EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
Differentiating scalar implicature from mutual exclusivity in language acquisition
[Authors and Affiliations Blinded]
Total Word Count: 9,597
Abstract Word Count: 205
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EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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Abstract
When acquiring language, children must not only learn the meanings of words, but also how to
interpret them in context. For example, as part of acquiring the quantifiers some and all, children
must learn to differentiate the logical semantics of the scalar quantifier some from its
pragmatically enriched meaning, “some but not all”. Many studies report that this type of
inference, generally referred to as “scalar implicature”, poses a difficult challenge to children
until quite late in development – as late as 9 or 10 years of age. In contrast, more recent studies
find successes as early as 3 years of age. We ask whether the computation of exclusion
inferences (like those licensed by contrast or mutual exclusivity) – rather than an ability to
compute scalar implicatures – might account for children’s performance on tasks showing early
success on distinguishing some from all. We find strong evidence that young children (N = 214;
ages 4;0-7;11) compute exclusion inferences when relating some and all to one another even
when such inferences are inappropriate in the context. We also find evidence that, in some
contexts, performance that is consistent with the computation of scalar implicature can actually
be explained by the computation of exclusion inferences like contrast and mutual exclusivity.
Keywords: Pragmatics, mutual exclusivity, contrast, scalar implicature, inference
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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When children encounter new words, they assume that they differ in meaning from
previously learned words. For example, when shown a pair of objects – one novel, and the other
familiar – and told to “Find the blicket”, children as young as 18 months of age preferentially
select the novel referent (Halberda, 2003; Markman, Wasow, & Hansen, 2003; Spiegel &
Halberda, 2011). Results like this have been reported in relation to children’s acquisition of
nouns, verbs, adjectives, proper names, and even number words (e.g., Au & Markman, 1987;
Carey & Bartlett, 1978; Clark, 1987; 1988; 1990; Wynn, 1992), suggesting that children very
generally assume that different words encode different meanings. According to many accounts,
this reasoning reflects a more general pragmatic approach to language: Children assume that
speakers are cooperative Gricean interlocutors who seek to be truthful, informative, relevant, and
clear (Grice, 1970). Thus, they reason that if the speaker had intended to refer to the object with
the known label then they would have used that word, and thus must have intended to label the
novel object. In this way, children can infer that utterances like those in (1) differ in meaning,
even if they lack meanings for the words some and all or understand how some and all are
related to one another.
(1a) I ate some of the cookies.
(1b) I ate all of the cookies.
Taken alone, word learning assumptions like Clark’s (1987) Principle of Contrast and Au
and Markman’s (1987) Mutual Exclusivity Assumption are useful, but incomplete, cues to word
learning and interpretation. In the best case scenario, assumptions like these can indicate that two
words differ somehow in meaning – even if only in connotation or conversational register. In the
worst case, they can lead to false inferences – e.g., that a cat is not an animal. Very generally, in
order to arrive at adult-like interpretations of words, the assumption that they have mutually
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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exclusive meanings (or simply contrast) must be supplemented with additional information about
the words under consideration (e.g., whether they are relevant alternatives to one another;
whether one entails the other). For example, to interpret the sentences in (1) in an adult-like way
(e.g., that the speaker is intending to convey that they ate some but not all of the cookies),
children must know the literal meanings of some and all, including that all is strictly stronger
than some in this context, and that if (1b) were true, then it would have been a more
informative/optimal thing to say. Only with this knowledge is it possible to infer that (1a) implies
the negation of (1b).
This particular inference – a “scalar implicature” – is in some respects similar to
inferences based on contrast or mutual exclusivity. Just as interpreting the novel word blicket is
easier if one can use contrast to rule out “cat” as a possible meaning, interpreting an utterance
containing some to mean “not all” involves negating a corresponding utterance that contains all.
Indeed, several researchers have argued that contrast and mutual exclusivity rely on similar
computational architecture to scalar implicature (Barner & Bachrach, 2010; Clark, 1990;
Gathercole, 1989; Grice, 1970, 1991; Katsos & Wilson, 2014; Wynn, 1992). However, despite
their similarities, these types of inferences exhibit important differences, both in their structure
and their developmental trajectories. Below, we explore one property of scalar implicature that is
not described by word learning constraints – what linguists call “asymmetric entailment”. In
particular, we ask whether studies which claim to show early abilities to compute implicatures
actually do so, or whether they might instead rely on simpler inferences, like those required by
contrast and mutual exclusivity. In doing so, we not only ask whether previous studies provide
valid tests of implicature, but also whether the ability to compute implicatures might arise
initially from the same machinery that supports word learning.
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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In order to understand how contrast and mutual exclusivity are related to scalar
implicature, it is important to first characterize the computations that they involve. First, consider
contrast (for discussion see Clark 1987; 1988; 1990). Contrast inferences arise from the
assumption that differences in linguistic form signal differences in meaning, and are relatively
weak, in the sense that they do not, in isolation license strong assumptions about reference. For
example, contrast allows expressions like couch and sofa to convey different connotations while
still labeling the same referent. Mutual exclusivity inferences can be described as enriched
contrast inferences: “Mutual exclusivity is one kind of contrast, but it is a more specific and
stronger assumption: many terms that contrast in meaning are not mutually exclusive.”
(Woodward & Markman, 1991; p. 141) Much like contrast, mutual exclusivity inferences arise
when listeners assume that each word has one meaning and each meaning is expressed by only
one word, such that word “A” implies not-“B”, just as “B” negates “A” (Woodward & Markman,
1991). In addition, mutual exclusivity inferences also involve the assumption that differences in
meaning predict differences in reference – a particular object labeled as a “blicket” cannot also
be called a “toma”. Thus, in this sense, they are stronger than contrast alone. For the purposes of
the present study, this difference between contrast and mutual exclusivity will not play a central
role, and therefore we will refer to both forms of inference collectively as “exclusion inferences”,
except in cases where the difference is important.
According to Clark (1990), exclusion inferences can be characterized as Gricean in
nature, and can therefore be thought of as being importantly similar to scalar implicature. For
example, in a context including a cat and a novel object, a speaker who intends to refer to the cat
is expected to say, “Look at the cat!” rather than, “Look at the blicket”. In this case, on a
standard Gricean analysis, the listener hears the word blicket and assumes that the speaker's
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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intended referent is not a cat, since if they had intended to refer to the cat then they would have
chosen the word cat instead. This is much like the inference proposed by Gricean models of
scalar implicature. In (1a), if the speaker had actually eaten all of the cookies then they should
have said so; thus, saying they ate some of the cookies licenses the implicature that the statement
containing all is false.
While exclusion inferences are structurally similar to scalar implicature, they also differ
in critical ways. First, exclusion inferences differ dramatically from scalar implicatures with
respect to their developmental trajectories. While children readily compute exclusion inferences
by the age of 2 or earlier (Au & Markman, 1987; Carey & Bartlett, 1978; Halberda, 2003;
Heibeck & Markman, 1987; Markman & Wachtel, 1988; Wynn, 1992), the literature on scalar
implicature is divided, with some studies reporting difficulties among children as old as 9 or 10
years of age, and others finding evidence of scalar implicature in 3-year-olds (Chierchia et al.,
2001; Miller, Schmitt, Chang, & Munn, 2003; Noveck, 2001; Papafragou & Tantalou, 2004;
Papafragou & Musolino, 2003; Stiller, Goodman, & Frank, 2015; Yoon, Wu, & Frank, 2015). A
second difference is that, whereas exclusion inferences involve a symmetrical exclusion
relationship (hence “mutual exclusivity”), implicature generally does not. For example, in (1a)
and (1b) the utterances not only contrast, but also exhibit what linguists call “asymmetric
entailment”: Whereas the truth of the utterance in (1b) entails that (1a) must also be true – i.e., if
I ate all of the cake I must have eaten some of it – the opposite is not true. This observation has
led some linguists to posit the existence of ordered lexical classes, sometimes called Horn scales,
which are deployed in the service of scalar implicature (Horn, 1989; Gazdar, 1979; Levinson,
2000). According to this view, the ability to compute scalar implicatures involves not only the
ability to contrast utterances, but also the ability to relate them to one another according to their
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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relative informational strength in context. Specifically, upon hearing, e.g., “I ate some of the
cookies”, the listener must infer that were the stronger alternative statement true – i.e., “I ate all
of the cookies” – then the speaker would have said so, and consequently they must not believe
this stronger statement to be true, but instead believe that they ate some, but not all, of the
cookies.
As already noted, whereas children compute exclusion inferences almost as soon as they
can talk, they often fail to compute scalar implicatures until well into elementary school
(Chierchia et al., 2001; Noveck, 2001; Papafragou & Musolino, 2003). Explanations for
children’s failures vary, but there is increasing evidence that at least part of their difficulty lies in
summoning relevant scalar alternatives – e.g., they fail to spontaneously conjure utterances
containing all as relevant alternatives to utterances containing some, resulting in an inability to
make a some-but-not-all inference (Barner, Brooks, & Bale, 2011; Hochstein, Bale, Fox, &
Barner, 2014; Skordos & Papafragou, 2016). In support of this view, children appear to perform
better when scalar alternatives are either primed, or explicitly contrasted with one another in
two-alternative forced choice paradigms (e.g., when one utterance is matched with one of two
pictures, or one picture is matched with one of two utterances; Chierchia et al., 2011; Katsos &
Bishop, 2010; Miller, Schmitt, Chang, & Munn, 2003; Papafragou & Tantalou, 2004; Stiller,
Goodman, & Frank, 2015). Critically, these are precisely the paradigms that would allow
participants to easily recruit mutual exclusivity to guide their judgments. Because of this, as we
describe below, although these studies can be interpreted as evidence for early abilities to
compute scalar implicature, it’s also possible that children’s earliest experimental successes rely
on a simpler exclusion inference, which does not involve computing asymmetric entailment.
Currently, no previous study has provided evidence to differentiate these two alternatives.
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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In one report of early implicature abilities, Papafragou and Tantalou (2004) showed 4and 5-year-old children a puppet who was asked to do a task – e.g., “Puppy! Paint all of the
stars”. After disappearing into a house, the puppet then returned and reported what he had done –
e.g., “I painted some of the stars”. In this case, children correctly judged that Puppy had not done
the right thing (e.g., that some implied, in this case, not all). While this study was interpreted as
providing evidence of scalar implicature in the early preschool years, it is also possible that
children’s success was driven by mutual exclusivity alone. To understand this, consider the
dialogue in (2).
(2a) S1: Did you buy all of the candy?
(2b) S2: I bought some of the candy.
Here, if children compute a scalar implicature, they should infer that not all of the candy
has been bought, because the statement containing all is stronger than the statement containing
some. However, they should also reach this conclusion if they use mutual exclusivity – some
implies “not all” simply because some and all are different words. In such cases, it is impossible
to differentiate which mechanism a listener has used to infer that some implies “not all”.
However, other cases do allow us to tease these two mechanisms apart. Consider now the
dialogue in (3), which contains an entailment relation.
(3a) S1: Did you approve some of the charges?
(3b) S2: I approved all of the charges.
Here, if children make
an exclusion
inference, then they should
assume
(counterintuitively and incorrectly) that the speaker of 3b did not approve some of the charges
because he approved “all” of them. On the other hand, if children represent the appropriate scalar
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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entailment relationship (that all entails some), they should infer that the speaker in 3b approved
some (and, in fact, all) of the charges.
In the present study, we investigated why different studies find discrepancies of up to 8
years in their estimates of when children can compute implicatures. First, we asked whether
recent reports of early implicature computation in children necessarily involved true
implicatures, or instead might be explained as being supported by exclusion inferences alone.
Second, our study addressed the question of whether scalar implicature might be rooted, in part,
in the same inferential capacities that underlie exclusion inferences like contrast and mutual
exclusivity.
To test these questions, we built on Papafragou and Tantalou’s (2004) study with two
important modifications. First, in addition to trials like those used in the original study (which
could be solved either by computing scalar implicatures or by using exclusion inferences), we
also included trials that required sensitivity to asymmetric entailment, as in (3). This allowed us
to ask whether children’s inferences reflect the computation of exclusion inferences, or whether
they also involve assumptions regarding asymmetric entailment, as required by scalar
implicature. Second, we included trials in which logically equivalent statements nonetheless
contrasted in form (e.g., a request to paint “3” out of 3 stars, fulfilled by a Puppy painting “all”
of the stars), and trials containing novel words (e.g., blick, as in 3) about which the child should
have no previous expectations about meaning. This allowed us to ask whether, outside of the
special case of scalar implicature, children relied more heavily on mutual exclusivity than other
sources of information when making judgments about contrasting utterances. If children rely on
simple exclusion inferences to guide their judgments, then they should perform as though any
contrasting statements (regardless of their logical relations to one another) negate one another
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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(e.g., arriving at the false inferences that all implies “not some”; three (out of 3) implies “not
all”). In contrast, if children can compute scalar implicatures, then they should perform in a way
that suggests understanding of asymmetric entailment – namely, that stronger alternatives entail
weaker ones but not vice versa.
Experiment 1
Materials and Methods
Participants
A total of 95 monolingual English participants between the ages of 4;0 and 7;11 from
[BLINDED] participated (7 additional participants were tested but were out of our age range).
Children were recruited from [BLINDED], a local museum, and preschools and daycares in
[BLINDED]. Parental consent and verbal child assent were obtained prior to testing. Three
participants were excluded for failing to complete at least half of the task or for experimenter
notes of inattention, 2 were excluded for being bilingual, and 1 was excluded due to
experimenter error. Finally, 8 additional participants were excluded for only providing one type
of response (e.g., always giving Puppy a prize or withholding a prize). Thus, a final N of 81
children (4 YOs n = 21; 5 YOs n = 27; 6+ YOs n = 33) was included in analyses; our data
collection goal was to have a minimum of 20 participants in each age group. An additional 16
adult (undergraduate) participants participated for course credit, and there were no exclusions of
adults.
Materials and Procedure
Our methods were modeled after Papafragou and Tantalou (2004). A toy puppy was used during
the task, and an Experimenter served as narrator. A plastic container full of approximately 25
small plastic grapes served as “prizes” for Puppy. For each trial, there was a “Before” picture of
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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three items (e.g., a picture of 3 unpainted stars; see Fig. 1 left panel). Pictures were presented on
an 8.5” x 11” piece of paper, with all three items laid out horizontally across the page.
Puppy painted
some of the stars!
Okay, Puppy, you
get a prize if you
paint all the stars!
Make sure to
paint
all of the stars!
Puppy painted
some of the
stars!
Look what
Puppy did!
Request
Exp. 1
Exp. 2
(Words
and
Pictures
Exp. 2
(Pictures
Only)
What Puppy Did
Figure 1. Schematic of methods for Exp. 1 and Exp. 2. Left panel indicates the experimenter’s
request (e.g., Puppy’s task), while the right panel demonstrates how the child learned of what
puppy did.
For each trial, the experimenter requested that Puppy complete a task. For example, the
Experimenter requested that Puppy e.g., paint all/some/two/three/blick of the stars (list of all
trials is in Table 1). Puppy’s task was always described verbally and repeated twice (see below),
with the request first stated in a conditional “if…” statement, where scalar implicatures are
typically not calculated, minimizing the likelihood that participants would compute implicatures
on the request (e.g. some) itself. Participants were informed that they would have the option to
give Puppy a prize (toy grapes that they could feed to Puppy) if he did his job well.
On each trial, the experimenter showed a Before picture (e.g., three unpainted stars) and
told the participant that Puppy had to complete a task. On each trial, the experimenter said,
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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“Wow, look! There are three [objects]. Okay Puppy, you get a prize if you [requested task].
Make sure to [requested task].” The participant then learned what Puppy actually did via a verbal
description (e.g., “Alright, Puppy, did you [task]?” followed by the summary of his actions:
“Puppy painted some of the stars”), but saw no visual evidence of his actions (i.e. the picture did
not change). After hearing about Puppy’s actions, the participant was given an opportunity to
offer a prize to Puppy (indicating that Puppy had successfully done what was asked of him), and
to give justifications for their decision. Participants completed 22 trials. Within each set of
stimuli, there were two trial orders to reduce the likelihood of order effects. We had seven trial
types, described in detail below and in Table 1. In Table 1, we make the content of and
predictions for each trial explicit (e.g., what task the Experimenter requested Puppy to do, what
Puppy actually did, the number of trials each participant received, and the predictions for the
trial).
There were two types of control trials: ‘Good Job’ Controls and ‘Bad Job’ Controls. For
the ‘Good Job’ Control trials, the experimenter’s request exactly matched what Puppy did,
allowing us to measure whether participants would give Puppy a prize if he did the right thing
(see Table 1 for a description of how – regardless of strategy – all participants are predicted to
give a prize on these trials). For the “Bad Job” Control trials, the experimenter’s request clearly
didn’t match what the Puppy did, allowing us to measure whether participants would withhold a
prize from Puppy if he did the wrong thing.
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
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Table 1. Trial types, names, actions involved, and predictions for trials in Experiment 1.
Exclusion
n of Experimenter Puppy's Implicature
Inference
trials
Request
Actions Prediction
Prediction
1
three
three
prize
prize
3
some
some
prize
prize
Trial Type
Trial Name
Good Job
Controls
request 3, did 3
request some, did some
Bad Job
Controls
request 3, did 2
request blue, did green & red
request green, did red & blue
1
1
1
three
blue
green
two
green/red
red/blue
no prize
no prize
no prize
no prize
no prize
no prize
Scalar
scalar implicature
scalar entailment
request 3, did some
3
1
3
all
some
three
some
all
some
no prize
prize
no prize
no prize
no prize
no prize
Novel
request all, did blick
request blick, did all
1
1
all
blick
blick
all
no prize
prize
no prize
no prize
Contrast
Mismatch
request 2, did some
3
two
some
prize
no prize
Numerical
Entailment
request 2, did all
1
two
all
prize
no prize
1
1
blue
hat
blue/green
hat/shirt
prize
prize
no prize
no prize
Contextual request blue, did blue and green
Entailment
request hat, did hat and shirt
There were five critical trial types: Scalar Implicature, Novel Im-“blick”-ature, Contrast
Mismatch, Numerical Entailment, and Contextual Entailment. For the Scalar trials (Scalar
Implicature and Scalar Entailment), we used some and all in the request and fulfillment. On
Scalar Implicature trials, we assessed whether participants computed implicatures (by inferring
that some implies “not all”), and on Scalar Entailment trials, we measured whether they also
computed entailment relations (that all entails some). For the Novel Im-“blick”-ature trials, we
replaced the word some from the Scalar trials with the novel quantifier blick in describing either
Puppy’s task or what he did. In other words, the Im-“blick”-ature trials were structurally
identical to the Scalar Implicature trials, but involved a novel word instead of the word some,
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
14
thus allowing us to test participants’ inferences in the absence of semantic or scale-specific
knowledge. For the Contrast Mismatch trial type, Puppy did what the experimenter requested,
but Puppy’s action was described using a different word from the request (see Table 1). This trial
type was important because if participants rely only on mutual exclusivity, they should withhold
a prize from Puppy, while if they use any other strategy that involves knowledge of the word
meanings (including computing scalar implicature), they should give Puppy a prize. For the
Numerical Entailment trials, Puppy was asked to do a number of actions (i.e., 2), but actually did
more. These trials were structurally similar to the Scalar Entailment trials in that Puppy’s actions
entailed the requested actions, but did not involve the sum/all scale – if participants rely on
mutual exclusivity, they should reject Puppy’s actions (since the request differed in format from
Puppy’s fulfillment), whereas if they recognize that a set of 3 includes a set of 2, they should
accept Puppy’s actions. Finally, the Contextual Entailment trials were again similar to the
Numerical Entailment and Scalar Entailment trials, in that Puppy did what was asked and more –
however, they did not require scale-specific knowledge of numerals and quantifiers, but instead
relied only on contextually-defined alternatives. Again, in this case, we predicted that if
participants compute entailment relations between the requests and reports of Puppy’s actions,
then they should give Puppy a prize, since Puppy did everything that was asked. However, if
participants rely on mutual exclusivity – and only reward actions that exactly match requests –
then they should withhold the prize.
Results
Data Management
A total of 9 trials were excluded prior to analyses due to experimenter error. Responses
were binary in nature (“prize” or “no prize”). As such, all analyses were binomial (though we
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
15
also report the proportion of trials on which participants gave puppy a prize). Whenever a
participant provided responses to multiple trials of a given trial type, we included participant as a
random factor when predicting binomial performance; analyses were conducted using the lme4
package in R (Bates, Machler, Bolker, & Walker, 2015). For all reported analyses, we first tested
for age effects on children's performance; unless reported otherwise, we found no differences in
performance between 4-, 5-, and 6-year-olds. Thus, all subsequent analyses compared children’s
performance to adults’ performance, although we visually display performance for each age
separately in our figures, in order to allow for comparisons with previous literature.
Results
Control Trials.
‘Good Job’ Controls. We first considered the control trials on which there was an exact
match between the experimenter’s request and Puppy’s actions – e.g., the experimenter asked
Puppy to perform an action on three of the objects, and, in fact, the Puppy performed an action
on three of the objects. Across all ages, participants successfully gave Puppy a prize on these
trials (see Fig. 2), and did so the vast majority of the time (see Table 2), and there was no
difference between children and adults (B = .44, SE = 1.84, p = .81).
‘Bad Job’ Controls. We next considered the control trials on which Puppy’s actions did
not fulfill the experimenter’s request. For example, the experimenter asked Puppy to perform an
action on three of the objects, and instead the child heard that Puppy performed an action on two
of the objects. Across all trial types and ages, participants nearly always withheld a prize (see
Fig. 2; Table 2), suggesting that they did not believe that Puppy’s actions fulfilled the
experimenter’s request. This suggests that participants attended to and understood the task, and
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
were willing to both give and withhold a prize from Puppy when they thought it was warranted.
Again, there were no differences between children and adults (B = .14, SE = 1.8, p = .94).
16
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
17
Figure 2: Mean rates of prize-giving for control trials; ‘Good Job’ Control trials are on the top
row and ‘Bad Job’ Control trials are on the bottom two rows. Error bars are SEM, dashed line is
50%.
Critical Trials
Scalar Implicature and Scalar Entailment Trials. The Scalar Implicature and
Entailment trials contained only the scalar terms some and all. On these trials, participants who
compute scalar implicatures should accept Puppy’s actions in the ‘request some, did all’ Scalar
Entailment case (because all entails some), but should reject Puppy’s actions on the ‘request all,
did some’ Scalar Implicature trials (because some implies that “not all” were done). Therefore,
performance on these two trial types should differ significantly. Consistent with this prediction,
adults gave puppy a prize 73.33% of the time in the ‘request some, did all’ Scalar Entailment
case, whereas they did so 8.33% of the time in the Scalar Implicature ‘request all, did some’
case; performance on these two trial types differed significantly for adults (B = -3.41, SE = .78,
p<.0001). Moreover, consistent with the use of true implicature, there was a strong
correspondence between performance on these two trial types: Nine out of the 11 adults who
withheld a prize on the scalar implicature trials rewarded puppy with a prize on the entailment
trials. 1
Note that whereas the use of scalar implicature predicts asymmetric judgments on these
different trials types, the use of exclusion inference predicts that participants should reject
1
To complete these analyses, we coded whether participants gave puppy a prize on Scalar
Implicature and Entailment trials. Only participants who provided consistent responses within a
given trial type were included in this analysis (Adult n = 11; Child n = 60).
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
18
Puppy’s actions for both trial types (‘request some, did all’ and ‘request all, did some’). This is
what we found in children. Children gave puppy a prize 43.21% of the time on the Scalar
Entailment ‘request some did all’ trials, and 38.24% of the time on the Scalar Implicature
“request all did some” trials, and performance on these two trial types did not differ statistically
(B = -.43, SE = .42, p = .31). Importantly, the same child participants who rejected Puppy’s
actions for the ‘request all did some’ trials also rejected Puppy’s actions for the ‘request some did
all’ trials. Unlike in adults, only 4/40, or 10%, of children who withheld a prize on the scalar
implicature trials then gave puppy a prize on the entailment trials. These judgments are unlike
those of adults’ and suggest that children did not compute scalar implicatures during our task, but
instead based their judgments purely on exclusion.
When the experimenter requested three, and Puppy reportedly did some, children gave a
prize 40.17% of the time, at a rate comparable to that of the scalar implicature ‘request all did
some’ trials. This performance is consistent with either exclusion inference or scalar implicature.
However, children’s performance on this trial type was not adult-like: children gave a prize
significantly more often than adults did (6.25% of adults gave a prize; B = 4.43, SE = 1.38, p =
.001), suggesting that overall they were less likely to judge that reported actions mismatched
requests. This finding is consistent with the possibility that at least some children interpreted
some as “some and possibly all” (not computing a scalar implicature) or “a relatively small
quantity”.
Novel Im-“blick”-ature trials. In order to understand the extent to which the above
pattern of performance relied on scale-specific knowledge of the word some, we next considered
trials that involved the novel word (blick) instead of the scalar word some. For one such trial,
Puppy was asked to do blick, and he reportedly did all. On this trial, both adults and children
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
19
rewarded Puppy around half of the time (Children: 44.87%; Adults: 53.33%; B = .34, SE = .57, p
= .55). For the request all did blick trials, adults consistently rejected Puppy’s actions (6.67%
gave Puppy a prize), suggesting that they did not believe that blick was a fulfillment of a request
for all. Children gave prizes at significantly higher rates (49.32% of the time) than did adults (B
= 2.54, SE = 1.06, p = .02). Importantly, children’s performance on the ‘request all did blick’ Im“blick”-ature trials was statistically indistinguishable from their performance on the Scalar
Implicature ‘request all did some’ trials (B = .21, SE = .37, p = .57). These data suggest that
scale-specific knowledge of the relation between some and all was not necessarily driving
children’s behavior on our scalar implicature and scalar entailment trials (Fig. 3).
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
20
Figure 3: Mean rates of prize-giving for Scalar and Im-“blick”-ature; error bars are SEM, dashed
line is 50%.
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
21
Contrast Mismatch. We next considered the case where reports of Puppy’s actions were
consistent with the experimenter’s request, yet contrasted in linguistic format (i.e. when puppy
was asked to do two, and said he did some). Critically, on this trial type, Puppy’s response was
described using a different linguistic term than had been used in the initial request, leading to
different predictions of performance for participants who computed scalar implicatures, relative
to those who computed exclusion inferences . Specifically, participants who computed a scalar
implicature (that some implies “not all”) should give puppy a prize, since some (and not all) is a
good fulfillment of a request for two items in this context (as adults did, see Table 1). However,
participants who (a) compute an exclusion inference (e.g., that two and some are different words
and therefore must refer to different quantities in this context) or (b) fail to compute a scalar
implicature (and believe that some might be compatible with doing 3 out of 3) should reject
Puppy’s actions, as children did around half of the time of the time (Fig. 4; Table 2).
Numerical Entailment. We next considered the trial on which Puppy was asked to do
some number of actions (e.g., “feed 2 of the lions”), but ended up doing too much (e.g., “feed all
of the lions”). On these trials, participants had three choices for how to interpret the
experimenter’s request. The first was to interpret the request for Puppy to do 2 as a lowerbounded request (e.g., interpreting the request like: “do at least two actions”), consistent with a
scalar entailment calculation. This predicted that participants would give Puppy a prize when he
did too much, as adults tended to do (Table 1). The second option was to compute an exclusion
inference, and the third was to interpret the request as an exact request (e.g., “do two, and no
more and no less”); both of these options predict withholding the prize. Children (and a plurality
of adults) tended to adopt this latter strategy, and withheld Puppy’s prize (Table 2, Fig. 4).
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
22
Figure 4: Mean rates of prize-giving for Contrast Mismatch and Numerical/Contextual
Entailment trials; error bars are SEM, dashed line is chance.
Contextual Entailment. Finally, we considered trials on which Puppy did more than what
was requested of him, and Puppy’s actions were described using contextual (as opposed to scalar
or numerical) alternatives. For example, these were trials where Puppy was asked to wash the
hat, but he actually washed the hat and shirt; or he was asked to eat the blue lollipop but actually
ate the blue and green lollipops (Fig. 4). These were important, because they involved entailment
(e.g., that washing a hat and shirt entails washing the hat), but included contextually defined
alternatives rather than lexical quantifiers like some and all. This allowed us to test whether
children’s reliance on mutual exclusivity was specific to quantifiers or reflected a more general
indifference to entailment relations in this task. Participants who correctly computed the
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
23
entailment relation should have preferred to give Puppy a prize. Consistent with this, adults gave
prizes on 81.25% of trials. On the other hand, we predicted that participants who compute
exclusion inferences across noun phrases should withhold Puppy’s prize. This is exactly what
children did, giving puppy a prize only 19.88% of the time; see Table 1).
Table 2. Percent giving puppy a prize in Experiment 1 (Words Only), and Experiment 2 (Words
and Pictures; Pictures Only).
Trial Type
Good Job
Controls
Stimuli
Four Year Olds Five Year Olds
Words Only
98.70%
91.51%
Words and Pictures
78.18%
87.50%
Pictures Only
67.79%
71.58%
Six+ Year Olds
93.08%
91.76%
85.56%
Adults
88.71%
98.75%
98.75%
Bad Job
Controls
Words Only
Words and Pictures
Pictures Only
8.06%
9.38%
11.11%
13.58%
6.38%
14.04%
8.08%
0.00%
5.56%
12.50%
0.00%
0.00%
Scalar
Implicature
Words Only
Words and Pictures
Pictures Only
38.33%
12.12%
13.89%
33.75%
10.42%
5.26%
41.84%
0.00%
7.41%
8.33%
2.13%
0.00%
Scalar
Entailment
Words Only
Words and Pictures
Pictures Only
57.14%
72.72%
58.33%
40.74%
43.75%
68.42%
36.36%
47.06%
72.22%
75.00%
93.33%
87.50%
Contrast
Mismatch
Words Only
Words and Pictures
Pictures Only
53.33%
90.91%
87.50%
66.67%
93.75%
86.84%
48.45%
97.06%
100.00%
78.05%
100.00%
100.00%
Numerical
Enatilment
Words Only
Words and Pictures
Pictures Only
33.33%
50.00%
33.33%
14.81%
31.25%
32.14%
9.09%
8.00%
12.96%
43.75%
52.08%
62.50%
Contextual
Entailment
Words Only
Words and Pictures
Pictures Only
36.59%
36.36%
41.67%
20.37%
28.13%
21.05%
9.09%
14.71%
31.42%
81.25%
75.00%
71.85%
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
24
Experiment 1 Discussion
Throughout the control trials in Experiment 1, participants of all ages demonstrated that
they understood and could complete the task, by giving Puppy a prize when appropriate, and by
withholding a prize when appropriate. Critical to the main question of this experiment, we found
that while both children and adults tended to (appropriately) withhold prizes from Puppy on
Scalar Implicature trials (when Puppy was asked to do all and actually did some), only adults
successful gave Puppy a prize on Scalar Entailment trials (when Puppy was asked to do some but
actually did all). Children, instead, frequently withheld a prize from Puppy on these entailment
trials. Importantly, the majority of children who initially appeared to “succeed” on Scalar
Implicature trials (by withholding a prize from Puppy when he did some after being told to do
all) failed to behave in an adult-like manner on entailment trials. And, when we replaced the
word some with the novel word blick for the Im-“blick”-ature trials, children’s performance
didn’t change, suggesting that their performance on Scalar Implicature trials didn’t necessarily
require scale-specific knowledge of the relation between some and all. The simplest explanation
of our data, therefore, is that children compute exclusion inferences instead of relying on scalespecific entailment relations: Whenever the form of the reported result differed from the form of
the request, children withheld the prize for the Puppy, even if the result entailed the request.
Thus, although children are clearly able to compute entailment relations in tasks that directly
probe this (e.g., Chierchia et al., 2001), they may not deploy this knowledge spontaneously, and
may instead prefer to base judgments on contrast. More generally, without explicit tests of
whether children deploy their knowledge of entailment, it is impossible to know whether their
behaviors reflect true scalar implicatures, or simpler strategies.
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
25
Further evidence for our conclusion that children computed exclusion inferences comes
from cases in which Puppy’s actions did not match the request in form but did in meaning. In
these cases, children did not reward Puppy’s actions, even when the two expressions were
otherwise compatible; e.g., when Puppy was asked to do two (out of 3) and reportedly did some.
We found that adults appeared to infer that some could, in this context, refer to 2, while children
believed that some was a poor fulfillment of a request for two. Similarly, on the Contextual and
Numerical Entailment trials where Puppy’s actions entailed the request (but did not linguistically
match the request), children withheld a prize much more frequently than adults did. These data
suggest that even in situations where adults readily use entailment information, children instead
computed simple exclusion inferences.
One possible objection to these conclusions is that children’s behaviors can also be
explained if we assume that they, unlike adults, computed scalar implicatures both at the moment
of request and at the moment when the Puppy’s behavior was reported. For example, when
Puppy was asked to paint some of the stars, children may have computed an implicature at this
time, interpreting the request as a demand to paint “some but not all of the stars”. This would
predict that on entailment trials (when Puppy painted all of the stars after being asked to paint
some) children should treat Puppy’s action of painting all as a violation of the demand (now
strengthened by scalar implicature) to paint “some but not all.”
One reason to be skeptical of this argument is that we couched the request first in an
“if…” statement before the direct request, which should help minimize implicatures on the
request. Another main problem with this argument, already alluded to, is that adults (who can
compute scalar implicatures) did not arrive at this interpretation of the stimuli, and consistently
rewarded Puppy when he painted all stars after a request for some. Thus, such an account would
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
26
require that early in life children are more likely to compute implicatures than adults, and then
gradually learn to compute them less frequently – the exact opposite of what is standardly
believed to occur. Nevertheless, in Experiment 2, we directly tested this alternative interpretation
of our data.
To rule out the possibility that children computed scalar implicatures at the moment of
request, we modified the stimuli from Experiment 1. Half of our participants in Experiment 2 did
not have access to linguistic information regarding Puppy’s behavior (e.g., Puppy was asked to
paint some of the stars, and the child saw visually that Puppy painted all of the stars), thus
removing linguistic contrast as a possible means by which children decided to reward Puppy.
The other half gained evidence of what Puppy did both linguistically and visually (e.g., Puppy
was asked to paint some of the stars, and the child both heard and saw visual evidence that Puppy
painted all of the stars). If children compute implicatures on the experimenter’s original request,
then they should reject Puppy’s actions (as they did in Exp. 1) when he does all after being asked
to do some, even in the absence of contrasting linguistic evidence. On the other hand, if our
results from Experiment 1 were driven by exclusion inference, then in the absence of contrasting
linguistic evidence (i.e. when the child learns of Puppy’s actions visually, not linguistically),
they should accept Puppy’s actions in entailment trials as fulfillments of the request. In other
words, if children no longer reject Puppy’s action when he completes all after being asked to
complete some) when this result is presented nonlinguistically, we can rule out the possibility
that children computed a scalar implicature at the moment of request.
Experiment 2
Materials and Methods
Participants
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
27
A total of 119 children between the ages of 4;0 and 7;11 were recruited from the same
population and using the same methods as Experiment 1 (an additional 6 participants were tested
but were beyond our targeted age range). Six participants were excluded for failing to complete
at least half of the task or for experimenter notes of inattention, 2 were excluded for being
bilingual, 2 were excluded due to experimenter error, and 3 were excluded for having
participated in a related study. Finally, 13 additional participants were excluded for only
providing one type of response (e.g., always giving Puppy a prize or withholding a prize). Thus,
a final N of 93 child participants (4 YOs n = 23; 5 YOs n = 35; 6+ YOs n = 35) were included in
analyses; our data collection goal had been to include a minimum of 20 usable participants in
each age group. An additional 32 adult (undergraduate) participants participated for course
credit, and there were no exclusions of adults.
Materials and Procedure
The procedure in Experiment 2 was identical to that in Experiment 1, with the following
exceptions. As in Experiment 1, participants saw a Before picture alongside the experimenter’s
request (e.g., a picture of 3 unpainted stars), but new to Experiment 2, they also saw an After
picture, showing what Puppy had done (e.g., a picture of 2 painted and 1 unpainted stars Fig. 1,
lower right panels). Thus, the new paradigm introduced in Experiment 2 provided all participants
with visual evidence of what Puppy did.
Participants were randomly assigned to one of two conditions: The Words and Pictures
condition, and the Pictures Only condition. As a result, participants learned of Puppy’s actions in
one of two ways (see Fig. 1). Participants in the Words and Pictures condition heard a verbal
description of what Puppy did (e.g., “Puppy painted some of the stars”; as in Experiment 1) and
saw a picture of what that looked like (e.g., one unpainted star and two painted stars; new to
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
28
Experiment 2). Participants in the Pictures Only condition saw a picture of what Puppy did (e.g.,
one unpainted star and two painted stars), but Puppy’s actions weren’t labeled except to draw
attention to the picture (e.g., “Look what Puppy did!”). Thus, between-subjects, we manipulated
access to linguistic information about Puppy’s actions in the presence of visual information
about Puppy’s actions. To aid in comparing methods across experiments, in Figure 1, we have
also depicted Experiment 1 (as Words Only).
There were several additional small changes to the stimuli in Experiment 2. While images
in Experiment 1 were hand drawn, images in Experiment 2 were computer generated. Second,
we removed the Im-“blick”-ature trial types in Experiment 2, since we could not develop an
appropriate picture of what it looked like to paint blick stars. We replaced these trials with (a) a
Control “Good Job” trial (‘request two did 2’) trial and (b) a Numerical Entailment (‘request two
did 3’) trial. In addition, we replaced one “Request two did some” with a “Request two did 3”
trial in Exp. 2.
Results
Nine individual trials were excluded due to experimenter error. All other analytic
procedures are as reported in Exp. 1.
Control Trials
‘Good Job’ Controls. As in Experiment 1, we found that participants of all ages
successfully accepted Puppy’s actions when there was an exact match between the request and
puppy’s fulfillment (Table 2; Children = 81.03%; Adults = 98.75%). However, a post-hoc
inspection of the data revealed that unlike in Experiment 1, children were less likely to accept
Puppy’s actions for the ‘request some, did some’ (72.76%) trial than for the theoretically
identical ‘request two, did two’ trial (91.40%), even though adults were at ceiling for both trial
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
types (puppy was given a prize on 100% and 97.9% of trials, respectively). This suggests that
children may have believed that the visual depiction of 2/3 actions was a poor match for the
request to complete some. Instead, some children appeared to interpret some as only true when
all was true, perhaps considering some to be ‘a handful’ or ‘at least 3’. Also, performance was
lower for children when they did not have a verbal description of puppy’s actions (as in the
Pictures Only condition: 75.8% vs. 86.82%; post-hoc Wilcoxon p = .044), suggesting that
children may have had difficulty spontaneously relating visual and verbal depictions (e.g., some
to visual depictions of ‘2 out of 3 items’).
‘Bad Job’ Controls. We next considered the trials on which Puppy’s actions clearly did
not fulfill the experimenter’s request. As in Experiment 1, at all ages and across all trials,
participants successfully rejected Puppy’s actions (Table 2; Children = 7.6% gave prize; Adults
= 0%). Thus, across control trials, we saw a similar pattern of performance in Experiment 1 and
Experiment 2, suggesting that the introduction of visual evidence of Puppy’s actions in
Experiment 2 did not interfere with participants’ understanding of the task.
Critical Trials
Scalar Implicature and Entailment Trials. Our critical finding from Experiment 1 was
that while children rejected Puppy’s actions on Scalar Implicature trials (when Puppy was asked
to do all but actually did some), they also rejected Puppy’s actions on Scalar Entailment trials,
(when Puppy was asked to do some, and Puppy did all). We first considered participants’
judgments for Scalar Implicature ‘request all did some’ trials.2 For these trials, adult responses
2
Note that it is possible to succeed on these trials without computing scalar implicatures,
because participants are shown visual representations of Puppy’s actions. For example, when
29
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
30
were not influenced by the presence of disambiguating visual information. As in Experiment 1,
adults in Experiment 2 believed that some (and/or a visual representation consistent with some)
was not a good fulfillment of a request for all, and withheld Puppy’s prize (Table 2). Children
also rejected Puppy’s some fulfillments for all, as they did in Experiment 1, both when they
heard that Puppy did some (only 6.8% accepted Puppy’s actions) and when they didn’t hear some
but only saw that Puppy did 2 out of 3 (only 8.2% accepted Puppy’s actions). Thus, like in
Experiment 1, children believed that some was not a good fulfillment of a request for all,
whether the information was presented linguistically or visually.
For Scalar Entailment (‘request some did all’) trials, adults gave Puppy a prize across all
conditions and experiments (Table 2). In contrast, children’s performance differed depending on
whether the learned about Puppy’s actions linguistically or visually. Similar to Experiment 1,
children in the Words and Pictures condition gave Puppy a prize around half of the time (Exp 1:
43.21%; Exp 2 Words and Pictures: 52.27%; no different from a chance rate of 50%, Wilcoxon p
= .77), once again raising the possibility that children computed a scalar implicature during
Puppy’s request – e.g., that Puppy was asked to do ‘only’ some. Against this interpretation,
unlike adults, children in the Pictures Only condition who heard that Puppy was asked to do
some and then saw that he did 3/3 (without hearing the word all) readily accepted Puppy’s
actions (67.34% of the time3; significantly higher than a chance rate of 50%, Wilcoxon p = .013),
asked to do all, child are shown that puppy did 2/3, and thus could use visual evidence as a basis
for rejecting Puppy’s actions.
3
Based on performance on the ‘Good Job’ Control trials, it also seems possible that
children included ‘3’ as a possible interpretation of ‘some’, causing them to accept Puppy’s
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
31
suggesting that they did not initially compute a “not all” interpretation for some. Instead,
crucially, the linguistic contrast between the words some and all (when both are spoken) appears
to cause children to assume that the action and request did not match.
Contrast Mismatch. We next considered the cases where Puppy’s response (performing
an action on some (2/3 objects) when asked to do two) matched the experimenter’s request in
content but not in form. Both adult and child participants in Experiment 2 overwhelmingly
accepted Puppy’s performance of the action on 2/3 of the items. While children frequently
rejected Puppy’s actions in Experiment 1 (accepting them only 55.74% of the time), when
children had visual access to disambiguating information (a picture showing that Puppy
completed the action on 2/3 of the objects), they now overwhelmingly gave Puppy a prize
(93.01%; Table 2). In other words, children who got both contrasting linguistic information
(hearing a request for two and hearing that Puppy did some) used visual information (a picture of
two stars colored) to remind them that, in this context, some is an appropriate fulfillment of two.
Numerical Entailment. We next considered trials on which Puppy was asked to do some
number of actions (e.g., “feed 2 of the lions”), but ended up doing more than this. For the trials
where Puppy was asked to do two and did three, adults typically accepted Puppy’s actions, while
children routinely rejected them (Table 2). For trials where Puppy was asked to do two and did
all, as in Experiment 1, children also withheld Puppy’s prize (awarding a prize only 24.73% of
actions at high rates in the Pictures Only condition. Still, if this was the strategy that children
adopted, it is inconsistent with either a mutual exclusivity-based or scalar-implicature based
computation.
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
32
the time). Interestingly, children withheld Puppy’s prize even in the Pictures Only condition,
where they did not have access to contrasting linguistic information.
Contextual Entailment. We next considered trials on which Puppy did more than what
was requested of him and his actions were described using contextual (as opposed to scalar or
numerical) alternatives. As in Experiment 1, adults overwhelmingly computed the entailment
relation and gave Puppy a prize (73.43% of the time). However, children consistently withheld
prizes (Pictures/Words: 25% gave prizes; Pictures Only: 29.90% gave prizes; Table 2).
Experiment 2 Discussion
The main goal of Experiment 2 was to test whether children’s apparent failure to compute
linguistic entailment (e.g., by recognizing that if puppy did all he also did some) might actually
be due to computation of a scalar implicature at the moment of request (i.e. inferring that a
request for some was a request to ‘not do all’). Across all conditions (Experiment 1’s ‘Words
Only’ and both Experiment 2’s ‘Pictures and Words’ and ‘Pictures Only’ conditions), the child
heard, “Puppy, paint some of the stars”, and therefore had the opportunity to compute the scalar
implicature, “Puppy, paint some but not all of the stars” at the moment of request. Had the child
computed a scalar implicature at the moment of the request (and therefore inferred that the
request was to do some but not all), then they should have rejected Puppy’s actions whenever he
was asked to do some but really did all. In Experiment 1 and the Pictures and Words condition of
Experiment 2 – the conditions in which the children had access to contrasting linguistic labels
(some and all) – children withheld a prize from Puppy when he was asked to do some but
actually did all. However, these results could have emerged either if children computed an
exclusion inference, or computed a scalar implicature both at the moment of request and at test.
In the Pictures Only condition, however, we could differentiate an exclusion-based strategy from
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
33
one in which the child computed a scalar implicature at the moment of request. This is because
the child didn’t hear contrasting linguistic labels in this condition – instead, they simply saw that
Puppy painted all of them. In other words, there was no some/all linguistic contrast, but there
was still the opportunity to compute a scalar implicature at the moment of request. Thus, if
children computed a scalar implicature at the moment of request, they should have rejected
Puppy’s actions. This is not what we found. Instead, without access to contrasting linguistic
labels, children no longer withheld a prize when Puppy did all after a request to do some. This is
inconsistent with the possibility that children spontaneously computed a scalar implicature at the
moment of request: If children did, then they should have interpreted the request as one for
‘some and not all’, and therefore should have found Puppy’s actions (doing all) incompatible
with the initial request. Importantly, adults’ performance was consistent across all trial types in
Experiment 1 and Experiment 2, suggesting that by adulthood, the presence (or absence) of
supporting visual information does not influence the mature linguistic processing of the types of
dialogues presented in our experiments (Table 2).
General Discussion
Many past studies have found that, whereas children readily apply the principle of
contrast and mutual exclusivity during word learning, they take many years to exhibit adult-like
behavior when computing scalar implicatures (e.g., that an utterance containing some implies
“not all”). However, a small number of recent studies have reported surprisingly early successes
at scalar implicature, usually using forced choice paradigms or direct contrast of scalar
alternatives (Papafragou & Tantalou, 2004; Miller et al., 2006; Skordos & Papafragou, 2016;
Stiller et al., 2015; Yoon, Wu, & Frank, 2015). Based on these findings, we explored the
possibility that children’s earliest successes on purported tests of scalar implicature might instead
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
34
be best explained by appeal to exclusion inference (e.g., inference driven by contrast or mutual
exclusivity): When children successfully judge that some is not a good fulfillment of a request
for all (Papafragou & Tantalou, 2004), they may do so either because they compute a scalar
implicature or because they note that some and all are different words, and therefore infer that
they must differ in some way in meaning (contrast) or even that they are incompatible (mutual
exclusivity).
Here, we asked whether it is possible to differentiate scalar implicature from simpler,
alternative exclusion inferences like contrast and mutual exclusivity. We began with the
observation that, unlike in the case of scalar implicature, exclusion inferences allow the
symmetric negation of alternatives and can therefore give rise to the judgment that an utterance
containing some implies “not all”, and also the false inference that an utterance containing all
implies ‘not some’. In contrast, scalar implicature generally involves asymmetric negation – e.g.,
such that “I ate some of the cookies” implies the negation of “I ate all of the cookies” but not
vice versa. Based on this logic, we asked whether children who successfully contrasted
alternative utterances also spontaneously invoked asymmetric entailment relations in the same
experimental context, as would be predicted if they truly computed scalar implicatures.
Consistent with the computation of exclusion inferences, we found that children rejected a
character’s actions whenever the descriptions of these actions linguistically contrasted with the
experimenter’s original request, independent of entailment relations. For example, if the
experimenter requested some and then said that Puppy did all, children rejected Puppy’s action
to the same degree as when all was requested and Puppy reportedly did some. This pattern of
performance is largely inconsistent with the possibility that children computed scalar
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
35
implicatures, because it suggests that children did not use asymmetric entailment relations to
constrain their responses.
As noted in Experiment 2, one alternative explanation of this pattern of results is that
children may have computed a scalar implicature both at the moment of the experimenter’s
request and when they learned of what Puppy did. Like an account based on exclusivity
inferences, this explanation also predicts that the child should reject Puppy’s actions when he
does all after being told to do some. For example, upon hearing the experimenter say “Puppy,
paint some of the stars”, children may have computed a scalar implicature and inferred that the
experimenter expected Puppy to paint some but not all of the stars, leading children to reject
Puppy’s action when he painted all of the stars, as we found in Experiment 1. Against this
interpretation, adults in Experiment 1 (who certainly can compute scalar implicatures) didn’t
reject Puppy’s actions, suggesting that it is unlikely that, in this context, a mature language user
would compute a scalar implicature at the moment of request. Nevertheless, in Experiment 2, we
tested this possibility in a condition where the child heard, e.g., “Puppy, paint some of the stars”
(and therefore still had the opportunity to compute a scalar implicature at the moment of
request), but then learned of Puppy’s actions visually instead of linguistically (and therefore no
longer had access to contrasting linguistic labels). Had children computed a scalar implicature at
the moment of request, then they should have rejected Puppy’s actions regardless of the modality
in which they learned about his actions (linguistic vs. visual). On the other hand, if performance
were driven by the computation of an exclusion inference, then they should have rejected
Puppy’s actions only when they had access to contrasting linguistic labels. We found that when
children didn’t have access to contrasting linguistic labels, they were much less likely to reject
Puppy’s actions, suggesting that the pattern we found in Experiment 1 was not due to children
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
36
computing a scalar implicature at the moment of request. This suggests that exclusion inferences
– and not scalar implicature – were driving children’s performance on our task.
While we found that children appeared to use exclusion inferences (instead of scalar
implicature) in our tasks, our claim is not that children are unable to compute entailment
relations, or even that their knowledge of the entailment relations between all and some is
incomplete. In fact, there is experimental evidence that young children of this age understand
entailment. For example, in a study by Chierchia et al. (2001), 3- to 6-year-olds demonstrated an
understanding of entailment by successfully choosing the more informative of two possible
utterances (by selecting e.g., “Every farmer cleaned a horse and a rabbit” instead of “Every
farmer cleaned a horse or a rabbit”) to describe a scene (Chierchia et al., 2001). Because there is
no reason to believe that children are incapable of reasoning about asymmetric entailment, our
claim here is simply that because exclusion inferences and implicature predict similar behaviors
in many contexts, it is critical to test whether children deploy their knowledge of asymmetric
entailment in a task, to be sure that they are indeed computing implicatures. Notice here that the
critical difference between implicature and exclusion inferences is not necessarily the form of the
inference itself, but instead the nature of the alternatives and how they are represented by
children in the service of this inference. In tasks like the one presented here, children do not
appear to interpret alternative utterances according to their scalar relations, but instead assign all
alternatives equal status, such that uttering an utterance A negates utterance B, regardless of
whether one entails the other.
This last point is important to understanding the significance of our findings to the
literature at large. A key difference between experiments which find early successes with
implicature and those which find later successes is that the former studies tend to use forced
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
37
choice paradigms that are similar to mutual exclusivity tasks, and which therefore present
children with a set of salient alternative referents. According to some past reports, children’s
main difficulty with implicature computation is their ability to spontaneously access relevant
alternatives – e.g., to access an utterance containing all when interpreting a sentence containing
some (Barner, Brooks, & Bale, 2011; Chierchia et al., 2001; Hochstein, Bale, Fox, & Barner,
2016; Skordos & Papafragou, 2016). Forced choice paradigms may help children appear to
succeed on implicature tasks by providing them with a pre-established set of relevant alternative
referents, which can be used by the child to generate linguistic alternatives. As evidence for this,
adult subjects are faster to compute implicatures in visual world paradigms when they are
allowed to preview the visual referents before hearing the test sentence (Snedeker, 2015).
According to Snedeker (2015), this suggests that such paradigms – and by extension forced
choice paradigms like those used in recent tests of implicature in children (e.g., Stiller,
Goodman, & Frank, 2014) – allow children to generate descriptions for different visual
alternatives, and to then use these descriptions to compute inferences. Consistent with this,
infants as young as 18 months appear to also spontaneously conjure the referents of pictures
upon viewing them, suggesting that even very young children can generate descriptions of
visually presented alternatives (Mani & Plunkett, 2010; for evidence in adults, see Meyer &
Belk, 2007; Meyer & Damian, 2007). How might this impact children’s ability to compute scalar
implicature? Upon seeing a picture with “all of the socks” and another containing “some of the
soccer balls” children may code the pictures with corresponding verbal descriptions, and use a
relatively simple matching strategy to guide their looking at test – e.g., looking to the picture
containing “some of the soccer balls” upon hearing “some” simply because it matches their prior
expectation, without involving any appeal to the stronger alternative containing “all”. In this
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
38
way, children may appear to succeed on scalar implicature tasks without needing to deploy any
knowledge of asymmetric entailment.
To summarize, we exploited the asymmetric relationship between scalar items to
investigate children’s understanding of the relation between words like some and all. We asked
whether children might rely on exclusion inferences (based in contrast or mutual exclusivity) –
which we already know children recruit for the purpose of word learning – in cases where adults
would typically compute scalar implicatures. We found strong evidence that young children rely
on exclusion inferences when scalar implicatures would be more appropriate. This suggests that
previous work reporting early success at computing scalar implicatures, which do not test
children's knowledge of entailment relations, may overestimate young children’s pragmatic
knowledge.
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
Acknowledgements: [Acknowledgments Blinded]
39
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
References
Au, T. & Markman, E. (1987). Acquiring word meanings via linguistic contrast.
Cognitive Development, 2, 217-236.
Barner, D., & Bachrach, A. (2010). Inference and exact numerical representation in early
language development. Cognitive Psychology, 60, 40–62.
Barner, D., Brooks, N., & Bale, A. (2011). Accessing the unsaid: The role of scalar
alternatives in children’s pragmatic inference. Cognition, 118, 84–93.
Bates, D., Machler, M., Bolker, B., & Walker, S. (2015). Fitting Linear Mixed-Effects Models
using lme4. Journal of Statistical Software, 67, 1-48.
Carey, S. & Bartlett, E. (1978). Acquiring a single new word. Papers and Reports on
Child Language, 15, 17-29.
Chierchia, G., Crain, S., Guasti, M.T., Gualmini, A., & Meroni, L. (2001). The Acquisition of
Disjunction: Evidence for a Grammatical View of Scalar Implicature. Proceedings of the
25th Boston University Conference on Language Development. Cascadilla Press:
Somerville, MA.
Clark, E. (1987). The principle of contrast: A constraint on language
acquisition. Mechanisms of Language Acquisition, 1, 33.
Clark, E. (1988). On the logic of contrast. Journal of Child Language, 15(2), 317-335.
Clark, E. (1990). On the pragmatics of contrast. Journal of Child Language,17(2), 417
- 431.
Gathercole, V. (1989). Contrast: a semantic constraint? Journal of Child Language, 16,
685-702.
Gazdar, G. (1979). Pragmatics: Implicature, presupposition, and logical form. New
40
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
41
York: Academic Press.
Grice, H. P. (1970). Logic and Conversations. Syntax and Semantics Volume Three: Speech
Acts, P. Cole and J.L. Morgan. New York: Academic Press, 41-58.
Grice, H. P. (1991). Studies in the Way of Words. Harvard University Press.
Halberda, J. (2003). The development of a word-learning strategy. Cognition, 87, B23-B34.
Heibeck, T. & Markman, E. (1987). Word learning in children: an examination of fast
mapping. Child Development, 58, 1021-1034.
Hochstein, L., Bale, A., Fox, D., & Barner, D. (2014). Ignorance and inference: Do
problems with Gricean epistemic reasoning explain children’s difficulty with
scalar implicature? Journal of Semantics, 0, 1-29.
Horn, L. (1989). A Natural History of Negation. Chicago: University of Chicago Press.
Katsos, N., & Bishop, D. (2011). Pragmatic tolerance: Implications for the acquisition of
informativeness and implicature. Cognition, 120, 67-81.
Katsos, N. & Wilson, E. (2014). Convergence and divergence between word learning and
pragmatic inferencing. Proceedings of Formal and Experimental Pragmatics, 2014, 1420.
Levinson, S. (2000). Presumptive Meanings: The theory of generalized conversational
implicature. Cambridge, MA: The MIT Press.
Mani, N., & Plunkett, K. (2010). In the Infant’s Mind’s Ear: Evidence for Implicit Naming in 18
- Month-Olds. Psychological Science, 21, 908-913.
Markman, E. & Wachtel, G. (1988). Children’s use of mutual exclusivity to constrain the
meaning of words. Cognitive Psychology, 20, 121-157.
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
42
Markman, E., Wasow, J., & Hannsen, M. (2003). Use of the mutual exclusivity assumption by
young word learnings. Cognitive Psychology, 47, 241-275.
Meyer A.S., Belke E., Telling A., Humphreys G.W. (2007). Early activation of object names in
visual search. Psychonomic Bulletin & Review, 14, 710–716.
Meyer A.S., Damian M.F. (2007). Activation of distractor names in the picture-picture word
interference paradigm. Memory & Cognition, 35, 494–503.
Miller, K., Schmitt, C., Chang, H., & Munn, A. (2005). Young children understand some
implicatures. Proceedings of the 29th Annual Boston University Conference on Language
Development.
Noveck, I. (2001). When children are more logical than adults: Experimental
investigations of scalar implicature. Cognition, 78, 165-188.
Papafragou, A., & Musolino (2003). Scalar implicatures: experiments at the semantics
pragmatics interface. Cognition, 86, 253-282.
Papafragou, A., & Tantalou, N. (2004). Children's Computation of Implicatures.
Language Acquisition, 12(1), 71–82.
Skordos, D., & Papafragou, P. (2016). Children’s derivation of scalar implicatures:
alternatives and relevance. Cognition, 153, 6-18.
Snedeker, J. (2015). Scalar implicature: A whirlwind tour with stops in processing, development,
and disorder. Tubingen, Germany. Slides available:
https://software.rc.fas.harvard.edu/lds/research/snedeker/jesse-snedeker/
Spiegel, C. & Halberda, J. (2011). Rapid fast-mapping abilities in 2-year-olds. Journal of
Experimental Child Psychology, 109, 132-140.
Smith, C. (1980). Quantifiers and question answering in young children. Journal of
EXCLUSION INFERENCES VS. SCALAR IMPLICATURE
Experimental Child Psychology, 30, 191-205.
Stiller, A. J., Goodman, N. D., & Frank, M. C. (2014). Ad-hoc Implicature in Preschool
Children. Language Learning and Development, 11(2), 176–190.
Woodward, A. & Markman, E. (1991). Constraints on Learning and Default Assumptions:
Comments on Merriman and Bowman’s “The Mutual Exclusivity Bias in Children’s
Word Learning”. Developmental Review, 11, 137-163.
Wynn, K. (1992). Children’s acquisition of the number words and the counting system.
Cognitive Psychology, 24(2), 220-251.
Yoon, E., Wu, Y., & Frank, M. (2015). Children’s Online Processing of Ad-Hoc Implicatures.
Proceedings of the 37th Annual Conference of the Cognitive Science Society.
43