Cognitive Psychology 75 (2014) 80–96

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Cognitive Psychology
journal homepage: www.elsevier.com/locate/cogpsych

Inferring word meanings by assumingthat speakers are informative
Michael C. Frank ⇑, Noah D. Goodman
Department of Psychology, Stanford University, United Statesa r t i c l e

i n f oArticle history:
Accepted 12 August 2014

Keywords:
Language acquisition
Pragmatics
Word learning
Bayesian models

a b s t r a c t
Language comprehension is more than a process of decoding theliteral meaning of a speaker’s utterance. Instead, by making theassumption that speakers choose their words to be informativein context, listeners routinely make pragmatic inferences that go
beyond the linguistic data. If language learners make these same
assumptions, they should be able to infer word meanings in otherwise ambiguous situations. We use probabilistic tools to formalize
these kinds of informativeness inferences—extending a model ofpragmatic language comprehension to the acquisition setting—and present four experiments whose data suggest that preschool
children can use informativeness to infer word meanings and that
adult judgments track quantitatively with informativeness.
Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction
Children learn the meanings of words with remarkable speed. Their vocabulary increases in leaps
and bounds relatively soon after the emergence of productive language (Fenson et al., 1994), and theyoften require only a small amount of exposure to begin the process of learning the meaning of an individual word when it is presented in a supportive context (Carey, 1978; Markson & Bloom, 1997). The
ability to infer and retain a huge variety of word meanings is one of the signature achievements ofhuman language learning, standing alongside the acquisition of discrete phonology and hierarchicalsyntactic and semantic structure (Pinker & Jackendoff, 2005).
⇑ Corresponding author. Address: Department of Psychology, Stanford University, 450 Serra Mall (Jordan Hall), Stanford, CA
94305, United States.
E-mail address: mcfrank@stanford.edu (M.C. Frank).
http://dx.doi.org/10.1016/j.cogpsych.2014.08.002
0010-0285/Ó 2014 Elsevier Inc. All rights reserved.

M.C. Frank, N.D. Goodman / Cognitive Psychology 75 (2014) 80–96

81Fig. 1. An example stimulus item for our experiments. The arrow represents a point or some gesture that signals that thedinosaur on the right is being talked about, but does not give away which aspect of it is being referred to. In our experiments,
the goal of the learner is to infer whether a novel word (e.g. ‘‘dax’’) means BANDANNA or HEADBAND.

Nevertheless, ﬁguring out what an individual word means can be a surprisingly difﬁcult puzzle. In
Quine’s (1960) classic example, he considers an anthropologist who observes a white rabbit running
by. One of his subjects points and says ‘‘gavagai.’’ Even assuming that the anthropologist interprets thepointing gesture as a signal of reference (Tomasello, 2008; Wittgenstein, 1953), he must still infer
which property of the rabbit the word refers to. Some properties may be logically impossible to distinguish from one another—think ‘‘rabbit’’ and ‘‘undetached mass of rabbit parts.’’ But beyond thesephilosophical edge cases, even useful properties can be strikingly difﬁcult to distinguish: how canhe decide between ‘‘rabbit,’’ ‘‘animal,’’ ‘‘white,’’ ‘‘running,’’ or even ‘‘dinner’’? We can think of this as
an easy—but perhaps more common—version of the Quinian puzzle: For any known referent (the rabbit), there are many conceptually natural referring expressions that include the referent in their extension (Gleitman & Gleitman, 1992).1 Our argument here is that many of these can be ruled out onpragmatic grounds, by considering the communicative context and the goals of the speaker.
Language learners have many tools at their disposal to help them limit the possibilities, including
patterns of consistent co-occurrence (Yu & Smith, 2007), the contrasting meanings of other words they
have learned (Clark, 1988; Markman & Wachtel, 1988), and the syntactic structure in which the word
appears (Gleitman, 1990). In the current work, however, we consider cases where these strategies are
ineffective, yet learners can nevertheless infer word meanings by considering the speaker’s communicative goal.2 These are cases where the pragmatics of the situation—roughly speaking, the fact thata particular communicator is trying to achieve a particular goal in this context, and that he or she is following a rational strategy to do so—help in inferring word meaning. In our Quinian example, the intuition we are pursuing is that the anthropologist may consider information necessary in the context inassigning a tentative meaning to ‘‘gavagai.’’ If the white rabbit is tailed by a brown one, perhaps ‘‘gavagai’’ means WHITE, while in the absence of such a context, a basic level object label might be more
appropriate.

1This easy puzzle is of course distinct from the harder version, the ‘‘true’’ Quinian puzzle: that there are inﬁnitely many
conceptually possible referring expressions that include the referent in their extension, and some of these are extensionallyidentical.
2
We use the term ‘‘inference’’ to distinguish between the process of ﬁguring out what a word means and the later retention ofthat meaning. Retention is a necessary component of learning (and there may be cases, for example ostensive naming, where
retention is the only component of learning). Nevertheless, we are interested here in the process of inference in ambiguoussituations. We also note that the use of the term ‘‘inference’’ does not connote to us that the psychological computation isnecessarily symbolic or logical. Statistical inferences of the type described below can be instantiated in probabilistic logics, neuralnetworks, or just about any other formalism (MacKay, 2003).

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Consider the analogous—though simpliﬁed—case in Fig. 1. If a speaker describes the dinosaur on
the right (marked by the arrow) as ‘‘a dinosaur with a dax,’’ the novel word could mean HEADBAND or
BANDANNA, or even in principle TAIL or FOOT. All of these meanings for ‘‘dax’’ would make the speaker’s
statement truthful. Nevertheless, several of these would be quite odd things to say: although that
dinosaur has one foot, it’s also true that he has two (and for that matter, so does the other dinosaur
as well). On the other hand, if ‘‘dax’’ meant HEADBAND, then it would be quite an apt description in
the current context. Hence, this example might provide evidence to a pragmatically-savvy learner that‘‘dax’’ has the meaning HEADBAND.
Importantly, there is no cross-situational information present in this single scenario, and neither
the learner’s previous vocabulary nor the syntax of the sentence reveal the word’s meaning. Yet theintuition is still quite clear that HEADBAND is a more likely candidate (and the experiments reported
below conﬁrm this intuition). Although not accounted for by the classic set of acquisition strategies,
inferences like this one ﬁt well with theories of pragmatic reasoning in language comprehension.
Philosophers and linguists have long suggested that language relies on shared assumptions about
the nature of the communicative task that allow comprehenders to go beyond the truth-functionalsemantics of speakers’ utterances. Most canonically, Grice (1975) proposed that speakers follow(and are assumed by comprehenders to follow) a set of conversational maxims. In turn, if listeners
assume that speakers are acting in accordance with these maxims, that gives them extra information
to make inferences about speakers’ intended meanings. Other theories of pragmatic communication
also provide related tools for explaining this type of inference. For example, Sperber and Wilson(1986) have suggested that there is a shared ‘‘Principle of Relevance’’ which underlies communication.
On their account, the key part of this interaction is the shared knowledge between speaker and listener that the headband is the most relevant feature of the dinosaur in this context; otherwise theinference is largely the same. Many additional neo-Gricean formulations have also been proposed(e.g. Clark, 1996; Levinson, 2000). Here we use the original Gricean language because it is best known,
but our ideas do not depend speciﬁcally on Grice’s formulation.
Returning to the example in Fig. 1, if the speaker is trying to pick out the dinosaur on the right, thenusing a word that referred to the HEADBAND would be a good choice. This choice would typically be motivated with reference to Grice’s Maxim of Quantity, which impels speakers to ‘‘be informative’’ (though
we return below to the question of how to provide an operational deﬁnition for ‘‘informativeness’’). The
inference that ‘‘dax’’ means HEADBAND goes beyond the simple application of Gricean reasoning, however.
To infer that ‘‘dax’’ means HEADBAND, the learner must presuppose that the speaker is being informative and then use this assumption, working backwards, to infer the meaning of a word (rather than theintended meaning of the speaker’s utterance, as is more typical in Gricean situations). This inference
has a counterfactual ﬂavor: If the speaker were being informative, they would have said somethingthat referred to the HEADBAND; they said ‘‘dax,’’ whose meaning I don’t know; therefore perhaps‘‘dax’’ means HEADBAND. Can children make this kind of inference in the course of language acquisition?
If so, such inferences could be an important tool for eliminating some of the referential uncertainty
inherent in learning a new word. We next consider related evidence on children’s pragmatic abilities.
While many theories of language acquisition assume that children bring some knowledge of thepragmatics of human communication to bear on the task of word learning (Bloom, 2002; Clark,
2003; Tomasello, 2003), evidence on children’s use of Gricean maxims speciﬁcally is mixed. On the
one hand, an inﬂuential body of work suggests that young children can use pragmatic inferences tolearn the meanings of words. For example, Akhtar, Carpenter, and Tomasello (1996) showed that
two-year-olds could use the fact that an object was new to an experimenter to infer the meaning of
a novel word that experimenter used. Baldwin (1993) found that 18-month-olds were able to map
a novel word to a referent that was hidden but signaled by the caregiver’s attention to its location.
And in a surprising recent demonstration of such abilities, Southgate, Chevallier, and Csibra (2010)
showed that 17-month-olds were able to use knowledge about a speaker’s false belief to map a novel
name to an object, based on the speakers’ naming of the location where she thought it was, not thelocation where it actually was. Thus, by their second birthday, children appear to be able to make relatively sophisticated inferences about speakers’ knowledge and intentions in word learning situations.
On the other hand, another body of work suggests that much older children still struggle to makepragmatic inferences in language production and comprehension—or at least that what inferences

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they do make can often be explained in other ways. Even ﬁve-year-old children have trouble understanding what information is available to communicative partners (Glucksberg, Krauss, & Weisberg,1966), though more recent evidence has shown some sensitivity to speaker knowledge in online measures (Nadig & Sedivy, 2002). In addition, Gricean reasoning has not been observed for children younger than four years, and is seen only inconsistently before the age of six. For example, Conti andCamras (1984) tested children on whether they could identify a maxim-violating ending to a story,
and found that while four-year-olds could not do so, six- and eight-year-olds were able to succeedin this task (but cf. Eskritt, Whalen, & Lee, 2008). In the same vein, children do not seem to be able
to compute scalar implicatures (one possible example of a Gricean implicature; though cf.
Chierchia, Crain, Guasti, Gualmini, & Meroni, 2001; Gualmini, Crain, Meroni, Chierchia, & Guasti,
2001; Guasti et al., 2005 for alternative accounts) until quite late (Noveck, 2001).
Nevertheless, accounts differ considerably on the age at which children ﬁrst succeed in making
implicatures (Guasti et al., 2005; Papafragou & Musolino, 2003) and on the factors that prevent themfrom succeeding (Barner & Bachrach, 2010; Barner, Brooks, & Bale, 2011; Katsos & Bishop, 2011). It
may be that the speciﬁcs of scalar implicature are difﬁcult for young children. Much younger children
are also sensitive to the informativeness of their own and others’ communication (Liszkowski,
Carpenter, & Tomasello, 2008; O’Neill & Topolevec, 2001; Matthews, Butcher, Lieven, & Tomasello,2012; Matthews, Lieven, & Tomasello, 2007). And some evidence indicates that preschoolers can makeother kinds of pragmatic inferences slightly earlier (Kurumada, 2013; Stiller, Goodman, & Frank,
2014), though none as early as the ‘‘pragmatic word learning’’ ﬁndings summarized above.
To summarize, the evidence on children’s pragmatic abilities is mixed. Children are sensitive toaspects of speakers’ goals and beliefs in word learning, and certainly they make substantial use ofsocial cues like eye-gaze and gesture. But it is still unknown how well they are able to use Gricean
reasoning to infer word meanings. We have suggested that the Gricean maxim of quantity (‘‘be informative’’) may help learners infer word meanings in otherwise ambiguous situations, but whether children—or even adults—are in fact able to make these inferences remains an open question. The current
work investigates this issue.
A key challenge in providing a Gricean account for word learning is deﬁning ‘‘informativeness,’’ aconcept that is often left frustratingly vague. Without a clear account of what makes a particular term
or utterance informative in context, we are left with a theory that fails to make concrete and easilytested predictions (Pea, 1979). For this reason, our work here uses a computational formulation of theidea that speakers are informative, using tools from information theory to make quantitative predictions in simple situations like Fig. 1. This framework builds on our recent work modeling adults’ pragmatic judgments as a process of probabilistic inference (Frank & Goodman, 2012). Its value here is thatit allows us to make quantitative predictions about behavior in a range of cases where previous theories have made at best directional predictions. The next section describes this framework and its
application to word learning.
Our experiments then test predictions derived from this framework. In Experiment 1, we make aquantitative test with adults and ﬁnd that there is high correspondence between adults’ aggregate
judgements about the meanings of novel words and the predictions of our model. Experiments 2
and 3 then test whether preschool children are able to make similar inferences in simpliﬁed cases.
Experiment 4 replicates the ﬁnding of Experiment 3 and rules out a number of alternative explanations. Together our results suggest that adults and children are sensitive to the relative informativeness of labels and can use this information to make inferences about the meanings of novel words
in ambiguous situations.

2. Modeling pragmatic inference in word learning
In order to motivate its use in word learning, we begin by giving a brief exposition of the probabilistic model of pragmatic inference introduced in Frank and Goodman (2012). We then show how thismodel can be adapted to make predictions from the perspective of a language learner who has uncertainty about what individual terms mean. The probabilistic modeling framework provides a convenient tool for formalizing this set of ideas. Related predictions can be derived in a game-theoretic

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framework for pragmatics (Benz, Jäger, & Van Rooij, 2005; Franke, 2009, 2013; Jäger, 2010), though to
our knowledge such a framework has not been used to model language learning.
The ‘‘rational speech act’’ model introduced in Frank and Goodman (2012) describes normative inferences in simple reference games under the assumption that listeners view speakers as having chosen
their words informatively—that is, relative to the information that they would transfer to a naive listener(see also Goodman & Stuhlmüller, 2013). The heart of our model is the idea that a rational3 listener willattempt to make inferences about the speaker’s intended referent rs , given the word w they uttered, the lexicon of their language L, and the context C. This inference can be described using Bayes’ rule:PðwjrS ; L; CÞPðr S Þ:00
r 0 2C Pðwjr ; L; CÞPðr Þ

Pðr S jw; L; CÞ ¼ P

ð1ÞIn other words, the posterior probability of some referent is proportional to the product of two terms:
the likelihood Pðwjr S ; CÞ that some word is used to describe a referent, and the prior probability PðrÞthat this referent will be the subject of discourse. Because the situations we treat here all assume thatthe speaker knows the intended referent rS , we do not discuss the prior term further (for more details
see Frank & Goodman, 2012).
We deﬁned the likelihood of a word being used to describe some referent as proportional to a formal measure of the information transferred by an utterance (its surprisal given the base context distribution). This information-theoretic deﬁnition of what it means to be ‘‘informative’’ leads to:PðwjrS ; L; CÞ ¼ P

jwj1
L

1
w0 2W jwjLð2Þ;

where jwjL refers to the number of objects in a particular context to which w can truthfully be applied,
given the known meaning of w in L. In other words, ‘‘be informative’’ translates to ‘‘say words that
apply to your referent and few others,’’ which seems to approximate the general Gricean intuition.
A Bayesian learner can use the assumption that speakers are informative to learn the meaning of
unknown words. A language learner often has uncertainty about both the speaker’s intended referent
and the lexicon mapping words to their meanings, which we notate L (a simple version of this case istreated in our work on cross-situational learning in Frank, Goodman, & Tenenbaum, 2009). But
although our framework can be extended to this case of joint uncertainty about meaning and reference, we focus here on the case where the referent is known and we must infer only word meanings.
(Given a set of extensionally-distinct possible meanings, this setup corrresponds to the Quinian casedescribed above, where the rabbit is indicated but the meaning of ‘‘gavagai’’ is unknown.)
In the case where we know the speaker’s intended referent, we can now reverse the inference andwrite the probability of a lexicon L, given the observation of a word w used to refer to some object r S :PðLjw; r S ; CÞ / PðwjL; r S ; CÞPðLÞ:ð3Þ

We next walk through the case shown in Fig. 1. We assume that the speaker’s intended referent (rS )has two truth-functional features f 1 and f 2 (HEADBAND and BANDANNA), and that there are two words in thelanguage w1 and w2 . We further assume that each word has exactly one meaning linked to it.4 Hence
there are only two possible lexicons: L1 ¼ fw1 ¼ f 1 ; w2 ¼ f 2 g and L2 ¼ fw1 ¼ f 2 ; w2 ¼ f 1 g, which areequally probable.
Under these assumptions,Pðw1 jL1 ; r S ; CÞ¼
PðL1 jw1 ; rS ; CÞ ¼
Pðw1 jL1 ; r S ; CÞ þ Pðw1 jL2 ; r S ; CÞj f 1 j1
j f 1 j1 þj f 2 j1
j f 1 j1
j f 2 j1
þ j f j1
j f 1 j1 þj f 2 j1
þj f 1 j1
2¼

j f 1 j1
j f 1 j1 þ j f 2 j1

;

ð4Þ

3
Note that the use of the term ‘‘rational’’ here does not imply a claim of human rationality, much less optimality (Frank, 2013).
Our current experiments test that the predictions of such a model are satisﬁed by the aggregate judgments of many humanobservers; these data leave open the question of the psychological mechanisms that produce the observed patterns of humanperformance.
4
Relaxing this assumption has interesting consequences with respect to ‘‘mutual exclusivity’’ inferences, which are treated in
more depth in Frank, Goodman, and Tenenbaum (2009) and Lewis and Frank (2013).

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85

where j f j indicates the number of objects with feature f (substituting Eq. (2) for the second step bynoting that word w would be used informatively depending on the extension of the relevant feature).
Note that, as in Frank and Goodman (2012), this computation requires no parameter values to be set
by hand.
Returning now to the example in Fig. 1, we can use Eq. (4) to calculate the probability that learners
judge that w (‘‘dax’’) means HEADBAND ( f 1 ) as opposed to BANDANNA ( f 2 ):Pðw ¼ f 1 jM S ; CÞ ¼

jheadbandj1
jheadbandj

1þ jbandannaj

11
2¼1 1 1¼
þ2 3
1

Thus, our prediction—all else being equal—is that learners should be around 67% conﬁdent that ‘‘dax’’means HEADBAND, because the feature HEADBAND has the smaller extension in context.
Of course, there are many other aspects of the situation that might alter this prediction. For example, we assume that there are no alternative competitor meanings for ‘‘dax’’ that are considered in participants’ judgments; indeed our experiments use a two-alternative forced choice for this reason. If wewere to allow participants to consider other competitor meanings (such as LONG NECK or ON THE LEFT), thedenominator in Eq. (4) would grow, causing the overall prediction for HEADBAND to go down. If suchcompetitors were included, a natural next step would be to attempt to measure learners’ prior expectations about the types of features that are typically named (rather than leaving this prior uniform as
we have here). In these initial experiments, however, we test the general form of the model rather
than how it would be extended to larger feature sets.
To summarize, given the set of simplifying assumptions we have made, the very abstract goal of‘‘being informative’’ reduces to a simple formulation: choose words which pick out relatively smaller
sections of the context. We recover the ‘‘size principle’’ of Tenenbaum and Grifﬁths (2001; see also Xu& Tenenbaum, 2007). This principle originated with Shepard’s 1987 work on generalization behavior
in psychological spaces and has more recently been rederived by Navarro and Perfors (2009). Our
work can be thought of as a third derivation of the size principle—based on premises about the communicative task, rather than about the structure of generalization—that licenses its application to thekinds of cases that we have treated here. In the following experiments we test whether adults and preschoolers are sensitive to contextual informativeness in their inferences about word meanings.
3. Experiment 1
Our ﬁrst experiment investigated whether adult word learners could make inferences about word
meaning on the basis of the relative informativeness of a word in context. We were additionally interested in whether these judgments conformed quantitatively to the framework described above. To
test these hypotheses, we asked adults for quantitative judgments about the meanings of novel words
in situations like Fig. 2, left. We used these slightly more complex displays to allow for the controlled
manipulation of the relative extensions of the two candidate features.
3.1. Methods
3.1.1. Participants
We recruited 201 unique individuals on Amazon Mechanical Turk (www.mturk.com), an online
crowd-sourcing tool. Mechanical Turk allows users to post small jobs to be performed quickly andanonymously by workers (users around the United States, in the case of our experiments) for a small
amount of compensation (Buhrmester, Kwang, & Gosling, 2011; Crump, McDonnell, & Gureckis, 2013).
3.1.2. Materials and methods
Each participant completed a short survey that included 4 questions about what words meant.
Each question showed a stimulus picture containing three objects (dinosaurs, rockets, bears, orrobots), with one target indicated by a box around it. Each object had two features (e.g. bandanna,
headband). Participants were told that someone had used a word in a foreign language (e.g. ‘‘daxy’’)
to refer to the object with the box around it and asked to make bets on which feature the word

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1/1

2/3

1/2

1/3

80

1/3

Average bet

70

1/2
60

2/3
1/1

50

40
40

50

60

70

80

Model prediction
Fig. 2. Top: Stimuli for Experiment 1 in one version of the four trial types (see text for description of condition labels). Bottom:
Data from Experiment 1. Points show participants’ mean bet with 95% conﬁdence intervals (computed via non-parametricbootstrap), plotted by the predictions of the informative communication model. The dashed lines show chance responding forhuman responders and model; the dotted line shows the diagonal, indicating perfect correspondence between model andhuman data.

referred to. An example stimulus is shown in Fig. 2, left. The assignment of object to condition, theposition of the target object, and target feature were all counterbalanced between subjects.
Trials were arranged into one of the four conditions (1/1, 1/2, 1/3, and 2/3). Conditions refer to thearrangement of features among the three objects: the numerator refers to the number of objects withthe ﬁrst feature. The denominator refers to the number of objects with the second feature. Consider
the 1/2 example in Fig. 2, top: the target dinosaur (with the box around it) has two features. The
ﬁrst—by convention, the one with a smaller extension, in this case the headband—is unique to that
object, so the numerator is 1. The second, the bandanna, is shared with another dinosaur. Thus, thistrial is a 1/2 trial.

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M.C. Frank, N.D. Goodman / Cognitive Psychology 75 (2014) 80–96
Table 1
Summary statistics and two-tailed one-sample t-tests against chance performance ($50) for each condition inExperiment 1. M, and SD denote the mean and standard deviation of bets on the target feature. Degrees of
freedom vary from condition to condition due to exclusions (see text for more details).
Trial

Model prediction

M

SD

t

df

p

1/1
1/2
1/3
2/3

50.0
66.7
75.0
60.0

50.2
66.8
70.3
56.7

14.1
23.1
27.7
19.8

0.21
10.01
10.19
4.65

193
189
193
188

.83
<.0001<.0001<.0001

Following this convention, a 1/1 trial was a trial in which a target object had two features, each ofwhich was unique to that object. A 1/2 trial was a trial in which one of the target object’s features was
unique and the other was shared with one other object (as in our example). A 1/3 trial had a target
with a single unique feature and a second feature shared with all three objects. Finally, a 2/3 trial target had no unique features, but had one feature shared with a single other object and one feature
shared with both other objects.
In each trial in the survey, the participant was asked to make one judgment, in the form of a ‘‘bet’’of $100 dollars on whether a novel adjective referred to one or the other property of the object withthe box around it, spreading the money between the two alternatives by entering two numerical values (the two alternatives were denoted by a picture next to each text box). This betting measure gives
us an estimate of speakers’ subjective probability, rather than a purely qualitative judgment (Frank &Goodman, 2012). For each trial, we also included two manipulation check questions, in which we
asked participants to write how many objects had each of the two target features (Crump et al.,2013; Oppenheimer, Meyvis, & Davidenko, 2009).

3.2. Results and discussion
In our analysis, we excluded trials on which participants’ bets did not sum to 100 (2.5% of trials)
and on which they failed to answer the check questions correctly (2.9%). These exclusions did notchange the qualitative or quantitative pattern of results. We also veriﬁed that there were no effectsof object type or target position in a simple linear regression predicting participants’ bets.5 Thus, weaveraged across these aspects of the data and analyzed bets on the target feature by condition. The target
feature was designated as the feature that constituted the numerator in the condition name, e.g. theunique feature in 1/2 trials (HEADBAND in our running example).
Participants’ mean bets on the target feature are plotted by model predictions in Fig. 2, right, and alldata are reported in Table 1. The primary prediction in our experiment was that participants’ bets
would favor the features that were more informative (had smaller extensions). We found that this prediction was satisﬁed: In the 1/2, 1/3, and 2/3 conditions (all the conditions where there was a difference in extension between features), participants picked the feature with the smaller extension
signiﬁcantly more than chance (t-tests are reported in Table 1). In addition, all three of these conditions differed signiﬁcantly from the 1/1 baseline condition (all ps < :001). Thus, participants in our
experiment reliably assigned the meaning of the novel word to the more informative feature of thetarget object in the context.
In addition, participants’ bets scaled with the relative informativeness of the two features. We
found a tight quantitative correspondence between (parameter-free) model predictions and humanbehavior. When there were equal numbers of objects with each feature, mean bets were very close
to $50, reﬂecting equal probability. In contrast, in the 1/2 case shown in Fig. 2, our informativenessmodel predicted a bet of $67 in this condition, nearly identical to the participants’ average bet of5
Due both to a desire to maintain comparability with the developmental experiments (Experiments 2–4) and due to concernsthat participants would pick up on consistencies in the type of inferences being studied, we limited the number of trials that any
given participant completed. Thus, the amount of data we collected for each participant did not allow us to make accurate
estimates of participant-level effects in a mixed-effects model (Gelman & Hill, 2006).

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M.C. Frank, N.D. Goodman / Cognitive Psychology 75 (2014) 80–96$67. Although there were only four conditions with distinct model predictions, the correlation
between mean bets and model predictions was quite high (r ¼ :98; p ¼ :02).6
Despite the high correlation between model and data, participants’ bets were slightly lower than
predicted by the model in some conditions (in particular, the 2/3 and 1/3 conditions are below thediagonal in Fig. 2). This trend is consistent with the idea that human judgments includes some‘‘lapses’’—cases where participants make errors or pick at chance—and hence behavioral measures
are biased towards chance relative to ideal observer model predictions (Wichmann & Hill, 2001;
see Frank, Goldwater, Grifﬁths, & Tenenbaum, 2010 for a recent exposition of this issue in the probabilistic language modeling literature).
Thus, our data suggest that adults’ judgments show a quantitative correspondence between the relative informativeness of a property in context and inferences about word meaning. Our next experiments test whether preschool children also show evidence of such sensitivity to informativeness.
4. Experiment 2
We next asked whether preschool children would also be able to make use of the informativenessof features to learn the meanings of novel adjectives. For this paradigm, we used a simpliﬁed version of
the 1/2 condition of Experiment 1 that used only two objects and two features, as in our original
example in Fig. 1.
4.1. Methods
4.1.1. ParticipantsParticipants were 24 children from an on-campus preschool, recruited from their classrooms by anexperimenter who had previously spent time in their classroom to establish rapport. Children wererecruited to fulﬁll a planned sample of 3–4 year-olds (N = 12, mean age = 3;7) and 4–5 year-olds(N = 12, mean age = 4;6).
4.1.2. Materials and methods
Children completed eight total trials, distributed into two conditions: ﬁller and inference. Inference
trials contained two objects: the target object (indicated by a point) had two features, while the distractor object had only one of these (as in the running example shown in Fig. 1). Filler trials were identical but the target had only one feature, which was not shared with the distractor. For example, a ﬁller
version of Fig. 1 would be identical but the target dinosaur would appear without a bandanna, so thatthe label would unambiguously refer to the headband (because this was the only salient accessory thedinosaur had). Trials were interleaved by condition, with a ﬁller trial always appearing ﬁrst.
At the beginning of the paradigm, children were introduced to a stuffed animal named Felix who
they were told was visiting a toy store and who they were to help in identifying some new toys. Experimental materials were presented via printed pictures shown in a binder, with training and testing
phases shown on subsequent pages. In the training portion of each trial, the experimenter pointed
to the target object and said e.g. ‘‘This is a dinosaur with a dax! How neat! A dinosaur with a dax.’’
This frame ensured that the target word (‘‘dax’’) was spoken twice. The ﬁrst part of the naming phrase
was always ‘‘this is a,’’ while the exclamation varied from item to provide variety. In the test portion of
the trial, children saw two additional images in which one object had each feature (e.g. a dinosaur
with a bandanna only and a dinosaur with a headband only; identical to the ﬁller trials). They wereasked ‘‘Here are some more dinosaurs. Which of these dinosaurs has a dax?’’ and responded bypointing.
6This ﬁnding additionally replicates the results of an adult experiment reported in Frank, Goodman, Lai, and Tenenbaum (2009)
with a distinct population and stimulus set. In that experiment, which used arrays of six geometric shapes, there were a total of 21
conditions ranging from 1/6 to 5/6, and the overall correlation between model predictions and participants’ mean bet was r ¼ :93.
We conducted this simpliﬁed version of the experiment in order to use stimuli more comparable to those used with children inExperiments 2–4.

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Experiment 2

Experiment 3

Proportion Correct

1.00
0.75
Trial Type
Filler0.50

Inference

0.25
0.00
3−4

4−5

3−4

4−5

Age (Years)
Fig. 3. Data from Experiments 2 and 3. Mean proportion correct is plotted by age group for both ﬁller and inference trials. The
dashed line shows chance performance. Error bars show 95% conﬁdence intervals, computed via a non-parametric bootstrap
over participant means.

Materials for the inference trials were identical to those used in Experiment 1; ﬁller trials usedmonkeys, dogs, cell phones, and cats as the objects. Novel words were ‘‘tupe,’’ ‘‘sep,’’ ‘‘zef,’’ ‘‘gabo,’’‘‘dax,’’ ‘‘ﬁd,’’ ‘‘keet,’’ and ‘‘toma.’’ We counterbalanced trial order, target position in both training
and test trials (crossed), and which feature was the target. Features were chosen to be equally salient
based on pilot studies using the same paradigm.
4.2. Results and discussion
If children were able to make use of the relative informativeness of the two possible word meanings, they should choose the more informative word meaning signiﬁcantly more often than chance.
Congruent with this hypothesis, we found that in inference trials, children chose the unique feature(the one that would have been more informative to name in this context) the majority of time
(3–4 year olds: M = 81%, SD = 39% and 4–5 year olds: M = 88%, SD = 33%) and nearly as often as theychose the correct feature in ﬁller trials (3–4 year olds: M = 83%, SD = 38% and 4–5 year olds:
M = 94%, SD = 24%). Results are shown in Fig. 3, left. These data suggest that children in our task weresensitive to the contextual distribution of features, even though the literal meaning of the utterance
did not strictly rule out the non-unique feature.
To quantify the reliability of this pattern, we ﬁt a logistic mixed effects model (Gelman & Hill, 2006;
Jaeger, 2008) to children’s responses, with age group and condition as ﬁxed effects, and with random
effects of condition ﬁt for each participant and each target item (a ‘‘maximal’’ random effect structure
Barr, Levy, Scheepers, & Tily, 2013). The resulting coefﬁcient estimates suggested that three-year-olds(the reference level) were above chance in their responding on inference trials (b ¼ 1:74; z ¼ 3:70;
p ¼ :0002). There was also a signiﬁcant coefﬁcient indicating higher performance on ﬁller trials(b ¼ 4:66; z ¼ 1:92; p ¼ :02). In this study there was no signiﬁcant effect of age group (b ¼ :47;
z ¼ :67; p ¼ :51). A model with an interaction term did not provide a better ﬁt (v2 ð1Þ ¼ :16; p ¼ :69),
though under this model the coefﬁcient estimate for ﬁller trials was slightly lower and only trended
towards signiﬁcance (b ¼ 3:91; p ¼ :09); the reliability of other results did not change.
Evidence from this study suggests that children successfully mapped words to features that would
have been more likely to be named by an informative speaker. The mean proportion of informativeness-congruent judgements by children in both groups was actually higher than the strict probability
assigned by our model (67%) and higher than that assigned by adults in the betting task in Experiment
1. There are several reasons to be cautious about this kind of quantitative interpretation, however. The
context of Experiment 2 was far less stripped down than that of Experiment 1, and the linguistic frame
for the novel label encouraged a contrastive reading (something we investigate in Experiment 3). In
addition, the two-alternative forced choice measure might have led children to maximize, more consistently choosing the highest-probability of the two alternatives (Hudson-Kam & Newport, 2005).
Thus, although the evidence strongly points in favor of informativeness, we do not believe a quantitative interpretation is warranted.

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5. Experiment 3
As mentioned above, one question about the ﬁndings of Experiment 2 comes from the use of thecontrastive sentence frame ‘‘This is a dinosaur with a dax.’’ The deictic ‘‘this’’ is, in the terminologyof Clark and Wong (2002), a ‘‘direct offer’’—the use of a deictic term for the exclusive purpose of providing a label. This exclusive purpose may have given participants a greater sense that the utterance
should be chosen with maximal informativeness. While the goal of the label is ambiguous—either toteach the label itself or to distinguish one dinosaur from the other—both would lead to a strong presumption of informativeness. In addition, the deictic ‘‘this’’ is easy to stress contrastively, implying tolisteners that ‘‘this [and not that other one] is a dinosaur with a dax.’’
In Experiment 3, we replicated the methods of Experiment 2 exactly but used the frame ‘‘here is a’’instead. By virtue of its focus on location, rather than identity, ‘‘here is a’’ provides an alternative goal
for the utterance: establishing in the common ground the location of a particular dinosaur (Clark,
1996). In addition, in Experiment 3, we avoided the strong prosodic phrase boundary between ‘‘here’’and ‘‘is’’ that would be necessary to imply contrastive stress in this condition (e.g. ‘‘here. . . is a dinosaur with a dax’’). A mapping of ‘‘dax’’ to the unique feature in this study would imply that the resultsof Experiment 2 are not speciﬁc to a single construction type.
5.1. Methods
5.1.1. ParticipantsParticipants were 25 children from the same on-campus preschool as Experiment 2. Children wererecruited to fulﬁll a planned sample of 3–4 year-olds (N = 12, mean age = 3;8) and 4–5 year-olds(N = 13, mean age = 4;3).
5.2. Materials and methods
Materials and methods for Experiment 3 were identical to those in Experiment 2 except that we
replaced the naming phrase ‘‘This is a’’ with the phrase ‘‘Here is a.’’5.3. Results and discussion
Results are shown in Fig. 3, right. Overall, performance in the inference trials was lower than inExperiment 2, but was still above chance (3–4 year olds: M = 69%, SD = 47% and 4–5 year olds:
M = 69%, SD = 47%). Filler trial performance remained quite high (3–4 year olds: M = 77%, SD = 42%
and 4–5 year olds: M = 94%, SD = 24%).
We again applied logistic mixed effects regression, though in this case we retained the interaction
between condition and age because it increased model ﬁt. We found that three-year-olds in the inference condition were signiﬁcantly above chance (b ¼ :93; z ¼ 2:17; p ¼ :03), and there was no main
effect of age group (b ¼ :04; z ¼ :06; p ¼ :95). Performance on ﬁller trials was higher than on inference trials, though not signiﬁcantly so (b ¼ 1:04; z ¼ 1:42; p ¼ :15), but there was a marginally significant interaction of trial type and age group (b ¼ 2:02; z ¼ 1:64; p ¼ :10). This interaction suggeststhat the age-related increase in ﬁller trial performance was not seen reliably in the inference trials—both 3–4 and 4–5 year olds were above chance, but they were not even numerically different
from one another.
Although children’s performance was lower in the inference trials in Experiment 3 than it was inExperiment 2, we nevertheless replicated the use of informativeness to make inferences about word
meaning. Either the ‘‘this is a’’ construction or the stress with which it was marked likely contributed
to the somewhat higher level of inferences in Experiment 2, and in naturalistic situations, these information sources both likely scaffold children’s performance in making similar inferences. But even in
their absence, children still appeared to notice the differential informativeness of the unique featureand treat that property as the extension of the novel word.

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91

Nevertheless, two alternative explanations remain possible. Because the unique feature could havebeen more salient to children, they might either have noticed that feature and then simply selected it
at test (a completely non-linguistic explanation) or they could have noticed it and assumed it was
being talked about, but failed to encode its link with any particular word. Both of these explanations
would bear against our hypothesis about the role of informativeness inferences for word learning.
Experiment 4 provides control conditions that rule these explanations out.
6. Experiment 4
In Experiment 4, we replicated Experiment 3 with a slightly larger sample of children (24, rather
than 12, per cell). In addition, we added two comparison conditions. The ﬁrst, the Disambiguation condition, was intended to test that children made a connection between the word they heard and thefeature they indicated at test. To test this hypothesis, we exploited the ﬁnding that children will reliably choose an unnamed or novel object when asked about the referent of a new word (Markman &Wachtel, 1988; Mervis & Bertrand, 1994). We taught a ﬁrst novel word using the same paradigm as inExperiment 3, but then asked for a second, distinct novel word at test. If they had made a connection
between the ﬁrst word and the informative feature, then children should choose the uninformative
feature in this test.
The second comparison condition, the Non-Linguistic Salience condition, simply asked children to‘‘ﬁnd another one’’ at test. This condition tested the hypothesis that children would choose featuresthat matched the unique feature at test irrespective of the presence of a label at all. We hypothesizedthat if children were relying on a linguistic inference (as proposed above), they would select featuresat chance in this condition.
6.1. Methods
6.1.1. ParticipantsParticipants were 144 children recruited from the San Jose Children’s Discovery Museum. Children
were recruited to fulﬁll a planned sample of 3–4 year-olds (N = 24 per condition, M rep = 3;6,
Mdisambig = 3;6, M salience = 3;8) and 4–5 year-olds (N = 24 per condition, M rep = 4;5, M disambig = 4;5,
Msalience = 4;7). In the replication condition, an additional 4 children completed the task but were
excluded from the ﬁnal sample (3 for falling under a pre-speciﬁed criterion of 75% parent-reported
English exposure, 1 for experimenter error); in the Disambiguation condition, 3 children were
excluded (2 for language, 1 for non-compliance); and in the Non-Linguistic Salience condition, 2 were
excluded (both for language).
6.2. Materials and methods
Materials and methods for Experiment 4 were identical to those in Experiment 3, except as noted.
In the inference trials of the Disambiguation condition, we used a different novel name at test than wasused in training. For example, if the child was taught about a ‘‘dax’’ in training, he or she might beasked about a ‘‘toma’’ at test. In both the inference and ﬁller trials of the Non-Linguistic Salience condition, we did not name the feature in training (‘‘Here is a dinosaur. How neat! Look at this dinosaur.’’)and we asked ‘‘Can you ﬁnd another one?’’ at test.
6.3. Results and discussion
We replicated the ﬁndings of Experiment 3: Children chose the more informative word meaning
more often than chance (3–4 year olds, M = 63%, SD = 29%; 4–5 year olds, M = 69%, SD = 27%). On theother hand, in the disambiguation condition, participants’ performance on inference trials ﬂipped(3–4 year olds, M = 37%, SD = 26%; 4–5 year olds, M = 27%, SD = 25%), indicating that they were choosing the feature that had not been informative at training, and hence that they had encoded the link
between the feature and the novel label used during the initial naming event. In the Non-Linguistic
Salience condition, participants chose at chance (3–4 year olds, M = 54%, SD = 25%; 4–5 year olds,

M.C. Frank, N.D. Goodman / Cognitive Psychology 75 (2014) 80–96

Proportion Inference Consistent92

Replication

Disambiguation

Non-Linguistic Salience

0.75
Trial Type

0.50

FillerInference

0.25

0.00
3

4

3

4

3

4

Age Group (Years)
Fig. 4. Data from Experiment 4. Mean proportion implicature consistent responding (and mean proportion correct for ﬁllers) is
plotted by age groups. The three panels show data from the replication of Experiment 3, the disambiguation condition, and thesalience condition. The dashed line shows chance performance. Error bars show 95% conﬁdence intervals, computed via a nonparametric bootstrap over participant means.

M = 51%, SD = 28%), indicating that the salience of the unique feature alone was insufﬁcient to drive
children’s choices. Results are shown in Fig. 4.
We ﬁt a mixed effects logistic regression across all three conditions. For ease of interpretation, we
ﬁt the model for only inference trials. A model that included condition by age interactions did not signiﬁcantly increase ﬁt (v2 ð2Þ ¼ 2:18; p ¼ :34), so we did not include an interaction in the ﬁnal model.
We set the three-year-olds’ performance in the Replication condition as the reference level—performance in this condition was signiﬁcantly above chance (b ¼ :78; z ¼ 3:81; p ¼ :0001). Performance
was reliably different from the Replication condition (and reliably below chance when set to the reference level) in the Disambiguation condition (b ¼ 1:54; z ¼ 6:24; p < :0001). Performance in the
Non-Linguistic Salience condition was reliably different from Replication condition performance(b ¼ :61; z ¼ 2:54; p ¼ :01). Finally, there were no reliable age effects, as would be expected averaging across conditions (b ¼ :12; z ¼ 0:19; p ¼ :53); the model including the interaction of age andcondition also did not yield any reliable age effects. The results of Experiment 4 thus support the
hypothesis that children noticed the differential informativeness of the unique feature and linked thisfeature to the particular word they heard.
7. General discussion
We began by revisiting a fundamental question in language acquisition: How do children infer themeanings of words in ambiguous situations? Although a variety of partial answers to this problem
have been identiﬁed by prior research, a large class of situations (including some construals of Quine’s
famous problem) are not addressed by these. We have argued here that in some of these cases, word
meaning can be disambiguated by the combination of knowledge of speakers’ communicative goals
and the assumption that they are using language informatively to achieve those goals (Grice, 1975).
Our contributions here are then to formalize this inference using a model of pragmatic reasoning
and to show that adults and children are able to use contextual informativeness in simple situations
to infer word meanings.
In our prior work, we described a framework for pragmatic inference that can be used to make predictions about the behavior of speakers and listeners in simple reference games (Frank & Goodman,2012). As we showed here, this framework can also be extended straightforwardly to make predictions about what novel words should mean, given that they are uttered by an informative speaker.
We then tested predictions from this framework. In Experiment 1, we showed that the aggregate
judgments of adult learners conformed quantitatively to the predictions of the pragmatic computation
we described. In Experiments 2 and 3, we provided evidence that preschoolers’ also made use ofcontextual informativeness in word learning inferences. In Experiment 4, we ruled out alternativeM.C. Frank, N.D. Goodman / Cognitive Psychology 75 (2014) 80–96

93

explanations of these ﬁndings in terms of general salience. Together these data suggest that adults andchildren can use Gricean considerations to infer word meaning in otherwise ambiguous situations.
Our work builds on a long tradition of considering pragmatic reasoning in early language learning(Bloom, 2002; Clark, 2003; Tomasello, 2003). Some of its closest antecedents come from early work on
the role of pragmatics in young children’s language, where Greenﬁeld, Bates, and their colleagues
developed the notion of informative use in context (Bates, 1976; Greenﬁeld, 1978; Greenﬁeld &Smith, 1976). These authors were interested in how children chose which aspects of the world to label
using their early language. They posited that children chose the most informative element of a situation and encoded it in speech.
Yet many of the ideas in this work did not see extensive further development. In a critique of thiswork, Pea (1979) noted thatthe term ‘informativeness’ is deﬁned in loose pragmatic terms. . . yet no pragmatic theory of information, with the intricacies which would be required in incorporating the belief-states of [speakers] A and B and their changes over time, has ever been developed. . . . So the allusion to a formal
pragmatic information theory is based on an illusion. (pp. 406–407)
Pea’s comment highlights a key weakness of these early approaches: they had no formal framework in which to ground observations about pragmatics. Our work here revisits the same set of questions posed in this earlier work (although from the perspective here of language learning as well as
language use): How can we formalize powerful Gricean notions of informativeness in context suchthat it can be applied to make quantitative predictions? We believe that the use of formal models
points the way forward for further investigations of children’s pragmatic abilities in early learning.
Our data leave open the question of the psychological mechanisms by which adults and children
compute the informativeness of a word in context. We note two particular issues here. First, we cannot differentiate between the case in which each participants’ judgments are slightly affected by
aspects of the contexts and the case in which some participants notice the informativeness of a featureand others do not. This is a general issue in translating computational-level models of human cognition to the psychological process level (Frank, 2013).
Second, and more speciﬁc to the particular domain at hand, it may be that the relative infrequency(uniqueness) of the most informative feature draws attention to it. We have not attempted to differentiate this psychological explanation experimentally because, to a ﬁrst approximation, unique features, objects, and events are in fact more likely to be referred to. Thus, the same mechanisms thatdraw our attention to the unexpected, surprising, and rare may be those that help us decide what
is informative to talk about. Experiment 4 rules out the explanation that non-linguistic salience or
attention alone could explain children’s choices in our target condition. It is nevertheless consistent
with this result that referential salience and joint attention could be major factors in everyday communication, as these factors can be combined with pragmatic inferences to yield good predictions
about reference judgments (Frank & Goodman, 2012).
More generally, the degree to which children (or adults) take others’ perspective in judging thenovelty of a stimulus is an open question. Experiments on discourse novelty suggest some degreeof perspective-taking (Akhtar et al., 1996), but it is controversial even for adults the degree to which
others’ perspectives are considered in language comprehension (Brown-Schmidt, Gunlogson, &Tanenhaus, 2008; Keysar, Lin, & Barr, 2003; Nadig & Sedivy, 2002). We found no non-linguistic coordination effects in this particular paradigm (indeed, our Non-Linguistic Salience condition was set up
to avoid a possible framing that would encourage non-linguistic coordination). But more generally,
non-linguistic coordination is an important phenomenon that suggests that ‘‘salience’’ as discussed
here is a construct requiring much more careful investigation (Clark, Schreuder, & Buttrick, 1983;
Schelling, 1980) Thus, this topic will be a fruitful direction for future work.
We proposed a simple model of word learning through informativeness here. A major strength of
this model is that it provides a precise, parameter-free ﬁt to adult judgments. But extending thismodel to more complex stimuli and scenarios will require substantial work. Smith, Goodman, andFrank (2013) presented an extension of the cross-situational word learning model of Frank,
Goodman, and Tenenbaum (2009) that included a pragmatic computation of the type described here.
That model was able to make a variety of pragmatically-motivated inferences in single- and multi-trial

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word learning scenarios, suggesting a possible uniﬁcation between single-trial ‘‘pragmatic’’ inferences(described here) and multi-trial ‘‘cross situational’’ inferences (Frank, Goodman, & Tenenbaum, 2009;
Yu and Smith, 2007).
Nevertheless, the encoding of context in that model remains as schematic as the one presented
here, leaving richer representations of context as another challenge for future work. In more complex
environments we expect that performance (especially children’s performance) would suffer. Toward
the goal of understanding this prediction, Vogel, Emilsson, Frank, Jurafsky, and Potts (2014) presented
a model that relied on a neural-network representation of pragmatic reasoning and showed more
graded generalization across contexts. The focus of that work was on understanding the depth of participants’ pragmatic reasoning (how deeply they reason about others’ beliefs), but the same model
might provide a platform for understanding how pragmatic computations would scale to larger ormore naturalistic scenarios.
Children can make many partial solutions to the Quinian puzzle of ambiguity, employing strategies
from cross-situational observation to disambiguation with prior linguistic knowledge, and such strategies can be very helpful. Yet there are still many examples where they fail, including the cases studied here. We have argued that cases where other strategies fail may still be disambiguated byconsidering the speaker’s pragmatic goals. In fact, as we have argued elsewhere (Frank, Goodman, &Tenenbaum, 2009), this consideration of the speaker’s communicative goals may form a broader
strategy for language acquisition, accounting for other phenomena as a byproduct of statisticalinference over social representations.

Acknowledgments
Many thanks to Allison Kraus, Kathy Woo, Janelle Klaas, Andrew Weaver, and Stephanie Nicholson
for assistance in stimulus design and data collection and to Susan Carey, Ted Gibson, Avril Kenney,Peter Lai, Rebecca Saxe, Jesse Snedeker, and Josh Tenenbaum for valuable discussion. Some ideas
described in this paper were originally presented to the Cognitive Science Society in Frank,
Goodman, Lai, et al. (2009). We gratefully acknowledge the support of ONR Grant N00014-13-1-0287.

Appendix A. Materials
Stimulus items for all four target items in each of the experiments are shown in Fig. A.1. For eachstimulus item (robots, dinosaurs, rockets, and bears), there were two possible features: robots had anantenna and a screen, dinosaurs had a bandanna and a headband, rockets had an antenna and awindow, and bears had a club and a headdress.

Fig. A.1. One version of all four stimuli for target trials in Experiments.

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