Guj) []{/] (w'.g) } ' f. ( 1O , e ) F M v G iff 3 ( w , g) E e( G) . g. (10 , e) FM -, v C; i ff -, ( 3 (10 , 09) E e r G ) ) . h . ( w , e ) F AI G Q H iff (A, B) E Q1JanLM ( Q ) , where A = { ( wl , g ) : ( wl , g) E e ( G ) &: W I E * ( 1O , e ( G) ) } & B = { ( wl , g) : (wl , g) E e( G) &: WI E * (w , e ( G) ) &: V(wl , g) : (WI , g) E erG) &: WI E * ( 1O , e ( G ) ) -+ 3 ( wl , h ) E e ( H ) } . 6 Co n t e rt reduction ( 2 1 . i ) is used for counterfactual s and deo n t i c m o dal i t y. 7 Yet , w e account for cases like l'vfa x do e s n t o wn a car. So h e does n 't h a ve to p a rk it. T he input referent of the negated condi tion of the second s e nt ence can refer to the a n n o t at i n g referent of the n e gated cond i t i o n of the fi r s t sentence. { ( A , B ) : P(cs ( A ) n cs ( B ) ) / P ( cs ( A ) ) :::8 E.g. , QuantM ( p mbab ly) ( A , B ) . 7 .5 } , with p rob ab i l i ty P defi ned for sets of worlds cS ( il ) , cs ( B ) , with A , B as i n ( 2 1 g ) a n d c s ( X ) = { W I : ( 3 .r /) ( WI , x ) E X } . 9 For indicative rn o d a l s the normalcy selection fu n ct i o n is cent e r e d . So, i n all of ( 2 9 a f ) t h e eval u ation wor l d is am on g t he normal worlds q uan t i fi ed over . T h i s p redicts the i n d i cat i ve (29i ) for ( 2 9 a c ) and subjunctive (2 9 i i ) for ( 29f) . 10 See Kibble( 1996 ) , who i n d e pe n d e n t l y i nves t igat e s m o d a l su bo rdinat i o n w i t h gr a d e d modal s , but doesn' t take into accou n t con strai n t s o n m o o d . 1 1 H oweve r , i n ( i ) , w i t h modal s u bo rd i n a t i o n rel at i ve to t h e r c s t ri ct o r a rgu­ m e n t indicative m ood i s l i censed , which is pr e d i c t e d ( see {n . 9 ) . (i) If I g o to China, i t 's u n l i k e ly that I 'll buy books. I ' ll v i s i t m onu lIlen t s . \ 2 The reason (32) might be considered as coh e re nt cou l d be due to t h e u s e o f t h e k i n d d e n oti n g N P g o l d in possessi ve c o ns truc t io n . C o n s i der ( i ) , for com ­ pari son , which is worse than ( 32 ) . Spe a k e r s who accept the G erm an e q ui v al e n t of ( i ) suggest that i t gets b e t ter i f t h e anaphor ihn for t h e carpet i s re p l ac ed by einen (one� a n a p h o ra ) , w h i ch i s genera l l y avai lable in pos i t i on s th a t do not al low for individual-�type an aphora, and t hu s cal l s for a separate an a l y s i s . I f A n d y m e t a u n i c o rn he'd b e delighted . U n i c o r n s som et i mes have a (i) fl y i n g c a rp e t . If A n dy asked i t k i Jl (lly, the uni corn m ight gi ve it t o h i m . n I nstead , i t corres pon d s to t h e p r es uppo s i t i on that i s t ri g ge r e d with in t h e co n d i t ional ' s an teceden t , b y t h e p h r ase really lucky, which is, t h en , r e s pons i bl e for the lo c a l a cco m m odation of t h i s m i s s i ng add i t i onal assum ptioll . . ' = � - , - , ' ' 1 67 ANETTE FRANK AND HANS KAMP 1 68 References Corblin, F . 1 994. 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