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1 Thisisanauthor-generatedprepublisheddraf
Thisisanauthor-generatedprepublisheddraft.Thenalversionisavailableonlineat CambrigeJournalsOnline (doi:10.1017/S0022226712000059).c\rCambridgeUniversityPress2012 Conjunction,cumulationandrespectivelyreadingsRuiP.ChavesLinguisticsDepartment{UniversityatBualoTheStateUniversityofNewYorkrchaves@bualo.eduAbstractSo-calledrespectivelyreadingshaveposedseriouschallengesfortheoriesofsyntaxandsemantics.SentenceslikeGeorgeandMartharespectivelydenouncedandweredenouncedbythegovernor(McCawley1998)showthatalthoughtheconjoinedverbalexpressionssharethesamesyntacticsubject,theydonotpredicatethatsubjectinthesameway;George(notMartha)denouncedthegovernor,andMartha(butnotGeorge)wasdenouncedbythegovernor.Postal(1998,160{163)andGawron&Kehler(2004,193{194)showthatthisphenomenonposesproblemsforcontemporarytheoriesofgrammarandarguethatitisparticularlyacutefortheorieswheresubcategorizationandpredicationarelinkedviaunication.Astheseauthorsnote,theproblemisevenmoresevereinrespectivelyreadingsinvolvingller{gapconstructions.InthispaperIarguethattheseverityoftheseproblemshasbeenoverstatedandthatthedatadonotentailanyspecialdissociationbetweenpredication,subcategorization,orextraction.InthispaperIproposeanaccountwhichisfullycompatiblewithunication-basedtheoriesofgrammar.Gawron&Kehler(2004)proposeanaccountofrespectivelyphenomenawhichcoversaremarkablywiderangeofcases.ThatapproachreliesonaRespfoperator,whichisstipulatedtobeoptionallyovert.However,thisanalysisisarguablyproblematicbecausetherearesignicantsemanticdierencesbetweenre-spectivelyreadingswithandwithoutanovertrealizationof`respectively'.Rather,thedatasuggestthatrespectivelyreadingsmaybespecialcasesofmoregeneralphe-nomenawhichhappentocreateinterpretationscompatiblewiththesemanticsoftheadverb`respectively'.Thisexplainswhyrespectivelyreadingscanarisewithouttheadverb,anddoesnotrequirepositingadisconnectbetweenpredicationandsubcate-gorization.Infact,asentencewitharespectivelyreadingwillnotdierinsyntacticorsemanticstructurefromsentenceswithoutsuchareading.1IntroductionEventhoughSueandKarenformsapluralNPthattriggerspluralsubject{ver

2 bagree-mentin(1),thissubjectphrasedoesno
bagree-mentin(1),thissubjectphrasedoesnotseemtobeinterpretedasapluralitybytheverbs IamgratefultotheanonymousrefereesoftheJournalofLinguisticsfortheircommentsandcriticism.Ialsothanktheaudiencesandrefereesoftheconferenceswherepreviousversionsofthisworkwerepresented,namelythe17thBiennialConferenceoftheLinguisticSocietyofNewZealand(UniversityofWaikato),andthe83rdAnnualMeetingoftheLinguisticSocietyofAmerica.ThanksisalsoduetoBrianGromforassistancesearchingGoogle'sN-Gramcorpus.1 in(1).Forexample,in(1a)KarenisnotanagentofjogandSueisnotanagentofdrive.Itisclear,however,thatsuchcoordinatesubjectNPsdoformasyntacticandsemanticsubjectbecauseofdatalike(2).Thus,respectivelyreadingsseemtocreateafundamentaldisconnectbetweensubcategorizationandpredication.(1)(a)SueandKarenjoganddriverespectively.(=`SuejogsandKarendrives.')(b)SueandKarenhiredBobandTimrespectively.(=`SuehiredBobandKarenhiredTim.')(2)(a)SueandKaren,wholoveeachotherverymuch,singanddancerespectively.(b)Theboyandthegirl(whoare)inthesamepictureareDutchandItalianrespec-tively.Postal(1998,136,160),Kehler(2002,125),andGawron&Kehler(2003,2004)pointoutthattheproblemismoresevereincasesof`long-distance'respectivelyreadings,suchas(3).Althoughbothpredicatessharethesamephraseextractedacross-the-board(ATB),theypredicateadierentsubsetofitsdenotation.Postal(1998,163)arguesthattheproblemisasseverefortransformationalapproachesasitisfornon{transformationalapproaches,andlikeGawron&Kehler(2004,193)concludesthattheidentityconditionimposedbycoordinationmustbeweakenedsomehow.Thispaperwillattempttosolvethisproblem.(3)(a)[Whatbookandwhatmagazine]didJohnbuyandBillreadrespectively?(b)[Where]didMaryvacationandBilldecidetoliverespectively?(c)InallymetSusan,Lynn,andMaryyesterday.Theyarethe[threesisters]thatBobhired,Johnpromoted,andBillredrespectively.Notethatthepresenceoftheadverbisnotnecessaryforrespectivelyreadingstoarise.Infact,iftheadverbisnotpresentthenotherreadingsareavailableaswell(collective,distributive,etc.).Forexample,SueandKarenhiredBobandTimcanmeanthatSuehiredBobandKarenhiredTim,orthatSueandKarencollectivelyhiredBobandTim,etc

3 ..InalltheaccountsthatIamfamiliarwith,th
..InalltheaccountsthatIamfamiliarwith,theoptionalityoftheadverbisleftwithoutanexplanationandassumedtobetheresultofarespectivelyoperator(Respf)whichcanbephoneticallynull.Iregardthisstipulationassuspect,andwillprovideanaccountthatexplainstheoptionalityoftheadverb.Kay(1989)arguesthatrespectivelyreadingsrequireaone-to-onemapping.Thus,in(1a)SueispairedwithjogandKarenwithdrive.Similarlyin(1b),SueisinsomesensepairedwithBob,andKarenispairedwithTim.Whensuchabijectivemappingisnotpossible,asin(4),boththerespectivelyreadingandtheadverbaredisallowed.(4)(a)SueandKarenjog(*respectively).(b)Suejogsandsings(*respectively).2 Moreover,McCawley(1998)notedthatthesebijectionscantargetanynumberofNPsinthesentence.Takeforexample(5a)below,whichismany{waysambiguous.Intheextreme,everyNPispair{wisemapped(i.e.`SuesentabooktoBobandKarensentamagazinetoTim'),butitcouldalsobethecasethatonlytwoNPsarepair{wisemapped(e.g.`SuesentabooktoBobandTim,andKarensentamagazinetoBobandTim',amongothers).Similarly,(5b)illustratesacasewhereonlythecomplementNPsareinvolvedinthebijection,notthesubject.Thepointisthatrespectivelyreadingscantargetanynumberofco{arguments.(5)(a)SueandKarensentabookandamagazinetoBobandTimrespectively.(b)IgaveTomandMaryabookandamagazinerespectively.Amajortenetofmosttheoriesofgrammaristhattheprocessofsemanticcomposi-tionshouldbeassimpleaspossible.Insometheories,semanticcompositionisviewedasideallybeingmonotonic.1Shieber(1988)statesthatagrammarissemanticallymonotonicif,foreveryphraseadmittedbythegrammar,thesemanticstructureofeachimmediatesubphrasesubsumessomeportionofthesemanticstructureoftheentirephrase.Inotherwords,forsemanticcompositiontooperatemonotonicallyitmustnotallowrepresentationspreviouslybuilttobesubsequentlychangedordeleted.Amono-tonicsemantictheoryismaximallyparsimoniousbecauseitsimplyjoinsmeaningswithoutresortingtonon{trivialcomputationsthatleadtolossofinformationaboutpreviouslyas-sembledrepresentations.Whetherornotallofnaturallanguagesemanticscanbehandledbymonotoniccompositionisdebatable,butoneofthephenomenathathastraditionallybeenevokedtonecessitatenon{monotonicoperati

4 onsispreciselyrespectivelyreadings.2Take
onsispreciselyrespectivelyreadings.2TakeforexampleSueandKarenjoganddrive.Allexistingaccountsof`respectively'arebasedontheassumptionthatSueandKarenyieldsaplurality{e.g.ani-sumlikesk,orsomeequivalentpluralmeaning{butthatatasubsequentstageofsemanticcom-position,skisdestroyedinordertoproducejog(s)^drive(k).ThepluralitythatwasassembledbyparsingthesubjectNPSueandKarenisnotpresentinthenalsemanticrepresentation.InthispaperIshowthatrespectivelyreadingscanbemodeledmonoton-ically,maintainingatightcorrespondencebetweensyntaxandsemantics.Inparticular,thesyntacticandsemanticrepresentationofsentenceslikeSueandKarenhiredBobandTimwillbethesameirrespectiveofarespectivelyinterpretation.ThesameappliestoSueandKarensinganddance.Inmyaccountthesesentencesallowareadingwhichiscompatiblewiththesemanticsoftheadverb`respectively'.Thepaperisstructuredasfollows.Section2reviewspreviousaccountsofrespectivelyphenomenaanddiscussestheirshortcomings.Newdataisprovidedtosuggestthatrespec-tivelyreadingsareofadierentnaturethanusuallyassumed.InSection3itisarguedthatthesentencemeaningswhicharecompatiblewiththepresenceoftheadverb`respectively'arespecialcasesoftwoindependentphenomena.Asaresultofthisreconceptualization, 1Thishasbeenadvocatedbyavarietyofauthors,foravarietyoftheoriesofgrammar,suchasAlshawi&Crouch(1992),Shieber&Schabes(1992),Pollard&Sag(1994,323),Steedman(1996,7,91),Steedman(2001,1,5{7,23,87),Halvorsen(1988),Dalrymple(1999),andAsher&Lascarides(2003,118),interalia.2SeePullum&Gazdar(1982,484)andGazdaretal.(1985,150).3 sentenceswithrespectivelyreadingsdonothavespecialsyntacticorsemanticrepresenta-tionsanddonotresorttonon{monotonicandoptionallycovertoperators.Myproposalcaninprinciplebeadoptedbyanytheoryofgrammar,andinSection4Ishow,byformal-izingmyaccountinHead-DrivenPhraseStructureGrammar(Pollard&Sag,1994),thatPostal(1998,160{163)andGawron&Kehler(2004,194)areincorrectinclaimingthatunication-basedframeworksareparticularlyill-suitedtohandlerespectivelyreadings.2Previousaccounts2.1SyntacticaccountsGoodall(1987),Moltmann(1992)andothersproposethat`respectively'triggersasyn-tacticoperationint

5 hepresenceofcoordinationthattransformsas
hepresenceofcoordinationthattransformsasentencewithphrasalconjunctionsintoclausalconjunctions.However,McCawley(1968,297),Chomsky(1972,123,note26),Stockwell,Schachter&Partee(1973),Pullum&Gazdar(1982),Kay(1989),Dalrymple&Kehler(1995),andMcCawley(1998)noteddatalike(6),whichrefutethisassumption.(6)(a)ThosevemenarePolish,Irish,Armenian,Italian,andChinese(respectively).(b)TheyliveinChicagoandNewYork(respectively).(c)Thesuccessivedescendantsofmyfruit\rywillbeheavier,respectively,thanthesuccessivedescendantsofyours.Kay(1989)showsthat`respectively'canonlyestablishaone-to-onemappingbetweendenotataifthereisanindependentranking.Thus,thesentencein(7a)isacceptablebuttheonein(7b)isnot.3(7)(a)Thethreebeststudentsreceivedthethreebestscoresrespectively.(b)#Thestudentswerepleasedbytheirscores,respectively.In(8)Iprovidemoreexampleslackingconjunctionaltogether.AsKay(1989,2004)observes,thecorrectgeneralizationisthataone-to-onemappingbetweenpluralitiesisestablishedviasomepragmaticrankingduetocontext,surfaceorder,orworldknowledge.(8)(a)Thefollowingtwosectionswilldealwiththesetwoissuesrespectively.(b)Twodierentformulasweretested,respectively,bytwogroupsofpatientswithvariousperiodontaldisorders.(c)Thiscontroversyrevolvedaroundtheplacewhereanewmeetinghouseshouldbeset,andasthepartiescouldnotagree,theybuilttwoinplacestheyrespectivelychose. 3AsKaynotes,thiscontrastswithexpressionslikerespective,whichonlyoccurifthemappingisnotachievedviaanindependentlyestablishedranking(e.g.thestudentswerepleasedbytheirrespectivescoresvs.#thethreebeststudentsreceivedthethreerespectivehighestscores).Formoreonrespective,dierent,andthesameseeCarlson(1987),Kay(1989,2004),Keenan(1992)andBarker(2007)amongothers.4 Insum,thedataindicatethattheso{called`respectivelyconstruction'cannotbeseenasasyntacticoperationoncoordinatestructures.Inthesedata,abijectionisestablishedbetweenplural{denotingnominalphrases,whichstronglysuggeststhatthecorrectaccountissemanticinnature.2.2SemanticaccountsLink(1991)proposesaspecialconjunctionmeaningthatformsorderedtuplesusinghigher{dimensional{abstractionslikexyandallowspredicatest

6 odistributeoverthem.Forexample,theconjun
odistributeoverthem.Forexample,theconjunctionGeorgeandNickyieldsatuple(g;n)whichisthenusedtoproduceapropositionalconjunctionasshownin(9).Suchanaccountisnotmonotonicbecausethei-sumscorrespondingtotheNPsGeorgeandNickandMarthaandHoneyaredestroyedwhencombinedwiththeverbalsemantics.4(9)(a)GeorgeandNickhateMarthaandHoney,respectively.x1x2:[y1y2[hate(x1;y1)^hate(x2;y2)](m;h)](g;n),hate(g;m)^hate(n;h)(b)GeorgeandMarthaaredrinkinganddancing,respectively.xy[drink(x)^dance(y)](g;m),drink(g)^dance(m)Gawron&Kehler(2004)proposeamorecomprehensiveaccount,whichscalesuptonon{coordinatecases.Conjunctionissystematicallyviewedassumformation:nominalconjunctionyieldsindividualsumswhileverbalconjunctionyieldspropertysums.ApragmaticallyestablishedsequencingfunctionfcanaccessthesurfaceofconjunctsandaRespfoperatorproducestherespectivelyreadings.TheRespfoperatorissimilartoadistributionoperatorDistrinthesensethatitattachestoapluralicentityandoperatesoveritsmembers.As(10)illustrates,Respftakestwoarguments:averbalrepresentationandanominalrepresentation.(10)SueandKarenjoganddrive.Respf(jogtdrive)(s_k)=jog(s)tdrive(k)TheanalysisofSueandKarenloveBobandTimproceedsasfollows.ThesubjectandobjectNPscorrespondtothejoinss_kand_k.ThedistributionDistrcopiestheverbmeaningovereachconjunctDistr(love(tt))=love()tlove(t),andthentheoperatorRespfcombinesthisVPwiththesubject:Respf(loves()tloves(t))(s_k)=loves()(s)tloves(t)(k).BasicallythesameappliestorespectivelyreadingswithoutNPconjunction.LikeLink's,thisaccountisnon{monotonic.Atsomepointintheprocessofsemanticcompositionwehaveani-sumfortherepresentationofaconjoinedNP,butlaterthatrepresentationdisappears.ThereisnorepresentationfortheNPpluralityinthenalsemanticsofthesentence.Thispointisimportantbecauseitreverberatesinthesyntax{semanticsinterface.IfGawron&Kehler(2004,193)areright,notheoryofgrammarmayassumethatverbsdirectlypredicatetheNPvalentsthattheysubcategorize.Thereisawaysthepotentialforarespectivelyreading,inwhichcaseRespfintervenesandcausesaverbtopredicateonlyastrictsubsetofitsargument'sdenotation.Mymaingoalisto 4Arelatedaccountthatfocusesontheverb

7 instead,vialexicalrules,isFast(2005).5 s
instead,vialexicalrules,isFast(2005).5 showthatthereisanalternativeanalysisofrespectivelyreadingswhichdoesnotcreatesuchadividebetweensyntaxandsemantics.Semanticcompositioncanremainsimpleandmonotonic,andsubcategorizationcanoperateintandemwithpredication,asassumedbycontemporarysyntactictheories.ThereseemtobethreeempiricalproblemswiththeaccountinGawron&Kehler(2004).First,althougheveryoccurrenceoftheadverb`respectively'isassumedtotriggertheinsertionofaRespfoperator,itispossibleforaRespfoperatortobeinsertedwithouttheovertpresenceoftheadverb.Theproblemisthatnothingbutastipulationcapturesthefactthattheadverbcanbeoptionalinrespectivelyinterpretations.Ideally,theoptionalityoftheadverbshouldfollowfromindependentlymotivatedfactors.Asecondproblemisthatthefmechanismthatcapturesthecontextually{determinedorderingsisclaimedtoonlyapplytonon{atomicreferents.AccordingtoGawron&Kehler(2004,174),thiscorrectlycapturestheoddnessofcaseslike#A/The/Everymansmiledrespectively,whereatleastoneoftheNPsissingularandthereforehasnopropersubpartsinwhichtomapanything.However,thisstancemaybeexcessive.ThenativespeakersofEnglishthatIhaveconsultedaccepttheexamplein(11)below,foundintheWeb1T5{gramVersion1ofGoogle'sN{GramCorpus,whichisalsothesourceoftheotherattestedexamplesincludedinthispaper,referencedbytheirURLs.Inthisdatapointthepresenceof`respectively'isallowedbecausearankingofpartiesandtheircostsiseasytoconceptualize,eventhougheachpartyisasingularNP.Theadverb`respectively'isfelicitousbecausetheuniversallyquantiedsubjectcanoutscopetheverbandobtainaninterpretationwherethereisadierent`bearing'eventforeachparty/cost.(11)Whiletherelationshipofthepartiesremainsamicable,itisessentialthatanagree-mentbereachedastothecosts[that]eachpartywillrespectivelybear.(www.innovasafe.com/doc/blatt.doc)ThethirdproblemisthatGawron&Kehler(2004)predictthatthereshouldbenodierencebetweenrespectivelyreadingswithorwithouttheadverb,becauseinbothcasestherelevantinterpretationsareproducedbyRespf.BelowIprovideempiricalevidenceagainstthisprediction.Considerthesentencein(12).Thereisapragmaticallyoddrstinterpretationwherethe

8 sametwentyexecutiveswerepromotedanddemot
sametwentyexecutiveswerepromotedanddemotedonthesameday.Thisisthe`strictidentity'reading,whereeachconjunctpredicatesexactlythesamedependent.However,thereisalsoa`weakidentity'reading,whereoutoftwentyexecutivessomewerepromotedandothersweredemoted.Thelatterseemstobewhatisusuallycalledarespectivelyreading,butinfactthisisnottrue.Theexamplein(12)actuallyworsenswiththeovertpresenceoftheadverb`respectively'.(12)Today,twentyexecutiveswerepromotedanddemoted(#respectively).Thissuggeststhatthereadingin(12)isrelatedto{butnotthesameas{are-spectivelyreading.Inthiscasetheadverb`respectively'isnotfelicitousbecausethereisnoindependentrankingofexecutives.SuchdataareunexpectedinGawron&Kehler(2004).In(13)Iprovidemoreexamplesofsentenceswithinterpretationsthatappeartoberespectivelyreadingsbutwhichcannotco{occurfelicitouslywiththeadverb.6 (13)(a)Thefrontandthebackoftheshiparecalledthebowandthestern,butwhichiswhich?(b)WeknowhousesfourandvearetheSwedeandtheGerman,butwhichiswhich?(www.everything2.com/index.pl?node id=984348)(c)GoodmanandIarelikeDrysdaleandKoufax.Yeah,butwhichoneiswhich?(sfgate.com/cgi-bin/blogs/mlasalle/detail?blogid=38&entry id=10946)(d)CaesarandIareasreandwater,butastowhichiswhichyoumustjudgeforyourself.(TalbotMundy,inTrosofSamothrace,Appleton-Century,1934,Chp.XXXI,p.168)Thedatain(13)alsoindicatethatthesurfacepairingbetweennominalconjunctsisnotagrammaticalconstraint,sinceitcanbecanceledbycertaincontinuations.Inotherwords,respectivelyreadingswithoutanovertadverbarebiasedtowardspresentationorder,whereasrespectivelyreadingswithanovertadverbarerestrictedtoit.5Anotherargumentagainstthenotionthatrespectivelyreadingswithorwithoutad-verbsarisefromthesameRespfoperatorisbasedonthecontrastin(14).Sincebothsentencesareonlyfelicitousifinterpretedwitharespectivelyreading,bothshouldrequirethepresenceofacovertoperatorRespf.Butwhereasexample(14a)toleratestheovertrealizationoftheadverb,(14b)becomeslessacceptablewiththeovertrealizationoftheadverb.Thefunctionoftheadverb`respectively'istosingleoutacertainkindofinterpre-tationinalargersetofpossibleinterpretations.Incaseslike(14b){where

9 noambiguityisusuallyperceivedbecausehusb
noambiguityisusuallyperceivedbecausehusbandandwifeissuchastrongbinomialexpression{thepresenceoftheadverbisunwarranted.ForGawron&Kehler(2004)itshouldnotmatterifRespfisovertorcovert,andyetthedataindicatethatitdoes.(14)(a)TomandMaryaretallandshort.(TomandMaryaretallandshortrespectively.)(b)TomandMaryarehusbandandwife.(?#TomandMaryarehusbandandwiferespectively.)Thefactthattheadverb`respectively'canaccesssurfaceorderisnotremarkable.Manyotherexpressionslike`theformer',`thelatter',`inthatorder',`conversely',`con-trariwise,and`viceversa',seemtoaccesssurfaceordermetalinguistically,evenintheabsenceofconjunction,asthedatain(15)illustrate.IconcludethatsuchexpressionsarecontextualinthesenseofKay(1989),andhavethemeanstoaccesssurfaceorder.Idonotdiscusshowsuchaccessworksasthisisanindependentquestionbeyond`respectively'.(15)(a)[CraigJones]iisadierentkindoflm{makerfrom[StuartLee]j.While[theformer]iismorecomfortablewithabstractconcepts,[thelatter]jlikestoconveyhisthoughtsasdirectlyaspossible. 5Iconjecturethatthesurfaceorderbiasisduetocognitivelimitationsalsoseenincross{serialdepen-dencies(Bachetal.(1986)showedthatserialdependencies`ABCABC'areeasiertoprocessthan`ABCCBA')andinmultipleextraction(seeFodor(1978)forprocessingdicultywhenextractionpathsarecrossed).7 (b)About20%of[men]'sunderwearisboughtby[women],andviceversa.(=`About20%ofwomen'sunderwearisboughtbymen.')(c)[Worms]mayhaveevolvedfrom[arthropods]ratherthantheotherwayaround.(d)[TheHobbit]waswrittenbefore[TheLordoftheRings],butIdidn'treadtheminthatorder.Ihavetriedtoarguethatso{calledrespectivelyreadingsarenothingbutasubsetofamoregeneralkindofreading.Thelatterareoftennotcompatiblewiththepresenceoftheadverb,asshownin(12)and(13).ThismeansthatRespfismissingimportantgeneralizations:ontheonehand,itistoorestrictivetomodelthe`respectivelyreadings'thatarisewithout`respectively'likein(12),whileontheother,itdoesnotcorrespondtotheactualsemanticcontributionmadebytheadverb.IthusrejecttheexistenceofanoptionallycovertoperatorlikeRespf,andseekanalternativeanalysis.3Analternativeaccountof`respectively'readingsInthissectionIexplorethepos

10 sibilityofrespectivelyreadingsbeingepiph
sibilityofrespectivelyreadingsbeingepiphenomenal.Theclaimisthattwodierentkindsofphenomenayieldinterpretationsthat{incertainconditions{happentobecompatiblewiththesemanticsofthe`respectively'adverb.Togivearoughanalogy,considerpluralsubject{verbagreement.Therearethreecom-pletelydierentphenomenainEnglishthatcantriggerit.Oneisnounpluralization(themorphologicalprocessbywhichasingularnouncanbeusedtoobtainapluralnoun),thesecondisnon-Booleanconjunction(whichyieldsapluralitywhenconjoiningsingularnominalexpressions),andthethirdiscollectivenouncoercion(e.g.Thefacultyarevotingthemselvesaraise).Althoughpluralization,conjunction,andcollective-to-pluralcoercionareclearlynotthesamephenomenon,theycanallyieldnominalexpressionsthatcanoccurassubjectsandtriggerpluralsubject{verbagreement.Myhypothesisisthattwounrelatedandindependentphenomenacanyieldinterpretationswhichincludewhatareusuallyviewedasrespectivelyreadings(i.e.casesinwhichtherearebijectionsbetweendenotata).Incertaincircumstances,theadverb`respectively'canbeaddedfordisam-biguationpurposes.Thispredictstheoptionalityoftheadverbandthesubtledierencesbetweenrespectivelyreadingswithorwithouttheadverb.Section3.1focusesoncasesthatdonotinvolveverbalconjunctionandarguesthattheseareakindofcumulativereadinginthesenseofScha(1981).Section3.2dealswithcasesthatinvolveverbalconjunction,andarguesthatthesefollowfromhowthesyntax{semanticsinterfaceofconjunctionintegratesshareddependents.InSection3.3theroleoftheadverbisdiscussed.3.1CumulativequanticationreadingsThesentencesin(16)haveacumulativequantificationinterpretaton(Scha,1981,497).6Forinstance,inacumulativereadingof(16a)therearemanypossiblemappings 6Othertermshadbeenusedintheliterature.E.g.,Kroch(1974)usestheterm`seriallydistributive'.8 betweenthesoldiersandthetargetstheyhit.AsBeck&Sauerland(2000)andothersnote,datalike(16)indicatethatsuchreadingsalsooccurwithconjunction.(16)(a)Twosoldiershittwotargets.(b)Severalcriticspraisedsomemovies.(c)700Dutchcompaniesused10000Americancomputers.(d)Thesedotscorrespondtothosecities.(e)JimandFrankwanttomarrytwodentists.Variousaccountshavebeenpropo

11 sedforsuchreadings.7Forexample,Kroch(197
sedforsuchreadings.7Forexample,Kroch(1974,205)andScha(1981,497)usemeaningpostulateslike(17).(17)P(;)=(802!902^P(0;0))^(802!902^P(0;0))Krifka(1989),Sternefeld(1998)andmanyothersmakeuseofa**-operatortoasimilareect.Formypurposes,itisnotimportantwhichanalysisisadopted,andIremainagnosticwithrespecttothischoice.Figure1showsthereadingsthat(17)allowsforacumulativeinterpretationof(16a).Crucially,twoofthesearebijections.Infact,whendiscussingasentencelike(16a),Link(1991)writesthat`thesituationdescribed(...)isaspecialcumulativereadingwhere,inaddition,therelationisabijectivefunction'.t1t2s1s2t1t2s1s2t1t2s1s2t1t2s1s2t1t2s1s2 bbbb bbbb bbbb bbbb bbbb bbbb bbbb bbbb bbbb bbbb bbbb bbbb bbbb Figure1:Respectivelyreadingsasaninstanceofcumulativereadings.Ithereforeproposethatsomerespectivelyreadingsaresimplyabijectivecumulativein-terpretation.Thefunctionsoftheadverb`respectively'istosingleoutoneofthebijectiverelationsinthesetofpossibleindependentlyobtainedcumulativeinterpretations.Thisexplainswhythepresenceoftheadverbisoptional,andwhyrespectivelyreadingsdonotarisewhentheNPsaredisjoinedratherthanconjoined.8Tobeclear,inthisviewrespectivelyinterpretationsareaconsequenceofcumulativereadings,andthefunctionoftheadverbistopickacumulativereadingthatisbijectiveandsatisesapragmatic-orlinearization-basedranking.Thisapproachmakesseveralpredictions.Cumulativequanticationcanapplytopredicateswithmorethantwoarguments,andwhenitdoes,itdoesnotforceallargumentstobecumulativelyinterpreted.Forexample,anytwoNPsin(18)canbeinterpretedcumulatively(orallthree). 7SeeforexampleBartsch(1973);Kroch(1974);Scha(1981);Krifka(1989);Roberts(1987);Schein(1993);Schwarzschild(1996);Sternefeld(1998);Landman(2000).8SeeGawron&Kehler(2004,202{204)formoreaboutdisjunctionand`respectively'.9 (18)Twostudentssentfourletterstothreecongressmen.Onestudentmayhavemailedtwoletterstothethreecongressmen,whiletheotherstu-dentmailedthetwootherletters;orthetwostudentscollectivelysentonelettertoonecongressmanandanotherlettertotheremainingcongressmen.Thetotalofcombinationsis24(=243),minusotherreadingsduetoscopeambigu

12 ity(e.g.Link1998:54).Thishasconsequences
ity(e.g.Link1998:54).Thishasconsequencesforthecurrentaccountofrespectivelyreadings.ItentailsthatsentenceswiththreepluralNPsareambiguousinessentiallythesameway.Thispredictionisborneoutindatalike(19),fromMcCawley(1998)andGawron&Kehler(2004),where`respectively'allowsalloranytwoNPstobemappedbijectively.Thisfollowswithoutstipulationifsuchreadingsarejustspecialcasesofcumulativereadings,asproposedabove.(19)GeorgeandMarthasentabombandanastylettertothepresidentandthegovernorrespectively.CumulativitycanalsotargetNPsthatarenotco-argumentsofthesameverb,asshownbyexamplesinvolvingadjunctslike(20).Inthesecasesthecumulationprocessseemstotargetthepredicatesinandcausing,whichcanbearguedtotakeasargumentsaneventualityandanominal.ItisthereforetemptingtoassumethateventsarestructuredmereologicallyasinBach(1986),andthatin(e;x)andcause(e;y)canbeinterpretedcumulatively.FormorediscussionseeforexampleSchein(1993,ch.9).(20)Fivealarmsmalfunctionedintwolocations,causingfouraccidents.Whatevertheproperaccountofcumulativereadingsis,myclaimisthatitwillpredictthebijectivemappingsthat`respectively'requires,amongmanyotherreadings.Iusetheadmittedlyoversimpliedaccountin(17)forexpositionpurposesonly,butmoresophis-ticatedapproachescanbeadopted,likethegeneralizedPPartoperatorofSchwarzschild(1990,1996).Crucially,however,noneoftheaboveaccountscandealwithrespectivelyreadingsthatinvolvepredicateconjunction,likethatin(21a).(21)a.Fortheirtalentexposition,thetopthreepageantwinnerssang,breathedre,andplayedthekazoo(respectively).b.Fortheirtalentexposition,[thetopthreepageantwinners]isang,theyibreathedre,andtheyiplayedthekazoo(#respectively).AsGawron&Kehler(2004,200)show,eventhePPartoperatoraccountinSchwarzschild(1996,88)cannotexplainwhy(21a)hasarespectivelyreadingbut(21b)doesnot.Gawron&Kehler(2004,199)alsoobservethatthePPartoperatorislimitedtorelationsamongindividual-levelgroups,anddoesnotextendtocasesthatinvolverelationsthatincludeproperty-levelgroups.Gawron&Kehlertakesuchdatatoshowthatpredicatescannotdirectlypredicatetheirdependents,butIargueotherwisebelow.10 3.2DependentsharinginconjunctionAsalreadydi

13 scussedinSection2.2,sentenceslike(12)abo
scussedinSection2.2,sentenceslike(12)above,repeatedherein(22),canbesaidtohavetwokindsofreadings.(22)Today,twentyexecutiveswerepromotedanddemoted.Inthe`strictidentity'reading,twentyexecutiveswerebothpromotedanddemoted(per-hapsbecauseofacomputerglitch).Thisreadingissomewhatimplausiblebecauseofworldknowledge,butwouldotherwisebethepreferredinterpretation(comparewithTwentyex-ecutiveswereinterviewedandsurveyed).Thereadingisonewheretheexecutivesthatwerepromotedaredierentfromtheexecutiveswhogotdemoted(a`weakidentity'read-ing).Thelatterinterpretationissimilar{butnotidenticalto{arespectivelyreading:thepresenceoftheadverbisnotallowedbecausethedenotataofthesubjectlackanindependentranking.Arguably,thesentencein(23)alsohasstrict/weakidentityreadings.Theweakreadingiswhatisusuallycalledarespectivelyreading,sinceitcanbeforcedbyaddingtheadverb`respectively'.Intheabsenceoftheadverb,thestrictreadingisthepreferredone.(23)TomandFredsanganddanced.Technicaldierencesaside,mostaccountsofVPcoordinationassumethatconjunctsmustnecessarilysharethesubject(i.e.musthavea`strictidentity'reading),asshowninFigure2.Thisexplainstheobservedsubject{verbagreementandsemanticinterpretation.S9x(man(x)^sing(x)^dance(x)) NPP:9x(man(x)^P(x)) amanVPx3:sing(x3)^dance(x3) VPx1:sing(x1) singsVPQ:x3:Q(x3)^dance(x3) ConjP:Q:x3:Q(x3)^P(x3) andVPx2:dance(x2) dancesFigure2:ShareddependentidentityHowever,inlightofambiguousexampleslike(22)above,Iwillrevisetheanalysisofconjunctionsothatanydependentsthataresharedbyconjunctsareeitherequated(`strictidentity')orcumulated(`weakidentity').Theformeryieldsthesameresultas11 inFigure2andthelatteryieldsakindofinterpretationofwhichrespectivelyreadingsareasubset.Fortunately,thereisasimpleoperationthatcansuccinctlycapturealltherelevantpatterns:Link's`'sumoperator.Inordertomodelnon-Booleannominalconjunction,Link(1983)resortstoasumrelation`'interpretedasajoinoperatorinamereologicaldomain:[[xy]]=[[x]]t[[y]].Thisdenitiondoesnotruleoutthepossibilitythatx=y,inwhichcasethesumdoesnotyieldaplurality.Thisfollowsfromthefactthatthejoin`t'isidempotent(i.e.8x[xtx=x]).9Formally,

14 Link'ssumencapsulatesexactlywhatisnecess
Link'ssumencapsulatesexactlywhatisnecessarytodealwiththetworeadingsof(22a),andconsequently,therespectivelyreadingsin(22b).Theproposedgeneralizationisstatedin(24)asaconditiononthesyntax{semanticsinterfaceofconjunction.InSection3.5Iarguethat(24)shouldbegeneralizedtootherkindsofdependencies.(24)SharedDependentConditionforConjunction(informal)Predicationdependenciessharedbyconjunctsarecombinedvia`'.Iwillformalize(24)byaugmentingthesemanticcontentoftheconjunctionand.Forsimplication,IassumethatthesemanticsofconjunctiononlytakestwoconjunctsQandP.10Ithusproposethelexicalentryin(25).Here,P[x0;:::;xn]andQ[y0;:::;yn]aretwoconjunctswithexactlyn(n0)freevariables,eachcorrespondingtoashareddependent.Thevariablescorrespondingtotheshareddependentsarecombinedvia`'.(25)Conjunction(preliminary)and:P:Q:z0:::zn:Q[x0:::xn]^P[y0:::yn]^z0=(x0y0)^:::^zn=(xnyn)InVPcoordinationthereisexactlyoneshareddependent:thesubject.ThismeansthatthevariablesofthesubjectsselectedbyeachoftheVPconjunctsarecombinedvia`'.Asaconsequence,thesevariablesareeitherequatedorcumulated.Ifequated,bothVPspredicatethesameentity(`strictidentity').Ifcumulated,eachVPpredicatesadierentpartoftheplurality(`weakidentity').ThisisshowninFigure3. 9PrincipleCofBindingtheorypredictsthatconjunctscannotbeco-referential,asin*TomiandTomileft,*BatmanandBruceWaynehasdiedtoday,and*myfatherandmydadarrived.Mattersaremorecomplexthanthis,however,sinceco-referentialconjunctscanoccurincertaincases:tellmeaboutJohnasafatherandJohnasahusband.SeevanEijck(1983,99)onexampleslikehisagedservantandthesubsequenteditorofhiscollectedpaperswaswithhimathisdeathbed,andHoeksema(1988)ondataliketheMorningStarandtheEveningStararethesameplanet,agreatmanandagoodfatherhaspassedaway,and*myheroandHoudinihaspassedaway.10SeeSection4.2foranaccountthatcandealwithanynumberofconjunctsanddependents.12 VPz:sing(e1;x1)^dance(e2;x2)^z=(x1x2) VPx:sing(x) singVPQ:z:Q(x1)^dance(x2)^z=(x1x2) ConjP:Q:z:Q(x1)^P(x2)^z=(x1x2) andVPx:dance(x) danceFigure3:Non-deterministicdependentsharingIftheobtainedcoordinateVPcombineswithasubjectlikeTomandSue,weobtainthe

15 representationin(26).Thearrow`7!'indica
representationin(26).Thearrow`7!'indicatesbeta-reduction.(26)TomandSuesinganddance.(z:sing(x1)^dance(x2)^z=(x1x2))(ts)7!sing(x1)^dance(x2)^(ts)=(x1x2)Ifx1=x2then`'doesnotformapluralityandweobtainareadingwhereTomandSuearebothagentsofsinginganddancing(i.e.z=x1=x2).Conversely,ifx1=x2then`'isinterpretedasaplurality-formingcumulationandweobtainareadingwheretts=x1tx2.Because`'isasymmetricrelation,inthelattercaseitisnotknownwhethert=x1ands=x2orift=x2ands=x1.Thisindeterminacycanberesolvedbyaddingtheadverb`respectively'.Thatistheadverb'sfunction.TheaccountscalestootherkindsofpluralNPsubjects,like(27).Asbefore,if`'isinterpretedasequalitythenallstudentssanganddanced,andif`'isinterpretedasaplurality-formingcumulationthensomestudentssangwhileotherstudentsdanced.(27)Severalstudentssinganddance.(P:9x(student(x)^P(x)))(z:dance(x1)^sing(x2)^z=(x1x2))7!9x(student(x)^sing(x1)^dance(x2)^x=(x1x2))AsdiscussedinSection2.2,thisfallsshortofbeingatruerespectivelyreadingbe-cause(27)doesnotallowthepresenceoftheadverb`respectively'.Theremustbeanindependentrankingbetweendenotatainordertoobtainatruerespectivelyreading.Outoftheblue,(27)exhibitsnosuchranking,andtherefore`respectively'isnotallowed.Conversely,incaseslikeRobinandKimarecousins.TheyliveinChicagoandNewYork(respectively),anindependentrankingisprovided,andthereforetheadverbcanbeused.Thebijectionforcedbythepresenceoftheadverb`respectively'insentenceslikeTomandFredsanganddancedholdsbetweentheatomsinthedenotationoftheplural13 NPandtheeventualitiesdenotedbytheconjoinedVP.IthusassumethatverbscomewithNeo-Davidsonianeventualityarguments,asarguedbyKamp(1979),Partee(1984),Higginbotham(1985),Bach(1986),Carlson(1987),Krifka(1989),Parsons(1990),andPustejovsky(1991),interalia.Supportforthiscomesfromwell-knownevidencethateventscanbeboundanaphorically,modiedbyanon-restrictiverelativeclause,dis-tributed,compared,andintensied:(28)(a)FredstabbedJones.Ithappenedatmidnight.(b)Kimevadedthepolice,whichisnotaneasythingtodo.(c)JohncalledeveryMonday.(=`ForallpastMondaysJohncalled.')(d)Iloveyoumorethanyouloveme.(e)Fredissogoingtojail.

16 Ifsucheventualitiesexist,thentheirconjun
Ifsucheventualitiesexist,thentheirconjunctionshouldalsoformapluraleventuality.Thisisempiricallysupportedbytheadverbialsin(29),whichpredicatetheconjoinedpluraleventuality.IthusfollowCarlson(1987,540{542),Lasersohn(1995,Chapter14),Gawron&Kehler(2004)andmanyothersinassumingthatplurality-formingconjunc-tioncanoperatecross-categorially:nominalconjunctionyieldsanominalpluralityandpredicateconjunctionyieldsapluraleventuality.(29)(a)Often,[[Igotothebeach]e1and[yougotothecity]e2]e1e2.(b)She[[gotdressed]e1and[driedherhair]e2]e1e2,[intenminutes].(c)Youcan'tsimultaneously[[drink]e1and[drive]e2]e1e2.(d)Whydidhe[[closethedoor]e1and[openthewindow]e2]e1e2?Accordingly,theconjunctionin(25)abovemustberevisedsothatitformsapluralitywiththedenotataoftheconjuncts.DrawingfromLink(1983)andKrifka(1990),Iadopttheconjunctionin(30),wherethe1and2variablescorrespondtoindividualsoreventu-alitiesdenotedbytheconjuncts.Iftheconjunctsareverbal,soistheplurality,andiftheconjunctsarenominal,soistheplurality.Nothinghingesonthisparticularformalization,however,asotherapproachestoconjunctionlikeLasersohn(1995),Schwarzschild(1996),andLandman(2000)canbeadoptedinstead.(30)Conjunction(revised)and:P:Q:z0:::zn:9(=(12)^Q(1)[x0:::xn]^P(2)[y0;:::yn]^z0=(x0y0)^:::^zn=(xnyn))Therevisedconjunctionin(30)allowsVPconjunctiontobemodeledasshownin(31).Thevariablesarerenamedaseforperspicuity.In(31a)wecombineandwithdanced.In(31b)wecombinesangwithanddanced.Notethatasumisformedwiththedenotationoftheconjuncts,andthesharedsubjectdependentiscombinedvia`'.Finally,in(31c)wecombineTomandFredwithsanganddanced.14 (31)[[TomandFred]NP[sanganddanced]VP]Sa.(P:Q:z:9e(e=(e1e2)^Q(x1)(e1)^P(x2)(e2)^z=(x1x2)))(x:e:dance(e;x))7!Q:z:(e3=(e1e2)^Q(x1)(e1)^dance(e2;x2)^z=(x1x2)b.(Q:z:9e(e=(e1e2)^Q(x1)(e1)^dance(e2;x2)^9z(z=(x1x2)))(x:e:sing(e;x))7!z:(e=(e1e2)^sing(e1;x1)^dance(e2;x2)^z=(x1x2))c.(z:9e(e=(e1e2)^sing(e1;x1)^dance(e2;x2)^z=(x1x2)))(tf)7!9e(e=(e1e2)^sing(e1;x1)^dance(e2;x2)^(tf)=(x1x2))Exactlyasbefore,thesemanticrepresentationobtainedin(31)allowstwodistinctinterpretations.If`'is

17 interpretedasequalitythenwehavethereadin
interpretedasequalitythenwehavethereadingwhereeachconjunctpredicatesthesameplurality(i.e.(ts)=(x1=x2)),andif`'isinterpretedasaplurality-formingcumulationthenwehaveareadingwhereeachverbpredicatesadierentindividual(i.e.(t=x1&f=x2)or(t=x2&f=x1)).Thesameaccountdealswithsentenceslike(32).Althoughthepreferentialinterpretationconveysthatbothmensinganddance,thereisalsoaninterpretationwheredierentmendodierentthings.11(32)Twomensinganddance.9z(men(z)^jzj2^9e(e=(e1e2)^sing(e1;x1)^dance(e2;x2)^z=(x1x2)))3.3Ontheroleoftheadverb`respectively'Inthisaccount,`respectively'issimilartootheradverbsinthatitsimplyaddsrestrictionstothesemanticsoftheverbalstructurethatitadjoinsto.Itdoesnotalteritinanyway.Letustentativelyassumethatthisadverbisrepresentedasin(33).Thesentencein(34)canthusobtaintheintendedrepresentation.(33)respectively:P:x:e:(P(x)(e)^respectively(e))(preliminary)(34)TomandFredsanganddancedrespectively.9e(e=e1e2^sing(e1;x1)^dance(e2;x2)^(tf)=(x1x2))^respectively(e))Therespectivelyreadingonlyarisesif`x1x2'isinterpretedasaplurality-formingcumulation.Inthatcase,eachverbpredicatesadierentreferent.Asbefore,thisisthe 11Therearealsodistributivereadingsforthesesentences,whichareorthogonaltothiswork,andwhichcanbemodeledintheusualwaybyapplyingadistributiontoeachverb.Forexample,inLinkeanterms:y:e:8x(xy!dance(e;x)).Notethatsuchadistributionneednotapplytotheverbdirectlygiventheexistenceofwell-wornambiguitieslikethetwentystudentsinmyclassspeaktwolanguages,wherethetotalnumberoflanguagesspokeniseithertwo(widescopereadingoftheindenitecomplement)orunknown(narrowscopereading).FormoreonthenatureofdistributivityseeSchein(1993),Lasersohn(1995,ch.9),Schwarzschild(1996,ch.5),Link(1991),andLandman(2000,452).15 weakidentityreadingofthesharedsubjects.Letusassumethatthissentenceistruebecause[[e]]=e01te02,wherehe01;ti2I(sing)andhe02;fi2I(dance).Sincetheadverb`respectively'canaccesssurfaceorder,itcanreadilyidentifytherankingstfande01e02.Iusetherelation`'tomean`outranks',inKay'ssense.Theadverbcanthendetectthebijectionf(e01;t);(e02;f)gbyinspectingthetuplesabove(i.e.denotedbyt

18 heverbsdescribedbythepluraleventualitye)
heverbsdescribedbythepluraleventualitye).Theadverboperatesinbasicallythesamewayinsentenceslike(35).AsdiscussedinSection3.1,anindependentlymotivatedcumulativeinterpretationallowsareadingwhereTomlovesSueandFredlovesMia.(35)TomandFredloveSueandMiarespectively.9e(sing(e;tf;sm)^respectively(e))Forexample,assumingthat[[e]]=e01te02wherehe01;t;si2I(love)andhe02;f;mi2I(love),thentherankingstfandsmallowthebijectionf(t;s);(f;m)gtobeevoked.The`love'eventsdenotedbyelackanindependentlyestablishedranking,andthereforecannotenteranybijection.Onecanassumethatexistentialclosureappliestoein(35).Nowletusconsidersomenegativeexamples.Thesentence#Amansmiledrespectivelyisnotfelicitousbecausethereisonlyoneeventandoneindividualparticipant.Thisfollowsfromthefactthat`'isarelation(i.e.requiresatleasttwoentities).In(36),however,theoddnessiscausedbytheabsenceofanindependentrankingfortheentitiesdenotedbythesubjectandthepredicate.(36)(a)#Thewomensmiledrespectively.(b)#Everymansmiledrespectively.(c)?#Eachwomanreadabookrespectively.AsdiscussedinSection2.2,thesameistruefor#Thestudentssmiledrespectivelyand#Thestudentswerepleasedbytheirscoresrespectively.AsKay(1989)correctlynotes,Thethreebeststudentsreceivedthethreebestscoresrespectivelymorereadilyelicitsacontextuallydeterminedrankingandthereforecanbefelicitous.Inowturntotheadverb.Thiswordcombineswithverbalexpressionsandpredi-catestheireventualityvariable,justlikemanyotheradverbials.Thedierenceliesinthesatisfactionconditionsintroducedby`respectively'.Putinformally,(37a)statesthat`respectively'construestwosets,XandY.SetXcontainsalltuplesdescribinganevente0,wheree0e.Here,eistheeventualitythattheadverbpredicatesand`'istheevent-mereological`part-of'relation.SetYiscomposedofallthepairsofentitiesoccupyingtwoxedpositionsnandminthetuplesofX.Finally,Ymustbeabijectionaccordingtoacontextualranking,asdenedin(37b).Arankingissimplyasetofcontextuallydeterminedrelationslike`12'.AlthoughIomitrankingsfrom(37b),IassumethattheyareestablishedalongthelinesofKay(1989,2004)andSection2.2.(37)a.[[respectively(e)]]=1iX=f:9P9e0(2I(P)&=he0;:::i&e0[[e]])g&9n

19 9m(Y=f(pn;qm):h:::;pn;:::;qm;:::i2Xg&[[B
9m(Y=f(pn;qm):h:::;pn;:::;qm;:::i2Xg&[[Bijr(Y)]])16 b.[[Bijr(Y)]]=1i:999c(==c&(f(a;b);(a;c)gY_f(a;b);(c;b)gY))Forillustration,letussupposethatthesentencein(38)istruebecausehe1;ti2I(sing)andhe2;fi2I(dance),for[[e]]=e01te02.Fromthetruthconditionsin(37)itfollowsthatX=fhe1;ti;he2;fig,andfromthesurfaceorderweextracttherankingtfande1e2.ThisyieldsthebijectionY=f(e1;t);(e2;f)g.ThesameanalysisappliestoThesetwomensinganddance,withthedierencethattherankingisnotduetosurfaceorder.(38)TomandFredsanganddancedrespectively.9e(e=e1e2^sing(e1;x1)^dance(e2;x2)^(tf)=(x1x2)^respectively(e))Nowletusconsidercaseswithoutverbalconjunction.AsdescribedinSection3.1,acumulativequanticationreadingofThesetwoboyslovethesetwogirlscanbeinterpretedsothathe01;b1;g2i2I(love)andhe02;b2;g1i2I(love).Byaddingthe`respectively'adverbwecanfelicitouslyobtainY=f(1;g1);(2;g2)gifthereisametalinguisticallydeterminedranking12andg1g2.Asdiscussedabove,e01ande02arenotsucientlydistinctandsalientinordertoestablishanindependentranking.Inmultiple`respectively'sen-tenceslike(39)(McCawley1998:294),thereisacumulativequanticationreadingoftheverbwhichyieldsX=fhe1t;b;pi,he2;m;l;gig.ThisallowsoneadverbtoevokeY=f(t;b);(m;l)gandtheothertoevokeY0=f(b;p);(l;g)g.(39)(a)TomandMartharespectivelysentabombandanastylettertothepresidentandthegovernorrespectively.(b)TomandMarthasentabombandanastyletterrespectivelytothepresidentandthegovernorrespectively.Thisanalysisisalsocompatiblewith(11),repeatedhereas(40).(40)Whiletherelationshipofthepartiesremainsamicable,itisessentialthatanagree-mentbereachedastothecoststhateachpartywillrespectivelybear.First,notethatmyaccountofraisingwillensurethattheverbbearpredicatesthesubjectreferenteachpartyandtheobjectreferentthecosts.12Second,inorderforthe`respec-tively'readingtobefelicitous,theremustbeadierenteventandadierentcostforeachparty,andcomprehendersmustbeabletoconceptualizetherespectiverankings.ThisispossiblebecausetheeventualityehasnarrowscopeundertheeachpartyNP.Thus,foreachpartytherewillbeadierent`bear'situationwithacertaincost.Onewaytomodeltherespectivelyreadingof(40)istoas

20 sumethattheadverb`respectively'hasaccess
sumethattheadverb`respectively'hasaccesstoallassignmentsmadetotheeventualityvariableethatitpredicates.Inthisapproach,thesetXwillcontainthetuplesformedbythevariousvaluesfortheevariableandforxandythatarerelevantfortheinterpretationoftheverbbearinthesentence.Consequently, 12SeeSection3.4andSection4formoreonrespectivelyreadingsinraisingandcontrolstructures.17 setYwillcontainpairsofcostsandparties,whichmustformabijectionforthesentencetobefelicitous,asusual,accordingtoapragmaticallydeterminedranking.Theremaybeanalternativeanalysis,however.Schein(1993)andKratzer(2003)notethatquantierslikeeveryallowcumulativereadings(e.g.Threecopy-editorscaughteverymistakeinthemanuscriptcanhaveaninterpretationwheredierenteditorscaughtdierentmistakes).Arespectivelyreadinglike(40)wouldbecomeunremarkableifeachcanhavethiskindofcumulativereadingaswell.3.4Otherkindsofdependentcumulationwithrespectivelyreadings3.4.1Inter-clausaldependenciesIn(41)wehavearespectivelyreadingentangledwithraisingandcontrolstructures.Thelogicalsubjectofhelpisthematrixsubject,afactwhichisindependentfromtherespectivelyreading.(41)FredandSueseemtowanttohelpKimandMia(respectively).Anyaccountofraisingandcontrolshouldpredictthatthelogicalformofthelowerverbishelp(fs;km),regardlessoftheexistenceofarespectivelyreading.Nothingmoreneedstobesaidbecauseacumulativequanticationinterpretationofhelp(fs;km)asdiscussedinSection3.1sucestoobtaintherespectivelyreading.IdiscussanexplicitaccountofraisingandcontrolinSection4.2inmoredetail,butitshouldbeclearthatanysuitabletheoryofraisingandcontrolwouldobtaintheintendedrepresentation.Amoreseriouschallengeisposedbycaseslike(42),notedbyananonymousreviewer.(42)Dierentnewspapersarerunningcon\rictingreports.TheGuardianandtheTele-graphreportedthatMichaelPhelpswonthesilvermedalandthegoldmedalrespec-tively.Theclause-embeddedVPconjunctionandthematrixsubjectsomehowlicensearespec-tivelyreading,eventhoughthesetwoconjunctionsareindierentclausesanddonotinvolveraisingorcontrol.ItisnotobvioushowtheGuardianandtheTelegraphandthesilvermedalandthegoldmedalallowarespectivelyreadingsincethereisnos

21 yntacticorsemanticrelationshipbetweenthe
yntacticorsemanticrelationshipbetweentheformerandthelatter.Isuspectthatanindependentphenomenonisatworkhere,whichcreatestheillusionthattherespectivelyreadingoccursacrosstheclausebarrier.Ithaslongbeenarguedthata`left-peripheryellipsis'phenomenon(Ross,1967;Sag,1976;Neijt,1979;Hudson,1984;vanOirsouw,1987;Wilder,1994)canpartiallyomitconjunctsasillustratedin(43).13(43)(a)[DidTomcallMaryand didMiacallSue]?(b)Thedoctor[examinedMiaonTuesdayand examinedTomonFriday].(c)He[drinkscoeewithmilkatbreakfastand drinks coee withcreamintheevening]. 13ButseeLevine(2011)forstructuresandreadingswhichresistanellipticalanalysis.18 (d)Mary[talkedaboutMonetonWednesdayand talked aboutRenoironThursday].(e)Margaret[spoketoMr.WimbleonFriday,and spoke totheDeanonSaturday].f)I[gaveyourbrotheracoloringbookand gaveabrandnewbiketoyoursister].Inparticular,Sag(1976,357)andBeavers&Sag(2004)assumethatthisellipsisprocesscantargetclausalconjunctsifsmallerellipsisdomainsarenotavailableforindependentreasons.Forexample,worldknowledgecausestheparsein(44a)tobemorelikelythantheonein(44b).Thelatteryieldsastrangereadingwherethesamemendietwice.(44)(a)TwomendiedinBaghdadonTuesday,and two men diedinTikritonFridaynight.(b)TwomendiedinBaghdadonTuesday,and diedinTikritonFridaynight.Similarly,(45a)ispreferentiallyinterpretedtomeanthatthereisatotaloftwotreesbecausecutdownisa`onetime'predicate.Thiseectvanishesin(45b)becausephotographisnotaone-timepredicate.(45)(a)Twooaktreeswerecutdownbymein1986,andbymywifein1999.(b)Twooaktreeswerephotographedbymein1986,andbymywifein1999.ThelattersentenceiscompatiblewithbothanellipticalScoordinationreadingwherethereisatotaloffourtrees(like(44a))andanellipticalVPcoordinationreadingwherethereisatotaloftwotrees(like(44b)).Crucially,ellipsissometimesyieldswhatlookslikeconstituentcoordination:(46)TwomendiedinBaghdadonTuesday,and two men diedonFridaynight.Forthesereasons,itisatleastplausiblethatthesamephenomenonoccursin(42)above,andcreatestheillusionof`respectively'spanningtwodierentclauses.Ifso,then(42)becomesunremarkable,asillustratedin(47).Thisparseyieldsallthatisneededforarespec

22 tivelyreading,viaacumulativequanticatio
tivelyreading,viaacumulativequanticationinterpretationofbelieve(jb;e1e2).(47)TheGuardianandtheTelegraphreported[[thatMichaelPhelpswonthesilvermedal]and[ that Michael Phelps wonthegoldmedal]]respectively.Letusconsidersomeevidenceinsupportofanellipticalanalysisof(42).Ifellipsisisatworkthenitshouldbeabletolicensenon-constituentremnants,asin(44a)and(45).Thisisconsistentwith(48).(48)JohnandBillbelievethatTomgaveabooktoSueandamagazinetoMia,respec-tively.Second,if(42)isellipticalthenitfollowswithoutfurtherstipulationthattheadverbcanappeartoberealizedinahigherclausalposition,totheleftoftheconjunctionthatitissemanticallylinkedto.Thisisshownin(49),wheretheobjectcoordinatephrasethat`respectively'mustinteractwithisembeddedintheclause.19 (49)JohnandBill[respectively[believedthatSuewantedtojogandwalk]].Notethatthisalsodispensesanyadditionalassumptionsabouttheadverbbeingallowedto\roattotheleftwhilecombiningsemanticallywiththelowerconjunction.Exampleslike(50)castseriousdoubtontheadverb'sabilityto\roatoutofitsembeddedclause.(50)*IrespectivelybelievethatTimandSueloveFredandMia.Finally,ifellipsisisatworkin(42)thenitispossibletomanipulatethesentencesothatworldknowledgecanforceanellipticalSinterpretation,asin(44a)and(45a)above.Althoughsuchasentenceisnecessarilycomplexandthereforediculttoprocess,thispredictionseemstobeborneoutin(51),whichcanrefertotwodierentcoinsbeingfound,asopposedtothesamecoinbeingfoundtwice(alessplausibleinterpretation).(51)JohnandFredclaimthatacoinwasfoundinthekitchenonMondayandintheyardonTuesdayrespectively.Iconcludethatthereisindependentevidencesupportingthehypothesisthat(41)followsasadirectpredictionofraising/control,andthat(42)followsasadirectpredictionofleft-peripheryellipsis.Thus,theserespectivelyreadingdatapointsarenotdierentfromthecasesdiscussedsofar.Idirectthereadertothereferencesgivenaboveforaccountsofleft-peripheryellipsisphenomena.InSection4.2Iillustratehowanindependentanalysisofraising/controlcaninterfacewiththeserespectivelyreadingswithoutfurtherstipulation.3.4.2Across-the-boardunboundeddependenciesItisgenerallyassumedsincetheseminalwork

23 ofRoss(1967)thatanidentityconditionmusth
ofRoss(1967)thatanidentityconditionmustholdbetweenelementsextractedacross-the-board.Forexample,inItwasRobinwhoFredhuggedandMiakissed,itmustbethecasethatthepatientofhugandkissisthesameperson,Robin.However,Postal(1998,136,160),Kehler(2002,125),andGawron&Kehler(2003,2004)notethattherearecertainller{gapconstructionswhichshowthatthisisnotalwaysthecase.Considertheconjunctionin(52),fromGawron&Kehler(2004,193).(52)InallymetSusan,Lyn,andMaryyesterday.TheyarethethreesistersxywthatBobhired x,Johnpromoted y,andBillred w.Thereisaninterpretation{possiblythemostprominentone{wherethepatientsof`hire',`promote',and`re'arethesame(strictidentity),andoneinterpretationwheretheyarenot(weakidentity).Thelatterreadingcanbemademoreprominentbyadding`respectively'.Asbefore,Irepresentbothreadingsof(52)via`',tomeanthatxandyareeitheridenticalorcumulateintoaplurality.In(53)Ioermoreexamplesofller{gapconstructionswithcomparableinterpreta-tions.14Someofthesesentences,suchas(53b,c,d),allowthepresenceof`respectively'andthereforecorrespondtowhathasbeencalledarespectivelyreading. 14Munn(1998,1999)arguesthatexampleslike(53a)donotviolatethestrictidentityconditionim-posedbycoordination.Instead,hearguesthattheseshouldbeanalyzedasfunctionalreadings(wherepair{listreadingsareavarietyoffunctionalreading),viaspecialdoubly-indexedfunctionaltraces.SeeGawron&Kehler(2003)forseveraltechnicalandempiricalproblemsinMunn'sanalysis.20 (53)(a)Whatxydid[Kim[eat xanddrink y]]?(b)Settingasideillegalpoachingforamoment,howmanysharksxydoyouestimate[[ xdiednaturally]and[ ywerekilledrecreationally]]?(c)The[shipsxythat[[aU-boatdestroyed x]and[aKamikazeplaneblewup y]]]]weretheLaconiaandtheCallaghan.(d)Thehousesxythat[[therereducedtoash x]and[the\roodleveleddown y]]wereneareachother.Postal(1998,136)andKehler(2002,125)alsonotedatalike(54),whichPostalclas-siesasaninterwovendependency.Iviewthesecasesasfallinginthesamecategoryas(53).AllofthesecasesfollowfromtheSharedDependentConditionforConjunctionproposedin(24).Basically,anyshareddependentiscombinedby`',evenifextracted.(54)(a)[[Whichpilot]xand[whichsailor]y]xywi

24 llJoaninvite xandGretaentertain yrespect
llJoaninvite xandGretaentertain yrespectively?(b)[[Whatbook]xand[whatmagazine]y]xydidJohnbuy xandBillread yre-spectively?(c)[[Howmanyfrogs]xand[howmanytoads]y]xydidGregcapture xandLucilletrain yrespectively?Thesameappliestoshareddependentsthatarerealizedtotherightoftheircanon-icalpositions,asincertainRight-NodeRaising(RNR)constructions.Vergnaud(1974),Abbott(1976),Jackendo(1977),Gazdar(1981,180),Postal(1998,136,178)andothersnotedcasesofadditiveRNRlike(55).(55)(a)FredspentandMialost[atotalof$10,000].(b)JohndefeatedandMarylostto[verydierentopponents].(c)GregcapturedandLucilletrained[312frogsbetweenthem].(d)JohnhummedandMarysang[thesametune](e)Iknowamanwholostandyouknowawomanwhospent[atotalof$10,000betweenthem].Sentenceslike(55a)haveatleasttwokindsofreading:oneinwhichFredspentandMialostthesameamountofmoney(atotalof$10,000),oronewherethesumoftheamountslostandspentis$10,000.Thismaybemodeledby`',asbefore.Sinceverydierentopponentsin(55b)denotesaplurality,itforcesthesummationinterpretation.Conversely,thesametunein(55d)forcesthestrictidentityreading.Theadverb`respectively'isnotfelicitousinthesecasesbecausetheRight-Node-Raisedconstituentdoesnotprovideanexplicitranking.Comparewith(58)below.ThesemanticsofadditiveRNRissimilartothecumulativereadingsinller{gapdependenciesin(52){(54).Inbothcasestheshareddependentsarecombinedintoauniqueandsemanticallyricherdependent.Carlson(1987)andSabbagh(2007)assume21 thatsuchreadingsonlyarisewithrelational/symmetricpredicates,butexampleslike(55a)suggestthatthisisnotalwaysthecase.Notethattheadditivereadingin(55a)isstillavailableevenifatotalofisomitted,althoughitisnotthepreferentialinterpretation.Othercasessuchas(56)providefurtherevidencethatadditiveRNRdoesnotrequirerelational/symmetricpredicates,andcaninprinciplearisewithanypluralNPinasuitablecontext.(56)TomrelocatedtoLondon,andSuespenthersummerinParis.Ican'timaginewhyTomwouldmovetoandSuewouldvacationin[twoofthemostexpensivecitiesinEurope].TherearetwokindsofevidencesuggestingthatadditiveRNRisduetotheShared-dependentconditionforConjunction.Likerespectivelyreadings,additiveRNRreading

25 sonlyoccurinplurality-formingconjunction
sonlyoccurinplurality-formingconjunctionstructures.Hence,thedisjunctionin(57),basedonBeavers&Sag(2004,66),onlyhasanon-additivereading.Theadditivereadingre-appearswithandinsteadofeither...or.(57)EitherFredspentorMialost[$10,000].(=`EitherFredspent$10,000orMialost$10,000.')Second,liketheleftwardextractioncasesin(54),additiveRNRallowsrespectivelyreadings.Thisisshownby(58),fromPostal(1998,136,178),Gawron&Kehler(2003)andAbels(2004),respectively.ThesereadingsshouldfollownaturallyifRNRaisedde-pendentsareallowedtobecumulatedby`'justlikeanyotherdependent.(58)(a)ErnestsoldcocaineandGeorgesoldheroin[totherstnurseandtotheseconddentalassistant]respectively.(b)IboughttravelguidesforParisandLondonyesterday.MaryvacationedandBilldecidedtolive[inthesetwocities]respectively.(c)MaryvacationedandBilldecidedtolive[inthetwomostexpensivecitiesinEurope]respectively.3.4.3AdnominaldependenciesAnotherconstructionwhicharguablyalsoexhibitscumulationofshareddependentphrasesisillustratedin(59).SuchdatawererstnotedbyRoss&Perlmutter(1970),Hintikka(1974),andMcCawley(1998,771).(59)(a)Amanxenteredtheroomandawomanywentout[whowerequitesimilar]xy.(b)Amanxenteredandawomanyleft[whohadmetinVienna]xy.(c)*Amanenteredorawomanleftwhowerequitesimilar.Here,arelativeclauseissimultaneouslylinkedtothesubjectsoftheprecedingconjoinedclauses.Likealltheothercasesdiscussedsofar,suchreadingsarenotpossiblewithlogicaldisjunctionandinvolveashareddependentthatisinterpretedcumulatively.22 Ifshareddependentcumulationisresponsibleforbothsplit{antecedentrelativeclausereadingsandrespectivelyreadingsthenonewouldexpectthemtobeabletoco-occurinthesamestructure,allthingsbeingequal.Thispredictionisborneoutin(60).(60)AmanenteredtheroomandawomanleftwhowereDutchandGreek,respectively.Somethingsimilarhappenswhenadnominaladjectivalphrasesconjoin,andsharethenominalheadthattheyselect.Theconjunctionofsingularadjectivescanyieldanadjec-tivalphrasecapableofmodifyingapluralnominal.Thiswasalreadyseenintheattesteddatapointin(13b)above,whichIrepeathereas(61).(61)WeknowhousesfourandvearetheSwedeandtheGerman,butwhichiswhich?Thisphenomenoni

26 snotobviousinEnglishbecauseofthelackofnu
snotobviousinEnglishbecauseofthelackofnumberagreement,butitcanbemorereadilyobservedinlanguageswhichrequireadjectivesandnounstoagreeinnumberovertly.Considerforexample(62)and(63),fromEuropeanPortuguese,wheretheconjunctionoftwosingularadjectivesyieldsaphrasethatcanadjointoapluralnominal.Ingeneral,itisnotpossibleforasingularadjectivetocombinewithanominalwithoutnumberagreement(e.g.*oschaspreto).(62)Oschaspretoeverdes~aoobtidosdathe.plteas.plblack.sgandgreen.sgare.plobtained.plfrommesmaplantasameplant`Theblackandgreenteasareobtainedfromthesameplant.'(63)OCarloseoManuelforamrespectivamenteossegundotheCarlosandtheManuelwererespectivelythe.plsecond.sgequartoclassicadosandfourth.sgranked-participants.pl`CarlosandManuelcameinsecondandthirdplacerespectively.'ThesedataareconsistentwiththeSharedDependentConditionforConjunction.Sincethetwoconjoinedadjectivalsselectanominaldependent,thelattershouldbesharedvia`'.Thepluraleventualityformedbytheconjunctionofadjectivalpredicatesyieldsapluralitythatrespectivelycanexploitintheusualway.15Furtherexamplesofthispatternarein(64).(64)(a)Theaveragelifespanwasbetween[[zeroandone][yearsold]].(b)Kowaldiscoveredthe[[13thand14th][moonsofJupiter]].(c)Ireadthe[[secondandthird][chaptersofyourbook]].(d)Theproductionofcarbonandnitrogenwillpeakon[days[sixandseven]]. 15Forexample,inhewassimultaneouslyhappyandtired.SeealsoLasersohn(1995).23 (e)BartandLisaare[players[threeandfour]].Sentence(64a),forexample,showsthatbyconjoiningonewithzerooneobtainsaphrasethatcannowcombinewithapluralnoun.Thiscontrastswith*oneyearsold,whichisungrammaticalbecauseonemustcombinewithsingularnouns.Eachconjunctispred-icatingadierentday,andhenceseemstoinvolveshareddependentcumulation.Asisexpected,theadverb`respectively'canbefelicitouslyadded,e.g.:(65)Theproductionofcarbonandnitrogenwillpeakondayssixandseven,respectively.Inconclusion,awiderangeofphenomenasuggeststhatshareddependentscanbesemanticallycombinedviasummation,andthatthismechanismcanyieldso-calledre-spectivelyinterpretationsasaspecialcase,whichcanbeforcedbytheovertrealizationofthe`respectively'adverb,incasether

27 eisapragmaticallyavailableranking.4AHead
eisapragmaticallyavailableranking.4AHead-DrivenPhraseStructureGrammaraccountPostal(1998,160{163)andGawron&Kehler(2004,194,195)arguethatrespectivelyphenomenaposefoundationalproblemsforcurrenttheoriesofgrammar,especiallyforunication-basedtheorieslikeHead-DrivenPhraseStructureGrammar(HPSG;Pollard&Sag1994).However,theaccountproposedabovesuggeststhatthesefoundationalproblemshavebeenoverstated.InwhatfollowsIshowthatHPSGcanmodeltherelevantphenomenawithoutanymajorchangestohowsubcategorizationandpredicationareusuallylexicallycoupled.Iwill,however,revisehowsubject{verbagreementisenforced.Allelsewillfollowfromthegrammarofcoordination.InSection4.1IpresentthebasicfoundationsofHPSGasoutlinedintheconstruction-basedapproachinSag(2010a,b),andinSection4.2Ishowhowthegrammarfragmentscalesuptorespectivelyphenomena.ThecumulativequanticationphenomenadiscussedinSection3.1aredealtwithatthelevelofsemanticinterpretationandthereforewillnotbediscussedhere.4.1BasicsHead-DrivenPhraseStructureGrammarisatheoryofgrammarwherephonology,syntax,semantics,andpragmaticsco-existlocallyinthesamekindoflinguisticstructure,calledasign.Centraltothisnon-derivationaltheoryisthenotionofconstraintsatisfaction(Carpenter,1992).Thegrammarrulesarenothingmorethandeclarativestatementsthatimposeconstraintsaboutlinguisticstructure,ratherthanoperationsthatalter,compare,ordisplacepreviouslyassembledrepresentations.Theinformationconveyedbyasignisencodedassetsoffeatures.Thefeaturephonencodesphonology,synencodesvariouskindsofsyntacticinformation(includingpart-of-speech,agreement,case,andsubcatego-rizationconstraints),andsemcontainssemanticrepresentations.Signscanbeoftypewordorphrase.ThesignforthepropernameTimisgivenin(66).24 (66)2666666666666666664wordphon/tIm/syn264catnounvalhislashfg375sem266664indexx264numsgper3genmas375restrhtim=xi3777753777777777777777775Valencyisrecordedinalist-valuedfeatureval,whichinthiscaseisempty(i.e.hi).Theemptysetvalueforslashmeansthattherearenoextracteddependents.Semanticsisrepresentedasalistofrestrictionsrestrcontainingpredications.ForexpositionpurposesIadoptthe`\rat'semanticformalismo

28 fCopestakeetal.(2005)andignorethetreatme
fCopestakeetal.(2005)andignorethetreatmentofquantierscope,butnothinghingesonthis.16FromnowonIusethesymbol`NP'asashorthandforafeaturestructuredescriptionofanominalsignwithanemptyvalencelist,asin(67).Hence,NPxisnothingbutanominalsignthathasemptyvalenceandareferentialindexx.(67)NPxisashorthandfor26664syn"catnounvalhi#semhindexxi37775Lexicalentriesandgrammarrulesarepartialdescriptionsoflinguisticstructure.Forexample,theverbsin(68)requireavalentwithnominalpart-of-speech,emptyvalence,andareferentialindex,butsaynothingaboutthephonologyorsemanticrepresentationofthatvalent.(68)(a)266666666666664wordphon/lEft/syn26664catverbvformniteval\nNPxslashfg37775semindexerestrh9eleave(e;x)i377777777777775 16InCopestakeetal.(2005)eachpredicationislabeled,andsemanticstructureisdeterminedincremen-tallyandmonotonicallybyhowthelabelsarerelated.Iomitsuchlabelsforforexpositionpurposesonly.SeealsoGinzburg&Sag(2000);Frank&Reyle(1995);Richter&Sailer(1999)andSag(2010b).25 (b)2666666666666666664wordphon/lIvz/syn266666664cat2664verbvformniteper3numsg3775val\nNPxslashfg377777775semindexerestrh9eleave(e;x)i3777777777777777775Anysignthatsatisesthesestatedconstraintswilldo.DrawingsomeinspirationfromKathol(1999),Iassumethatverbalmorpho-syntacticagreementinformationisappropri-ateforthetypeverb.Hence,theverbformin(68a)isunderspeciedandcancombinewithanykindofsubject(e.g./You/He/Theyleft),whereas(68b)canonlycombinewiththirdpersonsingularsubjects.Thetwooccurrencesofxindicatethatthetwoindicesmustbeunied.Inotherwords,thevariablecontributedbythesubjectNPisexactlythesameasthevariablepredicatedbytheverb;thetwoareinextricablyidentiedinthelexicalentryin(68).Ingeneral,variablebindingisensuredlexicallyinHPSG:predicatesdirectlylinktheirlogicalargumentstothevariablesoftheirvalents.Thisisoneoftheaspectsofunication-basedgrammarthatGawron&Kehler(2004)identifyasproblematicforrespectivelyreadings.Everythinginthegrammarisuniformlyrepresentedwithfeatures,andsyntactictreesarenoexception.ThisisshowninFigure4.Thefeaturemtrencodesinformationaboutthemothernodeandthelist-valuedfeaturedtrsencodesinformation

29 aboutthedaughtersoftheconstruction.Iuset
aboutthedaughtersoftheconstruction.Iusethetreenotationwhentalkingaboutstructureslicensedbythegrammar,andreservethefeaturematrixnotationwhentalkingaboutthegrammar.S NPVPisashorthandformtrSdtrshNP,VPiFigure4:AfeaturestructurerepresentationofatreeAs(69)shows,VPisshorthandforaverbalsignthatseeksanNP,andanSisshorthandforaverbalsignwithemptyvalence.(69)a.VPebaseisashorthandfor26666664syn2664cat"verbvformbase#valhNPi3775semhindexei3777777526 b.Sefiniteisashorthandfor26666664syn2664cat"verbvformnite#valhi3775semhindexei37777775Allgrammarrulesareoftheform),whereisatypeandisasetoffeaturesthatanyentityofthetypemustsatisfy.Theserulescancapturevaryingdegreesofgeneralizationbecausetheyarehierarchicallyorganized.Anypieceoflinguisticinforma-tionofagiventypemustnotonlysatisfyanyruleoftheform),butalsoeveryrule0)0,where0isa(directorindirect)supertypeof.Forexample,considerthetypehierarchyofphrasalrulesinFigure5.Theconstructions(cxt)inthisfragmentarephrasal,andcanbeeitherheadedornon-headed.Iviewcoordinatestructures(andperhapscertaincomparatives)asanon-headedconstructions,butnothinghingesonthisasfarasthisworkisconcerned.phrasal-cxtheaded-cxt specier-head-cxt ... ... head-comps-cxt ... non-headed-cxt coord-cxt ... Figure5:TopnodesofthehierarchyofphrasalconstructionsFornow,letusfocusontherulesgoverningheadedconstructions,i.e.thetypessub-sumedbyheaded-cxtinFigure5.Thehead-comps-cxttypeinFigure5modelsphrasesformedbyalexicalheadanditscomplements,andthespecier-head-cxtmodelsstruc-turesformedbyaspecierandahead.Otherruleswillmodeladjunctionconstructions,andsoon.Thefeaturehd-dtr,whichisonlyappropriateforheadedconstructions,isusedtoidentifywhichofthedaughtersisthehead.Throughout,IuseX,Y,asvariablesoverfeaturestructuresandLasavariableoverlistsoffeaturestructures.Thespecier-head-cxtconstructionruleallowsaheadphrasetocombinewithaspecier,asseenin(70).(70)Specier-HeadConstructionspecier-head-cxt)26666664mtrsynhvalhiidtrs*X,Z:synhvalhXii+hd-dtrZ37777775ThenotationX:meansthatthevariableXdescribesafeaturestructurewithatleastasmuchinformationasthefeaturestructuredescripti

30 on.Notethat(70)issilentaboutsemantics,p
on.Notethat(70)issilentaboutsemantics,part-of-speech,orphonology.Thisrulesimplyimposes(partial)syntactic27 constraintsonalocaltree,bystatingthataconstructionofthetypespecier-head-cxtcanbeformedbyasignXandaheadthatselectsXasavalent.Theresultingmothernodehasemptyvalence(i.e.[valhi]),liketheoneshownaboveinFigure4.FollowingMalouf(2000)andSag(2010a),Iassumethatthetypespecier-head-cxthasvarioussubtypes,eachcapturingspecicgrammaticalpatternsfordierentspecier{headconstructions.Forexample,Malouf(2000,15)modelsdierentcaseassignmentpatternsforgerundclauseswiththreedierentsubtypesofspecier-head-cxt:anaccusativesubjectruledealswithclauseslike(71),apossessivesubjectruledealswith(72),andanominativesubjectruledealswithcaseslike(73).(71)(a)Patdisapprovedof[[me][quietlyleavingbeforeanyonenoticed]].(b)Everyonewasimpressedby[[Pat][artfullyfoldingthenapkins]].(72)(a)Patdisapprovedof[[my][quietlyleavingbeforeanyonenoticed]].(b)Everyonewasimpressedby[[Pat's][artfullyfoldingthenapkins]].(73)(a)[[He][wearsatuxedo]].(b)Iinsistthat[[Sandy][leavemealone]].(c)[[Pat][artfullyfoldedthenapkins]].Thereareatleastfourotherkindsofspecier{headconstructionthathavetheirpe-culiarsyntactic,semantic,pragmatic,andprosodicconditions.First,wehave`Madmag-azine'sentences(Akmajian,1984),suchas(74),whichhaveanumberofidiosyncraticpropertiesthatcanbenaturallycapturedconstructionally(e.g.theycannotbeembed-ded,theirsubjectmustbeaccusative,andthetheyneverincludetense,modals,andsententialadverbials).(74)(a)[[Him][wearatuxedo]?!(Sure.)(b)[[Myboss][givemearaise]]?!(Ha.)(c)What![[Larry][beadoctor]]?Second,wehaveabsoluteconstructionslike(75),whichalsodierfrom(71)inseveralways:theprepositionwithisrequired,doesnothaveanNPdistribution,adjoinstoaclause,andhasvariablesemanticconnectivitywiththematrix.SeeStump(1985);Culicover&Jackendo(2005)fordiscussion.(75)With[[him][organizingthings]],we'llnevergetanythingdone.Third,structureslike(76)appeartobeakindofspecier{headfragmentconstructionwithanaccusativesubject.(76)Tom:I'dliketoseethatmovie.Kim:[[Me][too]].28 Finally,directiveandimperativesentenceslike(77)allow

31 optionalnon-rstpersonsubjects(butareonl
optionalnon-rstpersonsubjects(butareonlycompatiblewithsecondpersonre\rexiveobjects),andcomewithspecialpragmaticsandintonation.(77)(a)[[You][leavemealone]]!(b)[[Everyone][seatyourselves/*themselves]]!Theabovesubtypesofspecier-head-cxtcanbemodeledbythehierarchyinFigure6.Eachtypecanintroduceparticularsyntactic,semantic,pragmaticandprosodiccon-straints.Forexample,nom-subject-pred-cxtcorrespondstotherulein(78)below,whichlicensesstructuresformedwithanominativesubjectphraseandanagreeingniteverbalheadphrase.Sincenom-subject-pred-cxisasubtypeofspecier-head-cxt,itinheritsallitsconstraints:thespeciersignisrequiredtobetheonlymemberofthehead'sval,andthemother'svallistisempty.specier-head-cxtnom-subj-pred-cxt acc-subj-pred-cxt ... mad-magaz-pred-cxt Figure6:Hierarchyofspecier{headconstructions(extendinghierarchyinFigure5).DepartingfromPollard&Sag(1994)Iproposethatsubject{verbagreementiscom-putedatthephrasallevelratherthanlexically,asshownin(78),similarlytoSag,Wasow&Bender(2003:102).(78)NominativeSubjectPredicateConstructionnom-subject-pred-cxt)26666664dtrs*2666664syncathcasenomisem24indexperXnumY3537777752664syn2664cat264vformnperXnumY37537753775+37777775Basically,thisruleensuresthatwhateveristheagreementinformationXintheVPdaugh-ter,itmustunifywiththeinformationinthenominativesubjectdaughter.AHeadedConstructionrulediscussedbelowwillensurethattheagreementspecicationstheverb'scatarepercolatedtoitsphrasalprojections.Finally,theCoordinationConstructionruleinSection4.2willrequirethattheconjunctsandthemotherhavethesamecatvalue,andtherefore,verbalconjunctsshallimposethesameagreementspecicationsontheirshareddependents.AlthoughtheheadedconstructionsinFigure5aredierent,theyalsohavesimilaritieswhichcanbecapturedbythehead-cxtsupertype.Forexample,theHeadedConstructionrulein(79)ensuresthatforanyheadedconstructionthesyninformationoftheheaddaughterandofthemotherarethesame,bydefault(seeGinzburg&Sag2000:33).The29 defaultconstraint`='ensuresthatthefeaturesXoftheheaddaughterandofitsmotherareidentical,exceptifexplicitlycontradictedbytheapplicationofotherrules.Thus,(70)doesnotal

32 lowtheheaddaughterandthemothertohavethes
lowtheheaddaughterandthemothertohavethesamevalinformationinspecier{headconstructions,butdoesallowthemtohavethesamepart-of-speech.Thus,aVPprojectsanS,anN0projectsanNP,andsoon.17(79)HeadedConstructionheaded-cxt)"mtrrsyn/Xhd-dtrrsyn/X#SomerulesareevenmoregeneralandapplytoallphrasalconstructionsinFigure5,notjusttoheadedconstructions.Oneexampleisthesemanticcompositionrulein(80),whichstatesthatthesemanticcontentofthemotherofanyphrasalstructureistheconcatenationofthesemanticcontentsofthendaughters.The`'symboldenoteslistconcatenation.18(80)PrincipleofCompositionalityphrasal-cxt)264mtrhsemmrestrX1...XnidtrsDDsemmrestrX1,...,,semmrestrXnE375ThecumulativeeectofalloftheseconstraintsisshowninFigure7.Asmentionedabove,wheneverthegrammarrequirestwofeaturestohavethesamevalue,theresultisunication(ormoreaccurately,structure-sharing,sinceinmodel-theoreticalgrammartherearenoproceduraloperations).Inthelinguisticstructureslicensedbythegrammarconstraints,unicationisrepresentedviamultipleoccurrencesofaboxedtag,suchasthe 1 inFigure7.Thisstatesthatthespecier-head-cxthasidentiedthevalentsubcategorizedbytheheadwiththenon-headdaughter. 17Incertainotherconstructions,allofthesyninformationinthemotherandintheheadremainscom-patible,andthereforetheentiresynvalueissharedvia(79).Seeforexampletheadjunctionconstructionin(89).Theeectof(79)inadjunctionconstructionsisthatmotherandheadhaveexactlythesamesyninformation.Note,however,thatnothinginthisaccounthingesontheuseofdefaults,sinceeachclassofconstructioncanspecifyhowthevalenceinformationpropagates.18InmorerecentHPSGworkthesymbol`'isusedinsteadof`',butinordertoavoidconfusionwiththeLinkeansummationoperatorIreverttothelatternotation,originallyusedinPollard&Sag(1987).Thislistconcatenationrelationcanberecastasstandardstructure-sharingconstraints(Copestakeetal.,2001).30 26666664phrasesyn24cat 2 valhislashfg35semindexerestrhtim=x;9eleave(e;x)i37777775 1 266666666666664wordsyn2664catnouncasenomvalhislashfg3775sem2664indexx"numsgper3genmas#restrhtim=xi3775377777777777775 Tim26666666664wordsyn2664cat 2 verbvformnvalh 1 islashfg3775semin

33 dexerestrh9eleave(e;x)i37777777775 left
dexerestrh9eleave(e;x)i37777777775 leftFigure7:Representationofthesentence[[Tim]NP[left]VP]SConsidernowhowcomplementationconstructionsaremodeled.Ahead{complementruleallowsanylexicalheadtocombinewithitslexicallysubcategorizedcomplements(i.e.themoreobliquevalentsX2;:::;Xn)asdeterminedby(81).(81)PredicationalHead-ComplementConstructionhead-comps-cxt)26666664mtrhsynnvalhX1iidtrs*Y:"wordsynnvalhX1;X2;:::;Xni#,X2;:::;Xn+hd-dtrY37777775Notethatnothingissaidaboutthesemanticsorpart-of-speechofthedaughtersorofthemothernode.Anywordwithanon-emptyvalencecaninstantiatetheheadYandimposetherelevantlexicallyspeciedconstraintsontheXvalents.TheHeadedConstructionin(79)interactswiththisruleandmakessurethatthemotherandtheheaddaughterYhavethesamecatinformation.FollowingPollard&Sag(1994),asubjectraisingverblikecontinuelexicallyselectsaninnitivalVPcomplementandshareswithitssubjectvalentX.Theinnitivalauxiliaryverbtoisalsoaraisingverbandthereforealsosharesthesubjectvalentwithits(baseform)VPcomplement.TheanalysisofsubjectcontrolverbslikewantissimilarinthattheverblexicallyselectsabaseformVPandshareswithitthesamesubjectindex.Thelexicalentiresfortheseverbsareshownin(82).31 (82)(a)266666666666666666666664wordphon/k@ntInju/syn2666666666664catverbvformniteval*XVPinf24synhvalhXiisemP35+slashfg3777777777775semindexerestrh9econtinue(e;P)i377777777777777777777775(b)266666666666666666666664wordphon/wAnt/syn2666666666664catverbvformbaseval*NPxVPinf24synhvalhNPxiisemP35+slashfg3777777777775semindexerestrh9ewant(e;x;P)i377777777777777777777775Semantically,wantembedsthemeaningofthecomplementVPphrase,labeledbyl1.Thetwoverbsdierinthatcontinuedoesnotassignanysemanticroletoitssubject.Thus,thesubjectvariableofhelpin(83)isboundtothesubjectvariableofeverydominatingverbuptothematrixverbcontinue,andcumulativequanticationcanthenapplytohelp(e;x;y)asdiscussedinSection3.1above,andyieldtheintendedrespectivelyinterpretation.(83)FredandSuecontinuetowanttohelpKimandMia(respectively).Letusnowturntohowunboundedller{gapdependenciesaremodeledinHPSG.19Basically,certainlexicalconstraintsallowvalentstobelocatedins

34 lashratherthaninval.Thevaluesofslasharep
lashratherthaninval.ThevaluesofslasharepercolatedtothemothernodebytheHeadedConstructionin(79),sinceslashisasynfeature.Thisiswhythedependencyisunbounded,andcanbeiteratedindenitely.Thepercolationofgapscanbeinterruptedonlybycertainconstructions,namelythosethatimposeconstraintsonthevalueofslash.Onesuchconstructionisthetopicalizationconstruction,shownin(84),inwhichsomesignXisrealizedasasisteroftheheadclausethatcontainsthecorrespondinggap. 19SeeGinzburg&Sag(2000),Levine&Hukari(2006),andSag(2010a).32 (84)Filler{HeadConstructionller-head-cxt)26666666664mtrsynhslashYidtrs*X,Z:264syn264catverbvalhislashfXg[Y375375+hd-dtrZ37777777775Othergaps(ifany)arepercolatedtothemother,viatheremaindersetY.TheeectofthisheadedconstructionisillustratedinthetopicalizationsentenceinFigure8.ForexpositionpurposesIabbreviatecatinformation.Se26664synvalhislashfgsemhrestrhfred=ydana=x;9ehate(e;x;y)ii37775(ller-head-cxt) 2 NPyhrestrhfred=yii FREDSe26664synvalhislashf 2 gsemhrestrhdana=x;9ehate(e;x;y)ii37775(specier-head-cxt) 1 NPxhrestrhdana=xii DanaVPe26664synvalh 1 islashf 2 gsemhrestrh9ehate(e;x;y)ii37775 hatesFigure8:Atopicalizationconstruction.4.2ConjunctionandrespectivelyFortheanalysisofverbalcoordinationIassumeafamiliarbinarybranchingrulelikeX!XX,whichIformalizeinHPSGtermsas(85),drawingfromBeavers&Sag(2004).IleaveopenthepossibilityofrevisingthisruleasproposedinSag(2002)inordertogeneralizetoothercategories,andtodealwithcoordinationof`unlikecategories'phenomena.20 20Whereasnominalcoordinationmustallowagreementmismatchese.g.Tomandus,verbalcoordinationmustnot:twoverbalconjunctsmustbearstrictlyconsistentagreementinformationincat.However,other33 (85)VerbalCoordinationConstructionv-coord-cxt)2666664mtrsynhcatX:verbidtrs*24synhcatXicrd{3524synhcatXicrdcrd-marked35+3777775Thisconstructionallowstwoverbalconstituentstobecoordinatedaslongastheyhavecompatiblecatvaluesandrstdaughterisnotmarkedwithacoordinator(i.e.bearsthespecication[crd]),andtheseconddaughterismarkedwithacoordinator(i.e.bears[crdcrd-marked]).Iassumethatthecrd-markedtypehasseveralsubtypes,oneforeachkindofcoordinationmar

35 ker.Thus,thelexicalentryforandislexicall
ker.Thus,thelexicalentryforandislexicallyspeciedas[crdconj],theentryfordisjunctionorislexicallyspeciedas[crddisj],andsoon.Sincethemothernodein(85)isunderspeciedforthevalueofcrd,thisrulecanapplyrecursivelyasintended.Therearevarioustypesofcoordination,oftenwithspecialsyntactic,prosodic,semanticandpragmaticcharacteristics.Togivesomewell-knownexamples,considerpackagingconjunction(e.g.Eggs,cheeseandbaconwasallIneeded),numeralconjunction(e.g.countedvehundredandtwenty-twocats),arithmeticalconjunction(e.g.Twoandtwoisfour),conditionalconjunction(e.g.TakeonemorestepandI'llshootyouwhereyoustand),andintensicationconjunction(e.g.Thesoundbecamelouderandlouder),amongotherslikeBooleanconjunction,andplurality-formingnon-Booleanconjunction(TomandMaryagreed,Youcan'tsimultaneouslydrinkanddrive,Kimrarelysingsanddances,orRobinreadthenewspaperanddriedherhairinexactlytwentyseconds).Theseandothercoordinationpatternscanbemodeledwithatypehierarchyofconstructionsinwhicheachtypeintroducesthespecicconstraintsassociatedwiththatkindofcoordination.InthisworkIfocusonnon-Booleanconjunction,andontheformalizationoftheSharedDependentConditionforConjunction.InordertodescribesumindicesinHPSG,Iview`'asthefunctiondenedin(86).(86)(x;y)=zi[[z]]=([[x]]t[[y]])Plurality-formingconjunctionmustcreateapluralityfromthedenotationofthecon-juncts.Thisisdonebytakingtheindices1and2oftheconjunctsandcombiningthemvia`'.Similarly,thereferentsofeverysignselectedbytheconjunctsmustbecombinedvia`'.Thisisformalizedin(87),whichgeneralizestoanynumbermofshareddependents.21 verbalcatinformationneednotmatch,suchasaux:Kimlikebagelsandhecaneatalotofthem.SeeSag(2002).21TheLinkeansum`'conditionscanalternativelybeinsertedinrestrviathefeaturec(onstructional)-cont(ent)fromCopestakeetal.(2005)(cf.withChaves(2009)).Therulein(87)iscompatiblewiththetheoryofextractionproposedinGinzburg&Sag(2000),butnotwiththeoneadvocatedinChaves(2012b).Inordertomakeitso,(87)wouldberevisedasfollows.Themother'sslashvalueisinsteaddenedasX1[X2,whereX1istheslashvalueoftherstcon-junctandX2ofthesecond.The[relationcorrespondstoasymmetricaland

36 non-deterministicsetunionoperationwith`
non-deterministicsetunionoperationwith`'combination.Thisisdenedintermsofthreeconditions.Thebasecaseis34 (87)Non-BooleanConjunction(m0)nbool-cnj-cxt)266666666666666666666666664mtr2666664syn264valDXP(x0;y0)0,...,XP(xn;yn)nEslashnXP(xn+1;yn+1)n+1,...,XP(xm;ym)mo375semhindex(1;2)i3777775dtrs*26664synvalhXPx00;...,XPxnnislashfXPxn+1n+1;...,XPxmmgsemhindex1i3777526664synvalhXPy00;...,XPynnislashfXPyn+1n+1;...,XPymmgsemhindex2i37775+377777777777777777777777775InthisworkIfocusontheinstancesofv-coord-cxtwhicharealsosubtypesofnbool-cnj-cxt.Obviously,otherkindsofverbalcoordinationdonotformaplurality(e.g.BooleancoordinationslikeItisnotraininganditisnotsnowingordisjunctionslikeIcansingordance).ThecurrentgrammarthuslicensesstructuresliketheoneinFigure9,withthesemantics9z(men(z)^z=(x1x2)^sing(e1;x1)^dance(e2;x2)).Ifx1x2isinterpretedasequalitythenx1=x2andthereforethemenarebothsinginganddancing.However,ifx1x2isinterpretedasasumthenx1=x2andweobtainareadingwherethemensinginganddancingaredierent.Thisinterpretationisconsistentwiththeadverb`respectively'.Sevalhirestrh9zmen(z);9e1sing(e1;x1);9e2dance(e2;x2)i(specier-head-cxt) 1 NPzhrestrh9zmen(z)ii ThemenVPe=(e1;e2)valh 1 NPz=(x1;x2)irestrh9e1sing(e1;x1);9e2dance(e2;x2)i(nbool-cnj-cxt) VPe1valhNPx1irestrh9e1sing(e1;x1)i sangVPe2valhNPx2irestrh9e2dance(e2;x2)i anddancedFigure9:Valentsharinginconjunction:`Themensanganddanced'. fg[X=X,thesetunioncaseis(fg[X1)[(fg[X2)=f;g[(X1[X2),andthe`'caseis(fg[X1)[(fg[X2)=fg[(X1[X2).35 WhereasGawron&Kehler's(2004)accountobtainsthesereadingsfromdierentsyntactictreesanddierentsemanticrepresentations,thepresentaccountdoesnot.Infact,bothstrictandweakidentityreadingsaretheresultofasingletreestructureandasinglesemanticrepresentation.Asentencelike(88)ismodeledinthesameway,theonlydierencebeingthatthesubjectisani-sumratherthanaplural.(88)SueandKarensinganddance.z=(y1y2)^sue=y1^karen=y2^z=(x1x2)^sing(e1;x1)^dance(e2;x2)Thiscanbeinterpretedwithorwithoutarespectivelyreadingbecauseof`'.Moreover,ifzisapluralitythenbythesymmetryof`'itfollowsthateithery1=x1andy2=x2,ortha

37 ty1=x2andy2=x1.Instancesofrespectivelyre
ty1=x2andy2=x1.Instancesofrespectivelyreadingsinvolvingller{gapdependencieslike`whichbookandwhatmagazinedidyousaythatJohnboughtandBillread'andothersdiscussedinSection3.4.2arecapturedinaverysimilarway,asshowninFigure10.Theonlydierenceisthatthedependentsthataresharedandsummedareextractedsignsratherthansignsinsitu.Forsimplicity,Iomitthesemanticrepresentationbutitshouldbeclearthattheverbsboughtandreadpredicatex1andx2respectively,andthatthetwovariablesarecombinedvia`'attheconjunctionnode.ThesignsinslashpercolateinthetreeasaconsequenceoftheHeadedConstruction.Exactlyasbefore,if`'isinterpretedasequalitythenz=(x1=x2),butifitisinterpretedasplurality-formingcumulationthenzisapluralityformedwithx1andx2.Foranaccountofinterrogativeandsubject{auxiliaryinversionconstructionsseeGinzburg&Sag(2000)andSag(2010b).Theadverb`respectively'operatesessentiallylikeanyotherverbalmodier,syntacti-callyandsemantically.Thefeaturesel(ect)allowsmodiers,determinersandmarkerstolexicallyimposeconstraintsontheheadsthattheycombinewith.Suchstructuresaremodeledviathehead-functor-cxtruleprovidedin(89).22Sincethisruledoesnotim-poseanyconstraintsonthemothernode,theHeadedConstructionwillforceallthesyntacticfeaturesoftheheadandthemothertobeidentical.(89)Head{FunctorConstructionhead-functor-cxt)26664dtrs*X,24syn"selhXivalhi#35+hd-dtrX37775Thelexicalentryfor`respectively'isprovidedin(90),andconsistsofanadverbthatselectsaverbalheadviaselandpredicatestheverbevent. 22Asinalloftheconstructionsinthiswork,theorderoftheelementsindtrsisnotimportant.Asmentionedabove,alinearizationtheoryliketheoneofPollard&Sag(1987)orKathol(2000)determineswhichorderingsarepossibleinphon.36 Se3valhislashfg 1 NPz whatbookandwhatmagazineSe3valhislashf 1 g Ve3264inv+valh 3 , 4 islashf 1 g375 did 3 NP you 4 VPe3valh 3 islashf 1 g Ve3valh 3 , 2 islashf 1 g say 2 Se=(e1;e2)24valhislashD 1 NPz=(x1;x2)E35 Se1valhislashfnpx1g JohnboughtSe2valhislashfnpx2g andBillreadFigure10:Gapsharinginanacross-the-boardextractionconstruction.(90)26666666666666666666664wordphon/ô@spEktIvlI/syn266666666664cat266664adverbsel*264synhcatverbisemhindex

38 ei375+377775valhislashfg377777777775semi
ei375+377775valhislashfg377777777775semindexerestrhrespectively(e)i37777777777777777777775Notethatsincenoconstraintsareimposedonval,theverbalheadcanbeaverbphraseorasentence,coordinateornot.Figure11illustrateshow(90)and(89)interact.Iomitsomefeaturesforexpositionpurposes.TheadverbisinterpretedasinSection3.3.Ifwerevisetheconjunctionrulein(87)sothatthesigninselthatconjunctsshareiscombinedvia`'thenweobtainanN0liketheonein(91)andtherespectivesemantic37 VPe 1 VPeAdvPe2664syncathselh 1 iisemhrestrhrespectively(e)ii3775Figure11:Genericexampleofadverbialadjunction.representation.TheanalysisisshowninFigure12,andisparalleltowhathappenstoshareddependentsrecordedinvalandslashasdiscussedabove.(91)Theeventwilltakeplacebetween[dayssixandseven]N0.days(z)^9s1order(s1;x1)=6^9s2order(s2;x2)=7^s=s1s2^z=x1x2Basically,whenadjunctsareconjoinedanysignselectedviaseliscombinedviathe`'relation.Itistrivialtorevisetheconjunctionrulein(87)toachievethiseectonselvalues.N0zhrestrhdays(z);9s1order(s1;x1)=6;9s2order(s2;x2)=7ii(head-functor-cxt) 1 N0zhrestrhdays(z)ii daysAPs=(s1;s2)24cathselh 1 N0z=(x1;x2)iirestrh9s1order(s1;x1)=6;9s2order(s2;x2)=7i35(nbool-cnj-cxt) APs124cathselhN0x1iirestrh9s1order(s1;x1)=6i35 sixAPs224cathselhN0x2iirestrh9s2order(s2;x2)=7i35 andsevenFigure12:Conjunctionofadnominalexpressions.AsimilarapproachcanbeadoptedforshareddependentcumulationinRNRandinsplit{antecedentrelativeclauseextraposition,asdiscussedinSection3.4.2.ThereareseveralalternativeanalysesofRNRandExtraposition,whichIcannotdiscussbecauseofspacelimitations(butseeChaves2012a).MygoalhereistosuggestthatRight-Node-Raisedshareddependentsarealsosubjecttotheshareddependentcumulationphe-nomenon:anysignsselectedasdependentsbyeachoftheconjunctsarecombinedvia`',38 asshown,fortheexamplein(55a)above,inFigure13.If`'isinterpretedasequalitythenweobtainstandardnon-additiveRNR(thestrictidentityreading,wherethetotalofmoneyunderdiscussionis$20,000).If`'isinterpretedasplurality-formingcumulationthenweobtaintheadditiveRNRcases(theweakidentityreading,wherethetotalofmoneyis$10,000).IsuspectthattherearevariouskindsofRN

39 Rconstruction,andthatthekindillustratedb
Rconstruction,andthatthekindillustratedbelowisessentiallyacross-the-boardrightwardextraction,alongthelinesofGazdar(1981);seealsoChaves(2011).Theadverb`respectively'canadjointothecoordinateSeandevokeabijectionasusual,providedthatthereisarankingestablishedbysurfaceorder.InthecaseofFigure13nosuchrankingispossibleandthereforethepresenceof`respectively'isnotfelicitous.Ifarankingcanbeestablished,however,weobtaincaseslike(58)above.Se Se=(e1;e2) Se1 Fredspent x1Se2 andMialost x2NPz=(x1;x2) atotalof$10,000Figure13:Right-NodeRaising5ConclusionThispaperhasarguedthatrespectivelyreadingsaretheconsequenceoftwoindepen-dentlymotivatedphenomenaandthattheroleoftheadverb`respectively'isnottoalterpreviouslyassembledsemanticstructures,butrather,toaddconstraintsonthesemanticsoftheadjoinedphrase.TheadverbisbestviewedasacontextualoperatorinthesenseofKay(1989),whosefunctionistosingleoutone-to-onemappingsaccordingtoanindepen-dentlyestablishedcontextualranking.Accesstosuchrankingsisalsoavailabletootherexpressionsliketheformer,thelatterandinthatorder.Ihaveproposedthattwocom-pletelydistinctandindependentlymotivatedphenomenacanyieldcertaininterpretationswhicharecompatiblewiththepresenceoftheadverb`respectively'.Somerespectivelyreadingsfollowfromaphenomenonusuallycalledcumulativequantication(Scha,1981),andothersarisefromconjunctscumulatingtheirshareddependents.ThegeneralizationunderlingthelattercasesisencapsulatedbytheSubjectDependentConditionforCon-junction,whichstatesthatthei-sumoperationindependentlyproposedbyLink(1983)tomodelnon-Booleanconjunctionisalsorelevantformodelinghowdependentssharedbyconjunctsaresemanticallyintegrated.Inthisview,respectivelyreadingsarebutspecialcasesofawiderrangeofindependentlymotivatedinterpretations.AsfarasIamaware,thisistheonlyanalysisintheliteraturewhichexplainswhyrespectivelyreadingscanarisewithouttheovertrealizationoftheadverb.39 Theproposedanalysisismoreparsimoniousthanitspredecessorsintwocrucialways.First,sentenceshavethesamesyntacticandsemanticstructureregardlessoftherespec-tivelyreading.Second,thereisnoneedforaradicaldecouplingbetweensubcategori

40 zationandpredication.Predicatescandirect
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