Semantics & Pragmatics Volume 12, Article 1, 2019 https://doi.org/10.3765/sp.12.1

This is an early access version of

Champollion, Lucas, Dylan Bumford & Robert Henderson. 2019. Donkeys under discussion. Semantics and Pragmatics 12(1). 1–50. https://doi.org/ 10.3765/sp.12.1.

This version will be replaced with the final typeset version in due course. Note that page numbers will change, so cite with caution.

©2019 Lucas Champollion, Dylan Bumford, and Robert Henderson This is an open-access article distributed under the terms of a Creative Commons Attribution License (https://creativecommons.org/licenses/by/3.0/). early access

Donkeys under Discussion*

Lucas Champollion Dylan Bumford New York University University of California, Los Angeles

Robert Henderson University of Arizona

Abstract Donkey sentences have existential and universal readings, but they are not often perceived as ambiguous. We extend the pragmatic theory of non-maximality in plural definites by Križ (2016) to explain how hearers use Questions under Discussion to fix the interpretation of donkey sen- tences in context. We propose that the denotations of such sentences involve truth-value gaps — in certain scenarios the sentences are neither true nor false — and demonstrate that Križ’s pragmatic theory fills these gaps to gen- erate the standard judgments of the literature. Building on Muskens’s (1996) Compositional Discourse Representation Theory and on ideas from superval- uation semantics, we define a general schema for dynamic quantification that delivers the required truth-value gaps. Given the independently motivated pragmatic theory of Križ 2016, we argue that mixed readings of donkey sentences require neither plural information states, contra Brasoveanu 2008, 2010, nor error states, contra Champollion 2016, nor singular donkey pro- nouns with plural referents, contra Krifka 1996, Yoon 1996. We also show that the pragmatic account improves over alternatives like Kanazawa 1994 that attribute the readings of donkey sentences to the monotonicity properties of the embedding quantifier.

* We are grateful to Chris Barker, Justin Bledin, Adrian Brasoveanu, Simon Charlow, Cian Dorr, Jan van Eijck, Daniel Hoek, Makoto Kanazawa, Manuel Križ, Sophia Malamud, Chris Potts, Philippe Schlenker, Anna Szabolcsi, and audiences at SALT 26, New York University, and the University of Delaware for helpful feedback and comments. An earlier version of parts of this paper has been published by the first author as Champollion 2016. We wish to thank our reviewers and our editor, Paul Elbourne. We are also grateful to Todd Snider for his careful proofreading of the manuscript. All remaining errors are ours. early access 1 osre,i h iuto utdsrbd sentence described, just situation the in observes, Krifka As for As ekraigi h oial togro h two. the of stronger logically the is reading weak 1 ambiguity (existential/universal) truth-value weak/strong trivalence, gaps, interface, semantics/pragmatics Discussion, under Question medn eemnri onadmntn nisncersoe si h aeof case the in as scope, nuclear its in monotone downward is (a determiner embedding closed are doors Kanazawa As the of all that fact the any through ( accessible is that safe a doors. has three bank of local one the where situation a in the Krifka Imagine from definites. adapted plural sentences, of following interpretations non-maximal and maximal to or reading universal the as it to refer ∀ will we and interpretation, universal as paraphraseable following interpretation; existential is This or window). weak one a ( than Chierchia as more to has referred actually sometimes garage the that implication as paraphrased pronoun donkey the to which in interpretations aside Setting ( following The Yoon force. from understood universal adapted having be is as to pair others seem and pronouns force donkey existential some having that as observation old an is It Keywords: 2 1 Uuly famnhsagrg ihawno,... . . window, a with garage a has man a if Usually, ) ( antwsal orahtesf eas ) . . . because safe the reach to able wasn’t/was (I ) -reading. window a Introduction Yoon ( Tedosaeopen. are doors The closed. are doors b. The a. away. is he while closed away. it is keeps he he while open it keeps b. he a. 1 b) 1994 1 okysnecs yai eatc,hmgniy non-maximality, homogeneity, semantics, dynamic sentences, donkey nisms luil edn h enn ftepoonis pronoun the of meaning the reading plausible most its on , 1992 1994 ntems luil edn of reading plausible most the on , , 1996 , n ftewnosi i garage his in windows the of one oe,tewa/togtriooyi ilaig eas hnthe when because misleading, is terminology weak/strong the notes, 1995 l ftewnosi i garage his in windows the of all Krifka and ,w ilcl tteeitnilraigor reading existential the it call will we ), 1996 : 1996 ikti eairo okypronouns donkey of behavior this link 2 1996 hmolo ufr Henderson & Bumford & Champollion maximal tee mn akrobbers bank among uttered , ( 1 a) ecp htteei no is there that (except hspooncudbe could pronoun this hsi h togor strong the is This . nepeain,while interpretation), it sntanaphoric not is ( 2 a) expresses ∃ -reading. no the , early access ). dichotomy that try to re- 2 ∀ / ) is analyzed as referring to the in( ∃ 1 in( it 3 the doors -reading of donkey pronouns. On the basis convincingly shows that singular donkey pro- ∃ 2001 interpretation). These two readings naturally correspond expresses the fact that at least some of the doors are open for plural definites. In other words, donkey pronouns are not b) 2 ( dichotomy follows from the interaction of two relatively simple -reading and to the 2016 b. *Every farmer who owns a donkey gathers it at night. ∀ ∀ / ∃ The goal of this paper is to develop a theory that meets this challenge However, Kanazawa non-maximal ) a. Every donkey-owner gathers his donkeys at night. 3 are filled at the sentencepronouns, level, following not the at implementation the of levelin trivalence ofKriž resolution plural developed definites or donkey sums, we locate the parallelin between the donkey pragmatics pronouns rather and than pluralof in definites a the donkey semantics. sentence We does claimof not that logical generally the space draw denotation where a it cleantwo is line regions true between are and the the buffered region region by where possibilities it that is get false; apportioned rather, in those different the independently motivated formal systems: a pragmaticdisambiguates account plural of how definites context and donkeysemantics sentences, that delivers and truth-value a gaps leanthe for dynamic problems the that pragmatics arise to from fill. interpreting To singular avoid pronouns as referring to duce the behavior ofdescriptions. singular donkey pronouns to that of pluralbut definite succeeds at predictingembedded how by context determiners, disambiguates and donkey to sentences show that the apparent complexity of definites are compatible: ( one window or door. Apartmutandis from — with this, the it plural is definite essentially synonymous — mutatis nouns, unlike plural definites, cannotdonkey refer pronouns to are sums. incompatible For with example, collective singular predication, while plural to the of this kind of similarity, donkeyYoon sentences,and inKrifka whichdevelop the pronoun amereological sum-based sum of analysis all of the windowsas in the number-neutral; garage that in is, question. It it is does interpreted not presuppose that there is more than Donkeys under Discussion sentence (a This poses a challenge for analyses of the ways depending on the pragmatics. We assume that these truth-value gaps early access 2 rt odtosbcm oedffiutt seti nseaisw ilcall will we scenarios in ascertain to difficult more become conditions Truth ( 1989 1978 n eeostepamtcpr foracut Section account. our of part pragmatic the develops and Section it. biguating the of nature similar are that whole a definites. as plural sentences with donkey sentences is to it definites; plural to similar oepeiey h iiaiyi o ttelvlo onprssbta h ee fclauses of level the bonus at a but get phrases in will noun as I of sentences, level donkey the to at correspond not that is similarity the precisely, More are examples his heterogeneous other of Two has any it. he lets if father even some as car, soon the as false judged is it of is speak homogeneous will is we otherwise, scenarios; mixed relevant homogeneous in true judged readily is Parsons (e.g., beat not do they that donkeys additional own men some least mixed he donkeys the ( of none beats man false. some clearly instead is donkey if it every true; owns, beats clearly man is every ( it if in owns, sentence scenarios, he donkey such the In of differently. truth donkeys the two judge to easy is It by 2 and research. here of avenues developed new account suggesting and the questions of open benefits out pointing the of some Champollion work, highlighting present the of precursor Kanazawa Muskens particular, composi- (in Section standard semantics on dynamic building to by approaches needed tional as gaps truth-value delivers that 2016 4 Eeymnwoon okybasit. beats donkey a owns who man Every ) The h ae ssrcue sflos Section follows: as structured is paper The ewl a htadne etnehsa has sentence donkey a that say will We Heim , ( and , frpua ents Section definites. plural for ) aeytoeweeeeymnon n et n oky n at and donkey, one beats and owns man every where those namely , ∃ 6 / ∀ oprstepeetacutwt rvoswr,specifically work, previous with account present the compares 5 1994 1982 Chierchia from c), ihtm n h oeo context of role the and dichotomy estebde okysnecsaiefrteproe fti paper. this of purposes the for aside sentences donkey embedded set We . nepeain.A xml hs otsletinterpretation salient most whose example An interpretations. ∃ / Barker , Rooth , ∀ ( ihtm yfcsn nterl fcneti disam- in context of role the on focusing by dichotomy 5 a) 3 Rooth from adapted , Križ by developed theory the of summary brief a is 1987 1996 ). 10 Geurts , 1995 ya-l osta efrisfo driving from forbids he that sons -year-old 2 4 . feeysuetwoto ls rmm ie it, liked me from class a took who student every If ple hster odne sentences donkey to theory this applies ( 4 5 b) 2002 Shbr Pelletier & Schubert from adapted , heterogeneous Brasoveanu , 1987 hmolo ufr Henderson & Bumford & Champollion 2016 ti ooeeu because homogeneous is It . 2 ihihstepragmatic the highlights Section . 4 10 5 i omntet any treats man no if ) rsnsafragment a presents ya-l osdrive sons -year-old 2008 nepeaini it if interpretation 7 ocue by concludes , 2010 1995 n a and , , 1996 ). early access ) 7 , and b) 5 ( -readings, ∀ , and b) 5 ( . Hence it is not possible and b) 5 ( a) 5 ( -reading emerges, or a health -reading, it turns out to allow ∃ ∀ , and adverbial ones, such as 5 for a different context manipulation): c) , modulo the contrary-to-fact implication 5 ) observe that the interpretation of( -readings in suitable contexts. Chierchia ( ∃ ) reports that although it is most readily -year-old son lets him drive the car. 2011 and 1991 10 1995 a) 5 ( -readings, such as ∃ ) can be paraphrased in a context-independent way as 4 . It also cuts across the distinction between determiner-based , and upward monotone ones, as in Usually, if a man hasmeter. a quarter in his pocket, he will put it in the c) c) ) itself, Chierchia ( 5 5 ( ( 4 The farmers of Ithaca, N.Y., are stressed out. Theyapist. fight Her constantly recommendation is thatshould every beat farmer it, who and channel has his/her a aggressiveness donkey in acial way point of which, view. Theand farmers things of indeed Ithaca improve. follow this recommendation c. No man who has an umbrella leaves it home on a day like this. b. with each other. Eventually, they decide to go to the local psychother- while still morally questionable, is arguably less dangerous from a so- and The account of these facts that we will develop is based on the following The influence of context on donkey sentences has been noticed before: The distinction between homogeneous and heterogeneous readings cuts ) -reading surfaces. ) a. No man who has a ) Anyone who catches a Medfly should bring it to me. a) 7 5 6 5 that this paraphrase suggests. Just what it means to be equivalent for current ∀ intuition: sentence( Things are equivalent for currentdonkey-owner purposes beat to all the of way his they donkeys would be if every Gawron, Nerbonne & Petersis different ( depending onsamples whether on the a field speakerdepartment trip, is official in a engaged which biologist in case looking eradicating the for the Medfly, in which case the across the one between downward monotone embedding determiners, as in to reduce one of these distinctions to another. ( across the one between such as donkey sentences, such as quite clearly for (heterogeneous) gives this context asCasalegno a (see tongue-in-cheek also exampleAlmotahari and attributes it to Paolo interpreted in terms of a (homogeneous) Donkeys under Discussion ( ( ( As for( early access Križ in theory the to turn We hr h eatc osntpoieoe od hs err a resort may hearers this, do To one. provide not does semantics the where hs hr ti entl as isan a’ ado ie cnro.When scenarios. mixed of land man’s no a lies false definitely is it where those ( donkeys, his of ( any as beat just not false, does definitely donkey-owner some if ( donkey-owner that donkeys, every assume his if that of so all limiting reflexive, beats two is actually equivalence for hand, only one way the context-independent On a cases: in stated be can purposes l h or r pn n entl as falo hmaecoe,n matter no closed, are them of all if false definitely and open, if are be doors would the they Thus, all way open. the were to doors of purposes the terms current all the for in equivalent Put are them. things in that of arranged sentences, all are donkey doors through on the pass view if to our case needs the one longer and no sequence sentence is a by the this side open, But arranged are true. doors doors judged three these readily of of one two any if through and going side, by safe a reach can This plurality. whole as the definite Lasersohn to of plural true referred a speaking been by strictly has not denoted phenomenon is plurality predicate a a the of contexts, if hold certain even to In sentences. judged donkey be to can dif- way predicate in similar interpretations a different in contexts receive ferent can definites plural with Sentences 3 rests. account our of part pragmatic the to. have on they err than will equivalence they more or assuming judgments, not this any of make give side to to the fails classified hesitate context either be the will should Whenever hearers donkeys conversation. clear, their the of clear of is all purposes it not the whenever but for case some the beat will be who they will farmers value, this how truth Essentially, definite account. to a into purposes has that current sentence take for it donkey equivalent the makes as which context treated in be the scenarios can border when scenario clear particular, the a that In draw clear strategies. to pragmatic asked various effect sentence to in donkey are a to they value scenario, truth mixed definite a a such assign in to pressed are hearers Križ ewe h cnro nwihadne etnei entl reand true definitely is sentence donkey a which in scenarios the Between ofraieti hoy ene omk hs oin oeprecise. more notions these make to need we theory, this formalize To 2016 1999 npua definites plural on Malamud , 2 i entl as hnn ori open. is door no when false definitely is b) 2012 2016 h or r open are doors The h or r open are doors The .Freape smnindbfr,i one if before, mentioned as example, For ). 4 hc rvdstesaodn nwhich on scaffolding the provides which , i entl re nteohrhn,we hand, other the On true. definitely is ) 6 non-maximality hmolo ufr Henderson & Bumford & Champollion sjde entl reif true definitely judged is omncts roughly, communicates, h or r open are doors The (Brisson 1998 , 2003 4 is ) is , early access . w ) is ≈ 0 514 : , where w ). These 2016 Current Issue 2000 , 1987 . To characterize how itself or at some is judged true in a given 2012 3 (Löbner S w assumes a salient Question ). ). Consider for example the means that the QUD is resolved with respect to the QUD 0 2012 494 2016 w : w polarity instead of his preferred term ≈ or 7 w 2016 QUD and Malamud , Malamud 2003 , and any differences between these two worlds of the doors are open for the purposes of the 0 1999 ). In a scenario when some but not all doors are is literally (at the semantic level) neither true nor w true enough at . Intuitively, homogeneity ≈ and is the term most commonly used to refer to the salient subject 1993 enough because it is recent and lean; for similar and more elabo- w QUD , Lasersohn 2016 1979 b. The books were not written in Dutch. The doors are open , Schwarzschild Križ assumes that sentences can have truth-value gaps (van Fraassen Among the various accounts that formalize this process, we adopt the ) a. The books were written in Dutch. 8 matter that speakers andmotivated hearers to interpret seek sentences an alternative asthe notion being pragmatic of about. interpretation subject ofKriž matter definite ( becausequestions, plurals he which seems finds plausibly to cases establish be in the insensitive which immediate to conversational explicitly QUD. asked We preferquestions to that stick are asked and the questions that answers actually address. following sentences: ( We depart from Križ in adopting the term phenomenon known as terms refer to the factsuch that sentences sentences are with “neither definite true pluralsmixed nor and with false negations when respect of the to pluralityallowed the in property by question is ascribed non-maximality)” to (Križ it (modulo the exceptions open, false. These literal truthspeakers’ values intuitions. are They are not merely intended ancomputing intermediate to pragmatic step directly truth on the values. reflect way Križ native towards motivates truth-value gaps via the are irrelevant for current purposes.context A just sentence in case itbeing “true is enough” means being true either at rate accounts, see van Rooij these different interpretations arise, Križ under Discussion (QUD), a partitionan of equivalence the relation set of worldsin which the gives same rise way to in conversation, and hearers will havemore to like decide one whether in the which stateof all of them the affairs are. doors is are open or more like onesystem in in whichKriž none Donkeys under Discussion how they are arranged. Ifdepend some on but whether not all of them are open, judgments will 1969 (see Lewis with the common notion, and remain neutral about how to resolve mismatches between the We do this because 3 early access hr h or r ragdi sequence: in arranged are doors the where enough true are that Sentences world. actual the to equivalent is that world false. nor true neither are sentences both cases, other all in round; way olsta orsodt ie cnro.Te ecnapytetheory the apply can we Then scenarios. mixed to correspond that worlds Križ for seen, have we As hti,spoethat suppose is, That of value truth literal The tlcsatuhvleat value truth the a in lacks Quality it of Maxim sentence Gricean A the way. relax following to proposes Križ scenarios, mixed for while are, them of none if only and if false and Dutch eetdhr,tefloigtuhadfliyconditions: falsity and truth following the here, repeated at Križ gaps in truth-value claim have this make sentences now donkey us that Let assuming scenarios. by lack false precise likewise and the more sentences true to donkey At between respect that border false. with claimed clear is mixed have a is it We question which it. in in to plurality ascribed those the property from gap, true this is in plural worlds the definite a with sentence a 4 as homogeneously) hence (and maximally interpreted is it Since open. Instead, equivalent. hence, (and non-maximally proposition interpreted the be as will heterogeneously) it Accordingly, equivalent them. are of worlds both These and scenario). purposes, mixed current (a open for are doors three of two worlds two Consider w any at false be to true. it judged believe be not to do predicted they are as long as true, be to it believe not any and Križ Applying oacutfrtefc htsekr s ooeeu etne in sentences homogeneous use speakers that fact the for account To ups o xml htteQDi hte hr sawyt h safe. the to way a is there whether is QUD the that example for Suppose w 0 w 2016 ≈ 0 w ri neither in or w hsmasta paesmyutrasnec vni hydo they if even sentence a utter may speakers that means This . ( sentence assigns semantics the Suppose straightforwardly. all steol ol twhich at world only the is 2016 w w w some 0 all w w odne sentences donkey to ≈ ( 8 2016 sln si stu nuhat enough true is it as long as , hr l h or r pn and open, are doors the all where , a) w nor S seuvln oaworld a to equivalent is h or r open are doors The stu fadol faltebosaewitnin written are books the all if only and if true is a eue at used be may uti aetesf srahbeete nboth in either reachable is safe the case in just rt-au a iie h olsi which in worlds the divides gap truth-value a , w 0 a h or r ragdsd yside. by side arranged are doors the Say . { 8 w all h or r open are doors The w , hmolo ufr Henderson & Bumford & Champollion w w some all oadesteQDee if even QUD the address to onsa reeog at enough true as counts } and o osdracontext a consider Now . w none w some w ( 8 { hr odo is door no where w b) n o as at false not and stu enough, true is all r olonger no are w ti h other the is it } some . where , 4 ), early access . ) c) 4 5 ) as false 4 mixed mixed w w w ≈ ) receives 4 . This time, holds, true w true a) ) is interpreted 9 4 ( w If we change the sce- ) is mapped to the truth , sentence( 4 Things are equivalent 4 holds. Assume that the , repeated here, has the . Hence( c) mixed c) , let us first consider one 5 ( 9 w ( no does not treat a sentence like( mixed -reading. 5 ∃ w , every donkey-owner beats all of be a world where ≈ true w 9 true true one where w w . It is therefore pragmatically interpreted as mixed w mixed induced by the QUD. needs to be captured. This is precisely the role of w ≈ directly. Instead, at mixed worlds,( -reading. Thus, this theory predicts that the pragmatic } ∀ ) can be paraphrased roughly as otherwise; in particular, if everyone takes exactly one otherwise; in particular, if every donkey-owner beats ex- ) is whether every farmer follows the recommendation 4 ; this is a heterogeneous 6 } . For the purpose of exposition, though, pretend that there iff at least one donkey-owner does not beat any donkey he iff at least one leaves all his umbrellas home; mixed iff no umbrella-owner leaves any of his umbrellas home; iff every donkey-owner beats every donkey he owns; holds, and 5 equivalent -reading. Assume that sentence , w b) ∀ mixed 9 ( are now equivalent to each other, but not to umbrella along, and someone also leaves one home. true false neither owns; neither actly one donkey and someone owns a donkey he does not beat. true false . The pragmatics then treats this sentence as true just in case true , w w { , except that this paraphrase suggests that not every donkey owner . Since this proposition does not contain a. b. c. c. a. b. false } true neither w w Turning to donkey sentences headed by true ) No man who has an umbrella leaves it home on a day like this. =( { ) Every man who owns a donkey beats it. =( ) is not true enough at w 10 9 4 This is shorthand. The accountdenoting presented in Section that has the following truth and falsity conditions: ( donkeys actually beats all ofcontribution his of donkeys. For thisthe equivalence paraphrase relation to make sense, the { a homogeneous reading; and sincehis at donkeys, this is a interpretation of( to the way they would be if every man who owns a donkey beat all of his to beat at least oneas donkey. Then nario so that theand recommendation is to beat all of one’s donkeys, tions in Section are only three possible worlds.one Let where QUD in scenario( Donkeys under Discussion ( value ( We will present a theory that delivers exactly these truth and falsity condi- 4 early access 5 h ie hspriso oalo i os ekesftesaeabsent are fathers Reckless sons. his of all to permission this gives who sbfr,let before, As ( ( to both at take enough to true therefore fails he if at wet case at gets the nor man is A This wet. along. getting umbrella is any who umbrella an with man atrsnec,te“ie”seaiswudivlepol h aemr hnoeSocial context). one U.S. than current more the have in who impossible people (something involve number heart would Security by scenarios it “mixed” know the number sentence, Security logically latter Social scenarios a mixed have make who to men as as way such a impossible, such practically the in or is formulated are this sentences car, donkey the Some drive sons his of any lets father means This { QUD. the address to father a is as reckless, already who is father from car a the Clearly, drive to fathers. sons reckless his are of one there just whether allows is QUD the that Let ( conditions: falsity sentence that Assume ding. both all about say can we thing contains proposition means 10 11 11 w w i reeog nyat only enough true is ) N a h a a has who man No ) c) true a poe to opposed (as o e scnie okysnec eddby headed sentence donkey a consider us let Now w false r h aersetvl.Spoeta h U swehrteei a is there whether is QUD the that Suppose respectively. case the are w true } w c. b. a. ( true ( Therefore, . 5 , mixed c) , ( 5 w c) rv h a,adsm fte aeadtoa osta they that sons additional have them of don’t. some and car, the drive neither car; false true u rsn tboth at present but ilb rgaial nepee as interpreted pragmatically be will false a eue oadesteQDa both at QUD the address to used be can oteetowrd r qiaet ie hsQUD, this Given equivalent. are worlds two these so , w true ffn a esaysno i rv i car; his drive his of son any lets man no iff ffa es n a a o n esalhssn rv his drive sons his all lets and son a has man one least at iff and any tews;freape feeyfte losoesnto son one allows father every if example, for otherwise; , 11 w w w fhsubelshm.Hneti sa is this Hence home. umbrellas his of ) rcie ooeeu edn.Sneat Since reading. homogeneous a receives ) false mixed mixed 10 and w otfreswooneatyoedne etit beat donkey one exactly own who farmers Most hsi eeoeeu edn.Testrongest The reading. heterogeneous a is this , ( ( = car. the drive him lets son -year-old w 5 w ac hs rpstosa eoe Suppose before. as propositions these match a) true true w true eetdhr,hstefloigtuhand truth following the has here, repeated , w false mixed Since . and ( 5 and a) 10 and w ilb rgaial nepee as interpreted pragmatically be will w w ewrd nwhich in worlds be mixed false mixed w w mixed true hmolo ufr Henderson & Bumford & Champollion ti ete h aeat case the neither is It . sta oubel-we left umbrella-owner no that is Since . Kanazawa (see 6≈ so , { w ∃ w true -reading. w w false w no false true w , true ( , hthsthe has that mixed and ≈ 11 sntequivalent not is ( 10 1994 5 cnb used be can ) w ∀ a) w } mixed -reading. ic this Since . , : mixed 113 ( 10 w .Frthe For ). true Hence . b) or ( ∃ w This . 5 and , -rea- c) Most no , true 5 is a) early access b) 12 ( via the ] b) b) -readings, is naturally ∀ 12 12 ( ( a) 12 ( Were Peter’s courses : does it mean -readings, ∃ -reading so far. Arguably, ∀ dichotomy as a case of under- ∀ / ] can be judged true even ∃ ) remarks: b) Were Peter’s courses universally well- 12 11 ( 256 is transmitted to sentence : 1987 -reading and the ∃ generally ) reports, native speaker judgments suggest that Given this assumption, our account predicts that 116 : ] clearly requires every student to like every course is understood as addressing the QUD Things are equivalent for current purposes to the way they Most farmers who own a donkey beat it a) b) 1994 12 ( 12 ( b)] seem unclear. . On our account, the less-than-universal threshold that is inherent 12 b. Most students who took a course from Peter last year liked it. while [ he or she tookin situations from where Peter, half [ from of Peter didn’t the like students some. who of . . the took Responses courses from a they my course tookhas informants from the did him. weak not reading, indicate however. that[( The [ exact truth conditions of consistent opinions. Consider that most farmers who ownthey a own, donkey that beat most all farmers ofthe who the donkeys own donkeys they a own, donkey or beatbeat that most most some of farmers of who the ownand a donkeys informants donkey I they have own? consulted have I not am expressed simply strong or not sure, while These judgments are expected under the assumption that The theory we present here treats the We have focused on the ) a. Every student who took a course from Peter last year liked it. 12 in the generic quantifier liked? generally well-liked? is interpreted as would be if most studentsfrom in Peter Peter’s courses liked all of the courses they took understood as addressing the QUD following pair of sentences: ( specification rather than ambiguity, andas generates well as intermediatethe interpretations. QUDs Given that natural sentences assumptions address,availability our about of theory such makes intermediate predictions interpretations. about Consider the for example the difficult to probe. Thus Rooth ( Donkeys under Discussion these readings are endpoints on a continuum whose interior is notoriously As Kanazawa ( early access 6 htti U s pcfial netit bu htpooto fclasses of proportion what about uncertainty specifically is, QUD this what h ceti os nsieo nqeescniin eas tcno make cannot it because conditions uniqueness of spite in so do it accept who Heim by up brought was example This i)te r ie okysnec n cnrota ed oatruth-value a to leads that scenario a and sentence donkey a given are they (ii) ainta pol aefimitiin bu iutosweefresare farmers where situations about intuitions firm have “people that vation Jackson ossetaotterdne-etn”wiete ie“aidadguarded and “varied give they while donkey-beating” their about consistent class-liker. relevant a as count to order in like to about needs uncertainty to one in natural results is it threshold this, that capture about formally uncertainty to that attempt expect not do we although QUD; ( fathers. example reckless because are is there this whether that namely it QUD, take We ( be. example to car-lending them in the of (p.c.) variant Rooth a Mats on judgments by Section noted was in vagueness quantifiers Heim of of treatments not treatment supervaluation does to supervaluationist denotation connection our the foreshadows because idea situation This this in hesitate the judgments not in should clear (true) hearers give value that to truth predict classical consequently a We for. delivers described. stands hand scenario pronoun other the the plant on sage semantics which Our conditions truth to difference any Kadmon pronouns. on conditions uniqueness of following: to ( the analogously as them such treats situations simply consistent account are of Our they kinds situation. account; other consistent our on of one status kind most privileged one at any owns have farmer not every do uniqueness which donkey, meet in situations that example Situations for pronouns. conditions, to conditions uniqueness any Brasoveanu (e.g., controversial is proposal (Parsons sorts various of gaps. truth-value to rise give not and will QUD, situations the Consistent identify gap. easily cannot they (i) case in just hesitate will hearers ( (Rooth scenarios mixed in judgments” 13 ) n eeto h hoydvlpdhr sta tacut o h obser- the for accounts it that is here developed theory the of benefit One thsbe rpsdta okypoon ar nqeesconditions uniqueness carry pronouns donkey that proposed been has It 1990 ihit. with vrbd h ogtasg ln eebuh ih tesalong others eight bought here plant sage a bought who Everybody Scenario: 1994 n. : 11 : ssprautoitie ypitn u that out pointing by idea supervaluationist Kadmon’s against argues Heim . 136 aepat r odi ace fnine. of batches in sold are plants Sage .Ti eairi xetdo h aua supinthat assumption natural the on expected is behavior This ). 1978 Cooper , 12 1982 1979 1987 11 2008 predicts Kadmon than secure more are ) 11 hmolo ufr Henderson & Bumford & Champollion Kadmon , oageaantcrantypes certain against argue to mksi ayt comdt the accommodate to easy it makes ) Parsons also see ); Section : 1990 1990 5 rusta hearers that argues .W ontascribe not do We ). ;hwvr this however, ); 1978 5 The . and 6 early access ), 514 : 7 2016 for a different 2 . 6 : Section QUDs. Accommodation 2001 ). Following Križ ( ). Even though the uniqueness 13 ): 2008 ) to be false no matter what the QUD is. 9 152 : for further discussion). We return to Kanazawa accommodate 13 2 . 5 1994 ) is not met, we still predict that sentence 13 : Section 2008 ). There is evidence that both adults and children use 2012 of the sentence. . 0 1 . 6 donkey pronoun is met. Thesedonkey-beating are situations, a and special the class uniqueness ofbe condition consistent checked can just by lookingin at the the N extensions of the predicates [P]eople are capable of assessingsentence the without truth value resolving of thegiven a by donkey ‘vagueness’ the grammar of when thepurposes, there it is meaning is no enough to need assume tono that do problem underspecification so. causes for For people our insentence assigning in a situations truth where value the to uniqueness a condition donkey for the in Section Our account relies on the assumption that hearers interpret a sentence as ) will be judged true independently of any assumptions about the QUD, 13 and are therefore notowns dependent two on donkeys, the John QUD beatshis for neither donkeys, their of his our interpretation. donkeys, Thus semantics and if predicts everyone every sentence( else man beats onlybelieve one that of this is onperspective, the and wholeBrasoveanu correct (but see Kanazawa assume that hearers canthe try QUD to might be; infer thatof from QUDs is, sentences becomes they particularly and can relevant scenariossentences when out what hearers of are context. presented One donkey natural principleEven that mixed hearers scenarios are may sometimes use assigned to a infer classical truth value by the semantics here, this assumption to disambiguate sentences inhas context, been even explicitly when asked no question (Gualmini et al. the discourse participants, as relevantbut to need the not conversation. be These determined goals by can an explicit question in the conversation. We because the scenario does not fall into the sentence’s truth-valueaddressing gap. the QUD. This is astructure common (Roberts assumption in theories of information ations, such as the sage-plantcondition scenario for in( the pronoun in( Donkeys under Discussion depend on how pragmatic factors like the QUD are resolved. This is in line 1994 This leads us to expect that hearers should not hesitate to judge such a sentence false. We ( The present account extends Kanazawa’s perspective to all consistent situ- we take the formal notion of QUD to represent the overarching goals of with a speculation by Kanazawa ( 7 early access ( ievra omlzn usinase ogunewudrqie among require, would congruence question-answer Formalizing versa. vice ( Križ by proposed is Aboutness, of notion Lewis’s David by inspired QUDs, te hns lrfigwa tmasfratiaetpooiint match to proposition trivalent a for means it what clarifying things, other QUDs liked? the Likewise, addressing why affirmative. reason as the him? the understood in with be questions took well such they might answer classes congruence question-answer the to of used half be than cannot more and like students Peter’s of match all must alternatives Roberts focus (e.g., why its question reason and the of answer answers congruence, the possible that question-answer the notion by the constrained is, is that them address that tences owns? he donkey male calculable. every ( beat in moreover and sentence owns donkey classic the goals. as discourse of such to QUD case means the common in a example, as For hearer and speaker be by of must identifiable relevance they the that maximize and al. sentence must the et QUDs accommodated Kao that see propose Clark inference, QUD Clark to & Beaver approach and see accommodation literature, pragmatics. question the on on to literature constraints pointers the the in of open discussion currently relevant is For discourse the of state the judgments guarded” level, and ( semantic “varied Rooth the the by at hence observed false confused; nor become true may pragmatic neither they a are and assign that cannot sentences hearers they to When QUD, value sentence. the truth the accommodate from or QUD infer be the easily generally of cannot will properties they many principle, infer this to follow able speakers that assume hearers If 2016 14 ) ute osblt sta h eainhpbtenQD n h sen- the and QUDs between relationship the that is possibility further A given QUD the on converge interlocutors how of question broader The ): and sentence A drsigteQUD the Addressing w 2 eePtrscussgnrlywell-liked? generally courses Peter’s Were uhthat such ( 12 oseeydne-wigfre eta es n okyhe donkey one least at beat farmer donkey-owning every Does a) osntla err oacmoaeQD uhas such QUDs accommodate to hearers lead not does S 1987 a o eue oadesteQDi hr are there if QUD the address to used be not may w 1 ≈ adothers. and ) w 2 and S stu at true is calculable 14 eePtrscussuieslywell- universally courses Peter’s Were hmolo ufr Henderson & Bumford & Champollion 2008 2014 w hti,te utb jointly be must they is, that ; 1 u as at false but Section : Bae & Beaver particular, In . 2012 epcieyrte than rather respectively ol o omlybe normally not would .Ti ih ethe be might This ). ( 2 12 . 7 a) o Bayesian a for ; w 4 nunusual an ), 2 and . ( 12 w b) 1 and Did are early access , , 5 . 4 1996 , : Section 1994 2016 , Yoon ) could be paraphrased 1994 9 argues convincingly that 2001 8 15 conveys that Peter chose not to write the essay. (Lappin & Francez , many early theories assumed that singular 1 ). But as we have seen, Kanazawa dichotomy follows from the interaction of two relatively simple ∀ / 1996 Yes, he solved the math problems ∃ . This fits our overall strategy of showing how the apparent complexity As mentioned in Section To sum up this section, we have proposed a simple pragmatic theory that A trivalent dynamic compositional semantics the donkey or donkeys he owns the exam, and should leave it open whether he decided to write the essay. solving half of them andanswer writing an essay. When askedKriž whethernotes, Peter based passed on the observationsthat exam, by this the Benjamin is Spector unexpected (p.c.) if andon the an his explicitly anonymous theory asked reviewer, the question answer is should taken simply to entail be that the Peter QUD; solved in enough that problems case, to pass as Krifka singular donkey pronouns can onlythis have in atomic mind, discourse several frameworks referents. have With beenA proposed similar that question do is discussed not in interpret connection with plural definites in Križ of the independently motivated formal systems. donkey pronouns can pick upso both that atoms the and donkey sums pronoun as in discourse the referents, classic sentence( to deliver disambiguated readings, ourtrivalent next meanings task consists compositionally. in In deliveringon this these a section, simple dynamic we semantic do framework so originally by described in building Muskens that hearers can accommodate QUDsas by various exploiting features these of constraints the as context. well 5 together with worlds at whichhere the proposition treats is uniqueness true. as Thedonkey theory an pronouns developed come epiphenomenon with and uniquenesspredicting constraints. does how While not we interlocutors assume refrain converge from that QUDs on and a the QUD, sentences that we address have them proposed are that mutually constrained, and expects the semantic componentthe to QUD pass (formalized it as a antheory trivalent equivalence maps proposition. relation the over Given trivalent possible propositionthat worlds), to is the an true ordinary in bivalent mixed proposition scenarios whenever the QUD lumps those scenarios Donkeys under Discussion a possible answer to asentences question are; and we what leave the this focus for alternatives future of work. donkey 1995 who considers an exam that one can pass by either solving all the math problems, or by With a pragmatic theory in place that combines trivalent meanings with QUDs 8 10 early access 9 hc aedsorerfrnsaemdlda ucin rmassignments from functions as modeled are referents discourse case which use make not does that variant CDRT simpler a of favor in PCDRT eschew we easm htteagmnst l h ucin norcmoiinlfamn r always are fragment compositional our in functions the all to arguments the that assume we as such here, needed not are that but uses Muskens that types basic other as well as worlds, Muskens in while (Janssen ( 1983 fpua assignments. plural of (Champollion referents discourse manage PCDRT) and or generate CDRT to (plural theory representation discourse Section compositional in Stokhof plural discuss & we Groenendijk which work, of present tradition systems dynamic the particular, in in individuals, such sum as pronouns donkey singular Magri see arguments, trivalent allow Križ that and systems semantic and compositional sentences; For donkey bivalent. embed may about that the questions operators in aside other is set through appears we projects trivalence simple, trivalence where things this system keep how our To in determiners. place quantificational only of The outputs time. of possible periods suppress and we events section this following. throughout the readability, in and develop (which simplicity we quantifiers of system generalized interest the the static into In integrate entities) of to sets easier to somewhat apply it makes and simpler Muskens in that is between difference Muskens in described fact is CDRT in of is variant influential and most The possible be also would Muskens choice in converse adopted The we values. and their many) type to infinitely of are functions there as type that assignments only assume primitive represent are we the we which use (of Since we referents matter. individuals, course not to does anaphora options in two Heim interested in these cards between file choice the the to similar conceptually are they case this (in values to dis- from functions as or values, modeled their are to referents assignments course case which in referents, type of objects that way the conceptualizing for strategies and entities, of type the type, basic third a Muskens includes in semantics lean The etc. referents discourse relate Assignments ment. PCDRT. of power full the require not 2008 ttecr fdnmcssesfraahr stento fa assign- an of notion the is anaphora for systems dynamic of core the At .A oga hs ausalhv h aetp,sc sindividuals, as such type, same the have all values these as long As ). Muskens in variant the on instead build We it. on based is PCDRT ) 2015 1983 . Muskens , 1995 hyapyt niis h atroto sagal conceptually arguably is option latter The entities. to apply they 1991 9 t nSection In 1991 h yeo rt values. truth of type the , , 1995 s .Either ). (for , 1996 1996 s state 6 stknt etetp fasgmns in assignments, of type the be to taken is eblpeiae pl odsorereferents discourse to apply predicates verbal , eageta okyabgiisdo ambiguities donkey that argue we , 1995 16 s Brasoveanu in and stknt etetp fdiscourse of type the be to taken is or ssmlrt Ty to similar is 6 store . 6 hmolo ufr Henderson & Bumford & Champollion h ,e s, Baoen’ ( Brasoveanu’s on relied , ,e , f e, d, ,i diint h usual the to addition in ), i rmdsorereferents discourse from , 1996 1991 10 hr r w common two are There t. oentities to etc., Brasoveanu’s example, for ; rcro fthe of precursor A . 2016 2 2007 s (Gallin rc anaphora track .I hspaper, this In ). 1995 , 2008 1975 h main The . s o dis- for ,y z, y, x, Since . 2008 but ) 2014 e ) , early access as f x with 5 etc. . Prefixal , 0 R x o, o 11 for discourse : Section f as variables over input assignment 1995 , but free in and etc. assignment functions , respectively. Finally, , and primed versions 0 d Q x i, i ∧ d farmer P x . Finally, arguments are passed into d, e, f , , etc. d is a discourse referent. We want and d 0 is bound in λf . λx. f x 17 behave in the way o d x donkey applied to i donkey beats it = are based on Muskens 0 d 1 i d ) reduce to the following by a series of lambda for them. We let agree on all things except possibly on the value → 9 abbreviates o d represents , the variable respectively. When intermediate assignments are , the type of dynamic propositions. etc. 6= ii , i d R x 0 0 , and ∧ are assignments and x i . d λf x. f x 0 s j, j se, t o . In line with common practice in dynamic frameworks, we assignment objects h d a Q x) . This is guaranteed by the following definition: d se, ∧ and h ≡ ∀ i applied to — from the formulas that they quantify over. The scope of an operator extends f x. P x ∀ ∃ i[d]o ( to mean that output assignment ) with the relevant annotations: The lexical entries in Table Like many other dynamic theories, CDRT assumes that anaphoric links are Suppose Sentences denote relations between assignments, or what we will refer to , and ) Every farmer who owns a 9 ) ∃ abbreviates , 15 16 represents We use the following notationalλ conventions. Dots separate binding operatorsas — including far to the rightformula as possible (until the edgelambdas of are the collapsed: nesting group),functions so without for the instance, aid in the of parentheses (which are used only for grouping), so that of the indefinite treat indefinites separately from othernuclear determiners. scope The of restrictor( sentence and the conversions and equivalent simplifications: ( is( ( slight modifications. Determiners are given static entries, with the exception encoded in LFs through coindexation.discourse Indefinites referents are they superscripted introduce, with and anaphoric the are elements subscripted such with as the pronouns discourse referents they pick up. For example, here t i[d]o they assign to and needed, we write thereof range over discourse referents.keep To track make of it discourse easier referents,referents for we associated the use with reader the the to letters words do. Such axioms are unnecessary here. as dynamic propositions. By convention, wethe will first use component of a relation denoted by a main clause, and Donkeys under Discussion those works treat assignments asensure primitive, that they these provide sets of axioms to variables over the second. These letters are mnemonics for 11 early access hte hybt edt h aeotoe fte o h etneas sentence the do, they If outcome. same the to lead both they whether Table (Chierchia hl sasge htotoea lsia rt au;ohrie it otherwise, value; truth classical a as value truth outcome the that receives assigned is whole a like determiner embedding An sentences. options these of one to into corresponding lifted each be ways, can two determiners in these Static setting of them. dynamic one of the only all to to apply or scope assignments, embedding nuclear output the its whether that arises require for question and should one The one determiner different owns. relate a farmer will assignments, the it output donkey case, several each a to such assignment In input donkeys. same more the or two by owns out who picked farmer donkey the beats farmer the the whether on scope, to pass nuclear as to the assignment determiner to each embedding way In the this question. of in in job obtained donkey the assignments the is owns it who setting, farmer dynamic a a be must value its individuals; referent restrictor, the In ( 17 haeTp Translation Type every Phrase no a least) (at exactly farmer beats donkey a owns who it a. ) d d epooeta ohotosaeoeaiei h eatc fdonkey of semantics the in operative are options both that propose We a encounters restrictor the when happens what open leaves sketch This 1 b. d n 1995 n ae uei ik u oky h variable The donkey. a out picks it sure makes and n ai translations Basic λxio. λxio. h h h h h h hh h h hh h ). et, et, et, et, e, e e, e e e e t t t , , , beats farmer t t t t ( t i h h i , , h h h h 17 i e e t t t t et, t t et, t t et, t t et, i i t t a) e , e , , e , t h indefinite the , ii t t t id) (i x ii ii ii ii i i ii neither x ∧ λPQ. λPQ. λPQ. λPQ. Po i λPio. i λxio. λPQxio. G.G(yo i (λyio. G λGx. i λxio. λPQio. i (λyio. G λGx. i[d]o ∧ . i ∀ ¬∃ | | = P P ∧ = .Px P x. = = ∃ o ∩ ∩ .Px P x. donkey 18 j ∃ o o o ∃ Q Q .Qxij i x Q j. donkey a ∧ ∧ ∧ j ≥ | = | 0 id o i d) (i P i[d]j . farmer donkey → ∧ every n n = = hmolo ufr Henderson & Bumford & Champollion x Q od) (o x Q o o ∧ ∧ ∧ ∧ x , x o j x P nrdcstediscourse the introduces ∧ no beat own jd j j d) (j P owns or , ( y) x 17 y) x xcl two exactly b) od) (o x hc examines which , 0 ∧ x jd j d) (j Q agsover ranges checks 0 o d . early access of and D for the ) neither 1990 N completely 18 , where they and 138 R is the source of : ) as a whole. To this 1994 18 ) completely true; those who were in Kanazawa 18 s , which lift a static determiner the circles are blue A Q 19 . On the whole, participants who saw two and and cells, all the circles arecells, blue. at least some of the circles are blue. w E 4 4 Q cells, the circles are blue. neither 4 , which asked participants to evaluate the truth of of the of the 2 2 , and 2015 of the ) with respect to pictures that involved four cells, all filled 2 into its internally dynamic counterparts. These type shifters 18 ii ) neither true nor false when exactly two cells had any blue circles, et, t h 18 b. In exactly et, completely false h , Our proposal is independently motivated by the findings in Experiment of Križ & Chemla ) a. In exactly ) In exactly ) to have that truth value, and otherwise participants judged( 3 19 18 18 correspond to the schemata are attributed to Chierchia; similarattributed schemata to are unspecified sketched previous in literature.Heim restrictor Here and we nuclear write scope of these dynamic determiners; these variables In the following, wespecific generalize embedding this quantifier pattern and by fromfirst the abstracting define specific away source two from of type the trivalence.type shifters We have the same truth value (either both true or bothtrue false), nor participants judged false. ( false, as did those whojudged( saw more than twobut at all-blue most cells; one and of these participants can cells be was described all-blue. succinctly As Križ bynot & using Chemla shown thenote, following to this two the pattern sentences participants). (which In were any scenario where these two sentences purpose, they varied the numbersentence of constant, cells and on they display gave oftrue participants each the type, answer holding options the all-blue and two non-blue cellsshown judged( fewer than two cells with any blue circles in them judged it completely trivalence in this example. It is true inand cells neither that true contain nor only false in blue cells circles that contain bothin blue which and this non-blue trivalent circles behavior projects to sentence( sentences like( ( Donkeys under Discussion ( (“all-blue cells”), false in cells that contain no blue(“mixed circles cells”). (“no-blueKriž cells”) & Chemla ran their experiment to determine the way The plural definite in the subject of A with circles of different colors. early access eas qi h itddtrie ihtolmd lt o nu and input for slots lambda two with determiner lifted the equip also we ntebsso hs yesitr,w en e yesitrta takes that shifter type new a define we shifters, type these of basis the On ( proposition. dynamic type of both are ( follows: of as output of represented the be case account, can into the determiners this in Taking example, around. way For other way. simplified a the in presented be the can omit we themselves. reason, quantifiers by same introduced the referents For discourse of static. making treatment identical, externally be determiner to not lifted assignments does these the paper require this we because discourses, and with simple, deal things keep grammar, To the assignments. of output rest the with compatibility maintain to order In disagree. returns returns determiner this particular, In ( desired: as behaves determiner static a 20 22 21 ) ) a. ) nmn ae,tetuhcniin htrsl rmthe from result that conditions truth the cases, many In A rpsto smerclyetisthe entails asymmetrically proposition b. λRNio. D D false every = def A E λDRNio. = def = def hnte r ohfle n treturns it and false; both are they when = def                      DN.D(λx. D λDRNi. DN.D(λx. D λDRNi. D neither false true h ‚ e, every D t i          n eun nitral yai eemnrthat determiner dynamic internally an returns and neither false true eas hyec aea niiuladrtr a return and individual an take each they because ƒ otherwise if if = ∃ i ∀ i .( x. = = .( x. ∃ ∃ o o otherwise if if .Rxij (λx. j) i x R j. ∃ .Rxij (λx. j) i x R j. ∃ ∧ ∧ .Rxij) i x R j. .Rxij) i x R j. i i = = 20 o o true ¬ ∧ ∧ E ¬∃ ∧ E i N R D when ∀ → hmolo ufr Henderson & Bumford & Champollion i N R D E ∀ ∃ rpsto;for proposition; .Rxij i x R j. .Rxij i x R j. .Rxij i x R j. .Rxij i x R j. E ∧ and ¬ ∧ A i N R D A neither ∃ ∧ A ∃ → ∃ ∧ ∃ → i N R D r ohtu;it true; both are D .Nxjo) j x N o. o o .Nxjo) j x N o. D 0 o hs two these for 0 o j x N . o j x N . yeshifter type no hnthey when ti the is it , every 0 0 , early access     0

0 0 0 . N x j o 0 . N x j o . N x j o o 0 0 . N x j o 0 o o ∨ o an even number

An even number ∧

→ ¬∃ ) → ∃ → ∃ 0 or

→ ∃ 0 n . N x j o j. R x i j j. R x i j j. R x i j 0 . N x j o j. R x i j 0 exactly o o ∧ ∀ ∧ ∀ → ∀ ∧ ∀ ∧ ∃ ∧ ∃ is interpreted as definitely true just 21 : n j. R x i j) j. R x i j) j. R x i j) j. R x i j) j. R x i j j. (R x i j ∃ ∃ = ∧ ∧ ∃ ∃ ( ( o o | | ∃ | | ∃ nƒ x. ( = = x. ( exactly x x x x produces a definite truth value whenever it does     ∀ ∃ i i D

D ∧ ∧ if if otherwise = = o o exactly n < n n n > = = ‚ = i   i   D ƒ if if otherwise def = true false neither no propositions do not stand in an entailment relation. As a ‚ that a sentence embedded by a cardinality quantifier has a                      n E D def = 2015 true false neither and exactly no                                    A D λRNio. D Since our semantics interprets sentences as dynamic propositions (rela- ) ) , the 24 23 λRNio. entities that fall into a truth-value gap are counted. tions between assignments) but our pragmatics expects trivalent truth values, in case the number ofof farmers farmers who who beat beat all at theirjust least donkeys, in one and case donkey, the are these number both numbers& even; Chemla are and both definitely odd. false Thisdefinite reflects truth the value finding just by inKriž case that truth value does not depend on how ( in mind that the outputnot of matter how doubtful casesof are farmers resolved. For who example, have a donkey beat it In the case of nonmonotonicof determiners like result, these determiners look somewhatlifted. more For complex example, when here they is have been Donkeys under Discussion ( To understand the behavior of nonmonotonic quantifiers, it is helpful to keep we assume that dynamic propositions are mapped to trivalent truth values early access ersrc rdigPrinciple Bridging restrict We hr sa smer ntedfiiino rt eaiet nassignment. an to relative truth of definition the in asymmetry an is There ytefloigtobign rnils is,w en rt n falsity ( and truth follows: define as we assignment First, an principles. to relative bridging two following the by ( in sentence donkey classic the for conditions falsity and ( in to phrase duces restrictor the seen, have a we owns As examples. our for tions down sentence a constraint, of this like conditions Without truth universals. the corresponding collapsing and avoid pronouns to order in dependencies anaphoric ( assign- input over quantifying universally by ments: simpliciter falsity and some truth arrive. and not arrived did who who man man, a another contain as that such models entity, in other false like not sentences but dynamic true externally out that so is This to falsity. relative non-truth requires Falsity 25 26 ) ) 22 hs nre n rnilsdlvrtedsrdtuhadfliycondi- falsity and truth desired the deliver principles and entries These define we dependencies, anaphoric unresolved without sentences For estdown sat He adapyn h w rdigpicpe,w bantefloigtruth following the obtain we principles, bridging two the applying and ) ne hsscn principle. second this under d b. Let Principle Bridging a. Let Principle Bridging a. b. cases, other all In c. I l te cases, other all In c. donkey ( 17 i φ φ true. is φ o φ φ b) ea sinetand assignment an be uhthat such eatr ftype of term a be fe lgigteetrsit h hfe determiner shifted the into terms these plugging After . sflerltv to relative false is stu ffi stu eaiet vr nu assignment. input every to relative true is it iff true is sflei ti as eaiet vr nu assignment. input every to relative false is it iff false is stu eaieto relative true is eue to reduces ol aetesm rt odtosas conditions truth same the have would o i φ 1 2 ( sfalse. is 17 φ φ a) 2 t i i snihrtu o false. nor true neither is to relative false nor true neither is . n h ula cp phrase scope nuclear the and , osnecsta onthv unresolved have not do that sentences to ffteei nassignment an is there iff ffi snttu eaieto relative true not is it iff φ 22 eatr ftype of term a be i hl rt osntrqienon- require not does truth while , hmolo ufr Henderson & Bumford & Champollion t a arrived man A . 9 ): o i vr a sat man Every n hr san is there and uhthat such amrwho farmer et it beats i . D come o i φ every d re- early access x (j d) x (j d) x (j d) x (j d) dynamic; at ), as desired. x (j d)) beat x (j d)) 9 beat ), we obtain the → → ¬ own lets-drive 11 own     ∧ ∧ lets-drive → ¬ inherently →   x (j d)) x (j d)) x (j d)   (j d) (j d) x (j d) ∧ ∧ ∧ ∧ son son dnk own dnk own ∧ ∧ ∧ ∧ ∧ i[d]j ∧ i[d]j i[d]j ∧ i[d]j ∧ ∧ x ∧ i[d]j x (j d) i[d]j (j d) x x i[d]j i[d]j x (j d) (j d) x ∧ ∧ ) and the bridging principles: 23 ∧ ∧ x man son type shifter, which is a mechanism for x frm dnk x 23 x man son frm dnk     D     j. j. frm man man frm j. j. j. j. j. j. ∃ ∃ → ∀ → ∀ ∃ ∃ ∧ ∀ ∧ ∀ x. ( x. ( x. ( x. ( ∀ ∀ ∃ ∃ i i i i ∀ ∀ ∀ ∀ if if if if otherwise otherwise case states that there is no way of assigning a man to any true case states that there is a man who has at least one son and who true true false false neither neither                                                                       ). The false Our fragment attributes trivalence in donkey sentences to their embed- These are precisely the truth and falsity conditions listed in( 11 ) ) 28 27 scopes. But in all dynamic frameworks, indefinites are ers that antecede donkey pronounstrivalence should, as by well. analogy, We be expect takentrivalence that to the is introduce answer introduced to by thisreinterpreting is the static no. relations In between our properties fragment, such (generalized a quantifiers) way in that they accommodate dynamicity in their restrictors and nuclear son of his such that the man in questionlends lends every the one son of in his question sons his the car. car. ding quantifiers. This raises the question of whether the indefinite determin- Once again, these are preciselyin( the desired truth and falsity conditions listed their donkeys, and false onlytheir if donkeys. some Analogously, donkey-owning for farmer the beatsfollowing car-lending none result sentence( of from the entry in( ( ( Donkeys under Discussion The That is, the sentence is true only if every donkey-owning farmer beats all of early access ol diinlyrqieta amrt eteeydne eon.We owns. he donkey every beat to farmer that require additionally would easm htte aea es h ttctype static the least at have they that assume we ditdy ti o lases oda h iebtenteetoclasses; two these between line the draw to easy always not is it Admittedly, hscrepnst an to corresponds This 1 ( sentence for predicts fragment no is no there trivalence. that resulting only any not never is since there fact, thus In and dynamic, already apply are to our need they In any referents. never discourse is introduce there that framework operations denote they core, their ap& (Kamp types static with compatible is is that this operation that abstraction assume an we to referents, due discourse (external) introduce do numerals requires which type, static like numerals modified For see and context, aside. dynamic indefinites a numeral in set anaphora Kanazawa pronominal we plural simple, on things discussion keep more type to dynamic but the sums, of to entries additional numerals h bare giving by example as way same the Reyle & Kamp example Szabolcsi for see discussion, differential relevant the for DPs. quantificational by genuinely part and in indefinites dynamic of least behavior in at binding common and motivated scope is usually determiners is other and frameworks, from class semantic separate that fact the from (Geurts anyway see as will such we determiners correct, embedding be monotone to appears this While Section absent. in be to reading The this otherwise. predict false and donkey, some beats and owns farmer ( 29 e u rgetcnb xeddt ra lrlpooia npoa for anaphora, pronominal plural treat to extended be can fragment Our . t , Afre h wsadne et it. beats donkey a owns who farmer A a. ) opportunity Assigning h e t , b. t ii 1997 6 2001 htprle hto h nent article indefinite the of that parallel that λio. . 3 D htayputative any that htsi,frcnrtns esgettetn h word the treating suggest we concreteness for said, That . a od oi n ae o xml,teol edn htour that reading only the example, For case. any in so do to sol endo ttcgnrlzdqatfir,w predict we quantifiers, generalized static on defined only is ∃ Nouwen and 2002 a nihrnl yai yeadteeyptigi noa into it putting thereby and type dynamic inherently an .if]j i[f j. sfrohridfiiedtries uha aenumerals, bare as such determiners, indefinite other for As . D j[d]o antapyt medn ntne of instances embedding to apply cannot .I n ae u on eei htn rbe arises problem no that is here point our case, any In ). ∃ raigo h etne ti rejs ncs some case in just true is It sentence. the of -reading ∧ ∧ need D farmer donkey o n oto yaiiy hnsc modified such When dynamicity. of sort any for tmost at 2003 ∀ oapply to 29 raig fdne etne ihupward with sentences donkey of -readings sfrtu unieslike quantifiers true for As . jf) f (j ( in formula the by described is a) od) (o 24 n easm htte nyhv the have only they that assume we , ∧ ∧ D D own oidfiie,btta hr is there that but indefinites, to hmolo ufr Henderson & Bumford & Champollion a oidfiiedtries since determiners, indefinite to ol evr adt detect to hard very be would o od) (o ) (of h et, a yitouigreference introducing by h t t et, 1993 ii ∧ sse nTable in seen as , Chapter : beat a every . of)( d) (o ) f (o ∀ -reading 29 and 4 b). some and no , early access , ). We 1991 , and , Gawron, 2012 1996 1990 , Foppolo , Barker The following section ). 2002 1994 12 2016 ). We focus our comparison on , Geurts 1995 1996 , , 25 , that can disambiguate those sentences , Champollion 1992 1995 2016 2010 , ). Again to keep things simple, and because we do 2008 , Chierchia ) pragmatics as a separate component by which trivalent meanings 2003 1991 2016 ). In this respect, our theory is similar to many accounts couched . The related question of how to formally represent the ambiguity , Nouwen dichotomy has been taken on by many authors (Heim 1993 2002 ∀ 1993 / , which could interact compositionally in donkey sentences as we have interpreted them ∃ To summarize, this section has shown how a simple variant of CDRT Comparison with previous work ≈ could treat the notion “trueby enough” as a modal operatorhere. with This an would accessibility be relationthough, given an that interesting the result formal would system only to differ explore architecturally from in the future account work; presented here. we believe, more recent accounts that useambiguity Plural (Brasoveanu Compositional DRT to represent the While we treat Križ’s ( are (potentially) disambiguated, thereseparate components are into other a single interesting semantic options system. that For instance, collapse a these reviewer suggests we Geurts has been addressed thoroughlyDekker as well (e.g., Groenendijkin & ordinary Stokhof dynamic predicate logicas or compositional compositional DRT versions (Muskens thereof, such differences is far from establishedthe fact. The question of whichNerbonne factors & Peters affect first focus on three proposalsdo which not are postulate similar in a spirit semantic to ambiguity: oursKanazawa in that they donkey sentences. Different donkey sentencespeople’s seem intuitions to about differ them in in thethey neutral clarity are contexts of susceptible and in to the manipulation degree by to context. which The exact nature of such sentences. In each case, weable, argue either that in the terms account of presented its here formal is simplicity prefer- or conceptually in how it assigns 6 can be used to deliverpendently trivalent motivated meanings by toKriž a pragmaticthat component, are inde- neither true norcompares false our relative approach to to the previous QUD. accounts of the interpretation of donkey Donkeys under Discussion Reyle not model intersentential anaphora, we do not introduce abstraction here. There are factors other than the QUD that are involved in the interpretation of work to the semantics and pragmatics. 12 early access i h yesitr ehv eerdt as to referred have we shifters type the via 1981 aewt hs oooiiypoete.H oesthe models He and properties. describe corre- monotonicity readings to these universal with aims and late He existential how determiner. about embedding generalizations of the explain properties of monotonicity version the on static focuses the and clauses, relative and miners Kanazawa for determiner. that of properties monotonicity the to related availability systematically the equal, being things other of all that claims Kanazawa examples, two least at scope; nuclear its on Cooper & (Barwise conditions monotonicity their of and terms quantifiers in these characterized between difference the framework, static some the of examples with clear sentences that the is for sense preference his default fact, In available. readily more determiner like the determiners of other effect the that notes of Kanazawa Geurts trouble see the view, into this go of not critique will a to For consequently have inference. and not the invoking meant, does when is hearer that the what beginning, is out the suggestion figure from tentative in clear briefly His is only paper. meaning happens his speaker’s this of way paragraph the addresses last he the acknowledges role, Kanazawa a While plays context sentence. that donkey given a of interpretation semantics. a readings proposing the actually “modeling” not simply and ( be sentences Lewis to donkey & himself of King takes ambiguous, Kanazawa that are out determiners point that understood claim sometimes a have as the authors this constrain subsequent While and them. shifters between type choice these motivate that principles interpretive derived determiner, each for quantifiers generalized dynamic two defining 6 . 1 ∃ hl h tegho hs eals seilythe especially defaults, these of strength the While readings, universal and existential of distribution the to respect With an selecting in context of role the is work present the of topic main The no raig and -readings ): Kanazawa , a o oeucalne,oraayi a aesneo these of sense make can analysis our unchallenged, gone not has , every several 1994 r padmntn nbt ie.Bsdo hs n other and these on Based sides. both on monotone upward are sdwwr oooeo t etitrbtuwr monotone upward but restrictor its on monotone downward is and , 1994 netgtstepoete fdne etne ihdeter- with sentences donkey of properties the investigates ∀ tlatn least at raig fdne etne eddb eemnris determiner a by headed sentences donkey of -readings no ∃ raigwith -reading most sdwwr oooeo ohsds and sides; both on monotone downward is ∀ raig huhh cnwegsta hr are there that acknowledges he though -reading, , ecam htte aeonly have they that claims he , no and , every 26 tlattwo least at swl.A o h determiners the for As well. as hmolo ufr Henderson & Bumford & Champollion A and st aethe make to is , every E n ypostulating by and , ∃ raigpreference -reading tlatrltv to relative least at , ∃ 2002 / ∀ ∃ raig.I a In -readings. ihtm by dichotomy : every every 150 2016 ∀ some f. -reading n. : a be can aea have and 31 no ) , early access S that then 2012 2003 not all -readings ∃ ) only have monotone on and neither = ) 0 upward ) are precisely this not every at most n . The Big Question, a S(w 30 Did every card-owner For both sentences, to -reading. This accounts ∀ 2012 and , and few true , = no , this is the S(w) 27 . 3 . 6 , if every 0 w 13 and w -reading. ∀ Did Peter get all of his books back? This follows immediately from assuming that the default 14 extends this generalization to determiners that are and extends this generalization to determiners such as 1994 1994 . Our notion of a fact-finding context is inspired by what Roberts b. Not all students who borrowed a book from Peter returned it. 0 -reading. w ∃ We can also make sense of another generalization proposed by Kanazawa, ) a. No man who had a credit card failed to use it. 6≈ 30 are upward monotone on their restrictor and downward monotone onKanazawa their nuclear scope. both their restrictor and theirall nuclear intersective scope, determiners. and We his discuss formal these account determiners further later generalizes in it this to section. In virtue of worldmake knowledge QUDs and salient that their are truthpay not by conditions, fact-finding, card? such these as: sentences Kanazawa generalization; on our account, such exceptions are expected in non-default kind of exception: ( namely that determiners thatstrictor are and their downward nuclear monotone scopethe on (such as both theircontext re- is fact-finding, because fact-findingfor contexts these give rise kinds to of determiners. Kanazawa discusses exceptions from this For donkey sentences headed by for ’sKanazawa generalization that thethat default is interpretation downward of monotone a on determiner nuclear its scope restrictor is and the upward monotone on its calls the Big Question (“What iscalls the “What way is things the are?”) world andpartition like?”; what in seevan which also Rooij eachMalamud cellcase contains of just a one fact-finding possible context. world,finding A is context donkey an will sentence extreme always that be is interpreted interpreted as in having a a fact- homogeneous reading. QUD might be are typically interpreted as if they hadis been a uttered context in that what isQUD focused is on such truth that simpliciter; for thatw all is, it is a context whose Donkeys under Discussion preferences. We propose that donkey sentencesreading often because appear to sentences have presented a in default absence of any clues as to what the (that is, non-fact-finding) contexts. The sentences in( We discuss these determiners in Section we call a fact-finding context. For us, a fact-finding context for a sentence 13 14 15 early access hl ’ epnei iia oteqatrsnec in sentence quarter the to similar is response B’s While a hte h eatc sin it assigns semantics the whether way n ntal ocrsteQUD the concerns initially B and A hc rfr the prefers which eal ednso okysnecsi o e.I silsrtdb the by illustrated is ( It new. not override Kanazawa is can which sentences contexts example, following special donkey that of idea readings the default novel, is contexts fact-finding Kanazawa the in clear, noted are intuitions that extent the h ee sfdde o pl oso ahns n othe so and machines, (i) slot to apply not does fed is meter the Barker the have to expected is quarters? their QUD all stronger used the any, answering by between addresses dispute B the speaker that assumption the on this of sense makes account Our A. contradict to B for way ( weakest the is example, it and For it context. supports by material modification ( resist notes, raised he to examples as certain appear on that light Kanazawa shed the can by about This questions QUDs. as various readings of various availability of availability the about questions as such ( in discourse tation. the makes utterance the of example 31 32 Jh a ivrdla.H intpti ntecaiybox. charity the in it put didn’t He dollar. silver a has John A: ) A: ) hl u rpslta eal ednso okysnecsaiefrom arise sentences donkey of readings default that proposal our While sal,i a a ure nhspce,h ilpti nteso machine. slot the in it put will he pocket, his in quarter a has man a if Usually, Scenario: 1996 15 N,eeyoywohdaci u ti h box. the in it put coin a had who everybody No, B: B: i nbd epayo hi coins? their of any keep anybody Did hsmkssneo h rsn con fw sueta the that assume we if account present the on sense makes This , (i) in shown example, quarter classic the on tweak a example, similar a provides o vrbd h a ure eti,s ems aea least at have must he so it, left. kept quarter quarter one a had a who buy everybody to No, quarters his all used He Coke. quarters. any have doesn’t John 32 31 eaetligaottebhvo fmni abigcasinos. gambling in men of behavior the about talking are We ∀ de o aethe have not does ) i aual nepee sajitatmtt eov QUD a resolve to attempt joint a as interpreted naturally is ) ∃ raigfrcneta esn.I atclr h usino whether of question the particular, In reasons. contextual for -reading ntsta h otx rae yA’s by created context the that notes Kanazawa -reading, 1994 ∀ raigo ’ epneteol esbeinterpre- sensible only the response B’s of -reading ∀ . raigbcuei eovsteQDi h same the in QUD the resolves it because -reading ( in utterance B’s QUD, stronger this Against . ∃ raig vntog h surrounding the though even -reading, 1994 28 i onuealhsquarters? his all use John Did true ∀ raigi h otpoiet as prominent, most the is -reading trbtst ai evr(p.c.): Beaver David to attributes or hmolo ufr Henderson & Bumford & Champollion neither oegnrly ecnrecast can we generally, More ∀ hc ure-wes if quarter-owners, Which raigemerges. -reading hti osy slong as say, to is That . ( 5 b) hc saclassic a is which , which , 32 ) early access other than the one A and E ). Of course a different type 21 -reading are true, and false just in( ∀ D 29 ) justifies his choice of dynamic coercion 1994 -readings of donkey pronouns are taken at face -reading and its ∃ ∃ based on some Boolean combination of D a. So,b. every farmer who ownsSo, a every female farmer donkey who beats owns it. and feeds a donkey beats it. . We have accounted for the fact that a donkey sentence is readily judged There is a conceptual difference between our account and that of Kanazawa ) Every farmer who owns a donkey beats it. 33 number of townsmen own otherFor suits example, that some they townsmen did also not own wear tan to suits, the and funeral. some others own suits inference patterns. Once For example, imagine that athe funeral townsmen took showed place up, in and aexcept they for small all a college appropriately few town. dressed college All in students black who suits do not own suits. Imagine also that a that the interpretation of donkeyitly sentences by can various also conditions be that characterizedto formalize implic- his this explicit tendency, interpretive and principles. withoutthat For resorting maps example, static on determiners his to view,monotonicity dynamic the inferences determiners process such should as guarantee the that following are valid( by default. operations in terms of theminers. monotonicity Specifically, propertiesKanazawa ofclaims the that embeddingtendency his deter- for interpretive donkey principles sentences reflect to a sult preserve from valid properties inferential such patterns as thatsentences monotonicity re- and and their conservativity underlying of static non-donkey determiners. Based on this, he suggests dynamic framework via the typeshifter shifter would have led todefined different predictions; for example, we could have and stipulation, Kanazawa ( true just in case bothin its case both of them are false, by assuming that determiners are lifted into a Donkeys under Discussion as every quarter-owner kept atof least them one used quarter, all it their alreadymany quarters; follows quarter-owners and that kept this none all remains their the quarters. case regardless of how 1994 value, restrictors of universal quantifiers are no longer downward monotone. The problem with this view is that there are clear counterexamples to these we actually used. Reasoning about analogous possibilities of arbitrariness 16 early access h sthe is why would it proposal his on indeed, account: his for motivation the weakens hnvreeypeiicto ftepeiaemkstecasclquantifier classical the makes predicate the of precisification every whenever ( in inference valid the between difference The ( from inference the Thus, ( ( Then misplaced. they that iers otesrtsprdx noracut h omldffrnei htapeiaesuch predicate a that precisifications. is of difference number formal the account, our On as paradox. sorites the vagueness, to of rise give treatments supervaluationist and Fine account as our such between parllels clear are There applying applying by by obtained one is other one precisifications: different two as having such predicates dynamic irreducibly treat and false, quantifier classical the true, returns it context, the on depends interpretation a whose denotes cate scope nuclear its (e.g., whenever predicate counterpart classical static its like just behaves Chemla as & such Križ quantifier in generalized results pervaluationist experimental treatment the supervaluationist from original comes Fraassen motivation the van in of gaps extension truth-value natural of Eijck a (van is quantifiers turn generalized that in on note view we supervaluationist question, a this answer remains: itself To question language? the it, for offers he explanation the thus and posits of independently valid semantically not are context. examples these why This unclear constructed. be easily be can it like examples other patterns, inferential of ( ( Kanazawa like While cases validity. see semantic about evidence provide not ( 34 34 et it beats sget htteifrnepteni otx-eedn;tu,i does it thus, context-dependent; is pattern inference the that suggests ) Eeytwsa h wsasi oei ttefuneral. the at it wore suit a owns who townsman Every ) Kanazawa generalization underlying the doubt to reason is there While entl false definitely S,eeytwsa h wsatnsi oei ttefuneral. the at it wore suit tan a owns who townsman every b. So, a. a uttopeiictos hl au rdct like predicate vague a while precisifications, two just has 1975 o vr onmnwoon n ipae utwr ta the at it wore suit a misplaced and funeral. owns who townsman every So, D oee,w ontsedne etne svgebcuete onot do they because vague as sentences donkey see not do we However, . yesitra edfie tteoeaieoei natural in one operative the it defined we as shifter type 34 a eeecpin oagnrltnec fpreservation of tendency general a to exceptions mere as ) hnvreeypeiicto ftepeiaemakes predicate the of precisification every whenever A . sFrench is 16 34 34 ( to ) i rewhile true is ) 34 ;btwe ti ie ocasclpredi- nonclassical a given is it when but ); ete renrfalse nor true neither ( and a) 30 1969 sntdi Section in noted As . 34 hmolo ufr Henderson & Bumford & Champollion i invalid. is b) 33 et it beats ( vr a h wsadonkey a owns who man every 34 adteivldifrnein inference invalid the and ) a) and D snnlsia n as and nonclassical as rssntrlyfrom naturally arises nalohrcss We cases. other all in ( 34 tall b) a nunbounded an has r ohfalse. both are entl true definitely 1994 5 1996 empirical , 2015 E n the and , might ) .This ). su- A . early access ) 17 c) ) 5 30 65 ) and : 35 -reading ). Scenar- ∃ 1995 131 A boy who had : 2002 -reading. The account ∃ ), who considers( , where it appears as 2002 -reading? One reason may simply ∃ 1993 . 31 ) and some other authors assume that 1994 , which he claims only have the -readings in donkey sentences with upward monotone no ∀ To follow the traffic laws, drivers need to put exactly one , and -readings are difficult to observe in intersective determiners, Did everyone follow the traffic laws? ∀ -reading do not coincide. ∀ Scenario: dime into the parking meter.in Some their drivers pocket, have but more nobody thanQUD: overpays. one dime a. Yes,b. every man who hadNo, ac. at dime least put one it man inNo, who the one had parking man a meter. who dime had kept a it dime in kept his it pocket. in his pocket. At least one boy whobest had friend. an apple for breakfast didn’t give it to his (Chierchia at least n , Why, then, do Kanazawa ( Finally, the present theory parts ways with Kanazawa’s in its treatment ) No man who had a credit card failed to use it. =( ) ), comments that such examples should not be taken at face value because ) ) No man who has an umbrella leaves it home on a day like this. =( 38 35 36 37 36 Chierchia attributes this example to anvan apple der in Does his rucksack didn’t give it to his sister and flipping the resulting truthexamples valueGeurts afterwards.is That considering, may but beOur for true scenarios the for are following the constructed examples it toand is rule the less out clear. uniqueness, so that the ( overlook their existence unless onereason specifically may tries be to find the them. role Another of negation. Geurts ( they always seem to involvesentences are some often kind interpreted of by negation, removing and the because negation negative before evaluation intersective determiners can only havebe the the fact that relevantios examples that are give hard rise to to findembedding (Geurts determiners need to be carefully constructed, and it is easy to some here predicts that their interpretationNow, will while depend completely on thesome examples QUD. have already been noted in the( literature: Donkeys under Discussion of donkey sentences with intersective quantificational determiners such as ( ( ( 17 18 early access ( in sentences c. and b. The ( 178 ueashv ttclxcletis(slse nTable in listed (as entries lexical static have numerals ignoring the from for results account that We Principle Intersection the of version weakened a can sentences donkey intersective allow that shows This determiners. intersective that do determiners intersective the that generate ensures not Principle, Intersection arguments the both calls on monotone upward the are prefer that Kanazawa determiners in principle that monotonicity predicts not The arguments. to both is on forget monotone to and forget, not to is remember remember. to example, For Brasoveanu cases. see (though negation predicates implicit these an of contains one other that the claim not to difficult but be would It predicates. opposite Yoon with line the have sentences c. and ( ( 2016 40 39 ) ) h medn eemnr nb n .aebt nescieadupward and intersective both are c. and b. in determiners embedding The the have sentences a. the examples, these of all In o ieetprpcie,bcuetecoc em rirr ncertain in arbitrary seems choice the because perspective), different a for no n. : ∀ Ys n a h a engvnapswr ogtit. forgot password it. a forgot given password been a had given who been man had one it. who Yes, remembered man password one a least given at c. been Yes, had who man every b. No, a. both. given QUD: are some but passwords, the today. home at today. it home left password at umbrella it an left had umbrella who Scenario: an men today. had two him who Yes, with men it two took least umbrella at c. an Yes, had who man every b. No, a. of home. one at just ones take other QUD: they the case leave that and in along but them umbrella, one than more own Scenario: raig ncnet hr h niemdli eeat htsaid, That relevant. is model entire the where contexts in -readings sitretv e lal eevsthe receives clearly yet intersective is 30 ∃ ,ti atrpicpecno odi aeoia a,given way, categorical a in hold cannot principle latter this ), raig n nadtoa rnil epsuae,wihhe which postulates, he principle additional an and -reading, a n ebrual oacs h meeting? the access to unable member any Was day? rainy this on wet get umbrella-owner any Did 1996 ∀ oetrtesce oit’ etn,yune oremember to need you meeting, society’s secret the enter To ariga mrlaalw o osa r.Sm people Some dry. stay to you allows umbrella an Carrying raig fteb n .eape yasmn htmdfidadbare and modified that assuming by examples c. and b. the of -readings 1 ∀ rpassword or Yo ( Yoon by noted As -reading. hs xmlshv encntutdfo ar of pairs from constructed been have examples these , ∀ 38 raiga hi rfre interpretation. preferred their as -reading ( through ) 2 otnwmmesaegvnjs n of one just given are members new Most . 32 40 mk h aepitfrother for point same the make ) hmolo ufr Henderson & Bumford & Champollion 1 htaetp-hfe by type-shifted are that ) ∀ ( sentence in -reading 1996 ∃ Kn Lewis & King and ) raigadteb. the and -reading D . 2008 1994 18 37 In ). : early access b) 41 ( is naturally un- a) 41 for more discussion ( 3 . ): b) is about the number 6 41 , because the homogeneity 1996 c) presupposes that any woman 41 ( , each woman corresponds to a a) a) 41 ( 41 ( ). See Section 33 (HH, Barker 2002 is about linguist-job pairs (a symmetric reading). Barker’s main 1996 shares many aspects and predictions of the present theory and c) 41 ( The homogeneity hypothesis der a particular proportional readingthe presupposes same that quantificational members case of allnuclear agree scope. on whether they satisfy the b. Usually,c. if an artist livesUsually, in if a a town, linguist it hears is of pretty. a good job, she applies for it. The use of a proportional adverbial quantifier when construed un- 1996 Barker Barker defines quantificational cases as equivalence classes of variable Following earlier work, Barker distinguishes between symmetric and asym- ) ) a. Usually, if a woman owns a dog, she is happy. 2 . 42 41 quantificational case. According to HH, is happy either about allpresupposes of that her any dogs, town or about isit. none pretty No of or asymmetric them. readings not Likewise, are nopresuppositions available matter of for which these readings artists fail. live In effect, in homogeneity presuppositions assignments that agreebound on by what the they adverbial assign quantifier. In to those variables that are ( If a woman owns moreto than this one as dog, a she subject-asymmetric isof reading. counted towns( Sentence only that once. haveBarker artistssentence refers living in them (an object-asymmetricclaim reading), is and that asymmetrically interpreted adverbial donkey sentences come metric interpretations of donkey sentences.derstood Sentence as making a claim about how many dog-owning women are happy. has in part inspired it.headed However, by it determiners. only The briefly main touchessuch on focus as donkey is these: sentences on adverbial donkey sentences, ( of this point. 6 Barker Donkeys under Discussion irrelevant individuals is consistent withpsychologically our plausible theory and (Geurts has been argued to be with a homogeneity presupposition: early access h wssvrldnesbasalo oeo them. of none or all beats donkeys several owns who ( so, If ( well. example as of quantifiers reading nominal subject-asymmetric governs the it that assumes tentatively Barker observed. be could difference this which in scenarios any between difference the neutralize niista ontstl h U a ermvdfo h oan nthe In domain. the from removed be any can that QUD is the idea settle general not the do narrowing, that domain entities of theory formal no man’s a proposes in remain that at consideration from pocket quarters presupposition those this removing prevents by narrowing failure domain contextual that assumes and ∃ as ( case heterogeneously that the interpreted predict is correctly This will meter. account the present into quarter quarter one a least at have at both who putting men by most law whether the is follow QUD the that Suppose respectively. Let conditions: falsity and truth ( these has sentence the that predicts account Our ( from arises HH not for ( is challenge sentence that obvious Take sentence An readings. donkey enough”. heterogeneous a “true assume be we can which true in literally cases those all for failure 43 45 44 raigdet rspoiinfiueat failure presupposition to due -reading a. ) Ms e h w okyba it. beat donkey a own who men Most ) ) lhuhH sfruae oa oapyol oavrilquantifiers, adverbial to only apply to as so formulated is HH Although ycnrs,H speetds a rnl ue u h asymmetric the out rules wrongly far so presented as HH contrast, By presupposition a predicts it that in account present the from differs HH w true c. b. the in it put will he pocket, his in quarter a has meter. man a if Usually, w , true w w true xcl n ure notemtr n oto hs e have to men on these hold of they most that and quarters meter, additional the into quarter one exactly neither meter the false meter mixed false n at and ffms ure-wigmnptalterqatr nothe into quarters their all put men quarter-owning most iff and , ffms ure-wigmnptnn fterqatr into quarters their of none put men quarter-owning most iff Barker While satisfied. been have laws parking the after tews;freape feeyqatronn a puts man quarter-owning every if example, for otherwise; w w mixed mixed ( Hence . ewrd ecie by described worlds be { w ∀ true raig and -readings 34 44 w , i reeog at enough true is ) 5 mixed eetdhere: repeated b), 44 43 w hmolo ufr Henderson & Bumford & Champollion o t smercraigis reading asymmetric its on ) mixed } peupssta vr man every that presupposes ) the , ∃ i wr fthis of aware is Barker . ∃ raig yrln out ruling by -readings -reading. ( 45 a) , w ( 45 mixed b) and , n the and , ( 45 c) early access , ) is 44 ): ‘not every’, railway line cannot refer 1982 niet iedere ‘every’, ). the marble I dropped iedere and the present account differ clearly 2016 35 1996 , or with a “marginal” concept such as ‘no’ in mixed scenarios. Twenty native speakers were boy geen experimentally investigated the behavior of donkey sentences 2002 2002 I dropped ten marblesdropped and is found under only the nine sofa. of them. The marble I ‘some’ and Geurts By contrast, the present account does not treat donkey sentences as In the absence of an explicit theory of domain narrowing, it is difficult to )# 3 . 46 in the sense that the more marginal a concept is, the more leeway there is in rial representations. Aside from truethird and option false, in participants case were they alsoalmost could given never not a chosen. makeGeurts upalso theireye varied minds, towards the but whether scenarios this the and option embedding sentencescal” was determiner with concept combined an such with as a “prototypi- Geurts embedded by the four Dutch determiners enkele given truth value judgment tasks consisting of donkey sentences with picto- ( HH is tailored to donkey sentences and does notanalyses seem of to plural apply definites elsewhere, (i.e., Križ 6 speaker found, so that the uniqueness presupposition is satisfied. presuppositional and need not appealdirectly to compare domain our narrowing. approach While to wenarrowing, HH cannot we without do an think explicit there theory are of reasons domain to prefer our account. In particular, In this example, the definiteanaphorically; description the fact thatpresupposition is it not is satisfied ruled either. out If indicates domain narrowing that was its available, uniqueness is always available to rescuedoes sentences not from presupposition always failure; seem but to this be the case, as the following example shows (a find examples for which Barker in their predictions. That said,HH. our The theory two is theories not differassumes merely in that a how homogeneity formalization heterogeneity is of arises. a In presupposition particular, andBarker that domain narrowing Donkeys under Discussion restricted domain, the homogeneity presuppositionpredicted is true. satisfied, and( variation of an example attributed to Barbara Partee in Heim while the core ingredients of our account are independently motivated by we would expect it to rescue the example by removing the nine marbles the 19 early access slt nepeain r ofudta scue ymria individuals marginal by caused is that confound a are interpretations “split” mtra-rsesadteBusl-ai oncinmyb considered be may connection Brussels-Paris the and Amsterdam-Brussels a sdfrsnecswith sentences for used was Geurts lead sessions think-aloud The lotawy ugdfle(ugsigthe (suggesting false judged always almost the (suggesting interpreta- by “joint” true embedded (the judged sentences line that Amsterdam-Paris parts found the or Geurts line, interpretation) tion). same “split” the the this and call one will of (we lines railway two either example, For tokens. its individuating etne ihngto tfc value. face at negation with sentences B a is A Krifka every also not see that result; strategy the interpretive flipping one then least at that suggested pretest a in sessions think-aloud lets from that account our of sion between confound. symmetry this and The avoided farmers have as to such expect individuals therefore prototypical we townsmen; involve paper the in discuss spurious causes that and the to alent In ( “split” the Thus ( “cases”. like several sentence as a viewed of readily interpretation are they that argues QUD. ingly the using strategy by a gap adding truth-value as the seen resolve be list: “split” can this proposal a to Our remove to domain. to the “joint” considerations from a plausibility individuals using from or shifting possible, where infelicitous, such interpretation strategies, sentence different the using declaring it resolve as hearers that and crisis” terpretive for results the towards tended strongly the of towards case tended the slightly In prototypicality. in differences of 47 ( Eeyriwyln htcossara osoe it. over goes road a crosses that line railway Every a. ) 47 Geurts individuals, marginal of effect the to respect With Geurts b) b. the , 2002 o every not it a where case every In ∃ ∀ 2 . raigadthe and -reading raigo h jit nepeainof interpretation “joint” the of -reading r rmrl sdt eyuieslcam oteeetthat effect the to claims universal deny to used primarily are rusta ie cnro rge hth em n“in- an terms he what trigger scenarios mixed that argues every atr xcl h poiewya hs for those as way opposite the exactly pattern o every not not and ∀ pl oteotu ftepamtcmdl.Transcripts module. pragmatic the of output the to apply ∃ o every not raig oapa.Ms fteeape we examples the of Most appear. to -readings ∀ raigfrmr rttpclidvdasand individuals prototypical more for -reading ∃ raigwt oemria niiul.The individuals. marginal more with -reading raig,adtoeebde by embedded those and -reading), ∀ 2002 osse neautn h etnewithout sentence the evaluating in consisted 1996 1 raigcicd,adte r ohequiv- both are they and coincide, -reading 47 ala iecossa crosses line railway ( in as paraphrased be can a) ocuinaanttkn uget o donkey for judgments taking against caution to ssrkn,adwudb rdce ya exten- an by predicted be would and striking, is o h eae iwta etne fteshape the of sentences that view related the for 36 ala line railway ∃ hmolo ufr Henderson & Bumford & Champollion raiga el,independently well), as -reading every some atcpns responses participants’ , smria eas the because marginal is 2 eeams always almost were ( 47 od it road, a) nti sense, this In . 2002 47 1 vr saB a is A every osover goes b). every no convinc- not were . and 19 . early access , 1 of can 1 boy is except 1 (not) all a) some and possibly -reading of 48 ( and ∀ boy (‘Fred’, to give -readings. 1 ∀ (not) every boy is standing alone; 1 . By weak determiners, he means -readings independently of no girls, holding hands with ∃ 2 , to including Mary, the a) , he intends his reasoning to apply to other 48 ( 37 girl and not holding her hand; some 1 -readings, but he suggests that there is a robustly get ∃ boys altogether; , it is psychologically natural to understand mutatis mutandis a) no 4 girl and holding her hand; 1 48 ( and some, a few, at least n, at most n, (exactly) n, no, ), which is supposed to be available for all quantifiers. -reading is true, in the submodel without Mary both ∃ We have 1996 some ), he concedes that it may be an overstatement to claim that . Because the submodel selection procedure described in this subsection is 36 Context: boy is standing next to standing next to him a name) is standingthem between but not with the other (‘Mary’). many While stressing that he should not be taken to imply that hearers have b. Some of the boys that stand next to a girl hold her hand. and ) and( is false and its 20 35 few Now, ’Geurts claim entails that in situations where we can ignore parts Geurts explains this pattern by assuming that determiners like One of ’sGeurts findings is that among the donkey sentences that he ) a. b) b) as true: 48 48 48 Although Geurts focuses on the determiner intersective determiners like also only available for intersective determiners,for it example, differs by fromBarker domain ( narrowing as understood, for Mary. While in the original model readings are true. of a model while we interpret an intersective determiner, it is unobservable ( context he describes as in one strategy for verifying universalsentences, sentences he and proposes another one in forcertain effect existential circumstances that be intersective interpreted on determinersIf submodels may they of are under the judged model true inthey in question. might the have submodel, in this the can entire replace model. whatever For truth value example, Geurts suggests that in a on the other, in that only the latter readily giveinfluence rise the to way aintersective, they scene “allow is us to interpreted: concentrateelse”. as on positive he evidence, puts and ignore it, all because they are like( these determiners only lead to distinct asymmetry between donkey sentencesone with hand, such and determiners those on with the universal determiners like Donkeys under Discussion tested, those with ( ( The relevant submodel here consists of all the boys and girls in weak determiners as well, including, whether the individuals were prototypical or marginal. In view of examples 20 early access srn”adannmxmlo wa”itrrtto.We meddunder embedded When interpretation. “weak” or non-maximal a and “strong” ela ihohrtere.I orc,i a eoeo h atr htexplain that factors the of one be may it correct, why If theories. other with as well the to rise gives determiner that whether 6 nSection in as here, presented theory the with compatible is claim This model. original the of value the on agree state input donkeys. referent. their some discourse in out their assigments leave all assignments that whose check farmer-owned some Pronouns be no will that there way If indefinite a out. such left in is this donkey assignments do the assignments example, these For maximal, of set. state smaller output a any non-maximal assign in while to possible, free as are values indefinites many indefinites as Maximal ambiguity. introduce lexical simultaneously a as distinction weak-strong the models indefinite indefinites the and maximal as ∃ ∀ every or maximal a between ambiguous are indefinites that proposes Brasoveanu ( ( following: multiple the with as sentences such than donkey anaphora by rather donkey part assignments of in of instances it sets motivates are and states assignments, information just PCDRT, which introduces He in DRT. system assignments compositional a by or provided semantics that dynamic than ordinary state in information of notion richer a quires Brasoveanu 50 49 . ( in example, For -reading. raig hl hs hs neeet r o-aia iers othe to rise give non-maximal are antecedents whose those while -reading, 4 ) ) Brasoveanu In ∃ ∀ / Brasoveanu okypoon hs neeet r aia iers othe to rise give maximal are antecedents whose pronouns donkey , ∀ raig r adt bev nitretv eemnr,a enoted we as determiners, intersective in observe to hard are -readings her a bought who boy Every it for pay a buys who Everyone Brasoveanu However, dichotomy. 6 e hita gift Christmas a . ekaet rpit wrap to deskmate 2008 1 . d . rusta nacuto npoaadqatfiainre- quantification and anaphora of account an that argues 2008 2008 a h anproeo hsabgiyi oacutfor account to is ambiguity this of purpose main the , a d d snnmxml mn h uptsae fthe of states output the among non-maximal, is donkey and 49 d okoln n a a has and online book h indefinite the ), d girl a d rdtcard credit a hita itfra for gift Christmas . map 38 Brasoveanu Formally, strong. both are d ofre-we oky.If donkeys. farmer-owned to ∀ 2008 raigo the or -reading hmolo ufr Henderson & Bumford & Champollion ( in non-maximal; as book a : 164 e e onsotta having that out points rdtcr ssit uses card credit ili i ls asked class his in girl sesl understood easily is ∃ raigo the on -reading 50 the ), a e d to is early access . 40 : n. will be . There are 2008 man came in. . In particular, d 1995 sat down A d 2008 There is a man who ) and quantificational and 2008 is on the truth-conditional and ). Our work shows that the variety of 2010 39 man came in. They 2010 d A Exactly one man came in, and he sat down and did. Indefinites can still introduce their own discourse dichotomy to the pragmatics, we no longer require the 2010 treats indefinites as ambiguous, but takes a different route 2008 ∀ / is predicted to be ambiguous between ∃ 2010 Brasoveanu sat down. In addition to sidestepping these worries about overgeneration in non- d 5 . referents; when they do, they are always interpreted non-maximally, resulting anaphoric components of quantificationalpaper also and contains modal a discussion subordination,Brasoveanu and the an implementation of donkeythan anaphora. Brasoveanu readings available for donkey anaphorato does sets not of by assignments. itself necessitate a move 6 certainly arguments for PCDRT whichthey we go have beyond not donkey addressed sentences; here in because particular, PCDRT has beenof partly plural moti- pronominal anaphora (Brasoveanu modal subordination (Brasoveanu ulate sets of assignmentsresolving as the in PCDRT. Becausesemantics to we model delegate any the ambiguityindefinites. at work This the of level allows of us eitherspecifically, to the the pronouns rely version or on the of a CDRT relatively introduced simple in semanticMuskens theory, quantificational contexts, our analysis offersof a donkey more ambiguities parsimonious than treatment the account in Brasoveanu have adopted, one can analyzeanaphora most with if ordinary not assignments all as phenomena in involving CDRT, donkey without having to manip- it is incorrectly predictedtrue whenever that every manspeculates who that came such in a sat sentencerelated may down. to beBrasoveanu agreement ruled or out presupposition for maximization. independent reasons He came in and who sat down of the maximal indefiniteFor and that the reason, if uniqueness the condition singular of pronoun the is pronoun. swapped out for a plural one, Donkeys under Discussion two indefinites in the grammarquantificational predicts a contexts. subtle For ambiguity example, even outside a of discourse like vated by the need to capture quantificational dependencies for the purpose The uniqueness inference in the latter reading arises from the interaction we have shown that in the presence of a pragmatic theory such as the one we While the main focus of Brasoveanu early access od,tefis okypooni aual nepee xsetal n the and existentially interpreted naturally is pronoun donkey first the words, h utpyslciequantifier selective multiply The Dekker of spirit the in is move this notes, he As up. pick can Brasoveanu referents; discourse additional introduce 2010 to determiners ability Embedding the indefinite referent. given the discourse are referent, introduced discourse previously In a novel definite. up a anaphoric picks introducing an of to instead identically case, translated that be can assumes indefinite now an Brasoveanu readings, that universal model To readings. existential in eodoeuiesly o osdrastaini hc vr a owns man every which in situation other a In consider shining. Now is universally. sun one the second when raining, home is at it umbrellas when his along of truth umbrella all its one leave for to take required and to is umbrella-owner what sentence, every this for of is reading natural most the On ( the pronouns: which two in antecedes sentences indefinite existential-universal same mixed from arises indefinite the indistinguishable be would referent the reading discourse from resulting the the up determiner, pick embedding to the able were definite the If is following: stipulation ( the a like example, sentences For discourse-initial out terms. rule semantic to in stipulated required explained be must be them cannot between and differences distributional any reading, a definite anaphoric the as tion indefinite the pairs; farmer-donkey ( ( sentence of follows: readings as universal be the and somewhat, existential Simplifying the selective. for singly LFs of make instead determiners selective embedding multiply of them translations the to adjustments necessary 53 52 51 Every a. ) ) Every ) oegnrlpolmwt prahsta oaeteabgiyin ambiguity the locate that approaches with problem general more A share definites and indefinites since that is approach this to downside One sue htteeaeteol icus eeet htindefinites that referents discourse only the are these that assumes vr a h a nubel ae taogo an asbtleaves but days rainy days. on sunny along on it home takes it umbrella an has who man Every b. ∀ ( in -reading Every ,d f amrwoon the owns who farmer ,d f f amrwoon a owns who farmer amrwoon a owns who farmer 51 b). the d every donkey a 40 d d d okybasit beats donkey donkey d okybasit beats donkey ,d f okybasit beats donkey would. in hmolo ufr Henderson & Bumford & Champollion ( 51 eevstesm interpreta- same the receives b) unie neetover effect in quantifies d d . . d . xseta reading existential 9 nvra reading universal aeasmdto assumed are ) d nrdcdby introduced 1993 the ; early access . 2010 leads 2016 . This of course 2008 relies on the strong and Brasoveanu will contain, between a) were tasty. 2016 above when indefinites ap- 2008 54 ( d 4 were tasty. . 6 d leans on the PCDRT framework 2016 41 , the full power of PCDRT is not needed 4 . sandwich. They 6 d sandwich. #They d ) as true only if every umbrella-owner takes all his ), Champollion 53 , augmented with designated “error” referents/objects, 2016 could at least avoid this possibility in principle by stip- 1995 2010 2008 — a precursor of the current work — sketches a dynamic frag- b. Every student ate a ) semantic clauses into a simple compositional dynamic framework Champollion 2016 , the assignments coming out of sentence As we have seen in Section On the present account, the ambiguity is located in the pragmatics, and ) a. A student ate a b), but this is impossible. a 6 . 54 2016 54 are necessarily interpreted weakly (non-maximally). But since Champollion ( Brasoveanu ulating that indefinites outside the arguments of generalized quantifiers pear outside of quantificational contexts.of For instance, given the maximality them, as many sandwiches asnoun were ought eaten then by to students. The be subsequent able pro- to refer to this discourse plurality, as it can in for our purposes. In addition,to the specific several setup empirical in Champollion issues. First, Champollion inherits the difficulties mentioned in Section mixed scenarios. But where the current approach fairly directly lifts Križ’s of Brasoveanu together with explicitly supervaluationist lexical entries for determiners. lion ment intended to generate effective truth-value gaps for donkey readings in dry). While this isDid not everyone the stay case dry in when the it situation rained of and interest, unburdenedumbrellas a when with QUD it them, such was as as sunny? desired. 6 assigned the wrong meaning on both Brasoveanu generating the plausible reading posestics no treats particular sentence( problem. Theumbrellas seman- with him when it is rainy (even though one would suffice to stay Donkeys under Discussion two umbrellas, so thatantecedent the is two interpreted readings strongly do or not weakly, collapse. one No of matter the if pronouns the will be ( (maximal) entry for indefinites proposed in Brasoveanu ( (that of Muskens will lump this situation together with those where everyone took multiple With essentially the same goals in mind as in the project here, Champol- 21 early access hte h icus referent discourse the whether oacrandsorerfrn.Frisac,i h sentence the respect in a with instance, owns uniformity For who for referent. update discourse local certain its a of to outputs the tests that meaning maximal single a to committed is everywhere. it indefinite sentences, donkey comprise that ments 2016 hnst io hro o onigti out. this pointing for Charlow Simon insulters. respect to their Thanks with with mixed fights are in students got whether they all on whether insulted; depend to were to where they ought cases whether readings those to its respect in of with just mixed error are an behaviors throwing students’ by obtained conditions truth ( But The clause. worry. pronoun relative undergeneration the the the instead, is that high This is scope information. worry take this overgeneration cannot of it all island, see clause to relative enough insulted the the who in quantifier: somebody embedded the with is of fight pronoun scope a nuclear in entire getting the of is property case this in uniformity for of each of honor Its ( islands, scope of issues. presence over-generation the ( and In in under- test. both uniformity to its leads of this basis the as uses it the by injected donkeys the of none or all either maximal when beats words, John other that sure In make is. moment John, the farmer of considering farmer in particular stored the values whoever the by to referent respect discourse with the uniformly behaves — farmer owning beats 55 ) ∀ 55 Champollion Second, omk hswr,tepoonms aesoeoe h rdct that predicate the over scope take must pronoun the work, this make To raig o xml,i rejs ncs vr student every case in just true is example, for -reading, si atmtvtdb eiet vi eatcabgiyi h ele- the in ambiguity semantic avoid to desire a by motivated part in is ): hc ili ahdsrbtv yl ee osm atclrdonkey- particular some to refer cycle distributive each in will which — h nutdit insulted who vr tdn h ruh a brought who student Every a d . d okybasit beats donkey x sbcpcs h rprythat property The backpacks. ’s d . d 55 hc ilpc u l ftednesowned donkeys the of all out pick will which — 2016 it hsn edn hc ol orsodt the to correspond would which reading no has ) d d ilts h noigst fasgmnsto assignments of sets incoming the test will h rnu ilb ncag finspecting of charge in be will pronoun the , f sin otesnua okypoona pronoun donkey singular the to assigns soitdwt h ujc ftepredicate the of subject the with associated d 42 akakgti gtwt somebody with fight a in got backpack hmolo ufr Henderson & Bumford & Champollion can 21 it osdrtesentence the Consider aesoejs within just scope take d ol edt test to need would d x Every u ic the since But . eeddthe defended f farmer early access , -rea- ) and ∃ treats 1996 dichotomy 2016 ∀ / ∃ -reading. Because different ∀ , we propose to treat the classical , we have given plural definites and 43 1996 ). The pragmatic component of our account , but does not assume that donkey sentences -reading and the 1991 ∃ 1996 Things are equivalent for current purposes to the way while keeping the context constant (Yoon and Krifka Things are equivalent for current purposes to the way as 1996 -reading can flip-flop when one switches between predicates closed , , we have identified this equivalence relation with an implicit ∀ and 1994 2016 open By shifting some of the explanatory burden from the semantics to the To specify what it means to be equivalent for current purposes, we have Conclusion is broadly similar to Barker involve a uniqueness or homogeneityyet-unconstrained presupposition notion and of does domain not narrowing. rely on a pragmatics, we have avoided problems that arise from trying to make plural ding and the like tion participants are working; wethe have QUD. identified this This implicit accounts questionQUD, for with is the fully fact specified that andas when held ambiguous between the fixed, the a context, donkeydonkey including sentence sentences the are is used not in perceived evoke different conversational different settings settings (or when naturally presented in isolation), the QUD may well modeled this notion as anunderspecified equivalence by relation the between semantics worlds anding that determinedKriž is by left the pragmatics. Follow- question that represents the overarching goal towards which the conversa- donkey sentence as they would be if every farmermodulo who the owns contrary-to-fact a implication donkey that beatpragmatic all these account the paraphrases captures donkeys suggest. he the Our owns exceptionand tolerance donkey of sentences both in plural a definites simple and uniform way. scenarios, and leaves truth-value gapsby for theYoon pragmatics to fill.donkey As anaphora suggested a uniform pragmaticThe treatment. doors Just are open as Križ they would be if all the doors are open in donkey sentences followsindependently from motivated the formal interaction systems: a of pragmaticdisambiguates two account plural relatively of how definites simple context and donkeysemantics sentences, which and abstains a lean from dynamic drawing borders between true and false Donkeys under Discussion 7 vary from one donkey sentence to another. This explains why the (Gawron, Nerbonne & Peters This work has shown that the apparent complexity of the when one switches between contexts while keeping the sentence constant early access work. etgto a pndu.Frt hr sa ct edfrtere fhow of theories for need acute an is there First, up. opened has vestigation con sflycmail ihasmn lrlidvdasa eeet of referents as individuals plural our assuming said, with That compatible pronouns. fully donkey is singular account of interpretation the of in individuals semantics the in involved be Kanazawa as because, problematic that assumption Yoon problematic owns particular, the In on rely uniform. Krifka semantically and anaphora donkey and definites ie ihsc hoist aepeitosaotdne etne in sentences donkey about predictions make com- to be theories can such account pragmatic with Our bined QUDs. on converge jointly interlocutors choice the down narrow to evidence sufficient them. re- common between provide the hearers’ when not from QUDs stems does possible hesitation several ground of the one and accommodate judgments QUDs, to in the in luctance variation which variation The in value. to truth scenarios traced definite is the a precisely deliver not are does these semantics scenarios: mixed in ments pronouns. donkey two Brasoveanu ( in like out sentences laid been have with systems Problems of antecedent. Section types indefinite second the and of first ambiguity the an to Brasoveanu back or traced determiner; is embedding the of Kanazawa level pronoun; from the donkey apart the it of sets ambiguity This an ambiguity. Chierchia semantic as the of such avoids sort systems also any it postulate components, motivated to independently need and lean on rely it of number a avoid to able Champollion were in we identified issues states, empirical information Brasoveanu plural in on those relying like pluralities states evaluation-level of information terms plural in and anaphora donkey treat that systems the (Muskens for CDRT of fragment a to plural ecoeb onigotsvrlnwaeuso eerhta u in- our that research of avenues new several out pointing by close We judg- guarded and varied give hearers why explains account our Finally, does only Not parsimonious. theoretically is explored have we system The streamlined semantics the keep to us allows also component semantic Our a egvnaprle nlssi em fpua niiul.Ti is This individuals. plural of terms in analysis parallel a given be can Kanazawa by suggested as pronouns, donkey 6 ∃ . / 1 ∀ sw aeson h hr yeo ytmhspolm with problems has system of type third the shown, have we As . ihtm ndne etne osntrqiemvn to moving require not does sentences donkey in dichotomy 53 i hc h aeidfiiesre sa neeetto antecedent an as serves indefinite same the which in ) 1995 hr the where , 1995 it u con vistene o plural for need the avoids account Our . 2001 44 , 1996 hw,pua niiul cannot individuals plural shows, .W aesonta accounting that shown have We ). 2016 ∃ hmolo ufr Henderson & Bumford & Champollion / ∀ 1994 rcro ftepresent the of precursor a , ihtm satiue to attributed is dichotomy 2001 hr ti oee at modeled is it where , it and 2008 2008 . h okys he donkey(s) the , 2010 , 2010 hr it where , ynot By . 2008 : early access . / . If 1007 , it is . or — as Natural . Seen in take the 10 00372821 D neither /bf Linguistic Inquiry 1007 . . were all best-sellers 10 d . https://doi.org/ , Chierchia, Fox & Spector 00056 219 – 2000 book; they 159 /ling_a_ d ). ), we have assumed a globalist view of 2 ( 1162 4 . https://doi.org/ 45 . . Generalized quantifiers and natural lan- 2016 10 259 – ) is externally static, so we have no account 1981 237 21 ). 3 . An antinomy about anaphora. ( 4 Not every farmer who owns a donkey beats it 2011 — Every student read a . Presuppositions for proportional quantifiers. 3 . 6 schema( in . https://doi.org/ D . 1996 517 – Linguistics and Philosophy 509 ). 3 ( 00350139 ). For example, a localist version of our account could let Although we have implemented our semantics in a dynamic fragment, Language Semantics guage. bf 42 Barwise, Jon & Robin Cooper. References Almotahari, Mahrad. Barker, Chris. every student who tookargued a in class Section from methis liked way, it, donkey sentences I constitute willbetween a localist get novel and a testing globalist ground bonus accounts for of the the debate semantics-pragmatics interface. into the compositional semantics (Levinson 2011 QUD as an additional argumentdetermining and the output dynamic a potential bivalent of semantics,be the as helpful sentence. well for Such as the a interpretation model of could embedded also donkey sentences such as discourse referent of the embedding determinerin makes subsequent available sentences. for Like anaphora Križ ( the semantics-pragmatics interface, in whichflow there from is the a semantics one-way to information reformulate the our pragmatics; account but in it localist would terms not so be as difficult to to allow pragmatic intrusion particular, the for discourses like In contexts where theplausible that truth the value same pragmatic ofcontext factors also that a influence determine donkey which its individuals truth sentence — which value is donkeys, in for example — the mation, and what is theRelatedly, role of we question-answer have congruence in leftcongruence this to open process. the how trivalent setting. to extend theories of question-answer Donkeys under Discussion context. More generally, theories ofsuch QUDs as should address how related hearers questions accommodate QUDs in the face of incomplete infor- we do not handle anaphora to maximal sets or evaluation pluralities; in early access rsvau Adrian. Brasoveanu, Adrian. Brasoveanu, Clark. Z. Brady & I. David Beaver, ekr Paul. Dekker, Robin. Cooper, Spector. Benjamin & Fox Danny Gennaro, Chierchia, Gennaro. Chierchia, Gennaro. Chierchia, Lucas. Champollion, Christine. Brisson, Christine. Brisson, Adrian. Brasoveanu, //doi.org/ 11245 10 1023 10 semantics 9783110253382 chap. Communication (HSK)), and Science Linguistics of Handbooks / nikationswissenschaft Claudia Heusinger, meaning language von natural (eds.), Klaus Portner In Paul phenomenon. & Maienborn grammatical a as ture grammar https://doi.org/ of theory the and Philosophy 3765 (SALT Conference Theory Linguistic and predication. http://ling.rutgers. dissertation. edu/images/ University Rutgers NJ: Brunswick, New Semantics individuals. non-atomic http://ling.rutgers.edu/ images/diss_brasoveanu_ dissertation. University Rutgers NJ: Brunswick, meaning determines . . 1002 61 /a: /salt.v / – 1 92 1022771705575 . / 392554 9781444304176 . http://hdl.handle.net/ dissertation. Amsterdam of University . 10 1993 27 26 15 1979 . igitc n Philosophy and Linguistics 10 ( 1007 i ( 4 0 2 ). . . . . ). . 2297 1 3864 1998 10 2003 rnsneta eiain:usaddwsi dynamic in downs and ups meditations: Transsentential 2008 437 . h nepeaino pronouns. of interpretation The . 111 2016 1995 1 1992 /s 2010 2007 . . 121 7208 10988 . – – https://doi.org/ Publishing. Blackwell UK: Oxford, . . . 527 183 Plurals, . 87 okypuaiis lrlifrainsae versus states information Plural pluralities: Donkey . ooeet ndne sentences. donkey in Homogeneity . . . . itiuiiy aiaiyadflaigquantifiers floating and maximality Distributivity, npoaaddnmcbinding. dynamic and Anaphora . 4641 eopsn oa quantification. modal Decomposing . yaiso enn:Aahr,presupposition, Anaphora, meaning: of Dynamics . /chicago/ , . https://doi.org/ . igitc n Philosophy and Linguistics https://doi.org/ . tutrdnmnladmdlreference modal and nominal Structured 2297 2007 - 008 vol. , .pdf. hcg,I:Uiest fCiaoPress. Chicago of University IL: Chicago, . – .pdf. - 2331 all 9035 3 eatc:A nentoa adokof handbook international An Semantics: 2008 9780226104515 46 n h ouiomt fcollective of nonuniformity the and , Hnbce u pah n Kommu- und Sprach- zur (Handbücher https://doi.org/ Gruyter. de . - 0 . . 26 es n estvt:Hwfocus How sensitivity: and Sense 26 hmolo ufr Henderson & Bumford & Champollion ( 10 10 2 ) ). . . . 684 1093 1007 129 – – . 704 001 /jos/ffq /bf 184 ytxadSemantics and Syntax 31 2011 00635805 https://doi.org/ . . https://doi.org/ . 0001 ( 2 ). clrimplica- Scalar . igitc and Linguistics 008 129 26 . hSemantics th – . 209 ora of Journal . 10 https: . New . . 1515 10 10 / . . . early access . . – a . 156 335 213 – . The -z. . New e , . https: 2 Linguis- 91 129 . Jeroen – ). 2008 9029 . 300 2 - 67 ( – 00628304 . de Gruyter. , , vol. 744110 25 4 / . Stanford, CA: 008 /bf 265 Linguistics and 9 - 189 – . The absorption ). ce 144 4 Natural Language 8 - – 1007 00630732 3 164 . ( , chap. 11050 1991 , 10 105 /bf 30 /s , 1007 1007 . . . 10 A. 10 . 164 Synthese 22 . . Dynamic predicate logic. (Mathematics Studies). Amsterdam, 1991 19 47 Linguistics and Philosophy . https://doi.org/ . . . Milan, Italy: University of Milano-Bicocca .pdf. 100 . Vol. – 3581 / 1014624331450 39 903 . https://doi.org/ . https://doi.org/ The dynamics of sophisticated laziness 9783110852820 c YTJmN. ). /a: / 2 9 . 1 The logic of pragmatics. an experimental investiga- Situation theory and its applications 2011 ( . Presuppositions, supervaluations and free logic. In 178 . 237 00485047 ce The logical way of doing things – – 14 1023 1515 . . 46 1993 /bf f Intensional and higher-order modal logic, with applica- 137 1969 2012 . Quantifiers and partiality. In Jaap van der Does & Jan 205 The semantics of definite and indefinite noun phrases Quantifiers, logic, and language 10 10 . ). 76 . . E-type pronouns and donkey anaphora. ). . File change semantics and the familiarity theory of def- . Donkey business. 2 c 3 ( 1007 ( 7 . 1996 1975 13 . Vagueness, truth and logic. 16 be 1982 10 1990 1983 2002 02 e Meaning, use and interpretation of language 1975 517 . Saarbrücken, Germany: CSLI Publications. http://scidok.sulb.uni- d Philosophy initeness. In Rainer Bäuerle, Christoph Schwarze & Arnim vonhttps://doi.org/ Stechow question-answer requirement for scope assignment. Semantics archive.net/Archive/jA https://doi.org/ tics and Philosophy principle and E-type anaphora. In& Jon Syun Barwise, Jean Tutiya Mark (eds.), Gawron,362 Plotkin saarland.de/volltexte/ Karel Lambert (ed.), Haven, CT: Yale University Press. tions to Montague semantics Netherlands & Oxford, UK: North Holland. tions with children and adults dissertation. CSLI Publications. https://pdfs.semanticscholar.org/ 88 Groenendijk (ed.). DYANA deliverable R van Eijck (eds.), (eds.), Amherst, MA: University of Massachusetts dissertation. http://semantics //doi.org/ Heim, Irene. Heim, Irene. Heim, Irene. Geurts, Bart. Groenendijk, Jeroen & Martin Stokhof. Gualmini, Andrea, Sarah Hulsey, Valentine Hacquard & Danny Fox. Gawron, Jean Mark, John Nerbonne & Stanley Peters. Gallin, Daniel. Foppolo, Francesca. van Fraassen, Bas C. van Eijck, Jan. Fine, Kit. Donkeys under Discussion van der Does, Jaap. early access ap as&UeReyle. Uwe & Hans Kamp, Nirit. Kadmon, Theo. Janssen, Griffin. Eric Jackson, eisn tpe C. Stephen Levinson, Peter. Lasersohn, Francez. Nissim & Shalom Lappin, Chemla. Emmanuel & Manuel Križ, Manuel. Križ, Manuel. Križ, Manfred. Krifka, Lewis. S. Karen & C. Jeffrey King, Goodman. D. Noah & Bergen Leon Wu, Y. Jean T., Justine Kao, Makoto. Kanazawa, Makoto. Kanazawa, //doi.org/ mtra,Ntelns nvriyo mtra dissertation. Amsterdam of University Netherlands: Amsterdam, 1007 1010766724907 17 9114 anaphora. homogeneity. of problem Semantics projection Language the to application their and tics guage 6 sentences. donkey entries/anaphora/. http://plato.stanford.edu/archives/sum University. Stanford Lab, Philosophy of Encyclopedia Stanford Sciences words. number of understanding Philosophy and Linguistics setting. dynamic a in inference monotonicity https://doi.org/ Kluwer. lands: https://doi.org/ statements general and ) . ( 2 136 ). 33 . -z /bf 109 ina uti:Uiest fVen dissertation. Vienna of University Austria: Vienna, . ( – 3 153 00985574 ). 111 – 493 10 2016 158 https://doi.org/ . 2015 igitc n Philosophy and Linguistics ( 1990 1983 . 33 2307 – https://doi.org/ . 1996 539 ). ooeet,nnmxmlt,and non-maximality, Homogeneity, . 1999 . . 2001 10 1994 12002 set fhmgniyi h eatc fntrllan- natural of semantics the in homogeneity of Aspects . Uniqueness. . 2000 . / https://doi.org/ . 1994 onain n plctoso otgegrammar Montague of applications and Foundations . 417059 6 rgai teghnn npua rdctosand predications plural in strengthening Pragmatic . 1007 hSmnisadLnusi hoyCneec (SALT Conference Theory Linguistic and Semantics th rgai halos. Pragmatic . iglrdne rnusaesmnial singular. semantically are pronouns donkey Singular . 23 ekv.srn ednso okysnecsand sentences donkey of readings strong vs. Weak . – . . tnod A tnodUiest dissertation. University Stanford CA: Stanford, . 1993 ( 12007 rsmtv meanings Presumptive /bf 3 eaieplrt,dfiie ne quantification under definites polarity, Negative ). . 00627710 205 24 10 . 2016 rmdsoret logic to discourse From https://doi.org/ . . ( 1994 – 2015 3765 10 10 3 igitc n Philosophy and Linguistics 248 ). . . npoa nEwr .Zla(ed.), Zalta N. Edward In Anaphora. . rceig fteNtoa cdm of Academy National the of Proceedings 48 1007 1007 383 w ehd ofidtuhvlegaps truth-value find to methods Two . -yepoon,ism,addonkey and i-sums, pronouns, E-type . 10 https://doi.org/ . Summer , /salt.v . . – 1093 17 /bf / 403 978 Language ( 4 hmolo ufr Henderson & Bumford & Champollion 00984775 6 ). https://doi.org/ . /jos/ffv i - 0 94 391 . 2016 2769 abig,M:MTPress. MIT MA: Cambridge, . igitc n Philosophy and Linguistics - 10 011 – 428 . 1073 eahsc Research Metaphysics . . - 006 75 all . 2066 https://doi.org/ . 10 odeh,Nether- Dordrecht, . ( . 3 /pnas. . . ora fSeman- of Journal ). 1007 - 2014 1 522 . 13 /s 1407479111 – ( 3 10 Nonliteral . 551 11050 ). . 273 Natural 1023 hts: https . 2016 – - 015 324 The /a: 10 / . - . . . early access . . 69 – 1 ). . Linguis- 6 5 / b : ling . ( . London, _ 5 Linguistics 145 (Amsterdam 1023 – . . https://doi. 1005571202592 99 /full.pdf. . 58 114 10 . https://doi.org/ . Berlin, Germany: – /a: 1 630 186 / ). 430 Debrecen Symposium – /TENSEAND.PDF. – 3 , vol. ( 1023 Journal of Philosophical . 9781137333285 5 / 143 1874 414 10 00258436 . , 1987 ). 2 ( 842427 90 /bf 1057 . 19 . Amsterdam/Philadelphia: John 10 1007 . 0018456 183 – Semantics and Pragmatics 10 . https : / / doi . org / 49 /bfb 147 763 – . . Budapest, Hungary: Akadémiai Kiadó. . https://doi.org/ 6 1007 . . 727 5 94 – 308 10 ). – 6 81 . The meaning of plural definites: A decision- /sp. ( . Combining Montague semantics and discourse , . Tense and the logic of change. In Urs Egli, Peter E. 213 f. . Anaphora and the logic of change. In Jan van Eijck 26 Semantics and Pragmatics . . Questioning to resolve decision problems. . Polarity in natural language: Predication, quantifica- 8 . The conceptual nature of natural language quantifi- ). . 3765 2012 3 . https://doi.org/ . . . Information structure in discourse: towards an inte- ( 1996 Pragmatics, semantics and the case of scalar implicatures 3 Plural pronominal anaphora in context: Dynamic aspects 1995 . . Pronouns as paraphrases. Manuscript. . Utrecht, Netherlands: Utrecht University dissertation. 1991 . An account for the homogeneity effects triggered by plu- 10 . 23 5 Linguistics and Philosophy 1987 2003 2000 359 . Scorekeeping in a language game. – 2012 98658 . 1978 /sp. 2014 2003 00635836 339 1979 ). 1 /bf 3765 ( . 8 Logics in AI: European workshop JELIA ’ 10 1007 . 0000004548 grated formal theory of pragmatics. https://doi.org/ tics and Philosophy of quantification https://dspace.library.uu.nl/bitstream/handle/ Studies in the Theoryrent and Issues History in of Linguistic Linguistic Theory), Benjamins. Science:https://pure.uvt.nl/portal/files/ Series IV: Cur- representation. Springer. https://doi.org/ Pause, Christoph Schwarze, ArnimLexical von knowledge Stechow in & the Götz organization Wienold of (eds.), language UK: Palgrave Macmillan. https://doi.org/ theoretic approach. org/ and Philosophy ral definites and conjunction basedPistoia on Reda double (ed.), strengthening. In Salvatore cation. In Imre Rusza &of Anna Logic Szabolcsi and (eds.), Language tion and negation in particular and characterizing sentences. Logic 10 (ed.), (Palgrave Studies in Pragmatics, Language and Cognition), Roberts, Craige. van Rooij, Robert. Nouwen, Rick. Muskens, Reinhard. Parsons, Terry. Muskens, Reinhard. Malamud, Sophia A. Muskens, Reinhard. Magri, Giorgio. Löbner, Sebastian. Löbner, Sebastian. Donkeys under Discussion Lewis, David. early access usn AZ Tucson, 10 cuet ehr .&FacsJffyPelletier. Jeffry Francis & K. Lenhart Schubert, Mats. Rooth, [email protected] Room Bldg. Communication Arizona of University Linguistics of Department Henderson Robert [email protected] NY York, New University York New Linguistics of Department Champollion Lucas Youngeun. Yoon, Youngeun. Yoon, Anna. Szabolcsi, Roger. Schwarzschild, ahntnPlace Washington //doi.org/ 10 org/ interpretations. Korean tion. and English in NPs definite taking scope of Ways distributivity. org/ Philosophy), issues and Semantic II: (eds.), volume Turner meaning, Raymond and & Gennaro Partee In H. generics. Barbara interpret Chierchia, to Theory Representation Discourse using https://doi.org/ Reidel. approaches Netherlands: logical and (ed.), Linguistic Gärdenfors quantifiers: Peter eralized In Semantics. Situation and Semantics, Change . 1007 10 10 . . 1007 1007 85721 /bf 10003 1987 10 01256743 /bf / . 1007 978 aua agaeSemantics Language Natural 1996 1997 1994 onprs nepeaini otgeGamr File Grammar, Montague in interpretation phrase Noun . 00372820 aua agaeSemantics Language Natural - 94 193 / 978 taeisfrsoetkn.I naSaoci(ed.), Szabolcsi Anna In taking. scope for Strategies . oa n ata rdctsadtewa n strong and weak the and predicates partial and Total . . - . 1993 009 ekadsrn nepeain fqatfir and quantifiers of interpretations strong and Weak – , 268 - 109 109 94 - . lrl,peupstosadtesucsof sources the and presuppositions Plurals, . 2723 - https://doi. Kluwer. Netherlands: Dordrecht, . 011 – 154 - - 5814 0 https: Kluwer. Netherlands: Dordrecht, . _ 6 50 nvriyo ea tAsi disserta- Austin at Texas of University . . [email protected] CA Angeles, Los 3125 Angeles Los California, of University Linguistics of Department Bumford Dylan - 5 10 _ 4 apelHall Campbell . . 1007 hmolo ufr Henderson & Bumford & Champollion vol. , 1989 2 ( / 3 978 ). 4 39 eeial paig or, speaking, Generically . 201 ( 3 - ). 94 90095 Suisi Linguistics in (Studies – 217 248 , - 009 237 – rpris types, Properties, https://doi.org/ . 236 – - 268 3381 https://doi. . Dordrecht, . - 1 _ 9 . Gen-