LinguistandPhilos DOI10.1007/s10988-014-9162-8 RESEARCH ARTICLE The interaction of compositional semantics and event semantics LucasChampollion ©TheAuthor(s)2014.ThisarticleispublishedwithopenaccessatSpringerlink.com Abstract Davidsonianeventsemanticsisoftentakentoformanunhappymarriage withcompositionalsemantics.Forexample,ithasbeenclaimedtobeproblematicfor semanticaccountsofquantification(BeaverandCondoravdi,in:Alonietal.(eds.)Pro- ceedingsofthe16thAmsterdamColloquium,2007),forclassicalaccountsofnegation (Krifka,in:Bartschetal.(eds.)Semanticsandcontextualexpression,1989),andfor intersectiveaccountsofverbalcoordination(Lasersohn,inPlurality,conjunctionand events,1995).Thispapershowsthatnoneofthisisthecase,onceweabandontheidea thattheeventvariableisboundatsentencelevel,andassumeinsteadthatverbsdenote existentialquantifiersoverevents.Quantificationalargumentscanthenbegivenase- manticaccount,negationcanbetreatedclassically,andcoordinationcanbemodeled asintersection.Theframeworkpresentedhereisanaturalchoiceforresearchersand fieldworkerswhowishtosketchasemanticanalysisofalanguagewithoutbeingforced tomakecommitmentsaboutthehierarchicalorderofarguments,theargument-adjunct distinction,thedefaultscopeofquantifiers,orthenatureofnegationandcoordination. Electronicsupplementarymaterial Theonlineversionofthisarticle(doi:10.1007/s10988-014-9162-8) containssupplementarymaterial,whichisavailabletoauthorizedusers. A30-minutevideoofatalkthatsummarizesandcomplementsthispaperisavailableathttps://www. youtube.com/watch?v=21KxSsIceNgandhasbeenpostedasasupplementalmaterialtothispaper, availableathttp://dx.doi.org/10.1007/s10988-014-9162-8.Thevideowalksthroughthederivationsinthe paperbyusingtheLambdaCalculator(Champollionetal.2007).Thissoftwareapplicationhasalsobeen usedtocheckthederivationsforcorrectnessandtogeneratethefiguresinthispaper.Informationonthe calculator,aswellasabasicversionofthetool,isavailableathttp://www.lambdacalculator.com.Please contactmeviaemailatchampoll@gmail.comforamoreadvancedversionofthecalculator,alongwitha filethatimplementstheformalsystemandderivationspresentedhere. B L.Champollion( ) DepartmentofLinguistics,NYU,NewYork,NY,USA e-mail:[email protected] 123 L.Champollion Keywords Eventsemantics·Thematicroles·Quantifiers·Negation·Coordination· Conjunction·For-adverbials 1 Introduction Ever since Montague famously rejected the contention that there is any important theoretical difference between formal and natural languages, research on composi- tional semantics in his spirit has produced successful accounts of the behavior of scope-takingexpressions(Montague1970).Inparticular,thoseexpressionsinnatural languagethathavecounterpartsinpredicatelogicandrelatedsystems,suchasquanti- fiers,negation,andconjunctions,havebeengivenformalaccounts.Ithasturnedoutin manycasesthatthesecounterparts,orsuitablegeneralizations,areviablecandidates fortheformalrepresentationsofthecoresemanticmeanings,andinparticularofthe scopalproperties,oftherelevantnatural-languageexpressions.Thiscanbeseen,for example,inaccountsofquantificationalnounphrasesintermsofgeneralizedquan- tifiers(BarwiseandCooper1981),inaccountsoftruth-functionallinguisticnegation in terms of logical negation (Horn 1989) and in accounts of coordination in terms of generalized logical conjunction and disjunction (Partee and Rooth 1983). This is perhapsnotsurprisinggiventhat,historicallyspeaking,thedesignofpredicatelogic wasinspiredbynaturallanguage. Another successful tradition in semantics stems from Davidson’s proposal that thelogicalformofactionsentencesmakesreferencetounderlyingevents(Davidson 1967).Buildingonthisidea,semanticresearchhasdevelopedsuccessfulaccountsofa largenumberofphenomenasuchasverbalmodification,therelationsbetweenadjec- tivesandadverbs,therelationsbetweennominalizations,nominalgerunds,andverbs, thesemanticsofperceptionverbs,andthesemanticrelationsbetweenrelatedmembers ofsemanticalternationssuchascausativesandinchoatives(Parsons1990,1995). Iwillcallthetwoframeworksjustmentioned“compositionalsemantics”and“event semantics”.Forthepurposeofthispaper,Itaketheadvantagesofeachofthesetwo frameworkstohavebeenfirmlyestablished.Thenaturalnextquestiontoaskiswhat isthebestwaytocombinethetwo.Thisquestionisrelevantforatleasttwokindsof addressees. – The theoretical researcher may be primarily interested in interactions, such as whetheracommitmenttoeventsimpliesorsuggestsacommitmenttothisorthat analysisofascope-takingexpression–say,whethereventsrequireananalysisof quantifiersinsyntactictermsandacommitmenttoarepresentationalleveldistinct fromsurfaceform.Iwillarguethatitdoesnot,andIwillpresentsimilarkindsof resultsinthecaseofanalysesofnegationandcoordination. – The student and the semantic fieldworker who wish to sketch an analysis of a language without making implicit semantic commitments about the difference between arguments and adjuncts may want to adopt event semantics because it provides the ability to treat them on par. They may also be interested in giving standardanalysesofsuchcommonplacephenomenaasquantifiersandnegation. Thereiscurrentlynoconsensusonwhatisthebestwaytocombinecompositional semanticsandeventsemantics,whetheritispossibleoreasy,andwhatconsequences 123 Theinteractionofcompositionalsemanticsandeventsemantics thepresenceofeventshasontheanalysesofscope-takingexpressionsincompositional semantics.Inmanyimplementationsofeventsemanticsincompositionalframeworks, accountsofscope-takingexpressionssuchasquantifiers,negation,andconjunctions need to be complicated compared with the more standard treatments that would be availableifeventswerenotpresent.Perhapsforthisreason,textbooksofcompositional semanticstendtoavoidusingevents(HeimandKratzer1998).Anaspiringsemanticist or a fieldworker might be discouraged by this situation, particularly when a given languageorphenomenonthatseemstobewell-suitedtoeventsemanticsalsoinvolves scope-takingexpressionsthatneedtobeanalyzedinsomeway. Thispaperaimstoremedythissituationbypresentinganimplementationofevent semantics that combines with standard treatments of scope-taking expressions in a well-behavedway.Iwillcallthisimplementation“quantificationaleventsemantics”. The implementation is then used to show that event semantics is compatible with the standard accounts of scope-taking expressions that have been developed in the traditionofMontague,andthatthepresenceofeventsdoesnotmakeitnecessaryto choosebetweenaccountsoftheseexpressionsinthewayithasbeenclaimed. Forexample,therehasbeenalongdebateonwhetherthescopeofquantificational argumentsisdeterminedsyntactically,forexamplebyquantifierraising(May1985), or semantically, for example by type-shifting (Hendriks 1993). It has been claimed more recently that adopting event semantics bears on this choice in a way that is notseenasadvantageous.Thus,BeaverandCondoravdi(2007)holdthat“[i]nDavid- sonianEventSemanticstheanalysisofquantificationisproblematic:eitherquantifiers aretreatedexternallytotheeventsystemandquantifiedin(Landman2000),orelse the definitions of the quantifiers must be greatly (and non-uniformly) complicated (cf.Krifka1989)”.Theysuggestasanalternativeanonstandardframeworkinwhich verbaldenotationsholdofpartialfunctionsthatmapdesignatedconstantslike“agent” and “theme” to individuals. For related criticism and similar proposals, see Eckardt (2010)andWinterandZwarts(2011).ItakeBeaverandCondoravdi(2007)asarepre- sentativeexampleoftheseproposals(thoughthereareimportantdifferencesbetween them)andIdiscussitinSect.5. Contrary to such claims, I argue that the analysis of quantifier scope does not poseanyspecialproblemsinaneventsemanticframework.Thatis,adoptingoneor the other view on quantifier scope does not entail a commitment on whether events are present in the system. For semanticists who reject quantifying-in or quantifier raising as an option, such as Beaver & Condoravdi and Eckardt, it is possible to adoptasemanticapproach toquantifier scopeinacompletely standardevent-based framework.Conversely,adoptingoneortheotherviewonthepresenceofeventsdoes not force the semanticist to take a stance on whether quantifier scope is determined syntacticallyorsemantically.Schematically,mystrategyconsistsinfillingacornerin the2-by-2matrixthatisopenedbytheparametersmentionedabove(seeTable1). Themaintechnicalinnovationinthispaperwillconsistinabandoningtheideathat theeventvariableisboundatsentencelevel,asisgenerallyassumedincompositional approachestoeventsemantics.Instead,Iwillassumethatverbsandtheirprojections (suchasverbphrasesandsentenceradicals)denoteexistentialquantifiersoverevents. Aswewillsee,thismoveismotivatedbythefactthattheeventquantifieralwaystakes lowestpossiblescope,anditwillturnouttogiveusadditionaldegreesoffreedomthat 123 L.Champollion Table1 Analysesofquantificationandevents Noevents Events Syntacticaccount e.g.May(1985) e.g.Landman(2000) Semanticaccount e.g.Hendriks(1993) Thispaper we can exploit in order to give a semantic account of quantifier scope. Later on we willseethatthesamemovealsomakesitpossibletoadoptaccountsofnegationand conjunctioninwhichtheirdenotationsmirrorthoseoftheircounterpartsinpredicate logic(¬and∧). Thispaperdoesnotpresentindetailsyntacticapproachestoquantifierscope,since theycanbeextendedtoeventsemanticframeworksstraightforwardly;seeLandman (1996, 2000) for an overview. However, let me briefly mention why syntactic ap- proaches have been considered problematic. In these approaches, type mismatches between verbs and quantificational arguments are resolved by movement. This is sometimes perceived as cumbersome. As Eckardt (2010) observes, “the semantic composition of even a simple sentence like John likes most Fellini movies requires quantifierraising,interpretedtraces,coindexing,andlambdaabstraction.”Sincesyn- tacticapproachesrelyoncovertmovement,theyentailthepresenceofarepresenta- tionallevel(LogicalForm)thatisdistinctfromthesurfacelevel.Assuch,theyarenot directlycompositional(Jacobson1999;Barker2002).Finally,thereisanovergenera- tionworry:Inlanguagesandconfigurationswheresurfacescopedeterminessemantic scope(seee.g.BeghelliandStowell1997forEnglish,andC.-T.J.Huang1999;S.-F. Huang1981forChinese),nothingshortofadditionalassumptionsensuresthatraised quantifierskeeptheirrelativeorderthesameasbeforetheyraised. Two caveats before we begin. First, the nonstandard systems in the papers cited abovearemotivatednotonlybytherepresentationofquantificationalargumentsbut alsobyadditionalconsiderations,suchastherepresentationofstackedtemporalmod- ifiersasinOnmostdays,itrainedintheafternoon(BeaverandCondoravdi2007)and theabilitytomakeallargumentsofaverbsemanticallyaccessibleatanypointinthe derivation(Eckardt2010).Second,Idonotconsiderscopelessreadingsofquantifiers, suchascumulativeandcollectivequantificationasinTwentycomposerscollaborated onsevenshows(Schein2002).Thesereadingsincreasethecomplexityofbothevent- basedandeventless grammarsbecause itisnotpossibletoderivethesereadingsby givingonequantifierscopeovertheother.Myomissionisjustifiedbecausetheclaims by Beaver & Condoravdi and Eckardt about the difficulty of integrating quantifier scope and event semantics are not based on these complex cases. In principle the presentaccountcanbecombinedwithmereology-basedanalysesofscopelessread- ingsofincreasingquantifiers,alongthelinesofKrifka(1989)andLandman(2000). Asforscopelessreadingsofnon-increasingquantifiers,thecompatibilityquestionis open;forrelevantdiscussionseeSchein(1993),Krifka(1999)andBrasoveanu(2012). Therestofthepaperisorganizedasfollows.IfirstshowinSect.2thattheexistential quantifierthatbindstheeventvariablealwaystakeslowestpossiblescope.Isuggest that this is because it is contained in the lexical entry of the verb, rather than being introducedatsentencelevel.Ishowthatinthepresenceoftypeshiftingrules,eventse- 123 Theinteractionofcompositionalsemanticsandeventsemantics manticsdoesnotrequireacommitmenttoarepresentationalleveldistinctfromsurface formasfarasquantifiersareconcerned.IthenshowinSect.3thatfixed-scopeoperators likenegationandmodalscanbegivenastraightforwardandstandardtreatment,and thatinparticulareventsemanticsdoesnotmakeitnecessarytoresorttoanon-standard accountofnegationintermsofmereologicalfusionasclaimedbyKrifka(1989).Sec- tion4showsthatcoordinationcanbegivenastandardintersectivedenotationinthe present framework, and critically reviews a claim to the effect that event semantics favorsacollectiveaccountofcoordination(Lasersohn1995).Section5discussesthe eventless system by Beaver and Condoravdi (2007) and shows that most aspects of thatsystemcanbereproducedinthepresentframework.Section6concludes. 2 QuantificationinaNeo-Davidsonianframework Thedifferencebetweensyntacticandsemanticapproachestoquantifierscopeistradi- tionallystudiedinclassicalMontagoviansemanticsystems,whereverbsaretranslated asn-aryrelationsthatholdbetweentheirarguments.Suchatranslationdrawsafirm semanticdistinctionbetween(obligatory)argumentsand(optional)adjuncts.Expres- sions in which some arguments are missing, like kiss Mary or John kissed, are not assignedatruthvalue.Amongalternativesthattreatargumentsandadjunctsonapar, the best-known one is the Neo-Davidsonian approach (Parsons 1990). In a typical instantiation,verbsandalltheirprojectionsuptothesentencelevelaretranslatedas predicatesofevents,andverbalargumentsmodifyeventsviathematicroleslikeagent andtheme.Variationsofthissetuparefound,forexample,inCarlson(1984),Krifka (1989), Parsons (1995) and Landman (2000). At the sentence level, a silent opera- tor (called sentence mood operator in Krifka (1989) or more commonly existential closure)thenbindstheeventargument,typicallywithanexistentialquantifier.Some syntacticmechanism(e.g.thethetacriterion)isassumedtomakesurethattheoperator canonlyapplyonceallthesyntacticargumentsoftheverbhavebeenintroducedtothe derivation,andnotearlier.Forexample,asentencelikeJohnkissedMaryistranslated asfollows,disregardingtense: (1) [[JohnkissedMary]] =∃e.kiss(e)∧ag(e,john)∧th(e,mary) Neo-Davidsonian approaches to event semantics make no difference between argu- ments and adjuncts. They rely on syntactic devices, for example on the theta cri- terion, to label subjectless sentences like kiss Mary as ungrammatical; as far as meaningisconcerned,theycouldassignsuchexpressionsatruthvalue,inthiscase, ∃e.kiss(e)∧th(e,mary).Thedifferencebetweensuchexpressionsandfullsentences is determined by syntax, not by semantics. The specific approach I will adopt is alsoNeo-Davidsonian,butmanyoftheproblemsIwillpointoutwithexistingNeo- DavidsonianapproachesaresharedbyclassicalDavidsoniansystemsinwhichaverb likekissisrepresentedasathree-placerelationbetweenakisser,akissee,andakissing event.Toalargeextent,althoughIwillnotdemonstrateit,thegeneralprinciplesof thesolutionthatIwilladoptcarryovertoclassicalDavidsoniantreatments,because theseprinciplesdonotrelyinanycrucialwayontheassumptionthattheargument- 123 L.Champollion adjunctdistinctioneitherisorisnotrepresentedinthesemantics.Essentially,Iwill adapt type-shifting techniques originally developed for eventless verbal denotations byHendriks(1993).ThesetechniquescanbeadaptedtotheclassicalDavidsoniancase withslightmodificationsandtotheNeo-Davidsoniancasewithlargermodifications. IwilldemonstrateonlytheNeo-Davidsoniancase. Whenaverbalargumentisitselfquantificational,itneedstotakescopeabovethis eventquantifier.Thisisawell-knownfactanditisreflectedinmanyNeo-Davidsonian theories.Forexample,theScopeDomainPrincipleinLandman(1996)statesthatonly nonquantificationalnounphrasescanbe“enteredintoscopedomains”.Inthecontext ofLandman’stheory,where“scopedomain”means“verbaldenotation”,thisprinciple ineffectsaysthatonlynonquantificationalnounphrasescanbeinterpretedinsitu,and ithastheconsequencethatallquantificationalnounphrasesmusttakescopeoverthe eventargument.Forexample,thecorrecttranslationofJohnkissedeverygirlaccording totheScopeDomainPrincipleis(2).Thisrepresentsthefactthatthesentenceentails thatforeverygirl,thereisaseparateeventinwhichJohnkissedthatgirl.Forexample, thesentenceJohnkissedMaryisrepresentedas(3).Itfollowslogicallyfrom(2)given theadditionalassumptionthatMaryisagirl(4). (2) [[Johnkissedeverygirl]] =∀x[girl(x)→∃e[kiss(e)∧ag(e,john)∧th(e,x)]] (3) [[JohnkissedMary]] =∃e[kiss(e)∧ag(e,john)∧th(e,mary)] (4) [[Maryisagirl]] =girl(mary) The alternative translation in which the event quantifier takes wide scope, (5), expressesthatthereisasingleeventwhichwasaneventofJohnkissingeverygirl. This contradicts not only the Scope Domain Principle and related assumptions, but alsoourintuitionsaboutkissing,sincewethinkofdifferentkissingsasdifferentevents andtheseeventsarenotrepresented.Thefollowingtranslationthereforedoesnotseem torepresentanyreadingofthesentence. (5) [[Johnkissedeverygirl]](problematictranslation) =∃e[kiss(e)∧ag(e,john)∧∀x[girl(x)→th(e,x)]] The translation is problematic, not because it makes available a single event, but becauseitdoesnotmaketheindividualkissingeventsavailable.Thisisnottodeny thatasingle(complex)mightbeultimatelyneeded.Thesentencemightbetrueeven iftheindividualkissingsonlytookasecond.ItispossibletofollowitupwithIttook verylong,asareviewernotes.Thissuggeststhattherepresentationneedstoprovidea complexeventthatmightbethoughtofasthefusionofallthedistinctkissingevents. Theanaphoricvariableitcanthenreferbacktothatcomplexevent.Otherarguments for this kind of complex events are provided by Schein (1993) and Kratzer (2000) onthebasisofcumulativereadingsofsentenceslikeThreecopyeditorscaughtevery mistakeinthemanuscript.Forasummaryandacriticaldiscussionofthesearguments, seeChampollion(2010a).HereIfocusontheindividualeventsthatcorrespondtothe 123 Theinteractionofcompositionalsemanticsandeventsemantics separatekissings.IcomebacktofusioneventsinSect.3.TheendofSect.5sketches anextensionofthepresentaccounttointersententialanaphorathatislaidoutinmore detailinChampollion(toappear-a). In general, the event quantifier always takes lowest possible scope with respect tootherscope-takingelements.Forexample,sentence(6)onlyhasthereading(7a) and cannot mean (7b). While (7b) might be ruled out for independent reasons (for examplebecausealmosteveryeventwilltriviallymakeittrue),thefactremainsthat thequantifiernoboymustbeabletotakewidescopewithrespecttotheeventquantifier in order to derive the reading (7a). Even with respect to fixed-scope operators like negation,theeventquantifieralwaysseemstotakelowscope(8). (6) Noboylaughed. (7) a. ¬∃x[boy(x)∧∃e[laugh(e)∧ag(e)= x]] ¬∃x (cid:6)∃e “Thereisnolaughingeventthatisdonebyaboy.” b. ∃e[¬∃x[boy(x)∧laugh(e)∧ag(e)= x]] *∃e(cid:6)¬∃x “Thereisaneventthatisnotalaughingbyaboy.” (8) Johndidn’tlaugh. (9) a. ¬∃e[laugh(e)∧ag(e)=john] ¬(cid:6)∃e “ThereisnoeventinwhichJohnlaughs.” b. ∃e¬[laugh(e)∧ag(e)=john] *∃e(cid:6)¬ “ThereisaneventinwhichJohndoesnotlaugh.” Anadditionalreasonforgivinglowscopetotheeventquantifierismoretheory- internal:ManyNeo-Davidsonianframeworksassumethatthematicrolesarefunctions (theUniqueRoleRequirement,Carlson1984;Parsons1990;Landman1996,2000). Thishastheeffectofmakingthewrongtranslation(5)acontradictioninallmodelsin whichthereismorethanonegirl,sincetheUniqueRoleRequiremententailsthatno morethanonegirlcanbethethemeofakissingevent.Theanalysistobedeveloped here can accommodate the Unique Role Requirement. For clarity, I will represent thematic roles using functional notation from now on, e.g. “th(e) = x” instead of “th(e,x)”. Asdescribedabove,typicalinstantiationsoftheNeo-Davidsonianframeworkapply existentialclosuretotheeventquantifieratsentencelevel(e.g.Krifka1989;Parsons 1995; Landman 1996). Therefore, any theory of quantifier scope needs to give all argument quantifiers the ability to take scope above the sentence level to derive the correcttruthconditions.[SomeinstantiationsapplyexistentialclosureattheVPlevel, andregardsubjectsasoutsidetheVP,e.g.Carlson(2003)followingDiesing(1992). In this case, only argument quantifiers within the VP, such as the object quantifier, needtobegiventheabilitytotakescopeaboveVPlevelinordertoderivethecorrect truthconditions.]Itisherethatadifferencebetweensyntacticandsemantictheories ofquantifierscopearises. ForsyntactictheoriessuchasMay’sQuantifierRaising(QR),itisnoproblemto raise a quantifier above sentence level; this is in fact their normal operating mode. ThisisillustratedinFig.1.Forconvenience,IhavefollowedLandman(1996,2000) inplacingthethematicrolesdirectlyintotheverbmeaning,butthisisnotcrucial. 123 L.Champollion Fig.1 “Johnkissedeverygirl”inaneventframework,usingquantifierraising By contrast, many semantic theories are designed to allow quantifiers to be in- terpreted in situ. Some examples are the argument raising rule of Hendriks (1993), thetype-shiftingruleforquantifiers presented inthetextbook byHeimandKratzer (1998), and the continuation passing style transforms used in Barker (2002). Many such theories amount to lifting the type of the verb or verbal projection so that it expectsaquantifierinsteadofanindividual-typeargument.Incaseaverbcombines withmultiplequantifiers,itstypecanbeliftedseveraltimes.Theorderinwhichthese liftingoperationsareappliedtotheverbdeterminesthescopeofitsarguments.Forex- ample,inHendriks’system,theorderinwhichtheargumentraisingruleisappliedto atransitiveverbdeterminesthescopethatitsquantificationalargumentstaketowards eachother. IntheNeo-Davidsonianframeworkdescribedabove,theeventquantifierisintro- ducedbyexistentialclosureafteranyotherquantifiers,butitalwayshastotakescope under allofthem.InaHendriks-stylesystem,thisrequires thatevery verbbetype- liftedfortheeventquantifierthatcomesintheguiseofexistentialclosure.Butsince every sentence contains this event quantifier, one might then as well rewrite lexical entriesofverbstoincorporatetheexistentialclosureovertheireventargument. Thisleadsmetothemaintechnicalinnovationandthecentralclaimofthispaper. Iproposethatverbsarenotinterpretedaspredicatesofevents(10),butaspredicates that hold of sets of events (11). Conceptualizing Neo-Davidsonian event semantics thiswayrequiresashiftinthinking.Insteadofdenotingthesetofallrainingevents, 123 Theinteractionofcompositionalsemanticsandeventsemantics thinkofapredicatelike“rain”asbeingtrueofanysetthatcontainsarainingevent.I letthevariable f rangeovereventpredicates. (10) Previous(Neo-Davidsonian)approachestoeventsemantics: [[rain]]=λe[rain(e)] (11) Thisapproach: [[rain]]=λf∃e[rain(e)∧ f(e)] Onthenewview,whichIwillrefertoasquantificationaleventsemantics,averbwill betrueofanysetofevents f solongas f contains(possiblyamongotherthings)an eventthatsatisfiestherelevanteventpredicate. Assumingthattheverbraindoesnottakeanysemanticallyvisiblearguments,and ignoringtenseandaspectfornow,thetruthconditionsofasentencelikeitisraining canbeobtainedbycheckingwhetherthesetofalleventswhatsoever,λe.true,hasthe propertydenotedbytheverb.Themeaningofitisrainingcomesoutasfollows: (12) [[Itisraining]] a. =λf∃e[rain(e)∧ f(e)](λe.true) b. =∃e[rain(e)∧(λe.true)(e)] c. =∃e[rain(e)∧true] d. =∃e[rain(e)] Sincethisproposalisthecoreofthispaper,letmerestatethemotivationforthis move to the extent that I have presented it so far, and provide some explanation of theintuitionbehindthisidea.Thereisaconceptualdifferencebetweenthequantifiers that are used to capture the semantic behavior of quantificational noun phrases and theexistentialquantifierthatbindstheeventvariable.Theformernotonlycapturethe semanticsofquantificationalnounphrasesbutalsotheirscopalambiguityinlanguages likeEnglish.Thevariouswaystoarrangequantifiersinlogicalformulascorrespondto thedifferencesinmeaningbetweenreadingsofscopallyambiguoussentenceslikeA diplomatvisitedeverycountry.Thelattercapturestheindefinitenatureofevents.But herethereisnocounterparttothescopalambiguityofquantificationalnounphrases. As we have seen above, event quantifiers always take lowest possible scope. In this respecttheyarearguablylesslikeordinaryquantificationalargumentsandmorelike bareplurals(seeDayal2011forarecentoverview).Thesimplestwaytomodelthis factcompositionallyistointroducetheeventquantifierattheplacewhereitisobserved tooccur,namelyaslowaspossible.Puttingexistentialclosureintothelexicalentryof theverbwillautomaticallyderivethefactthatallotherquantifiersalwayshavetotake scopeaboveexistentialclosure.ThismoveisreminiscentofthewayCarlson(1977) puts existential quantification over stages into the lexical semantics of stage-level predicates, thereby ensuring that bare plurals can denote kinds and their existential importtakesnarrowestscope. Theentryin(11)canbederivedfromtheonein(10)bythetype-shiftingprinciple AinPartee(1987),butthisparallelshouldbetakenwithagrainofsalt.Typeshifting is generally understood to occur “online” during the computation of the meaning ofasentence,whilequantificationaleventsemantics,thepresentproposal,appliesit 123 L.Champollion “offline”inthelexicon.Themovefrom(10)to(11)isbetterunderstoodasanoperation that rewrites an entire grammar, similarly to the continuization procedure in Barker (2002). Wewillletnotonlyverbsbutalltheirprojectionsholdofsetsofevents.Forexample, wecanthinkofaverbphraselike“seeMary”asbeingtrueofanysetthatcontainsa seeingeventwhosethemeisMary. (13) [[seeMary]]=λf∃e[see(e)∧ f(e)∧th(e)=mary] Changingthetypeofverbsandverbalprojectionsfromsetsofeventstosetsofsets ofeventspavesthewayforanumberoftheoreticalmoves,andtherestofthispaper is devoted to them. For example, quantificational event semantics gives us a handle oninterpretingquantifiersinsitu.Ontheoldapproach,averbphrasehadtobetrue ofanevent,soitwasnotclearwhatkindofeventaverbphraselike“kisseverygirl” couldbetrueof.Nowthatverbphrasesholdofsetsofevents,wecanformulatethe meaningofverbphrasescontainingquantifiersinanintuitiveway:“kisseverygirl” istrueofanysetofeventsthatcontainsapotentiallydifferentkissingeventforevery girl. (14) [[kisseverygirl]] =λf∀x[girl(x)→∃e[kiss(e)∧ f(e)∧th(e)= x]] Forsimpledeclarativesentences,westillneedasentence-leveloperator,butithasa functionsomewhatdifferentfromexistentialclosure:Itassertsthatthepredicateistrue ofthesetofallevents.Intuitively,onemightthinkoftheworldasthesetofallevents that exist. Then, the sentence-level operator asserts that the sentence is true of the world.Asusual,Iassumethatsyntaxisresponsibleformakingsurethattheoperator onlyappliesonceallthesyntacticargumentsoftheverbhavebeenintroduced. (15) [[[closure]]]=λe.true Thissimplepicturecanberefinedbyrestrictingthesetofeventsdenotedbytheclo- sureoperatorinvariousways,and/orbyintroducingadditionaloperators.Forexample, if we believe that certain sentences involve definite rather than indefinite reference, saytoaparticularevente ,wecouldsupplythisbyadefiniteclosureoperatorwith 0 themeaningλe.e=e .Or,wemaywishtoaddprojectionsfortense,aspect,perfect, 0 etc.abovetheeventlevel,inthestyleofIatridouetal.(2001).Iwillnotspelloutthese refinementshere,butSect.3hasanimplementationofasimpletreatmentoftense. ThisclosureoperatorissimilartothedownarrowoperatorofDynamicMontague Grammar,whichmapsthedynamicinterpretationofasentencetoatruthvalue(Groe- nendijk and Stokhof 1990), and to the Lower operator of Barker and Shan (2008), which does the same for a continuized interpretation by applying itto a trivial con- tinuation.Allthesetypeshiftersareusedtosimilareffectintheirrespectivesystems: Theystripawaythelayersofcomplexityintroducedbythesemanticmachineryand mapapredicatetowhatareintuitivelyitstruthconditions. Itreatnounphrasesasgeneralizedquantifiersoverindividuals(type(cid:7)et,t(cid:8)).This partoftheanalysisiscompletelystandard.Iuse P forpredicatesofindividuals(type (cid:7)et(cid:8)): 123