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Parts of a whole: Distributivity as a bridge between aspect and measurement Lucas Champollion Final preprint, as submitted to the publisher on June 15, 2016 Contains table of contents, introduction, and conclusion Distributed with permission of Oxford University Press Contents ￿Overview ￿￿ ￿.￿ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ ￿ecentralmetaphor . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Overviewofthingstocome . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Waystoreadthisbook . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿ ￿estage ￿￿ ￿.￿ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Notationalconventions . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Mereology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Foundationsofalgebraicsemantics . . . . . . . . . . . . ￿￿ ￿.￿.￿ Axiomatizationsofclassicalmereology . . . . . . . . . . ￿￿ ￿.￿.￿ Mereologyversussettheory . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Algebraicclosure,atomicityandgroups . . . . . . . . . ￿￿ ￿.￿.￿ Higher-orderproperties . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Ontology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Ordinaryobjects(type e) . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Kinds(type e) . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Events(typev) . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Intervals(type i) . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Degrees(typed) . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Numbers(typen) . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ ￿ematicroles(type v,e ). . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Tracefunctions: runtimeandlocation(type v,i ) . . . ￿￿ ￿ ￿ ￿.￿.￿ Measurefunctions(types e,d and v,d ) . . . . . . . ￿￿ ￿ ￿ ￿.￿.￿ Unitfunctions(types d,n and i,n ) . . . . . . . . . . ￿￿ ￿ ￿ ￿ ￿ ￿.￿.￿ ￿ecardinalityfunction(type e,n ) . . . . . . . . . . . ￿￿ ￿ ￿ ￿ ￿ ￿.￿ Nouns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿ ￿ ￿.￿.￿ Singularcountnouns . . . . . . . . . . . . . . . . . . . . ￿￿ CONTENTS ￿ ￿.￿.￿ Pluralcountnouns . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Measurenouns . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Groupnouns . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Massnouns . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ Kind-referringreadings . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Verbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿.￿ ￿eNeo-Davidsonianpositionanditsalternatives . . . ￿￿ ￿.￿.￿ Lexicalcumulativity . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Nounphrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Prepositionalphrases . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿￿ ￿ecompositionalprocess . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿ ￿ecastofcharacters ￿￿ ￿.￿ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Pseudopartitives . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ For-adverbials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿ ￿.￿ Adverbial-eachconstructions . . . . . . . . . . . . . . . . . . . . ￿￿ ￿ ￿etheory ￿￿￿ ￿.￿ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Whatisdistributivity? . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Quanti￿cationaldistributivity . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Relationaldistributivity . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Predicativedistributivity . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Distributiveconstructions . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ For-adverbialsaredistributiveconstructions . . . . . . ￿￿￿ ￿.￿.￿ Pseudopartitivesaredistributiveconstructions . . . . . ￿￿￿ ￿.￿ ￿ecomponentsofadistributiverelation . . . . . . . . . . . . . ￿￿￿ ￿.￿ ￿econstraintsondistributiveconstructions . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Capturingpredicativedistributivity . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Adverbialeach . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Temporalfor-adverbials . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Pseudopartitives . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Unifyingtheconstraints . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Compositionalimplementation . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿ CONTENTS ￿ Minimalparts ￿￿￿ ￿.￿ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ ￿eminimal-partsproblem . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ ￿eminimal-partsproblemforverbalpredicates . . . . ￿￿￿ ￿.￿.￿ ￿eminimal-partsproblemformassnouns . . . . . . . ￿￿￿ ￿.￿ Previousaccountsoftheminimal-partsproblem . . . . . . . . . ￿￿￿ ￿.￿.￿ Dowty￿￿￿￿ . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Hinrichs￿￿￿￿ . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Moltmann￿￿￿￿,￿￿￿￿ . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Link￿￿￿￿b. . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Borik￿￿￿￿ . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Summingup . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Strati￿edreferenceasasolutiontotheminimal-partsproblem ￿￿￿ ￿.￿ Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿ Aspectandspace ￿￿￿ ￿.￿ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Subregionsversusstrata . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Implementationsofbothapproaches . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Dowty￿￿￿￿andmyproposal . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Krifka￿￿￿￿ . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Comparingtheapproaches . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ ￿esubregion-basedapproach . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ ￿estrata-basedapproach . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿ Measurefunctions ￿￿￿ ￿.￿ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Constraintsonmeasurefunctions . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Previousaccounts . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Stratatheoryandmeasurement . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿ Covertdistributivity ￿￿￿ ￿.￿ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Atomicdistributivity . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ CONTENTS ￿ ￿.￿ Nonatomicdistributivity . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ ReformulatingtheDandPartoperators . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Previousworkonevent-baseddistributivityoperators . . . . . ￿￿￿ ￿.￿ ￿escopalbehavioroffor-adverbials . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿ Overtdistributivity ￿￿￿ ￿.￿ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Overtdistributivityacrosslanguages . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Relatingovertandcovertdistributivity . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Somemorecomplicatedcases . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ EachasaPPmodi￿er . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ Jeweilsdistributingoveraconjunctionofverbs . . . . . ￿￿￿ ￿.￿.￿ Jeweilsinsubjectposition. . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿.￿ ReverseDP-internaldistributivity . . . . . . . . . . . . . ￿￿￿ ￿.￿ Distributivedeterminers . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Zimmermann’sgeneralizationexplained . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Previouswork: Zimmermann￿￿￿￿b . . . . . . . . . . . . . . . . ￿￿￿ ￿.￿ Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿￿ Collectivityandcumulativity ￿￿￿ ￿￿.￿ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿￿.￿ Allandmaximality . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿￿.￿ Numerous-typepredicates . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿￿.￿ Gather-typepredicates . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿￿.￿ Whyalldistinguishesbetweennumerousandgather . . . . . . . ￿￿￿ ￿￿.￿ Meaningshi￿e￿ectstriggeredbyall . . . . . . . . . . . . . . . . ￿￿￿ ￿￿.￿ Fromalltoeach: Di￿erentgranularitylevels . . . . . . . . . . . ￿￿￿ ￿￿.￿ For andallblockcumulativereadings . . . . . . . . . . . . . . . ￿￿￿ ￿￿.￿ Openproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿￿.￿￿ Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿￿ Conclusion ￿￿￿ ￿￿.￿ Chapter-by-chaptersummary . . . . . . . . . . . . . . . . . . . . ￿￿￿ ￿￿.￿ Futurework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ￿￿￿ Acknowledgments ￿is book is a substantially revised and extended version of my dissertation, Champollion￿￿￿￿b,whichintroducedtheframeworkofstratatheorycentered around the notion of strati￿ed reference. It incorporates subsequent work as describedbelow. ￿estoryofthisworkbeginsinthesummerof￿￿￿￿. Ihadbeenagraduate studentattheUniversityofPennsylvaniaforfouryears,andIwasjustaboutto ￿nishasummerinternshipatthePaloAltoResearchCenter(PARC).Partlydue toitsproximitytoStanfordUniversityandSiliconValley,PARCwasagreatplace todoresearchattheintersectionoflinguisticsandcomputerscience. Among otherthings,Ihadbeentryingtohacksomenotionofaspectintothenatural languagesemanticpipelinetheywererunningatthetime. Ienjoyedthistask: I couldfeelliketherealcomputationallinguistthatpartofmehasalwayswanted tobe,andstillreadsemanticspapersalldaylong. ￿enmysupervisors,Cleo CondoravdiandDannyBobrow,askedmeifIwantedtomovetotheWestCoast andturnmyaspectprojectintoadissertationthere. Noneofusknewbackthen whatitwouldbeaboutandhowmuchcomputersciencetherewouldbeinit. In theend,thereisnoneinitatall. I’mdeeplygratefultoCleoandDannyforthe trustandenthusiasmwithwhichtheyembarkedonthisprojectwithme. Cleowasthenaturalchoiceasmydissertationadvisor,andIhaven’tregretted that choice a single time. Perhaps most importantly for me, she le￿ me the freedom to take this enterprise in whatever direction I wanted. ￿is is not to say that she was ever disinterested or not fully engaged, despite her many responsibilitiesatPARC.Cleokepto￿eringpatientencouragementthroughout themanyunexpectedturnsthisworktook,andshealwayshadtherightamount ofclearadviceattherighttime. SheintroducedmetothePARCandStanford communities,andoverthecourseofnumeroushikingtrips,alsotothebeauty oftheBayArea. I’m deeply grateful to the chair of my dissertation, Aravind Joshi. He has beenunerringlysupportiveashesponsoredmy￿rststayatPennasanexchange student,andlateronasIfoundmywaythroughgraduateschoolbetweenformal languagetheoryandformalsemantics. Hesel￿esslysupportedmydecisionto CONTENTS ￿ moveawayfromPennandfromhisownresearchagenda. ￿e other members of my dissertation committee were Maribel Romero andFlorianSchwarz. Maribeldrewmerightintosemanticsfromthevery￿rst classItookwithheratPennin￿￿￿￿. HerclasseswerethebestIevertook. Her approachtosemanticsmightwellshapemyownworkmorethanIknow. Like everyoneelse,Ilookedoninamazementasshechangedjobs,movedacrossthe oceantoKonstanz,foundedafamily,becamedepartmentchair,andkeptaneye onmydissertationallatonce. Iamgratefultoherforhergeneroushelp. ￿ere’s nowaytosneaka￿awedlinguisticargumentpasther,thoughI’msurethisbook containsmanythatshehaslonggivenupontryingtocorrect. AlthoughFlorianSchwarzjoinedPennandthecommitteeonlyshortlybe- fore the dissertation was completed, he worked his way into the project with remarkablespeedandmadeanimpactonit,especiallybychallengingtheway Ioriginallycharacterizedstrati￿ed-referenceconstraintsaspresuppositions. I thankhimfornumerousdetailedcommentsandforhisenthusiasticapproach totheenterprise. Itwasagreatpleasuretohavehimonthecommittee. TonyKrochservedonthedissertationcommitteeforagoodyearorso. I’m gratefulthathedid,andI’mgladhestayedaroundevena￿erheo￿ciallyle￿. I thankhimforgivingmethebene￿tofthedoubtearlyon,forencouragingmeto bebold,andfornotthinkingthathise￿ortswerelostonme. Tonynevermadea secretofhisopinionwhenhethoughtIwasheadedthewrongway,andgiven mypersonality,Ithinkhedeservescreditforthat. Ihavealotofpeopletothankforteachingmelinguistics,engagingwithmy ideas, and making sure that writing the dissertation and this work was not a lonelybusiness.Itwouldbeimpossibletothankeveryone,andifyoufeelunjustly omittedfromwhatfollows,youmostlikelyare. ￿e late Ellen Prince took me seriously when I was still green behind the ears,andIhearsheputinagoodwordformewhenIwantedtojoinPenn. I regretnothavingspentmoretimewithher. MyMaster’sdegreeadvisor,MitchMarcus,hasbeensupportivethroughout mytimeatPenn,anditislargelythankstohisandAravind’se￿ortsthatIcould navigatethegapbetweenlinguisticsandcomputerscience. I am grateful to my fellow graduate students at Penn from ￿￿￿￿ to ￿￿￿￿, particularlyAviadEilam,KeelanEvanini,EvaFlorencioNieto,JonathanGress- Wright,CatherineLai,LucyLee,LaiaMayol,Jean-FrançoisMondon,andJosh ￿ CONTENTS Tauberer. ￿eyplowedthroughtheendlesscourseworkwithme,enduredmy islandviolations,andneverlostpatiencewithmyunendinghungerforgram- maticalityjudgments. It’sbeengreatlivingwithmylinguistroommatesAriel Diertani,JonathanGress-Wright,LaurelMacKenzie(nowmycolleagueatNYU), LaiaMayol, andSatoshiNambuat￿￿￿￿SpruceSt. IespeciallythankSatoshi forhelpingmeprintandsubmitthedissertationwhileIwasinEurope. Ithank Yanyan Sui for being who she is, for giving me a glimpse of Chinese, and for showingmethemanywayshowtoopenanorange. JeeyoungKim,AngelaLee and her Highness Leslie Williams of Sansom Place helped me get away from linguisticsonceinawhileandmadesureIdidn’ttakemyselftooseriously. Iamgratefultothefacultyandadministratorsatthelinguisticsdepartment atPenn,particularlytoGeneBuckleyandAmyForsyth,fortheirsupportand formakingitpossibleformetospendtimeatPARCandStanford. Ialsothank PennforsupportingmethroughaBenjaminFranklinfellowship,aDissertation Completionfellowship,andvarioustravelgrants. ComingtoPenninthe￿rstplacewasn’teasy,andmanypeoplepreparedand supportedmeontheway. Ithankmyteachers,especiallymyhighschoolEnglish teacher,PeterSchneider. AttheUniversityofFreiburg,UdoHahnintroduced metocomputationallinguistics,recommendedPenntome,andspentagreat deal of his time helping me get there. I’m grateful to the German Academic ExchangeService(DAAD)for￿nancingmy￿rstyearofstudiesatPenn. Ithank theStudiensti￿ungdesdeutschenVolkesfortheirsupportaswell. MovingontoCalifornia,IgratefullyacknowledgePARCforprovidingme withastipendandano￿ce. Manythankstothelinguistswhowereworkingat PARCwhileIwasthere,especiallytoDannyBobrow,CleoCondoravdi,JiFang, LauriKarttunen,JohnMaxwell,andAnnieZaenen. ImetLizCoppockatPARCwhenshewasworkingonspatialaspect.￿rough workingwithher,IwaseventuallyledtotheideasinChapter￿.I’mgratefultoher forhercommentsonthatchapterandformanyconversationsonsemantics.Scott GrimmwasalsoatPARCandattheStanfordlinguisticsdepartmentwhenIwas thereando￿eredcommentsandgeneroushelponpseudopartitives(Chapter￿) and other topics. Also at Stanford, I thank the faculty, especially Johan van Benthem,PaulKiparsky,BethLevinandChrisPotts,forgivingmeopportunities tositintheirclassesandtopresentmywork. I’mgratefultoEricActon,David Clausen,AlexDjalali,JasonGrafmiller,ChigusaKurumada,SvenLauer,Jack CONTENTS ￿ Tomlinson,andmyotherfriendsatthelinguisticsdepartmentformanyfunand thoughtfulconversations. IthankPennandStanfordforlettingmetakepartin theexchangescholarprogram,whichwashighlybene￿cialtothiswork. I￿nishedthedissertationin￿￿￿￿asapostdocattheuniversityofTübingen, where Sigrid Beck, Fritz Hamm, Gerhard Jäger have been fostering a lively research environment with help from their wonderful administrators, Sonja Haas-GruberandBeateStarke. Iamgratefultoallofthemandtothelinguist friendsImadethere,particularlyNadineBade,VeraHohaus,AnnaHowell,and SonjaTiemann. SvetaKrasikovahadunfortunatelyalreadyle￿Tübingenbythe timeIarrived,butshewasstillthereo￿enenoughtogivemevaluablecomments. I applied for my current position at NYU with a research program based on the dissertation. I have pursued it since I joined the department in ￿￿￿￿. ￿is book summarizes its current state, and I believe it is a stable foundation for future theory-building. I am grateful to the remarkably talented students here and to my semanticist colleagues, Chris Barker, Philippe Schlenker, and Anna Szabolcsi, for the vibrant research environment they have created and formanyconversationsinvolvingvariousaspectsofthiswork. Forhelpingme inmanyways,Iamalsogratefultothesta￿,particularlyAuraHolguin,Mike Kennedy,TeresaLeung,andEddieQuiles.Amongmynonsemanticistcolleagues, IowespecialthankstoChrisCollinsforhisencouragementandforhisdetailed commentsonChapters￿and￿. Amongthestudents,Iamespeciallygrateful to Hanna Muller and Linmin Zhang for helping me run web surveys that I occasionallyusedtocon￿rm(orinonecase,asdescribedbelow,todiscon￿rm) assumptionsIhadmadein￿￿￿￿aboutthemeaningandacceptabilityofvarious sentences. Inthisconnection,IthankMichaelYoshitakaErlewineandHadas Kotekforprovidingtheopen-sourceso￿warepackageTurktoolstothesemantics community(Erlewine&Kotek￿￿￿￿). Ihavebene￿tedfrommanydiscussionsingraduateseminarsaboutthiswork that I taught at NYU in ￿￿￿￿ and ￿￿￿￿, and in summer school courses that I taught at ESSLLI ￿￿￿￿ and at the ￿￿￿￿ LSA summer institute. Teaching these courseswasincrediblyinspiring,andIamverygratefultothestudentswhotook partinthem. Someofthechangesinthisbookoriginatedindiscussionsinthese courses. IowespecialthankstoJeremyKuhn,whotookpartinthesecondNYU seminarandwhosubsequentlypresentedhisworkonthewordallasKuhn￿￿￿￿. Jeremy’sin￿uenceisre￿ectedandacknowledgedthroughoutChapter￿￿. ￿￿ CONTENTS Ipublishedanoverviewofstratatheoryasatargetarticleintheopenpeer review journal ￿eoretical Linguistics (Champollion ￿￿￿￿c). I thank Manfred Krifkaforencouragingmetowritethatarticle,andIamindebtedtohimandto Hans-MartinGärtnerfortheirhelpaseditors. Iamgratefultotheauthorsof theresponsestothatarticle(Corver￿￿￿￿,Doetjes￿￿￿￿,Link￿￿￿￿,Piñón￿￿￿￿, Schwarzschild￿￿￿￿,Syrett￿￿￿￿). ￿eseresponsespromptedmetointroducea numberofre￿nementstothetheory,asdescribedindetailinmyreplyarticle (Champollion￿￿￿￿b). ￿isbookhasbeenupdatedtore￿ectthesere￿nements. AprecursorofChapter￿waspublishedasChampollion￿￿￿￿.Twohandbook articles,ChampolliontoappearandChampollion&Krifkatoappear,arebased inpartonthedissertation. Whilepreparingthem,Ihavedrawnprimarilyon the background material in Chapters ￿ and ￿. ￿is has led to revisions to the text,someofwhichIhaveincorporatedbackintothisbook. ￿epresentationin Chapter￿drawsinpartonSection￿ofChampollion￿￿￿￿bandonSection￿of Champollion￿￿￿￿c. Chapters￿,￿,￿,￿,￿,and￿havebeenonlylightlychanged,mostlytoimprove presentation. Chapter￿hasbeenpartlyrewritten. Ihaveremoveddiscussionsof frequencyadverbsthatwastangentialtoitsmainsubject,andofageneralization (labeled the “su￿ciently-many events” observation) based on subtle gradient judgmentsthatIhavesincethentriedandfailedtoreproduceexperimentally incollaborationwithHannaMullerandLinminZhang. Ihaveexpandedthe sectiondescribingmyaccount. Chapter￿hasundergonesigni￿cantexpansionandchangescomparedwith thedissertation,leadingtoitspublicationasanarticleintheopen-accessjournal Semantics&Pragmatics(Champollion￿￿￿￿a),whichisreprintedherewithslight modi￿cations. A closely related proceedings paper, Champollion ￿￿￿￿, is not includedinthisbook,butitscontentsarereferencedattheappropriateplaces. Chapter￿isbasedonworkIcarriedoutattheUniversityofTübingenand atNYUa￿erthedissertationwascompleted. Itsmainideashaveappearedas a short proceedings paper (Champollion ￿￿￿￿). Just as the previous one, this chapter has been published in its current form as a Semantics & Pragmatics article(Champollion￿￿￿￿c)andisreprintedherewithslightmodi￿cations. For theirhelpwiththetextofChapters￿and￿,Iamgratefultothejournaleditors, particularlyKaivonFintelandKjellJohanSæbø,andtothejournalreviewers, particularlyMalteZimmermann.

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For-adverbials are distributive constructions . . approach to semantics might well shape my own work more than I know. Like everyone I thank my teachers, especially my high school English teacher for future theory-building. is gives rise to the well-known Formally, this effect.
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