Centering in Dynamic Semantics
Daniel Hardt Department of Computing Sciences Villanova University Villanova, PA 19085 hardt@vill, edu
Abstract of phenomena involving sloppy identity in ellipsis and "paycheck pronouns". Since Montague, a major goal of semantics has been to describe a compositional method for con- verting a syntactic representation of a sentence into a logical representation of the sentence mean- Centering theory posits a discourse ing, and dmn to evaluate that representation with respect to a given context. A primary insight of center, a distinguished discourse en- dynamic semantics is that sentences have a sys- tity that is the topic of a discourse. tematic relation to context in two ways: not only A simplified version of this theory are they evaluated with respect to the current con- is developed in a Dynamic Seman- text, but they also systematically change that con- text. This insight has particular relevance ['or the tics framework. In dm resulting sys- apparent puzzle presented by sloppy identity and tem, the mechanism of center sh/ft related phenomena. While anaphoric expressions allows a simple, elegant analysis of are normally thought to be identical in meaning to a variety of phenomena involving dmir antecedents, they receive a different interpre- tation than their antecedents in these cases. Given sloppy identity in ellipsis at~d "pay- the dynamic perspective, the puzzle evaporates: check pronom~s". the anaphoric expression and its antecedent might represent exactly the same meaning, since mean- inn is fundamentally a potential to be evaluated with respect to some context. What changes is tile context, in the discourse intervening between antecedent and anaphoric expression. Consider the following example involving 1 Introduction sloppy identity in VP ellipsis: (1) Tom1 loves his1 cat. John1 does too. [loves hisl cat] Centering (Grosz et al., 1995) and Dynamic The sloppy reading results from a change in Semantics* both concern the sequential process- context, in which the value of 1 becomes John ing of discourses, with particular emphasis on the rather than Tom. This allows an extremely simple resolution of pronouns. In Dynamic Semantics, account of the "recovery mechanism" involved in the semantic structure of a discourse gives rise to sloppy identity; the elided VP is exactly identical constraints on the resolution of anaphoric expres- to its antecedent. Several authors (Garden% 1991; sions. Centering theory claims that a discourse Hardt, 1.994) have suggested a dynamic account always has a single topic, or center. Constraints along these lines, arguing that sloppy identity and on the resolution of anaphoric expressions arise, related phenomena reflect the reassignment of an in part, from the ways in which the center can index in tile discourse context. 2 change in a discourse. There is an important dif- Alternative approaches postulate complex re- ference in the way discourses are viewed in Cen- covery mechanisms for sloppy identity, such as tering and in Dynamic Semantics. In Dynamic higher-order matchiug (Dalrymple et al., 1991) Semantics, a discourse is viewed as a monotonic or the syntactic matching of parallel dependen- increase in information, as discourse referents are cies (Fiengo and May, 1994). Below, I will argue constantly added to the domain of discourse. Cen- that tile dynamic account is more general and em- tering draws attention to a particular role that a pirically adequate, as well as being simpler than discourse entity can hold; fl:om time to time, t,he alternative accotmts. current center will be shifted wit.h a new center. The clynamic account raises the following prob- In this paper, I will implement a simplified version lem: since the index of the tile initial "controller" of the centering theory in a dynamic system, and is reassioned, it becomes inaccessible in subse-
519 served tor the discourse center, and the discourse This is an abbrevial;ion for dm following type center will always occupy another index as well as logic formula: 0. We. will us(; the * to designate references to the discourse ce.nter. Thus tim above examt)le will be Aij (i[ut ]j Afarmer (u j) Awalks(u:, j) Alaughs(u, j)) notated as follows: (2) '.l.'omj, loves his, (:at. John2, does too. In the above formula, the variables i and j ret)- [loves his. cat] resent inpul: and output st;ates, and tim variabh~ In tile first senteIlce, To'm, is the value of ill- u, (akin to a discourse marker) is a flln(:tion froln dex 1, and ix also the discourse center, i.e., the states to individuals, lit what, folk)ws, we use value of index 0. The pronoun his* is equivalent the DltPF abbreviations without further comment,. to his0, and dins refers to tile discourse center. The reader is referred to (Muskens, 11996) for fur-- In tile secon(1 sentence, John becomes the value ther examl)les and the details of l;tl(', system. of index 2, and also replaces 5Ibm as the discourse We now define a siinple fragment of English, center and thus John becomes the value of index 0. base(1 on the one given in (Muskens, 1996). This center shift gives rise to the sloppy reading. -> P, llowever, both 'Ibm and John remain a('eessible in .lotu,,,, :W([u,,, = subsequent discourse. hc, where The paper ix organized as follows: In Section it ~ At,q [I I'~q] Two, i present a dynamic fl'amework based on an(l -> ; the system described in (Muskens, 1996), with walk -. Sv [I walk(v)] extensions for the discourse center, VP ellipsis, :at -* Xv [I cat(v)] and t)ayt:heck t)ronouns. Section Three (:oneerns l(,v,, Aq an "expanded paradigm" for sloppy identity; it; is shown that the t)roposed approach uniformly accounts for a broad range of sloppy identity phe- Not:e that the t;ransladon for h,e,, refers to nomena, including some not previously examined dr(ant(lte,~)). Tiffs is detined as the discourse re4> in the literature. Conclusions and plans for future. resentation of the antecedent of he~(see (Muskens, work are given in Section l~bur. 71.996, page 20)). The l;ranslation for and is the sequencing operator, ;. As described in (Musk(ms, 2 A Dynamic Framework 1996), the sequencing of two boxes K,K' is an ab- breviation for the following type logic expression: The basic dynamic framework is the dynamic logic system of (Muskens, 1996). This framework has, for the sake of simplicity, restricted l;he study [K~; g2]l -~ of anaphora to pronouns that are extensionally {
520 2.1 Discom'se (~('nt e,r 'l;h(; INFI, (:a,t('gory ra.ug('~s over verba,l inih~(: W(', de,film position 0 in Om context as t;h(; I)is- lions (PAST, PI~,I';S, ('¢(:.) and ;mxiliary v(,rbs ((lo, co'u,rse (,'cntc.r'. AI; any {~iv(m l)oi]~l; in the dis- should, el:('..)4 course, tim (liscours(~ (;Ifl;il,y d(}sigmtt;('.(1 as Lhc dis- Consid('x th(, folh)wint,, (~x~uni)l(~ of V] ) ellip- ('ore:s(; ('eJlt(;r o(:(:ut)ics posil,ion 0 as well as il;s sis: ot;he.r l)osil;iou. We (lesign;tl:c 1;his with a, *, as (d) a. Tom walks. ,lohn does too. iu th(; following (~Xaml)l(;: b. Ton,,* 1)l{.l",Sz w~flk. John:~* do(~s:e too. (3) A,* farmer walks, llc* la.ughcd. The, two s(',nt(,'n(:es r('('.(dve I,ll(~ following inl;cr This is r(!l)r('.se.nl;(xl ;t,q follows: 1)retal;ions: [,u,,,,, I,~0 : ,,,, fa,',n,;,(.,), ~alk(,,,),la,,~h@:,)] Total* l)l{,l",S2 walk. -~ In this (lis(:ours( h (:Ira enl;ity iill;rodu(:e.d /)y A I * i.~ - .\ x[I .v,.]k(~)], w,~lk@,)] farrn(:r is th(' discourse, (:(mi;('J, and thus o(:cut)i(~s ,/ohn:~* does2 Vlq~;2 too. :> position 0 a.s well as position ]. We must a(hl a,(hlitiomfl ]'uh's for indefinite (',x-- t)r(',ssions and n;un(',s, when t;hey add an ()t)j(~(:t l,o c(mtx;xt; t,hat, is (,tie dis(:oms('~ (:(~nter. Nex(;, we join t;he, two s(',nl;(m(;(', int, ert)r(,A;at, i()]]s with the s(!qucn(:ing Ol)exator , and we apply the. wdue of 1)2 1;o 11:~: a I', l'~@,,,,,,,,I ,,o :: ..1; l,, (,,.,);p..(..)) ,John.n* :5 TOlIII * l'l{,t']S2 walk../ohn:~* (loes2 VPE2 t;oo. -5
~l.([u,,,u,. lu0 :~ u.,,,~,, ~--.loh@;l'(H.)) [u(,, ul, Ih I u(, : : u,, u, --: Tom, ]% - A x[I w~lk(:~)], walk(u,)]; W(', will apply a v(',ry siinplili(',d version ot' (:en- [110, 113 I,*,, -: .:~, ,,:, :-.lot.x, w~lk(.:,)] tering ttmory, consisting o[ l;h(,, following con- sLra.ints: Next, we will (:o]mid(',r a,n cxmnl)h~ involving • Every discourse Hl, t;(!l'~tIl(:e ((;xceI)l; t;he dis- sloppy i(hml,ity, rib (to this, it will t)c n(',c,(~ssary cours(~' initial utl,(;ranc(;) musl; h~ve a (:(.'nt('.r. t:o add genitiv(,. Nl)'s, such as "his (:at" to ore sys- I;(HII. • If any t)rollOlllIS occ]lr ill an lt|;l;('.l'~lJl(;¢;, al; least one. t)I'OllO1111 liltlS|; r(~f(~l' to |;h(?. (:(;ll{;(w. his (he.,~'s,~) => We define, two types ()f transitions fi'om ()he ul> xl'. p~ ([,_~,. I of(u.,, H,.)]; P[0~,,,); ]'~(-.,) ) l;erancc i;o I;he n(;xI;: We n(',(~d two in(li(:e,s: n is the, index of h,c: this I. (](;'ll, te, l" (]oltl, i'lt?tatio'lt: tit(', (:('.Iil;(~l; w.nmius l;]le S3InO, is ml individual deline, d in input (:ont0,xt. The iu- (h'.x 7n, is 1;ira index of l:he obje.(:t 1)oss(~ssed 1)y h('..,d 2. (/c'nter Shift: tim (:(,alter (:hang('.s this obj('x:t is adde, d to th(', Ollti)ttt context. (For Tim ~wl:mfl (:ent('.ring theory involves ml ad(li- clarit;y, we will ofl;en write h,is,cat,,,.; 1)ut the '%1> tiona.l data struci;urc, the forward-looking centers, licial usage" is hc.,~ %, cat.) and define.s fimr transition types, with a 1)re[e.r- Now, we. examine a simph; case of sloppy iden- en(:e or(h;ring among tJmm. The reader is r('J'e,rred Lily in Vl' ellipsis: to (Gt'osz et al., 1995) for a fltll at:(:ount; of this. (5) }L. rlnOlIl IOV(Lqhis cat. ,Iohn does too. For our purposcs~ wc will ro.ly on t;hc mcdumisnl of center ,shift to iull)l('.m(ml; the ]'(;assignm(ml; i,ha|; t). 'Ibm,* l)l~.f';S2 love his* (:at:~. ,lolm4* we. argue, is (:ru(:ial to l;ho. dynamic a(:(:t)tlltI; o[ (10(;82 I;oo. slot)l)y id(mtity. Tom|* I'IH",S~ love his* (:a.t:~ -> [u,), ul, ]'~, u:~ [ Uo --ut, ul :-- Tom, 2.2 VP Ellipsis i'~ = Ax([ua] (>f(u:~, uo), Ne.xt, we extend tim system for VP (~llil)sis: tirsl;, ,:a; (.,:~), lov,,(x,~:, )1), verbs at'(; sep;uated into a base form and a,n infl(~(:-. ,,f(,~:,,,~,,),(:~(,~:,), lov,.0,, ,,,:,)] lion (INFI 0. This fa(:ilit;~)J;es |;hc |;reaJ;m(ml; of VP ,John4* (locs:~ (1oo) :-> ellipsis; the [NFI, (:ategory adds the. new prop(~rl:y [u(,, u4 lu4 -: u(), u4 = ,/ohn] ; l'~,(u4) l;o (;he (:Olfl;(;xl;~ just as the (lcgcrmin(~]' "a" a(l(ls ~ new individual to the (:ontexl;. An ;dt(',]nal;ive meaning for t]te INFL (:ateg(>ry is giv(;n for V])t;; Next, we join tim two scnt(',n(:es I,ogeJ;h(u' an(l OCCllrI'(}IIC(;S~ where a 1)rof)crl;y is acc(~sse,d from Lhe apt)ly th(, value of I)2 to u4: inlmt (:onl;(',xt. 4We ignore the. semantic conlailmtion of INFI,, INFLu => A I' Ax [1>,, I 1',~ = P] ; P(x) apm't f]'ont the above.-described interaction wil;h the. INFI,,z :& dr(ant(INH~,,)) discourse conte.xt.
521 Tom1* PRES2 love his* Cata (and) We use variables of the form ui to denote ordi- John4* doesu (too) => nary extensional individuals; we use variables of [U0, Ul, P2, U3 [ Uo = Ul, Ul = Tom, the form xi to denote dynamic individuals. There P2 = Ax[u31 of(u3, Uo), are two distinct effects on the output context. cat(ua), love(x,ua)], First, the dynamic individual Xm is added to con- of(ua,uo),cat(ua), love(u,,ua)] ; text: this object addsan individual Um to a given [Uo' U4 I U4 = 110' U4 = John] ; context, such that Um is of un in that context. [Ua I of(ua, uo), eat(ua), love(ua,u3)] Second, Xm is applied to the property P2. This actually adds u,~ to the current context. The antecedent for the VPE is "love his cat". Finally, we need an alternative form for pro- This object (PJ is introduced into the context by nouns thai; refer to dynamic individuals: PRES> P2 represents the property of "loving u0's hen ~ 6 where 6 = dr(ant(he,~)) cat", where uo is the discourse center defined in the input context. In the first sentence, the center is TOM. The second sentence shifts the center to The pronoun hen recovers xn from the current JOHN. It is this change in context that gives rise context. The desired reading can now be derived to the sloppy reading. Thus a sloppy reading is as follows: made possible when there is a center shift. Finally, we allow the possibility that, a property (7) a. Smith spent his paycheck. Jones saved might be the discourse center. This means we it. must add an alternative rule for INFL, so that it b. Smith1* PAST2 spend his* paychecka. adds a property that is the discourse CEntEr: Jones4* PASTa save ita. INFL,~* ::> We take the two sentences individually. The A PAx [Pn I P0 -=- P,~, Pn = P]; P(x) first sentEnCE introduces the dynamic individual xa, as follows6: 2.3 Paycheck Pronouns his* paychecka. => The phenomenon of "paycheck pronouns",5 is il- AP2 [xa I xa = IP([u3 ] of(ua,u0), paycheck(u3)]; P(ua)) ]; lustrated by the following Example xa(P2) (6) Smith spent his paycheck. Jones saved spend his* paycheck> => it. Av [xa I x3 = AP([ua [ of(ua,uo), paycheck(ua)]; The reading of interest is where the pronoun P(ua)) ]; "it" refers to Jones' paycheck, although its an- I spend(v,u')]) tecedent ("his paycheck") refers to Smith's pay- spend his* paychecka. check. Our account for this parallels the account Av [xa Ix3 : IP([u3 I of(ua,u0), paycheck(ua)]; of sloppy identity in VP ellipsis. The antecedent P(u:0) ]; "hisi paycheck" introduces a dynamic individual: [u3 I of(ua,uo), paycheck(ua)];[ I spcnd(v,ua)] a relation between contexts that introduces i's Smith ~* PAST2 spend his* paychecka. paycheck to the output context, where the value [u0,Ul,P2,xa ]u0 = ul,ul = Smith, of i is dEtErminEd by the input context. The fol- xa = AP([ua I of(ua,uo),paycheck(ua)]; lowing rule makes it possible for NP's like "his P(ua))]; paycheck" to add dynamic individuals to the con- [113 I of(ua,uo), payEheck(ua),spend(ul,ua)] text. his (he~'Sm) => We continue with the second sentence. P, I xm = I of(u..un)]; save it3 AQAv(Q()m'[ I save(v,u')])) dr(ant(ita)) xm(PJ We substitute the value of xa for dr(ant(ita)): 5This term comes from Kartunnen's example: The save ira man who gave his paycheck to his wife was wiser AQAv(Q(),u'[ I save(v,u')])) than the one who gave it to his mistress. Various ac- AP([ua I of(ua,u0),paycheck(ua)];P (ua))] counts of this phenomenon have been proposed, such as (Cooper, 1979; Engdahl, 1986; Jacobson, 1992; Gardent, 1991). (Heim, 1990) proposed extending the We perform A reductions, resulting in: Sag/Williams account of VPE to the case of paycheck pronouns. Gardent makes a proposal similar to the 6To simplify the representation, we omit the values current account: a dynamic approach in which pay- for VP variables P2 and Ps, since they are not relevant check pronouns and VPE are treated uniformly. to the current example.
522 save ita => (11) When Harry drinks, I always conceal Av ([ua [ of(ua,u0),paye.heck(ua)]; [NP my belief that he shouldn't [I save(v,,:,)])) [vp ] ]. When he gambles, i can't con- Jones4* I'AST.5 save ita. => ceal it. [Uo,U4,1'5,ua luo = u4,u4=Jones, of(ua,uo) , payeheck(ua), save(u4,ua)] ExaInlfles (8) and (9) have already been dis- cussed. (8) is the familiar (:as(', in which the VP an- tecedent (XP) contains a sloppy pronoun (YP). The coInplete discourse is rel)resented as fol- YI' switches from C1, ~lbm, to C2, John. In ex- lows: ample (9), we have at, NI' antecedent (XP) con- Smith :t* PAST2 st)end his* t)ayche(:k:~. taining a sloppy pronoun (YP), and the two con- .lones4* PAST5 save ita. => trollers tbr YI ) are Smith and Jones. l,',xample [u0,ul,P2,xa ] u0 = u~ ,u~ = Smith, (10) involves a VP anteee(lent ('ontaining a sloppy VP ellit)sis; l;he VP ellipsis switches from help you X 3 -= M'([ua I (,f(ua,u0),paydmek(u:,)];P (Ua)) to kiss you. Finally, example (1.1.) involves an NP [ua ] of(ua,uo), payeheck(ua),st,end(u~ ,ua)]; atttece(tent (:ontaining a sh)ppy VP ellipsis, switch- [uo,u4,Ps,ua luo = u4,u4=aones, ing froIn drinks to gambles. of(ua,no),l,ayeheck(u:0, save(u4,ua)] We have already seen how the sloppy reading is derived for (St and for (9). We now show the deriwttion tbr (10) (example (11) can be derived The dynamic individual xa adds the paycheck in a similar fashion.)8: of u0 (the discourse center) to the context. In the second sentence, the discourse center is ,]o'n,c& 1~ WILl;2* hell) youa [if] youa PRES4 want ntel 1;o2. Thus we get the reading in which "Jones saved I I WILL.;* kiss youa [even if] youa DO4 NOT. :-> Jones' tmyeheek", as desired. [Ul,l)0,Pe,ua,P4 I ul = 1,1)0 -- P:~,Ua - You, P= = av([ I help(v,u:d]), 3 An Expanded Paradigm tbr : av([ I want(v,po(u,))]), Sloppy Identity help(u, ,u:~),want (ul ,helt,(Ul,Ua))] ; [1'o,1',~, ] P0 = Ps, The proposed theory permits a simple, llniforln 1',~ -- ,\v([ I kiss(v,ua)]),NOT(P4(ua))] treatment of sloppy identity in VPE and pay- check pronouns. This uniformity extends fln'ther. We simply permit sloppy identity for any pro- The variable P4 represents the t)roI)erty of form, whenever the anliece(le.nl; contains a preform "wanting ul to Po". Below, we substitute the within it. This is schematicMly represented as fol- value Av([ I want(v,Po(t h))]) for P~, and then sub- lows: stitute the wflue Av([ [ help(v,u:0]) for P0, and apl)ly it to ua, giving the following, result: Cl ... b, .... [,,,] ...] ... c2... b,"] It WILL2* hel t) youa [if] youa PRES4 want me1 to2. (C1, C2: "controllers" of sloppy variable YP) It WlM, a* kiss youa [even if] youa 1)O4 NOT. :* [ul,Po,P2,ua,l'4 [ul = I,Po = P2,ua = "~2)u, Ilere, XP is the anl;ecedent for some preform P2 = Av([ I help(v,ua)]), XP', and YP is the sloppy variable~, i.e., a pro- = I form embedded within XP. A sloppy reading re- help(u1 ,nat,want (ul ,help(u, ,ua))] ; suits whenever there is a center shift involving [Po,Pa I Po = Ps, P5 = lv([ I kiss(v,ua)]), C1 and C2. That is, the interpretation of YP NOT([ I want(ua,kiss(u,,ua))]), switches from controller C1 to C2. Since the dynamic theory treats VP ellipsis uni- formly with NP proforms, XP and YP both range It is the. "center shiflT involving P2 ("help you") over NP and VP. This predicts four possibilities. and P5 ("kiss you") that inakes thedesired read- All four possibilities in fact occur, as shown by the ing possible. That, is, "what ua doesn't want is for following examples: 111 to kiss ua". The dynamic theory explains all four of these (8) Tom [v,' loves IN,' his] cat]. John eases in the same way; the embedded proform in does too. the antecedent (:an be sloppy, because the con- (9) Smith spent IN;' IN,' his] paycheck]. troller for the embedded proform can undergo a aeries saw;d it. center shift. The eases illustrated by (10) and (11.) (10) I'll help you if you [v*' want me to [v*' ] ]. I'll kiss you even if you don't, r 8We construct a representat, ion as if the connec- tives if and even if were simple conjunctions. This allows us to avoid the complex issues involved in rep- rThis example was provided by Marc Gawron resenting such "backwards conditionals" in a dynamic (p.c.), who attributed it to Carl Pollard. system.
523 have not, to my knowledge, been discussed t)revi- Robert Fiengo and Robert May. 1994. Indices ously in the literature. It is not clear how such ex- and Mentity. MIT Press, Cambridge, MA. amt)les could be handled by alternative theories, Claire Gai'dent. 1991. l)ynanfic semantics and such as (Fiengo and May, 1994) or (Dah'ymple el; vp-ellipsis, in J. van Eijck, editor, Logics i'tt al., 1991), since these theori(',s do not treat NP AI, Lect'ure notes in Artificial l'ntdli.qence J78. and VP anaphora in a uniform fashion. Springer, Berlin. 4 Conclusions and Future Work Jeroen Groenendijk and Martin Stokhof. 11992. Dynamic predicate logic. Linguistics and Phi- The dynamic perspective provides a Kamework losophy. for a silnple, intuitive account of sloppy identity Barbm'a Grosz, Aravind Joshi, and Scott Wein- and related phenomena, by explaining the inter- stein. 1.995. Centering: A fi'amework for mo(t- pretive facts in terms of changes in context. This eling tile local coherence of a discourse. Com- requires contexts to change in a way that is some- putational Linguistics , 21.(2). what foreign to the dynamic perspective; a given position in tile (:ontext must be reassigned, or shift Daniel Hardt;. 1994. Sense and reference in dy- its value. To implement this, I have incorporated namic senm ntics. Ill Procec,dings of the Ninth, the notion of discourse center, together with the Amsterdam Colloquium. me('hanism of center shift, into a dynamic sys- Irene lteim. 1982. 7'he Semantics of Definite and rein. This makes it possible to give a novel, dy- Indefinite Nou'n Phrases. 1)h.]). thesis, Univer- nalnie account of sloppy id(mtity t)henomena, i sity of Massachusetts-Amherst. have shown that this approach aeeotmts for an expanded paradigm of sloppy identity, going be- Irene Heiln. 1990. E-type pronouns and donkey yond tile data addressed in alternative a(:counts. anat)hora. Lmg'uistics and Philosophy, 13(2). In future work, we will investigate ineorI)orating Pauline ,Jaeobson. 1992. Antecedellt containe(1 additional aspects of centering theory, including delet,ion in a variabh>fl'ee selnantics. In i)~w~ the tbrward-looking centers list, and the prefer- cc.cdings of the Second Conference on Semantics en(;e orderings on transitions. and Ling'wistic ~lTlcory, Colunlbus, Ohio. Hans Kamp. 1980. A theory of truth and senlan- 5 Acknowledgments tic representation. In .I. (lroenendijk, T.M.V. Thanks to Claire Gardent, Aravind Joshi, Shah)m Janssen, and M. Stokhof, editors, Formal Mel;ll- Lappin, Mats Rooth, Stuart Shieber, Mark Steed- ods in the Study of Language, 1)ages 277 322. man, and Bonnie Webber for help in develoi)- Dordrecht;. Volume 136. ing tile basic aI)proach described in this pal)er. Chris Kennedy. 1993. Argumealt-contained ellip- Thanks to ll,einhard Muskens for helpful con> sis. ments on an earlier version of this work. This Ewan Klein. 1984. Vp ellipsis in dr theory. work was partially supported by a Villanova Uni- versity Summer Research Grant (1995), and an l{einhard Muskens. 1996. Combining montague NSF Career Grant, no. IRI-9502257. selnantics and discourse rel)reselfl;al;ion. Lin- .qv,i.stics and Philosophy. Jan van Eijck and Nissiln Francez. 11993. Pro- References cedural dynamic seinanties, verb-phrase ellip- sis, and presupI)osition. In CWI, E,cpor't C5'- Nicolas Asher. 1993. I~@:rcnce to Abstract Ob- l~931 l. jects in English. l)ordreeht. Cennaro Chierchia. 1992. Anaphora and dynalnic interpretation. Linguistics and Philosophy, 18. Alonzo Church. 1940. A formulation of the simple theory of types. Tile Journal of Symbolic Logic, 5:56 68. Robin Cooper. 1979. The interpretation of pro- nouns. In F. Heny and H. Schnelle, editors, Syntax and Semantics I0. Academic Press. Mary Dalrymple, Stuart Shieber, and Fernando Pereira. 1991. Ellipsis and higher-order unifi- cation. Linguistics and Philosophy, 14(4), Au- gust. glisabeth Engdahl. 1986. Constituent Questions. D. Riedel, Dordreeht, Netherlands.
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