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<Paper uid="C94-2120">
  <Title>INCREMENTAb INTERPRETATION: APPLICATIONS, THEORY, AND RF, LATIONSHIP TO DYNAMIC SEMANTICS*</Title>
  <Section position="4" start_page="750" end_page="750" type="metho">
    <SectionTitle>
3. IneremeiH;al Quantith~r Seeping
</SectionTitle>
    <Paragraph position="0"> So fa.r we have only considered semantie r(~presental.ions which do not involve (lll~uttiliel'S (except I'or the exist(mtial quantifier introduced by the mechanist, ~d)ove).</Paragraph>
    <Paragraph position="1"> In senten(:es with two oF more qmmtiliel;s, there is generally ~m ~mabiguity eon(:erning whiC |quantifier has wider s(:ope. 1&amp;quot;or exm:nple, in sentence (a) below tim preferred reading is lbr the same kid to have ('Aimbed every tree (i.e. the ml.iversal quantilier is within the scope of the existeutia.I) whereas in sentence (b) the preferred reading is where the universal quantifier has scope over the existential.</Paragraph>
    <Paragraph position="2">  7) a A I, ireless kid eliml)ed every tre.e.</Paragraph>
    <Paragraph position="3"> b There was ~ tish on every l~latc '.</Paragraph>
    <Paragraph position="4"> Scope prefiwenees sometimes seem to I)c esl, al)lished bel'ore the end of tz sentence. \],'or example, in seutenee (a) below, there s('.ellla a l)referell(:e for all Oll(,er seol)e reading for the first quantifier as soon as we inl;erl)rel; child. Ill (13) the i)refereu(:e, by the time we get to e.g. gram.mar, is \[~.)r adl ituwr scope re~ding for the lh:st qu a.ntiller.</Paragraph>
    <Paragraph position="5"> 8) a A te~eher gave every child a great deal of he-.</Paragraph>
    <Paragraph position="6"> mework Oll gralflnlar.</Paragraph>
    <Paragraph position="7">  91{ctractlon call be performed by using ~t tagged dattd)ase, whm'e e:tch In'OpOsition is l)alrcd with a sel: ,f s()tll'C(~ (!.~. given (P-~Q,{u4}), and (P,{nS})then(Q,{u4dtS}),:ml I,c deduced.</Paragraph>
    <Paragraph position="8"> Z~I b Every gM in the class showed a rather strict new teacher the results of her attempt to get the grammar exercises correct.</Paragraph>
    <Paragraph position="9"> This intuitive evidence can be backed up by considering garden path effects with quantifier scope tunbiguities (called jungle paths by Barwise 1987). The original examples, such ~s the fbllowing, 9) Statistics show that every 11 seconds a man is mugged here in New York city. We are here today to interview hiln showed that preferences for a particular scope are established and are overturned. 'Po show that preferences are sometimes established before the end of' a sentence, and before a potential sentence end, we need to show ga.rden path effects in examples such as the following: 10) Mary pttt the inIbrmation that statistics show that every 11 seconds a man is mugged here in New York city and that she was to interview him in her diary Most psycholinguistic experimentation has been concerned with which scope preferences are made, rather than the point at which the preferences are establishcd (see e.g. Kurtzman and MacDonald, 1993). Given tile illtuitive evidence, our hypothesis is that scope preferences can sometimes be established early, befbre the end ofa sentence. This leaves open the possibility that in other cases, where the scoping inIbrmation is not particularly of interest to the hearer, preferences are determined late, if at all.</Paragraph>
    <Section position="1" start_page="750" end_page="750" type="sub_section">
      <SectionTitle>
3.1 Increlnental Quantifier Scoping: hnple-
</SectionTitle>
      <Paragraph position="0"> lnent, ation Dealing with quantifiers incrementally is a rather simila.r problem to dealing with h'aglnents of trees incrementally, a,st as it is in-,possible to predict the level of embedding of ~r noun phrase such as John from tile fragment Mary thinL's John, it is also impossible to predict the scope of a quantifier in a fragment with respect ~o the arbitrarily large number of quantiliers which might appear later in the sentence. Again the problem can be avoided by a tbrm of pacldng. A particularly simple way of doing this is to use unseoped logical forms where qmmtifiers are left in situ (silnilar to the representations used by Hobbs and Shieber (1987), or to Quasi Logical Form (Alshawi 1990)). For example, the fl'agment Every man gives a boot&amp;quot; can be given the tbllowing representation:</Paragraph>
      <Paragraph position="2"> Each qnantitied term consists of' a quantitier, a va.riable and a restrictor, but, no body. To convert lambda expressions to unscoped propositions, we replace an occurrence of each argument with an empty existentia.l quantitier term. In this case we obtain: 12) gives(&lt; V,X,ITIall(X)&gt;,&lt; 3,y,book(y)&gt;,&lt; -~,z,'l'&gt;) Scoped propositions can then be obtained by using an outside-in quantifier scoping algorithm (Lewin, 1990), or an inside-out algorithm with a free w~riable constraint (IIobbs and Shieber, 1987). The propositions fbrlncd can then be judged for plausibility.</Paragraph>
      <Paragraph position="3"> To imitate jungle path phenomena, these pla.usi o bility judgements need to feed back into the scoping procedure for the next fragment. For example, if' every man is taken to be scoped outside a book after processing the fragment l?vcry man ga~c. a book, \[;hen this preference should be preserved when deterlnining the scope for the full sentence l?very uza~t gave a book lo a child. Thus instead of doing ~dl quantitier scoping at the end of the sentence, each new quantilier is scoped relative to the existing quantifiers (and operators such as negation, intensional verbs etc.). A preliminary irnplemenl, ation achieves this by annotating the semantic representations with node nantes, a.nd recording which quantifiers are 'discharged' at. which nodes, and in which order.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="750" end_page="752" type="metho">
    <SectionTitle>
DYNAMIC SEMANTICS
</SectionTitle>
    <Paragraph position="0"> l)ynamic semantics adopts the view that &amp;quot;the mea-ning of a sentence does not lie ill its truth conditions, but rather in the way ill which it changes (tile representation of) the in\[brmation of the intcrl)reter&amp;quot; (Groencndijk and Stokho\[', \] 991). At first glance such a. view seems ideally suited t.o incremental interpretation. Indeed, Groenendijk and Stokhof claim that the compositional nature o\[' l)ynamic Predicate Logic enables one to &amp;quot;interpret a text ir~ an on-line ntauner, i.e., incrementally, processing a.nd interpreting each basic unit as it comes along, in the context created by the interpretation of the t.ext so fa.r'.</Paragraph>
    <Paragraph position="1"> Putting these two quotes together is, however, misleading, since it suggests a more direct mapping between incremental sem~mtics and dyna.mh: semantics than is actually possible. In an incremental semantics, we would expect the informtttiou state, of an interpreter to be updated word by word. In contrast, in dynamic semantics, the ol:der in which states are updated is determined by semantic st;ructure, not by left-to-right order (see e.g. I,ewiu, 1992 \[br discussion). For example, in 1)ynanfic Predicate Logic ((~roenendijk ,~ Stokhof, 1991), states are threaded from the antecedent of a conditional into I, he conseque~d~, and from a restrictor of' a quantitier into I;he body. Thus, in interpreting, 13) John will buy it right away, if a car impresses him the input state for evMuation of .John will bug it right away is the output state from the a.ntecedent a ear hnp,vsses hhn. in this ease the threading through semantic structure is in the opposite order to the order in which the two clauses appear in the sentence.</Paragraph>
    <Paragraph position="2"> Some intuitive justification for the direction of threading in dynamic semantics is provided by cousidering appropriate orders for evaluation of propositions against a database: the natural order in which  l,o cvMual;e a, conditiona,1 is first, 1,o add the antecedenl;, illl(\[ thell see if I.he COllSC(lUOlll, c{i.ll 17c: l)roveli. \]to is ()lily ai, tile sentence lew;l iu ,siniple na,rrative texLs 0ha,t I,he l)l;esenl;al, ion ordor itlld I,ho iw, l, ur~d order o\[ 4&amp;quot;wahl3J;ion necx~s,&lt;sarily coincide.</Paragraph>
    <Paragraph position="3"> The orderhig of a,n~tl)hors and theii: autel:edent, s is o\[l;en used inl'orinMly/,o jusl,ify lefl,-l,o-riglll; i, hreadiug or thi:eadilig through selllaait, ic sl;rtlC(,llrO, llowew',r, (,\]iroa(lingj fl;Olll \]el'\[,-to-righ{ disa,llows cX;/llllJlcs (3\]&amp;quot; Ol) (;tonal c;d;aphoi;a,, as ill example (1'3), mid examI)les o\[' c:oiilpll|sory c,a.l;a,p}lora, a,s ill : 14) I lesitle her&gt; every girl could see a, large cl:acl~ Sitnihu:ly, l;\]irei~ding li'oin the aui;ccedeui,s o1' conditio-ua, lS into t;he COllSl'x\[llOll\[; fails f'()r (!X31ill)JeS sHCh &amp;s: 15) EVC'L'y boy will be a.I)lc t,(i s(!(', olLi, &lt;)\[' a window il he walll;s I,() I{, is also 1)ossilTle l;o gel; ,SOli{,ellCCS with &lt;(\[Olil,:cy' rea,dhlgs, })ill; whei:c the inde\[inil;c is hi I, hc conseqllOlil,: null \[6) A 81,11de, tit wilt a, tteud the COli\['creliCe it' we C(~II ~2~(\]0 l;ogei,hoi: enough lliOli(?y \[or her air \[are This ,qCli\[;OliCO ,q(!oHis \[;o g(;1L, ;i, reading where we aro liOt, lalking &amp;l)ollb it particul~u' sl0tl(i()tll, (~/11 O\[IL(H' exist, on 0ial), or ~d)Olil; i~ typic~d stu(\]cul, (a geiloric, reading). Mol;0Ovo, i;, as noi;ed by Zcewd; (\] {).90), t;}10 115(! of ~:llly kind o\[' o.rch?rcd i;hl:0a,dhig will tend 1;o tail Ibr l~ach-I)el;ers s(}ii\[a'~lll':os~ sllc, h {ts: 17) I,;vcry man who loves lwl: a.pl~reciai,es a wonlan who liw~s with him I&amp;quot;or tliis l,:hid of exainple, il, is still possible t,o il~;C ii sl,a, ndard tlyiittlnic SOliH'~.lll;\]c,q~ I)lll; only if i, hei!e is SOlile prior level of FOt'OI!el\]CC rcsohll;ioil which reorders the a.iil;ccedonl, s alld a.lla\])llors appropriately. FOI: c.X;llll I)le, \[\[' (I 7) is converl,ed into t, he ~(ionl,:ey' selil,el\]ce: 1 8) I,\]vel'y ill&amp;It who loves a. wollH/,ll who lives wMi hiin al)preciai, es hot Whe, n we consider t\]lreading (7\[' possible wor\]ds, as hi (JIMal, e Seuia,ui;\]cs (Ve\]tman 19{)0)&gt; l:he noed I;o (\]isi, inguish bci;woen L\]le orcler o\[ eva,\[uai, ion aitd l;he oi; (ler of I)resentat, ion I)ccolues inore cl(~ar cut,. (ton,sider I,i:yiug LO 17e\]'l()r\[n i;hroa,dh\]g hi le\['D-l;o-rigiil, Ol:dO..r tlil ring in/;el:ITrel, al;iol\] o\[ l,he s(~ll|;(~ltCO~ ,loire h:fl if Marg l&lt;ffl,. Afi, cr processiltg the 1)roposition ,ioh, left I;he set, o\[' worlds is refined down to those, worlds in which .lolu~ left, Now consider processing 0 Mary lejT. \[Iere we wa,nl; l,o ix;ilti;rodtlce 8OlllC' Wt)i:i(\[S, \[;\]lOSO in which noit, hor Ma.ry or &amp;)hn le\['L I lowever, 1,tits is nor allowed by {Jpc\[atc ,qenlanl,ics whMl is ~limilmtiv&lt; cacti new piece of in\[orma.t, ion cAlli ouly l'tii'l,\[lei: i'e\[hic l,hc set; of worlds.</Paragraph>
    <Paragraph position="4"> It is woiq;h liOl;ing t, hal; I.he diliii:nll,ic!,~ in l;l'3'illg 1;0 c, onll)ine c\]iuiinal;ive seiuaili;ics with le\['tq,o-righl, tlu:e~t(linp; a.pply t,o c, ousl;i:a.illl, basc(l ,Seliiaili,ic.s as welt as I;o Upda,te Sema.ntics. tladdock (1987) uses iucre.inentM re{inenient of sets of possible ret~rents, l,'or ex ainl)le , the ell'cot, of processing t/w rabbit in I;he ttOllli plll'aSc Utc ~ rabbil ht l/to hat is to provide it set of all l;~dol)ii,s. The pi:oces,sing o\[' i~t I't?IIII(!S this sel~ to ra.bbil;s which are ill SOlllCl,liillg;. h'inaHy, proccsSillg o17 \[hc \]lal relines the sol; t,o i:~d)lfits which al:(} ill a. ha, t. IIo &amp;quot;W(\]veI' 1 I1()'~Y= COllSid(;r \]l.i'oces,sing th&lt;~ rclblTit 71l #loltc of thc bomcs. Ily tile {inie Uu: rabbit in has been processo'd, the only ra.bloits i:eula,ining in c.onsidcra,l;ioll are r~d)bits which arc in solncl;hing. This im:orrecLly l:ule,~ (ml, the possibilii, y of the uoun phrase referring to a, I:~d)l)ii, which is in nothing a.l, a.\[l. The case is *u'l;ually a parMle/ to the earlier example of Mary introduced som, e, olm, to somethin,q being iimpl)rOl)rial;e if the final sontcncc is Mar.Is i*~h'odtu:cd noonc to asqjbodg.</Paragraph>
    <Paragraph position="5"> A/ldlough t, hi,s discussion has argued {haA i~ is no1.</Paragraph>
    <Paragraph position="6"> possilTle to i;hread the sti~t('s which are us(:d by a, (lyualille (71&amp;quot; eliHlimigive setlta.ill, ics troll\] 1(;\['1, 1;o i'ip;\[il,, word by woM, t;liis sliould not; Im taken as a.ll a, rgtlfiiOllt, against 1,he ilSf! 0|' SIlC,\[I ;I, ,S(~,IIItI, III;IcS ill il/creiitelll;a\[ iitl;erpretal, ion. \Y=hai, is rcqltired is it slight, ly IIIOl'O indirect al)proach, \[11 the I)l:f.',ql'!ltl, iUll)ielllenlLa, l, ioll , SOlllall-I;IC .M,I;tlCI, III'(;S (akin tt7 logica,l f(71HIIS) ;11:(\] built word I)y word, allel (;ach StlTIlCtltre i,~ then ewdlta.l;ed indcpclldcntly tiSillg ~t dynalnit: SOlilltlll, i(:8 (with t;hl;C/i..dili{{ l)erf'ornied ~c&lt;:ording I,o t;he sl,rHct;ure of 1;he logica.I \['Orlrl).</Paragraph>
  </Section>
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