RESEARCH
Dancing monkeys in Serbian and Korean – exhaustivity
requirements on distributive share markers
Ana Bosnić1,2
, Jennifer Spenader1
and Hamida Demirdache2
1
	 University of Groningen, Groningen, NL
2
	 University of Nantes, Nantes, FR
Corresponding author: Ana Bosnić (a.bosnic@rug.nl)
In some languages, distributive markers/quantifiers can attach to the argument that is being
distributed (the distributive share), as opposed to the restrictor of the sentence (the distributive
key). Researchers agree that distributive share markers can also distribute over events (and not
only individuals), but disagree as to what these markers are semantically – universal distributive
quantifiers or event plurality (pluractional) markers. In this paper, we experimentally probe ­spatial
event distribution. On a universal quantification account, exhaustive distribution over a spatial
distributive key is enforced, while on the pluractional analysis there is no such requirement. We
carried out two picture verification experiments to test exhaustivity requirements in intransitive
sentences with distributive share markers from two typologically different languages: the Serbian
marker po and the Korean marker -ssik. We found evidence for an exhaustivity requirement
over pluralities of non-atomic individuals (groups), but not over designated spatial locations.
We interpret these findings as evidence that the semantics of (spatial) event distribution with
distributive share markers involves a (spatial) distributive key. Specifically, po/-ssik have a
universal quantificational force (with a meaning akin to per (each)) establishing a distributive
relation between individual events and elements of the spatial distributive key. Plural individuals
made salient in the visual input can serve to divide up the spatial key into chunks of space that
have to be exhausted.
Keywords: event distributivity; event plurality; spatial distribution, exhaustivity; distributive
share/key; atomicity
1 Introduction
The fundamental question of how so-called distributive share (DistShare) markers should
be analyzed semantically is a matter of contention in the existing theoretical literature. A
pervasive line of analysis takes DistShare markers to be universal distributive quantifiers,
just like so-called distributive key (DistKey) markers, but that can distribute over implicit
spatiotemporal arguments unlike DistKey markers (Choe 1987; Gil 1995; ­Zimmermann
2002b; Balusu 2006 a.o.). Other researchers, however, take DistShare markers to be
pluractional markers, simply signaling event plurality without universal quantification
­(Matthewson 2000; Muller and Negrão 2012; Cable 2014; Knežević 2015; Pasquereau
2018 a.o.).
We bring novel empirical evidence to bear on these issues by experimentally probing
whether DistShare markers exhibit a required feature of universal quantification –
namely, that distribution over the members of the DistKey be exhaustive. While there is an
ever-growing interest in the semantics of DistShare markers across languages, especially
including lesser studied languages (see Gil 1982; 1995; Choe 1987; Farkas 1997; Oh 2006;
Glossa general linguistics
a journal of Bosnić, Ana, et al. 2020. Dancing monkeys in Serbian and Korean –
exhaustivity requirements on distributive share markers. Glossa: a journal
of general linguistics 5(1): 78. 1–28. DOI: https://doi.org/10.5334/gjgl.858
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
on distributive share markers
Art. 78, page 2 of 28
Zimmermann 2008; Henderson 2011; Cabredo-Hofherr & Etxeberria 2017 a.o.), these
markers have hardly been investigated experimentally. Knežević (2015) and Knežević &
Demirdache (2017; 2018) are among the few attempts to experimentally test DistShare
marker interpretations, investigating the Serbian DistShare marker po with both adults
and children. However, the focus in the theoretical literature has been mostly on individual
and/or temporal (as opposed to spatial) distributive readings. 
This paper reports on the first experimental investigations into spatial event readings,
as well as the first investigation into exhaustivity effects with DistShare markers, testing
Serbian and Korean, two typologically distinct languages that both have DistShare
markers. The question our experiments sought to address was whether DistShare markers
in Serbian and Korean should be analyzed as markers of event plurality, or as universal
quantifiers requiring a DistKey over which distribution takes place exhaustively. To test
for exhaustivity, we set up (with the first experiment and its follow up) different putative
distributive keys. Our experimental results do indeed provide evidence that the eventdistributive
reading that DistShare markers yield involves a covert (spatial) DistKey that
must be exhausted contra the event plurality hypothesis. But this exhaustivity requirement
is not realized as initially expected under the universal quantification hypothesis:
the exhaustivity requirement that speakers of both languages appear to impose is over
pluralities of non-atomic individuals (groups), but not over designated spatial locations.
We take this conclusion to argue in favor of a universal quantification analysis, on the
assumption that DistShare markers can distribute over entities that are non-atomic such
as time and space, as well as entities that are bigger than atoms – that is, groups/pluralities
of atomic individuals. 
The paper is organized as follows. Section 2 presents the basic concepts and issues
underlying the analysis of DistShare markers in the literature and the two main lines of
analysis investigated: universal distributive quantification and event plurality. Section 3
presents two picture verification experiments conducted to test exhaustivity requirements
using Serbian and Korean. The results actually revealed exhaustivity requirements, over
pluralities of non-atomic individuals (groups). Section 4 discusses how these findings
relate to the existing theoretical research. We then develop an analysis of spatial event
distribution along the lines of Zimmermann (2002b). DistShare markers are analyzed as
locative prepositions with universal quantificational force (with a meaning akin to per
(each)) establishing a distributive relation between individual events and elements of a
spatial/temporal DistKey. Plural individuals made salient in the visual input can serve to
divide up the spatial DistKey into relevant spaces that have to be exhausted. We close by
discussing this account in the context of Champollion’s (2016b) parameters of variation
for distributivity operators. Section 5 concludes by pointing out directions for further
experimental research.
2  Distributive share vs. Distributive key markers across languages
To illustrate the issues at stake, let’s start with (1), uttered in the context of a birthday
party with many presents and invitees, including four boys. (1) will be true if each of the
four boys in the context has individually bought two presents, yielding a total of eight presents
(bought by the boys). Each in (1) thus induces a distributive interpretation involving
pairs of presents distributed over the atomic members of a contextually restricted set of
boys. Importantly, the set of boys must be exhaustively distributed over, i.e. there cannot
be a boy who did not buy two presents.
(1) [Each boy] bought two presents.
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Art. 78, page 3 of 28
Gil (1982; 1995) distinguishes two major typological classes of distributive markers
crosslinguistically: Distributive key vs. Distributive share markers. The DistKey (or sorting
key) refers to the set that is being distributed over, and the DistShare to what is being
distributed (see also Choe 1987 and Zimmermann 2002b a.o.). Thus, in (1), the restriction
boy of the universal quantifier each is said to serve as the DistKey and the NP two presents
as the DistShare. Now consider a language that has DistShare markers, Serbian, which has
the distributive marker po.1
Consider the example in (2):
(2) [Dečaci DistKey
] su kupili [numNP
po dva poklona DistShare
].
boys.nom aux bought distr two presents.acc
a. ‘(The) boys each/individually bought two presents.’ – Individual distributive
reading
b. ‘(The) boys bought two presents at each/different place(s)/time(s).’ –
(Spatial/Temporal) event distributive reading
As shown in (2), Serbian po forms a syntactic constituent with the NP serving as the
DistShare (dva poklona “two presents”), i.e. the argument denoting what is being distributed.
(2) yields the reading in (2a), where distribution is over the plurality of individuals
denoted by the overt subject argument of the verb (boys), and which we refer to as
an individual distributive reading (four boys and eight presents). Crucially, (2) actually
yields the additional possible readings in (2b), where there is a plurality of events (of boys
buying two presents) distributed over contextually salient spatial or temporal locations.
For instance, four boys could have bought two presents on Monday and then again two
presents on Tuesday (the end result is then four boys and four presents).2
Note, importantly,
that these spatial and temporal locations are implicit arguments of the verb (they
are not denoted by an overt NP/DP in the sentence). We will refer to such readings as
event distributive readings.
Importantly, for intransitive sentences, the only overt argument that po can syntactically
combine with, and that can thus serve as the DistShare, is the single argument in subject
position. In other words, the DistKey will have to be a covert spatio/temporal argument,
which means that intransitive sentences only yield event distributive readings:
(3) Po dva dečaka pevaju.
distr two boys sing.pl
‘Two boys are singing at each/different place(s)/time(s).’
On the basis of a very broad and extensive typological overview of DistShare marking
across languages, Gil (1982; 1995; 2013) claims that DistShare markers are typologically
more marked than DistKey markers. Languages that have DistShare marking are typologically
diverse, including Korean, Japanese, the majority of Slavic languages, Hungarian,
German, Georgian, Karitiana, Hausa, and many others. We focus here on DistShare markers
from two typologically unrelated languages, Serbian and Korean, that show similar
syntactic and semantic properties.
	1
	Serbian also has universal DistKey markers (quantifiers) svi/svaki (all/every). For discussion of svaki as well
as its interaction with po, see Knežević & Demirdache (2018).
	2
	While these examples are more easily available, there are other possible, but increasingly more complex,
readings to get out of the blue (e.g. two groups of four boys each could have bought two presents, resulting
in eight boys and four presents in total).
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Art. 78, page 4 of 28
The DistShare marker po in Serbian attaches to numerals (henceforth num), reduplicated
numerals (num po num), bare singular nouns (analyzed in Knežević (2015) as having a
silent numeral one), and weak quantifiers such as few (e.g. po nekoliko).3
What is more,
po can attach to any argument in the sentence, e.g. the direct object, the subject (or even
both these arguments), or to adverbials. Importantly, Korean shows the same attachment
possibilities for its DistShare marker, the particle -ssik, and the range of interpretations
of -ssik sentences are similar to Serbian po sentences (see Oh (2001; 2006) for discussion
of -ssik). For the purposes of this paper, however, we confine ourselves to distributive
po/-ssik attaching to numeral phrases (numPs) in simple intransitive sentences.
The Korean example in (4) shows that the two properties that distinguish Serbian po (2)
from the determiner each in English (1) carry over to -ssik:
(4) Sonyen-tul-i [numNP
senmwul-ul twu-kay-ssikDistShare
] sa-ss-ta.
Boy.pl.nom present.acc two.clf.distr buy.past.dec
a. ‘(The) boys each bought two presents.’
b. ‘(The) boys bought two presents at each/different place(s)/time(s).’
Unlike determiner each that attaches to the NP serving as the DistKey (its restrictor boy
in (1)), but just like po, -ssik attaches to the NP serving as the DistShare (two presents). It
can also yield either the individual distributive reading in (4a), or the (spatial/temporal)
event distributive reading in (4b). It is specifically the latter property – the availability
of event distributive readings over implicit spatial or temporal arguments of the verb –
which distinguishes distributive markers such as po or -ssik, on the one hand, from both
determiner each in (1) and so called adnominal (or binominal) each in (5) on the other.
(5) Adnominal each: The boys bought two presents each.
As illustrated in (5), adnominal each appears to form a constituent with the NP serving
as the DistShare (two presents) just like po or -ssik. Adnominal each, however, just like
determiner each in (1), cannot distribute over implicit spatial or temporal arguments of
the verb. Thus, in (5), the only possible DistKey is the overt subject DP argument of the
verb, which results in simple individual distribution. Zimmermann (2002b) takes this
difference to reflect a more general typological generalization – namely, that distributive
markers that can also be used as determiners (e.g. each) are restricted to distributing over
individuals.4
2.1  Distributive share markers as distributive universal quantifiers
The idea that DistShare markers might be analyzed as a type of universal quantifier dates
back to at least Gil’s (1982) typological classification, according to which, DistShare
markers, just like DistKey markers, are subtypes of universal quantifiers, as shown by the
classification of universal quantifiers provided in Table 1 (Gil 1995: 349). DistShare and
DistKey quantifiers differ from “simple universal quantifiers” (e.g. all in English) in that
they enforce distributivity (do not permit collective readings).
The unifying assumption underlying this line of analysis is that the distributive interpretation
that DistShare markers involve universal quantification. This is a common idea
	3
	In addition, po can modify adjectives and adverbs, can also be a verbal prefix (indicating past repeated
actions) or a locative (distributive) preposition. This distribution is similar to that of pluractional markers
(see Hofherr-Cabredo & Laca 2012; Newman 2012; Knežević 2015).
	4
	For further discussion of the differences between adnominal each in English, elke in Dutch, and po in
­Serbian, see Rouweler & Hollebrandse (2015) and Knežević (2015).
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Art. 78, page 5 of 28
that is present in the work of e.g. Choe (1987) for Korean -ssik, Gil (1990) for Japanese
-zut(s)u, Faller (2001) for the Quechua particle -nka, Zimmermann (2002a/b) for German
adnominal and adverbial jeweils, po in Czech, Bulgarian and Russian, cîte in Romanian
and a dozen other languages, Balusu (2006) for reduplicated numerals in Telugu, or
Zimmermann (2008) for reduplicated numerals in Hausa.
Choe (1987), like Gil (1982), was one of the first to stress that the unifying function
of distributive markers crosslinguistically is to establish a dependency relation between
two arguments of a predicate – serving respectively as the DistKey and DistShare – with
distributivity derived by positing a universal quantifier interacting with an existential
in its scope. He distinguishes between regular quantificational determiners that form a
syntactic constituent with the DistKey argument (e.g. German jeder, or French chaque),
from so-called anti-quantifiers which appear to form a syntactic constituent with the
DistShare argument (e.g. Korean -ssik, adnominal each in English, and German je(weils)).
Zimmermann (2002b) replaces the term anti-quantifier with the notion of distance-distributivity
to refer to distributive items that appear (on the surface) to occur at a distance from
their DistKey. He contends that distance-distributivity is “a superficial phenomenon. All
instances of apparent distance-distributive quantifiers are reducible to regular adnominal
quantifiers.” (Zimmermann 2002b: 21). On this proposal, Serbian po (2), Korean -ssik (4),
English adnominal each (5) in English, and German adnominal jeweils (6) are all distancedistributive
(DD) universal quantifiers.
Zimmermann then develops a uniform compositional analysis of distance-distributivity
across languages, taking as a point of departure the analysis of adnominal jeweils in
German which, just like Serbian po or Korean -ssik, yields both individual and event distributive
readings, as illustrated with (6):
(6) German (Zimmermann 2002b: 291)
[Jeweils zwei Offiziere] haben die Ballerinen nach Hause begleitet.
each two officers have the ballerinas to home accompanied
a. ‘Each of the ballerinas was accompanied home by two officers.’
b. ‘Each time, two officers accompanied the ballerinas home.’
Jeweils in (6) forms a constituent with the subject NP zwei Offiziere “two officers” serving
as the DistShare. On the individual distributive reading in (6a), distribution is over
the direct object DP die Ballerinen “the ballerinas”, serving as the DistKey. While on
this reading, jeweils occurs at a distance from its overt NP-restriction/DistKey, on the
temporal/event distributive reading in (6b), distribution is over an implicit DistKey (a plurality
of times/events) that is not overtly expressed in the clause, but must be ­recoverable
from the linguistic context.5
	5
	We restrict our discussion here to adnominal jeweils which forms a constituent with a nominal expression
corresponding to the DistShare expression. Jeweils, however, can also occur adverbially, yielding ­temporal
Table 1: A classification of universal quantifiers (Gil 1995: 349).
Language Non-distributive DistKey DistShare
Warlpiri Ø Ø Ø
Hebrew kol Ø Ø
English all every Ø
Maricopa maṭ-čaamk Ø maṭ-čaamxperk
Georgian q’vela q’oveli q’vel-q’vela
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His proposal is that DD items such as jeweils are QPs embedded inside a PP, itself adjoined
to the NP serving as the DistShare. On Zimmermann’s proposal, DD quantifiers, just like
regular quantifiers, combine syntactically with their restrictor. The difference is that the
restrictor is not a lexical NP, but a pronominal NP which receives its value through coindexation
with a DistKey provided by the context. P°, covert in the case of German, provides
a relational variable R which specifies the relation that holds between the elements
of the DistKey and DistShare. Accordingly, the denotation of the jeweils-DP is given in (7)
and the analysis of the individual and event distributive readings of (6) are given in (8a)
and (8b), respectively (see Zimmermann 2002b: 250):6
(7) [[zwei Offiziere P°j
jeweilsi
]] = ∀z [z∈Zi
→ ∃X [2officers’ (X) ∧ *Rj
(X)(z)]]
For every element z of a given set Zi
, there is a set X of two officers such that z
and X stand in relation Rj
to one another.’
(8) a. ∀z [z∈[[the ballerinasi
]] → ∃X [2officers’(X) ∧ ∃e [*accompany’(X,z,e)]]]
For every element z of a given set of ballerinas, there is a group of two officers
X and an event e such that X accompanies z in e.
b. ∀z [z∈Zi
→ ∃X [2officers’(X) ∧ ∃e[*accompany’(X, [[the ballerinas]],z) ∧
R(e,z)]]]
For every element z of a contextually salient set (of events) Zi
, there is a set
X of two officers and an event e, such that the elements of X accompanied
the ballerinas in e, and event e is related to event z by a temporal, causal,
subpart, or other contextual relation.
On the individual distributive reading in (8a), the denotation of the DistKey die Ballerinen
“the ballerinas” provides the value for the set variable Zi
, while the denotation of the
transitive verb provides the value for the relation variable R, thus ensuring that the distributive
relationship between the elements of the DistKey (here, ballerinas) and elements
of the DistShare (here, sets of two officers) is one of accompanying the former home. On
the temporal event distributive reading in (8b), the restriction variable Zi
ranges over a
set of atomic events and must be anaphorically linked to an appropriate antecedent in
(or constructed from) the preceding discourse, and the free relation variable R is assigned
a value from the context. For example, if there is a ballet performance every Friday this
event distributive readings, as shown in (i), unlike po, which cannot occur in an adverbial position, as
shown in (ii).
(i) Peter hat jeweils gewonnen.
Peter has each.time won
‘Peter has won each time.’
(ii)*Petar je po pobedio.
Peter aux distr won
*’Peter has won each time.’
		This yields a three-way distinction across DD elements: those like adnominal each in English which only
allow individual distributive readings, those like adnominal jeweils and po which allow both individual and
event distributive readings with an indefinite DistShare expression, and those like adverbial jeweils, which
only allow event distributive readings.
	6
	The *-operator yields a cumulative predicate from a non-cumulative one. X stands for a variable over sets.
As defined in Krifka (1998), a predicate P is cumulative iff when P applies to two distinct elements x and y,
it also applies to the (mereological) sum of x and y, as stated in (i):
(i) ∀X⊆UP
[CUMP
(X) ↔ ∃x,y [X(x) ∧ X(y) ∧ ¬ x = y] ∧ ∀x,y [X(x) ∧ X(y) → X(x ⊕P
y)]]
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Art. 78, page 7 of 28
past year, then on this scenario, the DistKey is a set of Friday ballet performances and the
relation between the elements of the DistKey and elements of the DistShare (here, events
of two officers accompanying the ballerinas home) is plausibly one of temporal succession.
Importantly, R can take on a variety of values, including temporal, causal, subpart,
or other contextually determined relations.7
As the discussion in section 4.1 will show, the
assumption that the values of Z and R are quite free and pragmatically determined will
play an important role in capturing the truth conditions for spatial distribution with the
DistShare markers po and -ssik.
Another analysis of DistShare markers involving universal quantification is that of Balusu
(2006) and Balusu & Jayaseelan (2013) for reduplicated numerals (RedNum) in Telugu.
On their proposal, event distributivity is an instance of distributive quantification, involving
a Distributivity (D-) operator, a DistKey (the DP that is being distributed over), and
a DistShare (the (RedNum)NP that is being distributed). In Balusu & Jayaseelan’s (2013:
10) words, “a distributive operator is essentially a universal quantifier, that has a sorting
key, i.e. the quantifier’s restriction, and a distributive share, i.e. the quantifier’s scope”:
(9) D-operator DistKey DistShare
∀ set in restriction entities in scope
Balusu is one of the rare authors, to our knowledge, to address the issue of spatial event
distribution and, in particular, the question of how to recover implicit spatial (as well as
temporal) distributive keys from the context. Thus, consider the intransitive sentence in
(10a), which only yields spatio/temporal event readings, since the only overt argument
that can undergo numeral reduplication (and thus serve as the DistShare) is the subject
argument. On Balusu’s analysis, event distributive readings involve partitioning of an
event into non-overlapping subevents along spatial or temporal dimensions using “a contextually
salient method of division”. And it is these spatial/temporal dimensions (event
aspects) which serve as the covert DistKey. But how do we partition time and space? They
are not inherently partitioned into minimal atomic units, and thus can only be partitioned
into units along contextually salient parameters.
(10) Telugu (Balusu & Jayaseelan 2013: 38)
RenDu renDu kootu-lu egir-i-niyyi.
Two two monkey.pl jump.past.pl
‘Two monkeys jumped in each location/time interval.’
Balusu & Jayaseelan (2013: 40) explain the spatiotemporal portioning of the event
described by (10) as follows: “What do each time and each location refer to? […] The division
of the spatial and temporal regions into units happens according to the context. The
units need not be of equal duration in the case of temporal regions or of equal dimensions
in the case of spatial regions. […] Suppose that all the monkeys in the enclosure jumped
up all at once but they jumped up in pairs holding to each other, then the spatial key
	7
	As we shall see, to extend Zimmermann’s truth conditions to spatial/temporal distribution in Serbian/Korean
would involve assuming that, in the truth conditions for e.g. sentence (3) above in the text, the variable Z
is a set of spatial/temporal locations, and R is the relation be located in. (3) would thus come out meaning
roughly “For every element z of a contextually salient set of temporal/spatial locations Z, there is a set X
of two boys and an event e such that X sings in e and e is related to z because X is located in z.” The specific
extension we propose of Zimmermann’s analysis to account for our empirical findings is spelled out in
­section 4.1.
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Art. 78, page 8 of 28
reading is easily obtained. It could also be the case that the monkeys were not holding
one another in pairs but that they were sitting at different points on the branches of the
tree, and that there were two monkeys per branch. In such a situation too the spatial key
reading is felicitous.”
2.2  Distributive share markers as event plurality markers
Another prominent line of analysis found in the literature takes DistShare markers to be
pluractionals, i.e. markers of event plurality or pluractionality (a term coined by Newman
1980).
Pluractionals are markers on the verb or affecting the verb phrase, indicating event plurality
in a wide variety of manners (Cabredo-Hofherr & Laca 2012). For instance, Muller
& Negrão (2012) claimed that the distributive numerals in Karitiana should be analyzed
as adverbial operators that pluralize the events and restrict the cardinality of the entities
they modify. A plural event may involve the same action iterated several times (repetitions),
(same) actions distributed in space, time, or affecting multiple participants or
objects, either as a group or individually (Cusic 1981; Newman 2012; Lasersohn 1995).
An example of temporal pluractionals in English would be adverbial phrases such as again
and again or time after time.
Knežević (2015), and Knežević & Demirdache (2017; 2018)8
develop a pluractional analysis
of Serbian po, building on Lasersohn (1995) and Cable’s (2014) analysis for Tlingit.
Pluractional accounts have been defended for a typologically diverse set of DistShare
markers, in languages such as Kaqchikel (Henderson 2011; 2014) and Karitiana (Muller &
Negrão 2012), or St’at’imcets (Matthewson 2000).
There are two essential advantages for Knežević in using Cable’s analysis of the distributive
marker -gaa in Tlingit.9
First, Cable provides a single, uniform account of both
individual and event distributive readings of sentences with adnominal -gaa, deriving
both readings from the same truth conditions. Sentences with -gaa are thus not taken to
be ambiguous between individual and event distributive readings. Rather, the semantics
for -gaa yields weak truth conditions holding under both readings. What this essentially
means is that individual/participant distributivity is subsumed under event distributivity
and is not treated as a separate reading. Second, these weak truth conditions predict that
the semantics of distributivity with -gaa in Tlingit, just like with po in Serbian or -ssik in
Korean, does not involve a DistKey that has to be atomically and exhaustively distributed
over (section 2.2.1).
The readings that -gaa yields are illustrated in (11), together with the type of scenarios
provided by Cable for individual/participant and event distributivity:
(11) Tlingit (Cable 2014: 576)
a. Ax shaa yátx’i dáxgaa keitl has aawashúch.
my female children two.distr dog they.bathed
	8
	We henceforth use Knežević to refer to the work developed in Knežević (2015) and Knežević & Demirdache
(2017; 2018).
	9
	Note that -gaa also occurs adverbially, as shown in (i), yielding event distributive readings, as was
the case with German jeweils, but contrary to Serbian po which lacks an adverbial equivalent (see
footnote 5)
(i) Ax shaa yátx’i dáxgaa has aawashúch wé keitl.
my female children two.distr they.bathed those dog
‘My daughters bathed those dogs two at a time.’
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b. ‘My daughters bathed two dogs each/two at a time.’
i. Bathings Agent Theme Individual distributive
e1 Cléo dog1+dog2
e2 Kiya dog3+dog2
ii. Bathings Agent Theme Event distributive
e1 Cléo+Kiya dog1+dog2
e2 Cléo+Kiya dog3+dog2
iii. Bathings Agent Theme Individual+Event distributive
e1 Cléo dog1+dog2
e2 Cléo dog3+dog2
e3 Kiya dog4+dog5
e4 Kiya dog6+dog7
Cable treats distributive numerals (distributive markers) similarly to adverbials such as
piece by piece, as analyzed by Beck & von Stechow (2007). This analysis does not posit
quantificational D-operators of any sort. (12) gives the semantics assigned to adnominal
distributive numerals10
in Tlingit, and (13) the predicted truth conditions for the sentence
in (11) (Cable 2014: 586).
(12) [[ gaa ]] = [ λnn
: [ λQ<et>
: [ λP<e, εt>
: [ λeε
: ∃x. Q(x) & P(x)(e) &
<e , x> = σ<e’, y>
. participant(e’,y) & |y| = n & e’ < e & y < x ] … ]
(13) a. ∃e . ∃x . *dog(x) & *bathed(e) & *Agent(e) = σy.*my.daughter(y) &
*Theme(e) = x &
<e , x> = σ<e’, z> . z < x & |z| = 2 & e’ < e & participant(e’,z)
b. There is a plural event e of bathing, whose agents are the speaker’s daughters
and whose theme is a plurality of dogs x and the pair consisting of e
and x is the sum of those pairs <e’, z> such that z is a pair of dogs, e’ is a
(proper) part of e, and z participates in e’.
(13b) requires my daughters to have cumulatively bathed pairs of dogs, with each pair
being the theme of some sub-event of the larger event. Now, these truth conditions are
compatible with either the individual or the event distributive scenarios in (11i-ii), since
on a cumulative interpretation, the number of agents (here, one or two) is left unspecified.
Importantly, (11) is also correctly predicted to be true on a scenario such as (11iii) which
instantiates both participant and event distributivity (e.g. my daughters each bathed two
dogs at different times).
Knežević adapts the semantics of -gaa to po distributive numerals in Serbian.11
As shown
in (14), just like -gaa, po combines successively with a numeral n and a predicate Q supplied
by the modified NP. It then takes as an argument a relation P between individuals
and events and returns a predicate of events, holding of an event e iff there is an individual
x such that Q holds of x, and the relation P holds between e and x. The conjuncts “e ∈ *e’nQ
& e ∉ e’nQ
” require that e be a sum of events e’ in which exactly nQ dogs ­participate, but
	10
	σx
is the maximality operator involved in the semantics of definites DPs, σ<x, y>
a binary maximality operator
applying to a two-place relation Q(x)(y), and ε the semantic type of events.
	11
	Note that -gaa, just like po and -ssik, can attach to the subject, the object or to both arguments of the
­predicate.
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
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Art. 78, page 10 of 28
without itself being such an event. The claim is that the events described by a sentence
with a po nNP must necessarily involve a number of participating individuals described
by the NP that is a multiple of n.
(14) a. [[po]] = λn. λQ<e,t>
. λP<e, εt >.
λe. e ∈ *e’nQ
& e ∉ e’nQ
& ∃x Q(x) & P(x)(e)
b. Dečaci kupaju po dva psa.
boys bathe distr two dogs.acc
c. ∃e. ∃y. ∃x. e ∈ *e’2dogs
& e ∉ e’2dogs
& *boy(y) & *dog(x) & *bathe(e) &
*Agent(e)(y) & *Theme(e)(x)
d. There is an event e constructed out of (sub)events e’ each involving two dogs
and e is an event of boys cumulatively bathing dogs.
The sentence in (14b) thus comes out to have the truth conditions in (14c). In particular,
the events described by (14b) must be constructed out of events in which exactly two dogs
participate as themes, without being events of that kind themselves. This means that the
events described by (14b) must necessarily involve multiples of two dogs. (14b) will thus
not hold in collective scenarios involving exactly two dogs in total. It will, however, be
true as long as there are at least two subevents e’ of one big event e, spatially or temporally
separated, each containing exactly two dogs. That is, the number of dogs per subevent
has to be two, but there may be as many pairs of dogs as there are subevents e’ (the
total number of dogs is therefore context-dependent). Furthermore, there is no specification
in the semantics of how the agent participants partition across these events: the boys
can participate collectively, individually, or in groups in the event e, the only requirement
being that there be a bathing of two dogs per subevent e’.
In sum, po, on these proposals, is enforcing weak truth conditions, merely requiring
that there be at least two events involving the number of entities denoted by the -ssik
phrase. As we shall see in the next section, this crucially means the semantics of distributive
numerals should not involve a DistKey that has to be atomically and exhaustively
distributed over.
2.2.1  Lack of atomicity and exhaustivity requirements
As previously mentioned, on the semantics developed by Cable and Knežević, sentences
with distributive numerals are true under event distributive scenarios such as (11ii),
involving a partitioning into two subevents, each with agents acting collectively. This
is one of the generalizations that leads Knežević to claim that distributive markers such
as po are not distributive universal quantifiers: unlike distributive quantifiers such as
each, which enforce a partitioning of their restrictor set (DistKey) into atomic members,
DistShare markers like po do not require an atomic partition. So, for example, the Serbian
and Korean sentence in (16) should be judged true under all the situations depicted
in Figure 1,12
while the English sentence in (15) is only compatible with the scenario in
­Figure 1a.
(15) [Each boy DistKey
] is carrying [numNP
one piano DistShare
].
(16) a. Dečac-i nose po jedan klavir.
boy.pl.nom carry distr one piano.acc
	12
	Although this has not been tested experimentally, we checked with a few Korean and Serbian informants
who confirmed these judgments.
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Art. 78, page 11 of 28
b. Sonyen-tul-i phiano-lul han-tay-ssik nalu-ko iss-ta.
boy.pl.nom piano.acc one.clf.distr carry.prog.dec
i. ‘(The) boys each are carrying one piano.’
ii. ‘(The) boys are carrying one piano at each/different place(s).’
The second generalization that leads Knežević to explicitly argue against a universal quantification
analysis concerns another key property of universal quantifiers: the set denoted
by the noun phrase serving as the DistKey (the restriction of Q°) must be exhausted. To
quote Balusu & Jayaseelan (2013: 10): “the members of the distributive share need not
be exhaustively used up when being distributed, whereas the members of the sorting key
need to be exhaustively used up in being distributed over.”
Knežević contends that there are no exhaustivity requirements with po. That is, the
plurality over which the po numNP is distributed (be it a plurality of individuals, times,
spaces, or events) need not be exhausted. Thus, consider again the sentence in (15) and
(16), but this time under the scenarios in Figure 2.
English adults judge (15) as true under the scenarios in Figure 2a (since all members of
the set denoted by the DistKey (boy) are distributed over) and Figure 2b (the presence of
additional, uncarried pianos is irrelevant to the truth conditions of (15) since there is no
exhaustivity requirement on the DistShare). But English adults will judge (15) false under
the scenario in Figure 2c because the members of the DistKey are not exhaustively used up.13
	13
	Note, however, as is well-known from the acquisition literature, children up to the age of 8 or 9 reject
pictures like Figure 2b with universal quantifiers like (15) because of the extra object. This phenomenon
is known as quantifier spreading (The child exhaustively distributes all boys over all pianos and all pianos
over all boys in a one-to-one fashion; see Brooks & Braine 1996; Drozd 2001; Roeper et al. 2011).
Figure 1: Atomic and non-atomic scenarios (event distributive readings) for the sentences in
(15)/(16).
Figure 2: Exhausted and non-exhausted scenarios for the sentences in (15)/(16).
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
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Art. 78, page 12 of 28
In contrast, the Serbian example in (16) is predicted to be true in all of the situations
depicted in Figure 2 on a Knežević/Cable pluractional account of the semantics of distributive
numerals. In particular, the scenario under Figure 2c is compatible with the
truth conditions provided by Knežević for sentences with distributive numerals: there is
an event e constructed out of three (sub)events e’, each involving one piano exactly, and
e is an event of boys cumulatively carrying pianos.
These requirements, however, were never a subject of experimental investigation, and
have remained until now in the theoretical domain. This paper is thus the first attempt
to experimentally test whether there are indeed (no) exhaustivity requirements on an
implicit DistKey. We focus here on intransitive sentences in Serbian and Korean. The challenge
here is how to establish conditions with a covert (spatial/temporal) DistKey (set
of salient spatial/temporal units) that is either exhausted or not. Time and space are not
inherently partitioned into minimal atomic units, and thus can only be partitioned into
units along contextually salient parameters. The experimental set-up must thus provide
some kind of contextual restriction that will impose a partitioning of the event into nonoverlapping
subevents along spatial or temporal dimensions.
3  Testing exhaustivity requirements with spatial event distribution
Assuming that a key diagnostic for the Universal Quantification (henceforth UQ) account
is the exhaustivity requirement on the DistKey, we want to test experimentally whether
distribution over the members of the putative DistKey has to be exhausted or not (as
would be the case with the Event Plurality (henceforth EP) account). The experimental
investigations reported here targeted specifically spatial event distribution, in Serbian and
Korean, focusing on intransitive sentences14
with DistShare markers (po in Serbian (17a),
-ssik in Korean (17b)):
(17) a. Pleš-e po jedan majmun.
dance distr one monkey.nom
b. Wenswungi-ka han-mali-ssik chwum-ul chwu-koiss-ta.
monkey.nom one.clf.distr dance.acc dance.prog.dec
c. ‘DISTR one monkey is dancing at each location/in different locations.’
As previously mentioned, in intransitive sentences, where the sole overt argument of the
verb is marked as a DistShare, the only available DistKey will be an implicit spatial or
temporal argument of the verb – which means that the only available reading will be an
event distributive reading over covert spatial or temporal locations. Assuming that the
semantics underlying (17) does indeed involve exhaustively distributing events of a monkey
dancing over implicit spatial/temporal locations, the question is then how to recover
the covert spatial key from the context in order to test whether distribution over the
spatial key must be exhaustive. Our experimental set-up was largely inspired by Balusu
& Jayaseelan’s (2013) discussion of the contextual parameters involved in partitioning
an event into relevant spatial locations in order to obtain a spatial DistKey reading (see
discussion of (10) above).
The next section presents our experimental methodology, introducing the features that
are common to both Experiments 1 and 2. This is followed by a more specific discussion
of each experiment and their respective results.
	14
	Note that with transitive sentences, a number of confounding factors would have to be carefully controlled
for in languages such as Serbian or Korean which have bare/determinerless nominals and freedom of word
order, in particular, the interpretation of bare nominals in subject/topic position.
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
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Art. 78, page 13 of 28
3.1  Experiment 1
Both Experiments 1 and 2 tested two DistShare markers, Serbian po and Korean -ssik.
Although Korean and Serbian are typologically very different languages, po and -ssik show
similar syntactic and semantic properties and we thus expect them to pattern alike in their
interpretations.
Recall that in intransitive sentences, the only overt argument will be marked as the
DistShare. This implies that quantification is over events along a spatial or temporal
dimension and the DistKey is thus an implicit argument. Participants must therefore contextually
infer the DistKey. We sought to control this process with a frame story that
limits potential interpretations, and visual materials specifically designed to make spatial
units contextually salient. We only used materials depicting spatial distribution (primarily
for reasons of simplicity), but we believe our findings would carry over to temporal
distribution.
General set-up: We used a children’s visit to the zoo as a frame story for both experiments.
This setting allowed us to have cages or caves as identifiable spatial units over
which events could be distributed. This method of division into relevant spatial locations
is adapted from Balusu & Jayaseelan’s (2013) discussion of (10) above (scenarios involving
monkeys on each branch of the tree). We varied the visual contexts (pictures) across
subjects to test whether or not the spatial units need to be exhausted.
In our instructions we were careful not to explicitly mention cages/caves in order to
ensure that there is no linguistically explicit argument that could potentially serve as
a DistKey. Instead, the common context of the experiment was given at the beginning:
“Peter and Mary went to the zoo with their class. They brought a camera and took pictures
of animals they saw. After the visit, the teacher asked the children from the class to
describe their photos. Are the children describing the pictures well?”. Then, in a yes-no
picture verification task (a variation of a truth value judgment task), the participants had
to evaluate whether the descriptions of the photos were appropriate.
Test sentences: We started from the simplest structure – intransitive sentences, where
po/-ssik is syntactically attached to the subject. The subject has to be interpreted as the
DistShare, and the only alternative for the DistKey would be the implicit spatial units.
In addition, we also used the lowest numeral, so the target phrase was po one/ one-ssik.
Finally, the test items used a verb-subject word order for Serbian, see e.g. (17a), to avoid
po occurring at the beginning of the sentence (since Knežević’s (2015) previous research
showed that po-initial sentences sound odd). The word order in Korean remained subjectverb,
see e.g. (17b).
Our visual and discourse context aimed to make the cages/caves be considered as relevant
spatial units and to serve as the (implicit) DistKey. We designed experimental conditions
to try to investigate some basic questions about the different predictions that the
theories presented above make. These predictions are spelled out in the section below.
3.1.1  Method and design
Subjects: 53 adult native speakers of Serbian (mean age: 26.35; 37 female, 14 male, 2
unspecified) and 26 native Korean speakers (mean age: 34.00; 17 female, 8 male, 1
unspecified) completed a 5-minute Picture Verification task that was available online.
All Serbian participants and 6 Korean participants were recruited through social media
and did not receive remuneration. The remaining 20 Korean participants were recruited
through Amazon Mechanical Turk and were paid 65 cents for completing the experiment.
All participants gave their consent before starting the experiment.
Design and procedure: we used a 1 × 3 design with the same type of test sentence and
three different types of pictures as illustrated in Figure 3: A: Exhausted, B: Non-exhausted
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
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Art. 78, page 14 of 28
(empty spatial units) and C: Non-exhausted (not all spatial units contain Ving monkeys). The
experiment was preceded by detailed written instructions and a common context for all
items, discussed above.
Items: 12 unique sentences (target items) were created using 16 different animals and
eight verbs.15
Each verb was presented no more than twice in a target sentence (see
Appendix B for the complete list of items that were used for the target items and fillers).
Each condition had four observations and each participant saw only one condition combination
per item (see Figure 3 for test pictures where the background has been removed
for visual clarity. See Appendix B for an actual picture from the experiment).
Picture A was considered to be the baseline condition, in which spatial units (cages) are
considered exhausted since they each contain a dancing monkey. Pictures B and C showed
non-exhausted situations. Picture B showed two spatial units with monkeys carrying out
the target action, and two empty spatial units. Picture C showed two cages with a monkey
carrying out the target action and two cages with monkeys that are not carrying out the
target action. We always used two non-exhausted spatial units/cages, rather than one,
to avoid singling out the odd situation in the picture. All three conditions showed four
salient spaces in a rough 2 × 2 grid formation, and the position of the different types of
spaces, e.g. a cage vs. empty area, varied across items.
As previously stated, the test sentences all had imperfective intransitive verbs and the
following structure: [Verb [po-1(one)-Subject]] for Serbian (17a/18a) and [[Subject-
1(one)-ssik] Verb] for Korean (17b/18b).16
(18) a. Pleš-e [po jedan majmun].17
dance distr one monkey.nom
	15
	There was one additional non-exhausted condition (for the same test sentence) in the original design,
involving spatial units with other animals V-ing, e.g. hippos dancing in two of the cages. We considered this
condition to be a filler since it does not help in answering our research question. When this condition is
included, animals and actions were balanced across items.
	16
	The characters in the experiment we set up were animals typically found in a zoo: bears, parrots, owls, canaries,
hippos, rhinos, elephants, monkeys, chimps, gorillas, giraffes, zebras, horses, lions, tigers and panthers. The
verbs were: to jump, to cry, to sing, to dance, to sit, to lay down, to wave and to fly.
	17
	The actual animal in the picture is a chimpanzee but we use the term monkey in the examples because it is
a more common word.
Figure 3: Examples of three test pictures paired with test sentences in Serbian (18a) and Korean
(18b), giving three test conditions.
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
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Art. 78, page 15 of 28
b. [Wenswungi-ka han-mali-ssik] chwum-ul chwu-ko iss-ta.
monkey.nom one.clf.distr dance.acc dance.prog.dec
c. ‘DISTR one monkey is dancing (at different locations/each location).’
Control items were 12 numerically quantified sentences with a Verb-three-Subject(plural)
pattern (e.g. “Three tigers are sleeping” with one of the three pictures corresponding A,
B or C). These items had four yes and eight no responses and were used as true controls
– participants who made errors on more than 10% of control items were excluded. Each
participant also saw four filler items (see footnote 15). In sum, each participant saw 12
target items, 4 filler items and 12 control items, amounting to 28 items in total.
3.1.2 Predictions
What responses do we expect based on the two major lines of research? If we take the core
assumption underlying the EP account, all three pictures should be accepted (see Table 2),
since the only requirement is to have at least two events, and all scenarios satisfy this
requirement. If DistShare markers are a type of universal quantifier, then there must be a
DistKey that has to be exhausted. Because we made the linguistically implicit spatial DistKey
salient in the frame story and visually relevant in the individual items, these spaces
are contextually salient and the best candidate for the DistKey. The condition with Picture
A, the baseline, should be accepted. But a UQ account predicts that the two other pictures,
Picture B and Picture C, should be rejected because there are contextually relevant spaces
where no monkey is jumping. Also note that neither theory requires all the monkeys in
the context to satisfy the VP (dance), since the NP one monkey is marked as the DistShare.
3.1.3 Results
The results show us that the baseline picture (A) and the picture with non-exhausted
spatial units (empty cages/caves) (B) were overwhelmingly accepted (90.1% and 84.4%
respectively for Serbian and 96.1% and 97.1% respectively for Korean), unlike the picture
with non-exhausted spatial units in which no monkey is V-ing (C) (10.4% for Serbian and
8.6% for Korean) (see Figure 4).
Table 2: Predictions according to EP and UQ accounts on all test pictures in Experiment 1.
Picture A Picture B Picture C
Predictions EP   
UQ   
Figure 4: The results show the proportion of YES responses of Serbian (left) and Korean adults
(right) with the standard error bars for Picture A (blue), Picture B (red) and Picture C (green)
conditions.
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
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Art. 78, page 16 of 28
We performed a repeated measures mixed-effects logistic regression using glmer() function
of the lme4 package (Bates et al 2015) in R (R Core team 2014) for each language.
We started all analyses with a full and random intercept model that included Picture Type
(with levels A, B and C) as the only predictor (fixed factor) and Subjects and Items as random
factors. AIC values18
were compared to determine which model fit the data best, with
a complex model being preferred over a simpler model only if its AIC value is two or more
points lower. For both Serbian and Korean, model comparison did not show an effect of
the Items, so this random factor was removed. For both languages, the best fitting model
retained the fixed factor Picture Type and the random factor Subjects, with a random slope
by-Subjects for Picture Type (see the best model formulas for each language and the output
in Appendix A). The reference point was Picture A, and we see no significant difference
between Picture A and Picture B for Serbian (β = –1.70, z-value = –0.50, p = 0.62) or
Korean (β = –0.93, z-value = –0.14, p = 0.89). There was a highly significant difference
between Picture A and Picture C for both Serbian (β = –16.60, z-value = –4.79, p <
0.001) and Korean (β = –18.92, z-value = –2.83, p < 0.001).
We also combined data from both Serbian and Korean in one model, including a new
fixed factor Language with the levels Serbian and Korean. Models that included Language
were not significantly different from models without. This means that there is no significant
difference between Serbian and Korean participants in their responses.
3.1.4 Discussion
Going back to Table 2, we see that the baseline (Picture A) is accepted across the board,
as expected on all accounts. Picture B is also strongly accepted as predicted on the EP,
but not the UQ hypothesis. The situation is reversed for Picture C, which is overwhelmingly
rejected as predicted on the UQ, but not the EP hypothesis – see the updated table
(Table 3).
Taking stock: Our findings suggest that it is not necessary to exhaust spatial units.
Participants accepted Picture B with e.g. cages without monkeys. However, the rejection
of Picture C suggests that there is some form of exhaustivity requirement after all, since
cages with monkeys need to contain a dancing monkey to be acceptable. We state the
resulting descriptive generalizations in (19):
(19) Generalization 1: Empty contextually relevant spatial units (e.g. cages) need
not be exhausted, i.e. they need not satisfy the VP (by containing e.g. one dancing
monkey). While spatial units that contain individuals that fit the description
of the subject NP, e.g. monkeys, must exhaustively satisfy the denotation of the
VP (by containing e.g. one dancing monkey).
	18
	An AIC (Akaike information criterion) decrease of more than two indicates that the goodness of fit of the
model improved significantly (Akaike 1974).
Table 3: Predictions and results on all test pictures in Experiment 1.
Picture A Picture B Picture C
Predictions EP   
UQ   
Actual results   
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Art. 78, page 17 of 28
The overall experimental results thus seem to be a challenge to both theoretical approaches
of DistShare markers: the assumed UQ hypothesis makes predictions that are too strong,
while the EP hypothesis makes predictions that are too weak. To recapitulate, participant
responses suggest there is no exhaustivity requirement on individual monkeys, because
Picture A is accepted; there also seems to be no exhaustivity requirement on spatial units
(cages) because Picture B is accepted; however, participant responses suggest that there is
an exhaustivity requirement on groups of monkeys in cages. Thus, our findings are compatible
with a UQ account since this account correctly predicts there is an (implicit) spatial
DistKey that needs to be exhausted. The logical follow-up question is then: what is the
relevant DistKey and how is it recovered from the linguistic and visual input? We know
now that cages alone were not taken to be the relevant spatial locations, so the participants
must be reacting to something else in the experiment. When examined more closely,
the visual context, in fact, gives three possibilities to restrict the domain of quantification
– (a) cages, (b) groups (here, triplets) of monkeys in cages, or (c) groups (here, triplets)
of monkeys. The UQ account tested in Experiment 1 rules out option (a) as the DistKey,
i.e. cages as delimited spaces. We henceforth refer to this first option as DistKeyCAGE
. We
now need to determine whether (b) groups of monkeys in cages or (c) groups of monkeys
are serving as the DistKey. We refer to these two other options as DistKeyCAGED GROUP
and
DistKeyGROUP
, respectively. Experiment 2 was designed to test these two options.
3.2  Experiment 2
3.2.1  Method and design
Subjects: 31 adult native speakers of Serbian (mean age: 29.77; 23 female, 6 male, 2
unspecified) and 30 adult native speakers of Korean (mean age: 35.00; 24 female, 6 male)
participated in a picture verification task. The experiment was done online and took
approximately five minutes.
Design and procedure: we again had a 1 × 3 design but changed two picture types from
Experiment 1 (see Figure 5). Picture A was modified to create Picture A1: Exhausted
spatial units + monkey V-ing outside cages and Picture C was modified to create Picture
C1: Exhausted + no monkey V-ing outside cages showed groups of monkeys not bounded
by explicit spatial units.19
These pictures were designed to assess how necessary spatial
delimitation is. Control items and test sentences remained the same.
	19
	Picture B is named B1 but it is the same as in the previous experiment, to balance the design and have a
type of filler since, in essence, we are only testing pictures A1 and C1.
Figure 5: Pictures used in Experiment 2. Groups of monkeys appear outside clearly delimited
spatial units in A1 and C1.
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Art. 78, page 18 of 28
3.2.2 Predictions
The first experiment showed that a DistKeyCAGE
account taking cages to be the relevant
spatial DistKey is not correct, but the other two possibilities are to take groups of monkeys
in cages (DistKeyCAGED GROUP
) or only groups of monkeys (DistKeyGROUP
) to be the spatial
DistKey. This means that C1 is the crucial condition since it can tell us what the domain
of quantification for po/-ssik sentences is. (see Table 4).
3.2.3 Results
Figure 6 shows that participants accept Conditions A1 (96.8% for Serbian and 77.1% for
Korean) and B1 (90.9% for Serbian and 80.5% for Korean), but reject C1 (24.2% for Serbian
and 20.8% for Korean). The results match the predictions of DistKeyGROUP
, as seen in
Table 5.
For analysis, we again performed a repeated measures mixed-effects logistic regression
using glmer() function of the lme4 package (Bates et al 2015) in R (R Core team 2014). The
analysis and the procedure were identical to those used in Experiment 1. We started all
analyses with a full and random intercept model that included Picture Type (with levels A1,
B1 and C1) as the only predictor (fixed factor) and Subjects and Items as random factors AIC
values were compared to determine which model fit the data best, with a complex model
being preferred over a simpler model only if its AIC value is two or more points lower.
Model comparison showed that the model with the lowest AIC values for Serbian included
the fixed effect of Picture Type and a random effect of Items and Subjects, plus a random
slope for Picture Type for Subjects (the reference level (the Intercept) was set to be B1).
Table 4: Predictions according to the two possible DistKeys that must be exhausted.
Picture A1 Picture B1 Picture C1
Predictions DistKeyCAGED GROUP   
DistKeyGROUP   
Figure 6: The results show the proportion of YES responses of Serbian (left) and Korean (right)
adults with the standard error bars for Picture A1 (blue), Picture B1 (red) and Picture C1 (green)
of the (new) conditions.
Table 5: Predictions and results on all test pictures in Experiment 2.
Picture A1 Picture B1 Picture C1
Predictions DistKeyCAGED GROUP   
DistKeyGROUP   
Actual results   
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The model showed that B1 and A1 were not significantly different (β = 0.31, z
value = 0.10, p = 0.92), and that B1 had significantly higher rates of acceptance
than C1 (β = –11.41, z value = –4.43, p ≤ 0.001). The best model for Korean did
not include the Items and had a random slope for Picture Type for Subjects. Again, A1
was not significantly different from B1 (β = 4.31, z value = 1.46, p = 0.15) and C1
was significantly different than B1 (β = –9.99, z value = –3.99, p ≤ 0.001). The full
model is given in Appendix A. Finally, when the data was combined, the model with
Language as the fixed factor showed no significant difference compared to the model without
Language, meaning that Serbian and Korean participants responded similarly to the
conditions.
3.2.4 Discussion
The question we asked for Experiment 2 was whether we are exhausting groups (triplets)
of monkeys in cages, what we called DistKeyCAGED GROUP
, or simply (cageless) groups of
monkeys, i.e. DistKeyGROUP
. The results (the rejection of Picture C1 in particular) clearly
favor the latter answer – cages are completely irrelevant for the evaluation of the test
sentences and it is only the groups of monkeys that need to be exhausted. We thus modify
our previous descriptive generalization stated in (19), as in (20):
(20) Generalization 2: Empty contextually relevant spatial units (e.g. cages) need
not be exhausted, i.e. they do not satisfy the VP (by containing e.g. one dancing
monkey). Each (contextually/visually salient) group (here – triplet) of individuals
(e.g. monkeys) must be exhausted (must satisfy the VP by containing e.g. one
dancing monkey).20
We conclude that these groups/triplets of monkeys are defining the spatial locations that
are considered relevant and, as such, must be exhausted. But why did the participants
choose the triplets to be the relevant spatial DistKey and not the cages? In the pictures,
they are equally (visually) relevant. In fact, as mentioned before, the visual input yields
three potential DistKeys that can serve as the implicit restriction of a universal quantifier
– cages, triplets of monkeys in cages, or just triplets of monkeys.
We speculate the following: Our participants had to recover the spatial key on the basis
of two inputs provided by the experimental materials – visual and linguistic input. They
ignored the cages since they are not mentioned in the linguistic input. Monkeys, on the
other hand, are mentioned in the linguistic input and they are also salient in the visual
input, by being shown in clear groups of three, all distant from each other, resulting in
four clearly separated groups of monkeys (two in the case of the B conditions). This suggests
that when the preceding discourse context does not explicitly provide the spatial
DistKey, and the visual context is ambiguous as to what the right restriction is, participants
seem to use a strategy of prioritizing linguistic cues.
There is one caveat to this explanation. Namely, there is a 24% acceptance rate for
Picture C1 for Serbian and 20% for Korean, which is higher than the 10%/8% found
in the previous experiment. A Mann-Whitney U test indicated that the frequency of yes
answers for Experiment 1(Mdn = 0) was significantly lower than for Experiment 2 (p
< 0.01), so we examined individual response patterns for Picture C1 more closely. Only
4/31 Serbian participants and 4/30 Korean participants accepted C1 100% of the time
(and also accepted Picture B1 and A1 100% of the time). This observation is interesting
	20
	The groups of monkeys may contain other irrelevant individuals (animals) as well, but as long as there is
one monkey dancing in that relevant group, the generalization holds. This, however, is a separate observation
already discussed by McKercher and Kim (1999) and confirmed by several Serbian informants.
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
on distributive share markers
Art. 78, page 20 of 28
because, although it concerns a small subset of participants, these participants do appear
to show exactly the pattern of responses predicted on the event plurality account (all
three pictures accepted). On the other hand, this could easily be noise in the data and
since we, unfortunately, do not have these speakers’ explanations for the reason they
accepted all the conditions, we cannot make any further inferences. Lastly, some Korean
speakers (4/30) systematically rejected all three conditions, resulting in lower acceptance
rates even for the A1 (baseline) condition. We speculate the reason for this low
rejection rate may be that the pictures in Experiment 2 are showing a complex scene
and that some participants are very strict in their judgments, meaning that the sentence
may not be informative enough to capture everything that is happening in the picture.
We leave this as a speculation only, stressing again that this observation was statistically
insignificant.
4  General Discussion
The question our experiments sought to address was whether DistShare markers in Serbian
and Korean should be analyzed as markers of event plurality, or as universal quantifiers
requiring an implicit DistKey over which to distribute exhaustively. Let’s recapitulate
our main experimental conclusions (stated as Generalizations 1 in (19) and 2 in (20)).
(21) a. The results showed that individual members of the DistShare (e.g. monkeys)
need not be exhausted, as expected.
b. The result showed that the spatial argument made salient by the visual context
(i.e. cages/caves) need not be exhausted.
c. There is, however, evidence leading us to conclude that there is an implicit
DistKey: the set of triplets/groups of monkeys provided by the visual context
that needs to be exhaustively distributed over.21
We unpack the consequences of these observations in the following sections, and suggest
a possible universal quantifier analysis based on Zimmermann’s account.
4.1  Distribution over pluralities of non-atomic individuals
Our results provide intriguing evidence for a covert spatial DistKey. The visual context
supplies spatially separated groups/triplets of monkeys. This plurality, which is itself
made up of plural/non-atomic individuals, serves as the DistKey over which the members
of the DistShare (dancing monkeys) are distributed.
These conclusions clearly clash with the assumed predictions of the event plurality
analysis. Instead, they appear to provide evidence for the UQ accounts: (i) distributive
markers have an essentially relational function, that of establishing a relation between
members of the DistKey and members of the DistShare, and (ii) there is an exhaustivity
requirement on a DistKey. In our experiments with our materials we found that
the members of the DistShare contribute to spatially define the DistKey that has to be
exhausted.
To account for these findings, we suggest an analysis of event distributive readings
for both Serbian and Korean along the lines of Zimmermann (2002b) as presented in
	21
	It is important to bear in mind that distribution is taking place over pluralities/triplets of monkeys, not
individual monkeys, for the very simple reason that the numeral NP one monkey is marked as the DistShare.
We see clear empirical evidence for this in the ceiling acceptance for the baseline A/A1 condition that does
not exhaust the individual monkeys.
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
on distributive share markers
Art. 78, page 21 of 28
section 2.1.22
Consider again the intransitive sentences in (22b) and (22c), together with
their German translation in (22a):
(22) a. [Jeweils ein Affe] tanzt.
distr one monkey.nom dances
b. Pleš-e [po jedan majmun].
dances distr one monkey.nom
c. [Wenswungi-ka han-mali-ssik] chwum-ul chwu-ko iss-ta.
monkey.nom one.clf.distr dance.acc dance.prog.dec
‘DISTR one monkey is dancing.’
DD quantifiers across languages are assumed to have the uniform underlying structure
in (23a). Although all languages with DD quantifiers express the DistShare overtly, languages
differ with regards to which parts of the postnominal PP is overtly spelled out. In
particular, adapting Zimmermann, po in Serbian would be taken to spell out a complex
prepositional head derived via incorporation of a silent universal Q° into the overt P°head,
as shown in (23b). The PP is base-generated right-adjoined to the DistShare NP
([AP
one][NP
monkey]). While in Korean, this PP will stay in its base position,23
in Serbian it
raises to the Specifier of the whole DP (as does jeweils in German), yielding the observed
surface order (23c):
(23) a. [DP
D° [NP
[NP
NP DistShare
][PP
P° [QP
Q° je [NP
weili
-s DistKey
] QP
]PP
]NP
]DP
]
b. [DP
D° [NP
[NP
[AP
one][NP
monkey] DistShare
] [PP
[P°+ Q°
po [QP
teach
[NP
pro DistKey
]]]]]
c. [DP
[PP
[P°+ Q°
po [QP
teach
[ pro DistKey
]k
[ D° [NP
[NP
[AP
one][NP
monkey] DistShare
]
tk
]]]]
We now focus specifically on the analysis of Serbian, but conjecture that a similar analysis
could be applied to Korean as well. Zimmermann’s compositional analysis provides
a relational variable R specifying the relation that holds between the elements of the
DistKey and DistShare. The denotation for the PP headed by po is given in (24a). It will
combine with its argument, the value of the numeral NP in (24b), to yield the proposition
in (24c):
(24) a. [[ PP
poj
each proi
]] = λP. ∀z [(z∈Zi
) → ∃X [P(X) ∧ *Rj
(X, z)]]
b. [[ one monkey ]] = λX. 1monkey’(X)
c. [[ one monkey poj
each proi
]] = ∀z [z∈Zi
→ ∃X [1monkey’ (X) ∧ *Rj
(X, z)]]
For every element z of a contextually salient set Zi
, there is a set X of one monkey
such that X and z stand in relation Rj
to one another.
	22
	We choose to adopt Zimmermann’s proposal that DD items have a core prepositional meaning introducing
a free relation variable R for two correlated reasons: First, po is indeed a proposition with the meaning in
some contexts of per (each) (see (25a) in the text below). Second, the proposal that the value of the relation
R holding between the DistShare and the DistKey is pragmatically determined by context allows us to
capture the idea that event distribution here is over triplets of monkeys, with R in the case at hand being
the relation holding between monkeys and the triplets they belong to. We thank a reviewer for insightful
discussion of this point.
	23
	Note that there is also evidence from Korean for this analysis since, as Zimmermann (2002b) himself mentions:
the postnominal DistShare marker -ssik is a particle treated as a postposition.
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
on distributive share markers
Art. 78, page 22 of 28
The numeral NP24
one monkey in (24a) (which forms the DistShare) denotes a property
that is predicated of the set variable that is bound by the existential quantifier in the
nuclear scope of the universal. This ensures that elements of the DistShare are distributed
over elements of the implicit restriction of the universal quantifier.
The indexed variable proi
in (24) provides the restrictor of the universal quantifier, that
is, the DistKey. For event-distributive interpretations, proi
is simply left free, and understood
to denote a salient plurality (of events, on Zimmermann’s analysis of temporal event
distributive readings; see discussion of (8b)) that is recoverable from the context. Our
experimental results tell us that the DistKey in (24) is understood to be the set of sets/
triplets of monkeys made salient by the visual and linguistic input.
Turning now to the value of the relation variable R contributed by po, recall that for
participant distributive construals, its value is provided by an overt relation-denoting
expression in the clause (e.g. by the denotation of the verb in (8a)). For event distributive
interpretations, its value is pragmatically determined by the context (preceding discourse
and extra-linguistic context), together with world knowledge (see discussion of (8b)).
Zimmermann claims that R can take on a variety of temporal, locative, as well as other
values (in particular, causation, temporal succession/overlap/inclusion, homogeneous
subpart, etc.).
Focusing now specifically on Serbian, we can extend this analysis and assume that the
value of the free relation variable R is constrained/determined in part by the core lexical
meaning of po as a locative preposition. Evidence for the status of po as a locative
preposition, with plausibly (universal) quantificational content, is provided by the uses
of po, illustrated in (25), from Knežević (2015: 134–137) who points out that the earliest
diachronic use of po is that of a spatiotemporal preposition. Note, in particular, that
the translation provided for po in (25a) is very close to what we want as a value for R
in (24), i.e. one dancing monkey per triplet, and that we could paraphrase po in (25a) as
per (each). This falls out nicely on the assumption that po spells out incorporation of a
universal quantifier into a prepositional head, which we take to have a meaning akin to
that of per.25
(25) a. pet automobila po stanovniku. Quantitative locative
five car.gen.pl distr inhabitant.loc.sg
‘five cars per inhabitant.’
b. Igračke su (svuda) po Spatial-denoting locative
toy.nom.pl aux.3.pl (everywhere) distr
podu.
floor.loc.sg
‘The toys are all over the floor.’
c. Ivan spava po danu. Temporal-denoting locative
Ivan.nom sleep.3.sg.ps.impf distr day.loc.sg
‘Ivan sleeps throughout/during the day.’
Following Zimmermann, the value of R is contextually determined and can take on a variety
of meanings, that is, temporal, locative, subpart, causal, or other contextual relation.
	24
	A numeral n is taken to denote the property of being a set of n elements. The complex predicate n monkeys
thus denotes the complex property of being a set containing n monkeys, abbreviated “λX. n-monkeys’(X)”.
	25
	Indeed, Carlson & Filip (2001: 452) explicitly argue that “the [Czech verbal] distributive prefix po- also
involves universal quantification, because it requires that the property expressed by its base verb be attributable
to each such unit, namely to each atomic individual member or to each relevant group into which
the domain of interpretation is divided.” (emphasis added).
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
on distributive share markers
Art. 78, page 23 of 28
We take the relevant relation that po establishes between the DistKey (the set of triplets of
monkeys in the visual input) and the DistShare (a set of one monkey) to be the element-of
relation (∈). This constrains each subset/triplet of monkeys Z given in the visual input to
contain as one of its members a subset X of one monkey that is dancing.
The truth conditions ultimately derived for (22) are given in (26):
(26) ∀Z [Z∈ Z’i
→ ∃X [1monkey’(X) ∧ ∃e [*dance’(X, e) ∧ R(e, Z))]]]
For every set Z that is an element of a contextually salient set of sets Z’i
, there
is a set X of one monkey and an event e, such that X dances in e, and event e is
related to Z in that X ∈ Z.
For Zimmermann, event distribution involves distribution of events over an (implicit)
plurality of events. Importantly, (26) yields an event-based distributive interpretation,
even though distribution here is over non-atomic individuals (groups of monkeys). Recall,
in particular, that when quantification is over individuals, the DistShare and the DistKey
correspond to arguments of the verb and the value for the relation variable R in the
meaning of PP is provided by the denotation of the verb. This ensures that, in the case
of (8a) for instance, the distributive relation involves individual ballerinas and groups
of two officers, and is one of accompanying the former home. (26), on the other hand,
involves quantification over events, since po is establishing a relation between individual
events and elements (Z) of the DistKey (Z’i
), and the value of the relation variable R is
determined by the context. By imposing few constraints on either Z or R, Zimmermann’s
proposal allows us to nicely capture the generalization that the triplets of monkeys provided
by the visual input serve as the DistKey, with each triplet having to contain, as one
of its elements, a dancing monkey. Since both Z and R are pragmatically determined, the
interesting question is then why Z did not end up ranging over cages (with R as a locative
relation) so that distribution of dancing monkeys would be over cages and not triplets of
monkeys. We offered a speculative answer to this question in section 3.2.4, suggesting
that participants use both the visual input (triplets of cageless/caged monkeys) and the
linguistic input (mention of monkeys) provided by the experimental materials) to recover
the spatial DistKey.
On the proposal defended here, the truth conditions in (26) differ from those for runof-the-mill
cases of quantification over events only in that the members of the spatial
DistKey are plural individuals (i.e. groups of monkeys). We take up this issue in the context
of Champollion’s (2016b) parameters of variation for distributivity operators.
4.1.1  Distribution over spatio/temporal locations
Recall that not all DD items also distribute over spatio/temporal aspects of events. Those
that double as determiners (e.g. each) cannot, while DD items such as jeweils or po can.
Champollion (2016b: 4) takes this semantic variation to reflect the parameter settings for
distributivity operators: granularity and dimension. Granularity specifies the “size of the
entities over which we distribute: e.g. atoms or amounts of space or time.” Dimension
specifies the domain of distributivity: either participants/theta-roles or space/time intervals.
These parameters interact. If the granularity parameter is set to atoms (as is the case
for each), then distribution over spatial/temporal dimensions is excluded: since time is a
continuous and non-count dimension, there are no atoms to distribute over. If granularity
is left unspecified (as is the case for jeweils), distribution over non-count dimensions like
time is possible.
Clearly, the granularity parameter for po/-ssik is unspecified since they can distribute
over entities that are non-atomic such as time, as well as entities that are bigger than
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
on distributive share markers
Art. 78, page 24 of 28
atoms – that is, groups/pluralities of atomic individuals. Crucially, however, in the latter
case, distribution is over spaces, distribution is not over participants. Indeed, it cannot be
over the theta-role dimension, if only because the agent argument is itself marked as the
DistShare. The (locations of the) groups of monkeys serve to divide up the spatial key, to
partition the spatial region into relevant spatial units that have to be exhausted. So why
can po/-ssik distribute over pluralities of non-atomic individuals? The answer, we suggest,
is because this is yet another instance of distribution over the spatial dimension.26
We sought to capture this with the analysis developed for (22) in (25–26). Locative po
establishes a distributive relation between individual events (of monkeys dancing) and
plural individuals (triplets of monkeys), requiring that there be one dancing monkey per
each triplet of monkeys. The pluralities provided by the visual context thus serve to divide
up the DistKey into chunks of space.
We close by pointing out that this raises the issue of whether atomic individual/participant-based
distributive readings could not also be subsumed under spatial distributivity,
which is a controversial issue in the literature. As Cusic (1981) and Lasersohn (1995)
point out, although two atomic individuals can occupy the same space at different times,
they cannot occupy the same space at the same time (Lasersohn 1995: 250). The idea then
is that (atomic) participant distribution could be made to fall out from spatio/temporal
distribution: with events occurring simultaneously, distribution over singular individuals
would reduce to distribution over different spatial locations (since each atomic individual
defines his/her own spatial location), and with events occurring over different times,
to distribution over different temporal locations. We leave these issues open for further
research.
5 Conclusion
This paper experimentally probed the issue of whether DistShare markers show exhaustivity
requirements in two typologically very different languages, testing the Serbian marker
po and the Korean marker -ssik. The empirical findings were as follows. The sentence
“DISTR one monkey is dancing” in Serbian and Korean is true on a spatial event-distributive
reading if, in each caged group of monkeys (provided by the visual input), there is a
monkey dancing, and remains true when empty cages are added. When non-caged groups
of monkeys are added, the sentence remains true only as long as in each of these noncaged
groups, a monkey is dancing.
We took our empirical findings from Experiment 1 (corroborated by Experiment 2)
to provide evidence that the (spatial) event-distributive reading that DistShare markers
yield, involves a covert (spatial) DistKey that must be exhausted. This conclusion
argues in favor of a UQ analysis. The question, however, is how the spatial DistKey is
identified since it remains an implicit argument that must be recovered via context and
pragmatics. Having established in Experiment 1 that the DistKey was not ranging over
cages, we tested with Experiment 2, two other hypotheses made available by the visual
input – namely, that the spatial DistKey was either triplets of monkeys in cages, or
merely triplets of monkeys (whether they are caged or not). The later hypothesis neatly
proved to be the correct one. We suggested an analysis of spatial event distribution along
the lines of Zimmermann (2002b): po/-ssik is a locative pre/postposition with universal
quantificational force (roughly per (each)) establishing a distributive relation between
individual events (of monkeys dancing) and plural non-atomic individuals (triplets of
monkeys) serving as the DistKey, requiring that there be one dancing monkey per each
	26
	It goes without saying that quantification over groups coincides with quantification over spatial locations
occupied by these subgroups only to the extent that the subgroups in question occupy distinct spatial locations.
That is, if groups occupy the same location at different times, then we are distributing over time intervals
and not space. Likewise, if two different groups have the same participants, then distribution will again
necessarily be temporal (since the same individual cannot occupy at the same time two different spaces).
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
on distributive share markers
Art. 78, page 25 of 28
triplet of monkeys. This proposal receives empirical support from uses of po as a locative
(quantitative, spatial, or temporal) preposition. Moreover, it nicely captures Gil’s (2013:
222) definition of distributive numerals: “The meanings of sentences containing distributive
numerals can be described in terms of a binary semantic relationship of distributivity
that obtains between an expression containing the distributive numeral, the distributive
share, and some other expression in the sentence, the distributive key. This relationship
may be expressed by means of the English preposition per, in accordance with the formula
share per key.”
By experimentally probing the question of how spatial DistKeys are recovered from
the context (specifically, highlighting how both the linguistic and the visual input made
available together play a role in determining the relevant domain restriction) we hope
to have also contributed novel empirical evidence to bear on a long standing question in
the literature, that of how implicit quantifier domains are recovered (Von Fintel 1994;
Stanley & Gendler Szabó 2000).27
An obvious next step is to investigate how well the analysis developed here extends to
transitive sentences. The added complexity is that since transitive sentences have two
arguments, while one of them will serve as the DistShare (and as such be marked by po),
the other (unmarked argument of the verb) can potentially serve as an overt DistKey,
thus yielding an individual-distributive reading. This further gives a strong competitor to
event-distributive readings and again the challenge is in setting up the experiments, but
here to test both individual and event-distributive readings. This is one of the directions
of investigation we are currently developing.
Another line of investigation would be to test the hypothesis put forth that the critical
reading that sentence (22) yields arises as an instance of distribution over the spatial
dimension: distribution over non-atomic members of a plurality of individuals is possible
because the pluralities (made available by the visual input) can serve to divide up the
DistKey into chunks of space. The prediction would then be that no such reading should
arise if distribution is set up to be temporal, that is, over chunks of time and not space.
We hope that our work has shown the benefit of experimental data for probing empirical
generalizations and their theoretical accounts, and as such will encourage further experimental
research into the different uses of DistShare markers so that we can investigate
and comprehensively evaluate the best approach to semantically describe such markers.
Abbreviations
acc = accusative, aux = auxiliary, clf = classifier, dec = declarative, distr = distributive,
loc = locative, nom = nominative, past = past, pl = plural, prog = pro-
gressive.
Additional Files
The additional files for this article can be found as follows:
•		Appendix A. Complete model outputs for Experiments 1 and 2. DOI: https://doi.
org/10.5334/gjgl.858.s1
•		AppendixB.ExperimentalitemsinSerbianandKorean.DOI:https://doi.org/10.5334/
gjgl.858.s1
Acknowledgements
Jennifer Spenader and Hamida Demirdache should be considered joint senior authors of
this paper. The authors wish to thank Nataša Knežević, Boban Arsenijević, Orin Percus,
Bart Hollebrandse, Angeliek van Hout, Anamaria Fălăuş, Jakub Dotlačil, Ken Drozd,
	27
	We thank an anonymous reviewer for emphasizing this important point.
Bosnić et al: Dancing monkeys in Serbian and Korean – exhaustivity requirements
on distributive share markers
Art. 78, page 26 of 28
­Marijana Marelj and Anna de Koster, and three anonymous reviewers for invaluable discussions,
advice, comments and feedback they provided on different stages of this paper.
Special thanks go to Jiyoung Choi for Korean translations both for the experiment and in
the paper. We also thank our research groups and labs for useful meetings and discussions:
the Laboratoire de Linguistique de Nantes (LLING) UMR 6310 CNRS/University of Nantes,
the Acquisition Lab and the Semantics and Cognition group/University of Groningen. Conducting
this research would not have been possible without numerous informants, and
all the participants in our experiments, who we thank for their input and judgments. This
research was partly sponsored by Ammodo (Groningen – Nantes Van Gogh research grant).
Competing Interests
The authors have no competing interests to declare.
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and Korean – exhaustivity requirements on distributive share markers. Glossa: a journal of general linguistics 5(1):
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Submitted: 16 November 2018 Accepted: 17 April 2020 Published: 29 July 2020
Copyright: © 2020 The Author(s). This is an open-access article distributed under the terms of the Creative Commons
Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are credited. See http://creativecommons.org/licenses/by/4.0/.
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