Warm (for winter): Comparison class understanding in vague language
Michael Henry Tessler1 , Michael Lopez-Brau2 , and Noah D. Goodman1
mtessler@stanford.edu, lopez mic@knights.ucf.edu, ngoodman@stanford.edu
1 Dept. of Psychology, Stanford University, 2 Dept. of Electrical & Computer Engineering, University of Central Florida

Abstract
Speakers often refer to context only implicitly when using language. The utterance “it’s warm outside” could signal it’swarm relative to other days of the year or just relative to thecurrent season (e.g., it’s warm for winter). Warm vaguely conveys that the temperature is high relative to some contextualcomparison class, but little is known about how a listener decides upon such a standard of comparison. Here, we formalize
how world knowledge and listeners’ internal models of speech
production can drive the resolution of a comparison class incontext. We introduce a Rational Speech Act model and derive two novel predictions from it, which we validate using aparaphrase experiment to measure listeners’ beliefs about thelikely comparison class used by a speaker. Our model makes
quantitative predictions given prior world knowledge for thedomains in question. We triangulate this knowledge with afollow-up language task in the same domains, using Bayesiandata analysis to infer priors from both data sets.
Keywords: comparison class; pragmatics; Rational Speech
Act; Bayesian cognitive model; Bayesian data analysis

If it’s 75 ◦ F (24 ◦ C) outside, you could say “it’s warm.” If
it’s 60 ◦ F (16 ◦ C), you might not consider it warm. Unlessit’s January; it could be warm for January. Warm is relative,
and its felicity depends upon what the speaker uses as a basisof comparison—the comparison class (e.g., other days of theyear or other days in January). Comparison classes are necessary for understanding adjectives and, in fact, any part of language whose meaning must be pragmatically reconstructedfrom context, including vague quantifiers (e.g., “He ate a lotof burgers.”; Scholler & Franke, 2015) and generic language(e.g., “Dogs are friendly”; Tessler & Goodman, 2016a). The
challenge for listeners is that the comparison class often goesunsaid (e.g., in “It’s warm outside.”).
The existence of comparison classes for understandingvague language is uncontroversial (Bale, 2011; Solt, 2009).
Four-year-olds categorize novel creatures (pimwits) as either“tall” or “short” depending on the distribution of heights ofpimwits and not the heights of creatures that are not calledpimwits, suggesting the comparison class in that context isother pimwits (Barner & Snedeker, 2008). Adult judgmentsof the felicity for adjectives like “dark” or “tall” similarly depend upon fine-grained details of the statistics of the comparison class (Qing & Franke, 2014b; Schmidt, Goodman,
Barner, & Tenenbaum, 2009; Solt & Gotzner, 2012).
Any particular object of discourse, however, can be conceptualized or categorized in multiple ways, giving rise tomultiple possible comparison classes. A day in January is
also a day of the year; if it’s warm, it could be warm for winter or warm for the year. Why should one comparison classbe preferred over another? To our knowledge, this question
has not been addressed formally or empirically.1 We pro1 Theoretical work in semantics has instead focused on how in-pose that listeners actively combine category knowledge withpragmatic considerations to infer the comparison class implicitly used by the speaker. We introduce a minimal extension to the Rational Speech Act (RSA) model for gradable
adjectives (Lassiter & Goodman, 2013) to allow it to flexibly
reason about the implicit comparison class.
We derive two novel qualitative predictions from thismodel. Saying “it’s warm” in winter should signal it’s warm
for winter (as opposed to for the year) more so than saying“it’s cold”. The opposite relationship should hold in summer,
where “it’s cold” should signal it’s cold for summer more sothan “it’s warm”. This prediction is driven by the a priori
probability that the adjective could apply to the class (e.g.,
the probability that a given day in winter is warm; Prediction 1). In addition, regardless of the season and the adjective
form (e.g., “warm” or “cold”), listeners who expect speakers
to be informative will prefer classes that are relatively specific(e.g., relative to the current season as opposed to the whole
year), as they carry more information content (Prediction 2).
We test these predictions by eliciting the comparison classusing a paraphrase dependent measure (Expt. 1).
As with any Bayesian cognitive model, explicitly specifying relevant prior knowledge (e.g., beliefs about temperatures) is necessary for the model to make quantitative predictions. The current methodological standard is to measure
beliefs by having participants estimate quantities or give likelihood judgments (Franke et al., 2016). We pursue a different
methodology. The RSA model captures a productive fragment of natural language; thus, it makes predictions about arelated natural language task (Expt. 2). Critically, we can use
the model to predict natural language judgments that require
the same prior knowledge as in Expt. 1 and use Bayesiandata analysis to jointly infer the shared priors. This approachharnesses the productivity of language into experiment design and allows us to reconstruct priors without having participants engage in challenging numerical estimation tasks.

Understanding comparison classes
Adjectives like warm and cold are vague descriptions of anunderlying quantitative scale (e.g., temperature). The vagueness and context-sensitivity of these adjectival utterances canbe modeled using threshold semantics ([[u]] = x > θ, for utterance u, scalar degree x, and threshold θ), where the threshold is probabilistically set with respect to a comparison classc via pragmatic reasoning (Lassiter & Goodman, 2013; seealso Qing & Franke, 2014a):formation from a comparison class is used and what representations
might be preferred (Bale, 2011; Solt, 2009).

S1 (u | x, θ) ∝ exp (α1 · ln L0 (x | u, θ))(2)

L0 (x | u, θ) ∝ δ[[u]](x,θ) · Pc (x)(3)

This is a Rational Speech Act (RSA) model, a recursive
Bayesian model where speaker S and listener L coordinate on
an intended meaning (for a review, see Goodman & Frank,
2016). In this framework, the pragmatic listener L1 tries toresolve the state of the world x (e.g., the temperature) fromthe utterance she heard u (e.g., “it’s warm”). She imagines
the utterance came from an approximately rational Bayesian
speaker S1 trying to inform a naive listener L0 , who in turnupdates her prior beliefs Pc (x) via an utterance’s literal meaning [[u]](x). Lassiter & Goodman (2013) introduced into RSA
uncertainty over a semantic variable: the truth-functional
threshold θ (Eq. 1). θ comes from an uninformed prior andis resolved by the listener by reasoning about the likely statesof the world Pc (x) (e.g., possible temperatures) and the likelihood that a speaker would say the adjective given a state and athreshold S(u | x, θ). The prior distribution over world-states
Pc (x) is always relative to some comparison class c (Eqs. 1 &3) but where does the comparison class come from?
When a listener hears only that “it’s warm outside” without
an explicit comparison class (e.g., “. . . for the season”), we
posit the listener infers the comparison class using her world
knowledge of what worlds are plausible given different comparison classes P(x | c), what comparison classes are likely
to be talked about P(c), and how a rational speaker would
behave in a given world and comparison class S1 (u | x, c, θ)(Eq. 4). As a first test of this idea, we consider an idealizedcase where the comparison class can be either a relatively specific (subordinate) or relatively general (superordinate) categorization (e.g., warm relative to days in winter or relative
to days of the year). Crucially in this situation, the listeneris aware that the target entity is a member of the subordinateclass (e.g., aware that it is winter) and draws likely values ofthe degree (e.g., temperature) from the subordinate class prior
P(x | csub ). With these assumptions, the model becomes:
L1 (x, c, θ | u) ∝ S1 (u | x, c, θ) · P(x | csub ) · P(c) · P(θ)(4)

S1 (u | x, c, θ) ∝ exp (α1 · ln L0 (x | u, c, θ))(5)

L0 (x | u, c, θ) ∝ δ[[u]](x,θ) · P(x | c)

(6)

We are interested in the behavior of the model with the underspecified utterance (e.g., “It’s warm”), and we assume thespeaker has two alternative utterances in which the comparison class is explicit (e.g., “It’s warm relative to other days in
winter.” and “It’s warm relative to other days of the year.”).
The predictions of this model depend on the details of the listener’s knowledge of the subordinate and superordinate categories: P(x | csub ) and P(x | csuper ), as well as the prior distribution on comparison classes P(c) in Eq. 4.
Comparison class prior P(c) reflects listeners’ expectations of what classes are likely to be discussed. As a proxy

Degree priors (World knowledge) Only the relative values for P(x | csub ) and P(x | csuper ) affect model predictions.
Hence we fix each superordinate distribution to be a standard normal distribution P(x | csuper ) = N (0, 1) and the subordinate priors to also be Gaussian distributions P(x | csub ) =N (µsub , σsub ); the subordinate priors thus have standardized
units. We will eventually infer the parameters of the subordinate priors from experimental data.
Subordinate interpretation(1)

1

Probability density

L1 (x, θ | u) ∝ S1 (u | x, θ) · Pc (x) · P(θ)

for comparison class usage frequency, we use empirical frequency fˆ estimated from the Google WebGram corpus2 , andscale it by a free parameter β such that P(c) ∝ exp (β · log fˆ).

0
−2

0

2

medium

0.5

0.0
low

Degreelow

1.0

mediumhighSubordinate prior meanhighnegative

positive

Figure 1: Left: Three hypothetical subordinate class priordistributions over a degree (fixing the superordinate class to
be a unit-normal distribution, in grey). Right: Predicted listener inferences for an intended subordinate class interpretation given positive and negative form adjectives with different
subordinate degree priors.
Qualitative model predictions Figure 1 (left) shows
schematic superordinate and subordinate priors; e.g., temperatures over the whole year (super), in winter (low), fall(medium), and summer (high). The subordinate distributions
have lower variance than the superordinate, and the “low” and“high” distributions have different means (e.g., temperaturesin winter are expected to be lower and have lower variancethan temperatures over the whole year).
Two intuitions explain the inferences of the pragmatic listener model (shown in Figure 1 right). First, certain classes
are more or less likely to have an adjective felicitously apply.
For example, any given day in winter is less likely to be warm
than cold. Thus, hearing “it’s warm” (a positive-form adjective) in winter (low prior) will signal it’s warm for winter (thesubordinate class) more so than hearing “it’s cold” (negativeform), because it’s more likely to be true (Prediction 1).
2 Corpusaccessed via https://corpora.linguistik.
uni-erlangen.de/cgi-bin/demos/Web1T5/Web1T5_freq.
perl. Due to potential polysemy and idiosyncracies of our experimental materials (Table 1), we made the following substitutions
when querying the database for emprical frequency: produce →“fruits and vegetables”; things you watch online → “online videos”;
days in {season} → “{season} days”; dishwashers → “dishwashingmachines”; videos of cute animals → “animal videos”.

Scale (adjectives)
Height (tall, short)Price (expensive, cheap)
Temperature (warm, cold)
Time (long, short)
Weight (heavy, light)

Subordinate classes(professional) gymnast, soccer player, basketball player
bottle opener, toaster, dishwasher
winter, fall, summer (day in Maryland)
video of a cute animal, music video, movie
grape, apple, watermelon

Superordinate
peoplekitchen appliancesdays in the year
things you watch online
produce

Table 1: Items used in Experiments 1 and 2. Subordinate categories were designed to fall near the low end, high end, andsomewhere in the middle of the degree scale
Second, the amount of information conveyed by a vague utterance depends upon the variability in the comparison class.
Comparison classes that have higher variance will result in
relatively less information gain by the listener. All else being equal, listeners will prefer lower variance (e.g., subordinate) comparison classes because they are more informative(Prediction 2). Figure 1 (right) shows that subordinate classinterpretations are above baseline regardless of the adjective
polarity (positive or negative) or the mean of the subordinate
prior (low, medium, high).
In sum, we see two predictions: The pragmatic listeneroverall prefers subordinate comparison classes, though theextent of this preference is modulated by the a priori probability that the adjective is true of the subordinate category.
We test these two predictions in our first experiment.
Overview of data analytic approach As described above,
specifying the relevant prior knowledge yields two free parameters per subordinate class. We will put priors over theseparameters and infer their likely values using Bayesian data
analysis. The data from the comparison class experiment(Expt. 1) would be insufficient, however, to reliably estimate
all of the parameters of this data analytic model. To alleviate this, we use the same RSA model to predict additional
data about related language use in the same domains (Expt.
2). Specifically, we gather judgments about adjectives when
the comparison class is explicit: whether or not an adjective
would apply to a subordinate member explicitly relative to thesuperordinate category (e.g., Is a day in winter warm relative
to other days of the year?).
To model Expt. 2 data, we remove comparison class uncertainty by setting P(csuper ) = 1, since the sentences provide
an explicit comparison to the superordinate class. We model
sentence endorsement using a pragmatic speaker (following
Qing & Franke, 2014a; Tessler & Goodman, 2016a, 2016b):
S2 (u | csub ) ∝ exp (α2 · Ex∼Pcsub ln L1 (x | u))(7)

Note that L1 (x | u) is defined from Eq. 4 by marginalization.
Eqs. 4 and 7 define models for the data we will gather from
Expts. 1 and 2, and depend on the same background knowledge P(x | c). We can thus use data from both experiments
to jointly reconstruct the shared prior knowledge and generate predictions for the two data sets. Experimental paradigms,
computational models, preregistration report, and data for thispaper can be found at https://mhtess.github.io.

Behavioral experiments
Experiment 1 tests the qualitative predictions of the model.
Experiment 2 collects further data about adjective usage inorder to constrain the quantitative predictions of the RSA
model, which will be used to predict data from both experiments. The materials and much of the design of the two experiments are shared. Participants were recruited from Amazon’s Mechanical Turk and were restricted to those with U.S.
IP addresses with at least a 95% work approval rating. Eachexperiment took about 5 minutes and participants were compensated $0.50 for their work.
Materials We used positive- and negative-form gradable
adjectives describing five scales (Table 1). Each scale waspaired with a superordinate category, and for each superordinate category, we used three subordinate categories that
aimed to be situated near the high-end, low-end, and intermediate part of the degree scale (as in Figure 1 left). This
resulted in 30 unique items ({3 subordinate categories} x {5scales} x {2 adjective forms}). Each participant saw 15 trials: one for each subordinate category paired with either the
positive or negative form of its corresponding adjective. Participants never judged the same subordinate category for bothadjective forms (e.g., cold and warm winter days) and backto-back trials involved different scales to avoid fatigue.

Experiment 1: Comparison class inference
In this experiment, we gather human judgments of comparison classes in ambiguous contexts, testing the two predictions
described in Qualitative Model Predictions.
Participants and procedure We recruited 264 participantsand 2 were excluded for failing an attention check. On eachtrial, participants were given a context sentence to introduce
the subordinate category (e.g., Tanya lives in Maryland andsteps outside in winter.). This was followed by an adjective sentence, which predicated either a positive- or negativeform gradable adjective over the item (e.g., Tanya says toher friend, “It’s warm.”). Participants were asked “What do
you think Tanya meant?” and given a two-alternative forcedchoice to rephrase the adjective sentence with either an explicit subordinate or superordinate comparison class:{She / He / It} is ADJECTIVE (e.g., warm) relative toother SUBORDINATES (e.g., days in winter) or SUPER ORDINATES (e.g., days of the year)temperaturetimeweight0.5

form
negative
positivewatermelon

apple

grape

movie

music video

cute animal video

day in summer

day in fall

day in winterdishwasher

toasterbasketball player

soccer player

bottle opener

0.0
gymnastSubordinate paraphrase

priceComparison classdata

strength1
DegreepriorsPrior density

height1.0

low
medium
high

0
−2

0

2

−2

0

2

−2

0

2

−2

0

2

−2

0

2

peoplekitchen appliancesdays of the year

online videos

producestrength

1.0
Classpriors

0.5
0.0

low
mediumwatermelon

apple

grape

movie

music video

cute animal video

day in summer

day in fall

day in winterdishwasher

toasterbottle opener

basketball player

soccer player

highgymnastSubordinate probability

Degree value

Figure 2: Empirical comparison class data, inferred world priors, and empirically derived comparison class priors. Top: Experiment 1 results. Comparison class judgments in terms of proportion judgments in favor of subordinate comparison class.
Middle: Inferred prior distributions of world knowledge used to model Experiment 1 and 2 data. Bottom: Inferred prior probability of the subordinate comparison classes based on Google WebGram frequencies. Error bars correspond to 95% Bayesiancredible intervals (for bottom plot, derived from the posterior on the β scale parameter).
In addition to all of the above design parameters, half ofour participants completed trials where an additional sentence
introduced the superordinate category at the beginning (e.g.,
Tanya lives in Maryland and checks the weather every day.),
with the intention of making the superordinate paraphrase
more salient.
Results We observed no systematic differences between
participants’ responses when the superordinate category waspreviously mentioned in the context and those when it wasnot; thus, we collapse across these two conditions for all
analyses. Figure 2 (top) shows the proportion of participants
choosing the subordinate paraphrase for each item, revealing considerable variability both within- and across- scales.
The predicted effects are visually apparent within each scale(compare with Figure 1 right).
Our qualitative predictions are confirmed using a generalized linear mixed effects model with main effects of adjective
form (positive vs. negative) and the a priori judgment by the
first author of whether the sub-category was expected to be

low or high on the degree scale, and of critical theoreticalinterest, the interaction between these two variables. In addition, we included by-participant random effects of intercept
and by-subordinate category random effects of intercept anditeraction between form and strength3 . Confirming our two
qualitative model predictions, there was an interaction between form and strength (β = −3.75; SE = 0.58; z = −6.49)
and there was an overall preference for subordinate category
paraphrases (β = 1.21; SE = 0.37; z = 3.27). The main effects of form and strength were not significant.
We then test the simple effects. For items low on the degree
scale (e.g., temperatures in winter), positive form adjectives
were significantly more likely to imply subordinate comparison classes (β = 1.41; SE = 0.15; z = 9.43), while the opposite is true for items high on the scale (e.g., summer days;
β = −2.5; SE = 0.19; z = −13.15). Participants reason pragmatically to resolve the comparison class, combining world
knowledge with informativity as predicted by our model.
3 This was the maximal mixed-effects structure that converged.

Adjective production

Comparison class inference

Comparison class inference (subset)
1.0

Human endorsement

Human endorsement

1.00

0.75

0.50

0.25

0.9

0.8

0.7

0.00
0.00

0.25

0.50

0.75

1.00 0.00

0.25

0.50

0.75

1.00

0.7

heightpricetemperature

0.8

0.9

1.0

Model prediction

Model prediction
timeweightpositive

negative

Figure 3: Human endorsement of subordinate comparison class paraphrases (middle; Expt. 1) and adjective sentences (left;Expt. 2) as a function of listener model L1 and speaker model S2 predictions, respectively. The right facet displays a subsetof the paraphrase data (Expt. 1) to reveal good quantitative fit even in a small dynamic range. Error bars correspond to 95%
Bayesian credible intervals.

Experiment 2: Adjective endorsement
In this experiment, we collected data about adjective endorsement that would require the same prior knowledge relevant
for Expt. 1. We use this data to further constrain the RSA
model’s quantitative predictions.
Participants and procedure We recruited 100 participantsand 5 were excluded for failing an attention check. On eachtrial, participants were given a sentence introducing the subordinate category (e.g., Alicia lives in Maryland and steps
outside in winter.). This was followed by a question asking if
the participant would endorse an adjective explicitly relative
to the superordinate category (e.g., Do you think the day inwinter would be warm relative to other days of the year?).
Results The judgments in this experiment were consistent
with the a priori ordering of the subordinate categories on
the degree scale. On the y-axis of Figure 3 (left), we seethat the endorsement of adjectival phrases in these domains
is markedly more categorical than the comparison class inference task (compare vertical spread of left and middle facets).

Full model analysis and results
The RSA listener (Eq. 4) and speaker (Eq. 7) models makequantitative predictions about comparison class interpretation
and adjective endorsement, respectively. We construct a single data-analytic model with each of these RSA components
as sub-models in order to make quantitative predictions about
the data from both of our experiments.
The listener and speaker sub-models share their prior world
knowledge P(x | c) (e.g., temperatures in winter), describedin the Degree Priors section. We put the same priors
over the parameters of each subordinate distribution: µ ∼Uniform(−3, 3), σ ∼ Uniform(0, 5), since they have standardized units. The comparison class prior P(c) in Eq. 4

scales the empirical frequency fˆ by a free parameter, which
we give the following prior: β ∼ Uniform(0, 3).
The full model has three additional parameters not of direct
expt
theoretical interest: the speaker optimality parameters αi ,which can vary across the two tasks. The pragmatic listener
L1 model (Eq. 4) has one speaker optimality: α11 . The pragmatic speaker S2 model (Eq. 7) has two speaker optimality
parameters: {α21 , α22 }. We use priors consistent with the previous literature: α1 ∼ Uniform(0, 20), α2 ∼ Uniform(0, 5)
We implemented the RSA and Bayesian data analysis
models in the probabilistic programming language WebPPL(Goodman & Stuhlmuller, 2014). To learn about the credible
values of the parameters, we collecting 2 chains of 50k iterations (after 25k burn-in) using an incrementalized version of
MCMC (Ritchie, Stuhlmuller, & Goodman, 2016).
Results The full model’s posterior over the RSA and dataanalytic parameters were consistent with prior literature andintuition. The maximum a-posteriori (MAP) estimate and95% highest probability density (HPD) intervals for model
parameters specific to the L1 model used for Expt. 1 were
α11 = 1.6[1.1, 2.5], β = 0.13[0.11, 0.19]. Model parametersspecific to the S2 model used for Expt. 2: α21 = 3.5[0.6, 13.2],
α22 = 3.2[2.6, 3.8]. The inferred distributions corresponding
to subordinate class priors were consistent with the a priori ordering of these subordinate classes (low, medium, high)used in these tasks (Figure 2 middle).
Finally, the full model’s posterior predictive distribution
does an excellent job at capturing the quantitative variability in responses for Expt. 1: r2 (30) = 0.965, and Expt. 2:
r2 (30) = 0.985 (Figure 3). Because of the overall preference
for the subordinate comparison class, many of the data points
are distributed above 0.5. Even for these fine-grained differences, the model does a good job at explaining the quantitative variability in participants’ data (Figure 3 right).

Discussion
The words we say are often too vague to have a single, precise
meaning and only make sense in context. Context, however,can also be underspecified, as there are many possible dimensions or categories that a speaker might be implicitly referringto or comparing against. Here, we investigate the flexibility inthe class against which an entity can be implicitly compared.
We introduced a minimal extension to an adjective interpretation Rational Speech Act model to allow it to flexibly
reason about the comparison class. This model made twonovel predictions about how listeners should prioritize oneclass over another. It also made quantitative predictions about
how background knowledge about the degree scale should inform this inference in a graded fashion. Both qualitative predictions of the model were borne out in our first experiment,
and the quantitative predictions were confirmed using a novel
data analytic technique. To our knowledge, this is the first experiment to demonstrate how reference classes for adjective
interpretation can adjust based on world knowledge.
We observe in our modeling results for Expt. 1 that a uniform prior distribution over the experimentally supplied comparison class alternatives is unlikely (Figure 2 bottom). For
example, the comparison class of “people” for heights of individuals is relatively more salient than the class of “produce”
for the weights of fruits and vegetables. We used the frequency of the class in a corpus as a proxy for their prior probability P(c), which was sufficient to account for differences
in baseline class probability both between- and within-scales.
Corpus frequency is a composite measurement of factors
relevant for speech production. Its utility in this model suggests that utterances without an explicit comparison class(e.g., “It’s warm outside”) may in fact be incomplete sentences, in a way analogous to sentence fragments studied
in noisy-channel models of production and comprehension(Bergen & Goodman, 2015). Another (non-mutually exclusive) possibility is that the comparison class prior reflects
basic-level effects in categorization (Rosch & Mervis, 1975).
Future work should attempt to understand these factors toconstruct a more complete theory of the comparison classprior.
The second contribution of this paper is a novel dataanalytic approach, where prior knowledge used in theBayesian language model is reconstructed from converging
evidence gathered from related language experiments. In previous work, we have attempted to measure prior knowledge
by decomposing what would be a single, implicitly multilayered, numerical estimation question into multiple simpler
questions. Then, we construct a Bayesian data analytic model
to back out the prior knowledge (Tessler & Goodman, 2016a,
2016b). We extend this approach by using the same core RSA
model to model behavior across two language experiments.
The major feature of this method is that participants respond
only to simple, natural language questions rather than estimating numerical quantities for which complicated linking
functions must be designed (e.g., Franke et al., 2016). The

fully Bayesian language approach we pioneer here also provides a further constraint on the language model, which must
predict data from two similar but distinct language experiments. The productivity of natural language can thus be harnessed to productively design experiments that further constrain and test computational models of language and cognition.

Acknowledgements
The authors would like to thank Ali Horowitz for help in stimuli design. This work was supported in part by NSF Graduate Research Fellowship DGE-114747 to MHT, a Stanford
CSLI Summer Internship for MLB, and a Sloan Research Fellowship, ONR grant N00014-13-1-0788, and DARPA grantFA8750-14-2-0009 to NDG.

References
Bale, A. C. (2011). Scales and comparison classes. Natural Language Semantics, 19(2), 169–190.
Barner, D., & Snedeker, J. (2008). Compositionality and statistics inadjective acquisition: 4-year-olds interpret tall and short based on
the size distributions of novel noun referents. Child Development,
79(3), 594–608.
Bergen, L., & Goodman, N. D. (2015). The strategic use of noise inpragmatic reasoning. Topics in Cognitive Science, 7(2), 336–350.
Franke, M., Dablander, F., Scholler, A., Bennett, E., Degen, J.,
Tessler, M. H., . . . Goodman, N. D. (2016). What does the crowd
believe ? A hierarchical approach to estimating subjective beliefs
from empirical data. In Proceedings of the 38th annual meetingof the cognitive science society.
Goodman, N. D., & Frank, M. C. (2016). Pragmatic language interpretation as probabilistic inference. Trends in Cognitive Sciences,20(11), 818–829.
Goodman, N. D., & Stuhlmuller, A. (2014). The Design and Implementation of Probabilistic Programming Languages. http://dippl.org.
Lassiter, D., & Goodman, N. D. (2013). Context, scale structure,and statistics in the interpretation of positive-form adjectives. In
Semantics and linguistic theory (Vol. 23, pp. 587–610).
Qing, C., & Franke, M. (2014a). Gradable adjectives, vagueness,and optimal language use: A speaker-oriented model. In Semantics and linguistic theory (Vol. 24, pp. 23–41).
Qing, C., & Franke, M. (2014b). Meaning and Use of Gradable Adjectives: Formal Modeling Meets Empirical Data. In Proceedingsof the 36th annual conference of the cognitive science society.
Ritchie, D., Stuhlmuller, A., & Goodman, N. D. (2016). C3:
Lightweight incrementalized mcmc for probabilistic programs using continuations and callsite caching. In AISTATS 2016.
Rosch, E., & Mervis, C. B. (1975). Family resemblances: Studies
in the internal structure of categories. Cognitive Psychology, 7(4),573–605.
Schmidt, L. A., Goodman, N. D., Barner, D., & Tenenbaum, J. B.
(2009). How Tall Is Tall? Compositionality, Statistics, and Gradable Adjectives. In Proceedings of the 31st annual conference ofthe cognitive science society.
Scholler, A., & Franke, M. (2015). Semantic values as latent parameters: Surprising few & many. In Semantics and linguistic theory(Vol. 25, pp. 143–162).
Solt, S. (2009). Notes on the Comparison Class. In International
workshop on vagueness in communication.
Solt, S., & Gotzner, N. (2012). Experimenting with degree. In
Semantics and linguistic theory (Vol. 22, pp. 166–187).
Tessler, M. H., & Goodman, N. D. (2016a). A pragmatic theory ofgeneric language. ArXiv Preprint ArXiv:1608.02926.
Tessler, M. H., & Goodman, N. D. (2016b). Communicating generalizations about events. In Proceedings of the 38th annual meeting of the cognitive science society.