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<?xml version="1.0" standalone="yes"?> <Paper uid="C96-1088"> <Title>Centering in Dynamic Semantics</Title> <Section position="3" start_page="519" end_page="522" type="metho"> <SectionTitle> 2 A Dynamic Framework </SectionTitle> <Paragraph position="0"> The basic dynamic framework is the dynamic logic system of (Muskens, 1996). This framework has, for the sake of simplicity, restricted l;he study of anaphora to pronouns that are extensionally identified with their antecedents :~. I will extend Musk(ms' system to permit anaphora involving VP's as well as NP's, and to allow antecedents to be dynamic ms well as ordinary (extensional) objects.</Paragraph> <Paragraph position="1"> In Muskens' system, linearized I)RT boxes are integrated with the type logic (Church, 1940) that underlies Montague Semantics. Linearize(t DI{T boxes are simply a more concise way of writing standard DIt3 ~ boxes (Kamp, 1980). Muskens shows that DR~I' boxes can t)e viewed as abbreviations for expressions in ordinary type logic. Consider the following discourse.: tile; discourse: Aj farmer walks. H el laughed.</Paragraph> <Paragraph position="2"> This is represented by the following linearized I)RT box: \[u:t \[ farrner(ul ), walk(u1 ),taugh(u~ )\] 3There are several researchers who have extended dynamic frameworks to account tbr ellipsis and related phenomena: (Klein, 1984) is an early examt)le. lAsher, 1993) examines a variety of extensions to the I)R~.\[ ~ framework. (van Eijek and Francez, 1993) ex~ plorc similar issues of indexing and ellipsis in a dy~ namic setting. (Gardent, 1.99t) also extends a dy~ namie semantics system for ellipsis and anaphora.</Paragraph> <Paragraph position="3"> This is an abbrevial;ion for dm following type logic formula: Aij (i\[ut \]j Afarmer (u j) Awalks(u:, j) Alaughs(u, j)) In the above formula, the variables i and j ret)resent inpul: and output st;ates, and tim variabh~ u, (akin to a discourse marker) is a flln(:tion froln states to individuals, lit what, folk)ws, we use the DltPF abbreviations without further comment,.</Paragraph> <Paragraph position="4"> The reader is referred to (Muskens, 11996) for fur-ther examl)les and the details of l;tl(', system. We now define a siinple fragment of English, base(1 on the one given in (Muskens, 1996).</Paragraph> <Paragraph position="6"> Not:e that the t;ransladon for h,e,, refers to dr(ant(lte,~)). Tiffs is detined as the discourse re4> resentation of the antecedent of he~(see (Muskens, 71.996, page 20)). The l;ranslation for and is the sequencing operator, ;. As described in (Musk(ms, 1996), the sequencing of two boxes K,K' is an abbreviation for the following type logic expression: \[K~; g2\]l -~ {<i,j> I ~k (<i,k> ~ \[t~'t~ & <k,j> e \[K2~)} Typically, two DI/~.\[' boxes appearing in sequence can be 'm, evged inLo a single box, consisting of the union of the discourse markers ill the two boxes and the union of the conditions. This is described in the Mcwi'n9 Lcmma of (Muskens, 1996, page 8). In the representations that follow, we will often merge boxes without (;Oltli\[lellt to silllplify representations. Ilowever, the merge of two boxes is not always possible if there is a reassigmnent of an index, i(; will not be possible to perform the merge. This will arise in the cases of sloppy identity exalnined below.</Paragraph> <Paragraph position="7"> The above t\]'aginent, following the Kamp/lteim accounts, considers only one type of anaphora, involving individuals. We will extend the fragment in the following ways: * we will add the idea of a di.scour.se center to the system * we will allow dynamic properties to be added to contexts, as antecedents for VP ellipsis * we will allow dynamic individuals to be added to contexts, to accoullt for &quot;paycheck</Paragraph> <Paragraph position="9"/> <Section position="1" start_page="520" end_page="520" type="sub_section"> <SectionTitle> 2.1 Discom'se (~('nt e,r </SectionTitle> <Paragraph position="0"> W(', de, film position 0 in Om context as t;h(; I)isco'u, rse (,'cntc.r'. AI; any {~iv(m l)oi\]~l; in the discourse, tim (liscours(~ (;Ifl;il,y d(}sigmtt;('.(1 as Lhc dis- null ('ore:s(; ('eJlt(;r o(:(:ut)ics posil,ion 0 as well as il;s ot;he.r l)osil;iou. We (lesign;tl:c 1;his with a, *, as iu th(; following (~Xaml)l(;: (3) A,* farmer walks, llc* la.ughcd.</Paragraph> <Paragraph position="1"> This is r(!l)r('.se.nl;(xl ;t,q follows: \[,u,,,,, I,~0 : ,,,, fa,',n,;,(.,), ~alk(,,,),la,,~h@:,)\] In this (lis(:ours( h (:Ira enl;ity iill;rodu(:e.d /)y A I * farrn(:r is th(' discourse, (:(mi;('J, and thus o(:cut)i(~s position 0 a.s well as position \].</Paragraph> <Paragraph position="2"> 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.</Paragraph> <Paragraph position="3"> a I', l'~@,,,,,,,,I ,,o :: ..1; l,, (,,.,);p..(..)) ,John.n* :5 ~l.(\[u,,,u,. lu0 :~ u.,,,~,, ~--.loh@;l'(H.)) W(', will apply a v(',ry siinplili(',d version ot' (:entering ttmory, consisting o\[ l;h(,, following consLra.ints: null tiona.l data struci;urc, the forward-looking centers, and define.s fimr transition types, with a 1)re\[e.ren(:e or(h;ring among tJmm. The reader is r('J'e, rred to (Gt'osz et al., 1995) for a fltll at:(:ount; of this. For our purposcs~ wc will ro.ly on t;hc mcdumisnl of center ,shift to iull)l('.m(ml; the \]'(;assignm(ml; i,ha|; we. argue, is (:ru(:ial to l;ho. dynamic a(:(:t)tlltI; o\[ slot)l)y id(mtity.</Paragraph> </Section> <Section position="2" start_page="520" end_page="521" type="sub_section"> <SectionTitle> 2.2 VP Ellipsis </SectionTitle> <Paragraph position="0"> Ne.xt, we extend tim system for VP (~llil)sis: tirsl;, verbs at'(; sep;uated into a base form and a,n infl(~(:-.</Paragraph> <Paragraph position="1"> lion (INFI 0. This fa(:ilit;~)J;es |;hc |;reaJ;m(ml; of VP ellipsis; the \[NFI, (:ategory adds the. new prop(~rl:y l;o (;he (:Olfl;(;xl;~ just as the (lcgcrmin(~\]' &quot;a&quot; 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;; OCCllrI'(}IIC(;S~ where a 1)rof)crl;y is acc(~sse, d from Lhe inlmt (:onl;(',xt.</Paragraph> <Paragraph position="3"> lions (PAST, PI~,I';S, ('C/(:.) and ;mxiliary v(,rbs ((lo, should, el:('..) 4 Consid('x th(, folh)wint,, (~x~uni)l(~ of V\] ) ellipsis: null (d) a. Tom walks. ,lohn does too.</Paragraph> <Paragraph position="4"> b. Ton,,* 1)l{.l&quot;,Sz w~flk. John:~* do(~s:e too. The, two s(',nt(,'n(:es r('('.(dve I,ll(~ following inl;cr 1)retal;ions:</Paragraph> <Paragraph position="6"> 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.</Paragraph> <Paragraph position="8"> Next, we will (:o\]mid(',r a,n cxmnl)h~ involving sloppy i(hml,ity, rib (to this, it will t)c n(',c,(~ssary t:o add genitiv(,. Nl)'s, such as &quot;his (:at&quot; to ore sysI;(HII. null his (he.,~'s,~) => xl'. p~ (\[,_~,. I of(u.,, H,.)\]; P\[0~,,,); \]'~(-.,) ) We n(',(~d two in(li(:e,s: n is the, index of h,c: this 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 this obj('x:t is adde, d to th(', Ollti)ttt context. (For clarit;y, we will ofl;en write h, is,cat,,,.; 1)ut the '%1 > licial usage&quot; is hc.,~ %, cat.) Now, we. examine a simph; case of sloppy iden-Lily in Vl' ellipsis: (5) }L. rlnOlIl IOV(Lq his cat. ,Iohn does too.</Paragraph> <Paragraph position="9"> t). 'Ibm,* l)l~.f';S2 love his* (:at:~. ,lolm4* (10(;82 I;oo.</Paragraph> <Paragraph position="10"> Tom|* I'IH&quot;,S~ love his* (:a.t:~ -> \[u,), ul, \]'~, u:~ \[ Uo --ut, ul :-- Tom,</Paragraph> <Paragraph position="12"/> <Paragraph position="14"> The antecedent for the VPE is &quot;love his cat&quot;.</Paragraph> <Paragraph position="15"> This object (PJ is introduced into the context by PRES> P2 represents the property of &quot;loving u0's cat&quot;, 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 JOHN. It is this change in context that gives rise to the sloppy reading. Thus a sloppy reading is made possible when there is a center shift.</Paragraph> <Paragraph position="16"> Finally, we allow the possibility that, a property might be the discourse center. This means we must add an alternative rule for INFL, so that it adds a property that is the discourse CEntEr:</Paragraph> </Section> <Section position="3" start_page="521" end_page="522" type="sub_section"> <SectionTitle> 2.3 Paycheck Pronouns </SectionTitle> <Paragraph position="0"> The phenomenon of &quot;paycheck pronouns&quot;,5 is illustrated by the following Example (6) Smith spent his paycheck. Jones saved it.</Paragraph> <Paragraph position="1"> The reading of interest is where the pronoun &quot;it&quot; refers to Jones' paycheck, although its antecedent (&quot;his paycheck&quot;) refers to Smith's paycheck. Our account for this parallels the account of sloppy identity in VP ellipsis. The antecedent &quot;hisi paycheck&quot; introduces a dynamic individual: a relation between contexts that introduces i's paycheck to the output context, where the value of i is dEtErminEd by the input context. The following rule makes it possible for NP's like &quot;his paycheck&quot; to add dynamic individuals to the con-</Paragraph> <Paragraph position="3"> man who gave his paycheck to his wife was wiser than the one who gave it to his mistress. Various accounts of this phenomenon have been proposed, such as (Cooper, 1979; Engdahl, 1986; Jacobson, 1992; Gardent, 1991). (Heim, 1990) proposed extending the Sag/Williams account of VPE to the case of paycheck pronouns. Gardent makes a proposal similar to the current account: a dynamic approach in which paycheck pronouns and VPE are treated uniformly.</Paragraph> <Paragraph position="4"> We use variables of the form ui to denote ordinary extensional individuals; we use variables of the form xi to denote dynamic individuals. There are two distinct effects on the output context.</Paragraph> <Paragraph position="5"> First, the dynamic individual Xm is added to context: this object addsan individual Um to a given context, such that Um is of un in that context.</Paragraph> <Paragraph position="6"> Second, Xm is applied to the property P2. This actually adds u,~ to the current context.</Paragraph> <Paragraph position="7"> Finally, we need an alternative form for pronouns thai; refer to dynamic individuals: hen ~ 6 where 6 = dr(ant(he,~)) The pronoun hen recovers xn from the current context. The desired reading can now be derived as follows: (7) a. Smith spent his paycheck. Jones saved it.</Paragraph> <Paragraph position="8"> b. Smith1* PAST2 spend his* paychecka.</Paragraph> <Paragraph position="9"> Jones4* PASTa save ita.</Paragraph> <Paragraph position="10"> We take the two sentences individually. The first sentEnCE introduces the dynamic individual xa, as follows6:</Paragraph> <Paragraph position="12"> spend his* paychecka.</Paragraph> <Paragraph position="13"> We continue with the second sentence. save it3 AQAv(Q()m'\[ I save(v,u')\])) dr(ant(ita)) We substitute the value of xa for dr(ant(ita)): save ira AQAv(Q(),u'\[ I save(v,u')\])) AP(\[ua I of(ua,u0),paycheck(ua)\];P (ua))\] We perform A reductions, resulting in: 6To simplify the representation, we omit the values for VP variables P2 and Ps, since they are not relevant to the current example.</Paragraph> <Paragraph position="14"> payeheck(ua), save(u4,ua)\] The coInplete discourse is rel)resented as follows: null Smith :t* PAST2 st)end his* t)ayche(:k:~. .lones4* PAST5 save ita. =></Paragraph> <Paragraph position="16"> of(ua,no),l,ayeheck(u:0, save(u4,ua)\] The dynamic individual xa adds the paycheck of u0 (the discourse center) to the context. In the second sentence, the discourse center is ,\]o'n,c& Thus we get the reading in which &quot;Jones saved Jones' tmyeheek&quot;, as desired.</Paragraph> </Section> </Section> <Section position="4" start_page="522" end_page="523" type="metho"> <SectionTitle> 3 An Expanded Paradigm tbr </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="522" end_page="523" type="sub_section"> <SectionTitle> Sloppy Identity </SectionTitle> <Paragraph position="0"> The proposed theory permits a simple, llniforln treatment of sloppy identity in VPE and paycheck pronouns. This uniformity extends fln'ther.</Paragraph> <Paragraph position="1"> We simply permit sloppy identity for any proform, whenever the anliece(le.nl; contains a preform within it. This is schematicMly represented as follows: null Cl ... b, .... \[,,,\] ...\] ... c2... b,&quot;\] (C1, C2: &quot;controllers&quot; of sloppy variable YP) Ilere, XP is the anl;ecedent for some preform XP', and YP is the sloppy variable~, i.e., a pro-form embedded within XP. A sloppy reading resuits whenever there is a center shift involving C1 and C2. That is, the interpretation of YP switches from controller C1 to C2.</Paragraph> <Paragraph position="2"> Since the dynamic theory treats VP ellipsis uniformly with NP proforms, XP and YP both range over NP and VP. This predicts four possibilities.</Paragraph> <Paragraph position="3"> All four possibilities in fact occur, as shown by the following examples: (8) Tom \[v,' loves IN,' his\] cat\]. John does too.</Paragraph> <Paragraph position="4"> (9) Smith spent IN;' IN,' his\] paycheck\].</Paragraph> <Paragraph position="5"> aeries saw;d it.</Paragraph> <Paragraph position="6"> (10) I'll help you if you \[v*' want me to \[v*' \] \]. I'll kiss you even if you don't, r rThis example was provided by Marc Gawron (p.c.), who attributed it to Carl Pollard.</Paragraph> <Paragraph position="7"> (11) When Harry drinks, I always conceal \[NP my belief that he shouldn't \[vp \] \]. When he gambles, i can't conceal it.</Paragraph> <Paragraph position="8"> ExaInlfles (8) and (9) have already been discussed. (8) is the familiar (:as(', in which the VP antecedent (XP) contains a sloppy pronoun (YP). YI' switches from C1, ~lbm, to C2, John. In example (9), we have at, NI' antecedent (XP) containing a sloppy pronoun (YP), and the two controllers tbr YI ) are Smith and Jones. l,',xample (10) involves a VP anteee(lent ('ontaining a sloppy VP ellit)sis; l;he VP ellipsis switches from help you to kiss you. Finally, example (1.1.) involves an NP atttece(tent (:ontaining a sh)ppy VP ellipsis, switching froIn drinks to gambles.</Paragraph> <Paragraph position="9"> 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 in a similar fashion.)8:</Paragraph> <Paragraph position="11"> The variable P4 represents the t)roI)erty of &quot;wanting ul to Po&quot;. Below, we substitute the value Av(\[ I want(v,Po(t h))\]) for P~, and then substitute the wflue Av(\[ \[ help(v,u:0\]) for P0, and apl)ly it to ua, giving the following, result: It WILL2* hel t) youa \[if\] youa PRES4 want me1 to2.</Paragraph> <Paragraph position="12"> It WlM, a* kiss youa \[even if\] youa 1)O4 NOT. :*</Paragraph> <Paragraph position="14"> It is the. &quot;center shiflT involving P2 (&quot;help you&quot;) and P5 (&quot;kiss you&quot;) that inakes thedesired reading possible. That, is, &quot;what ua doesn't want is for 111 to kiss ua&quot;.</Paragraph> <Paragraph position="15"> The dynamic theory explains all four of these eases in the same way; the embedded proform in the antecedent (:an be sloppy, because the controller for the embedded proform can undergo a center shift. The eases illustrated by (10) and (11.) 8We construct a representat, ion as if the connectives if and even if were simple conjunctions. This allows us to avoid the complex issues involved in representing such &quot;backwards conditionals&quot; in a dynamic system.</Paragraph> <Paragraph position="16"> have not, to my knowledge, been discussed t)reviously in the literature. It is not clear how such examt)les could be handled by alternative theories, such as (Fiengo and May, 1994) or (Dah'ymple el; al., 1991), since these theori(',s do not treat NP and VP anaphora in a uniform fashion.</Paragraph> </Section> </Section> class="xml-element"></Paper>