Pragmatic language interpretation as probabilistic
inference
Noah D. Goodmana,∗, Michael C. Frankaa Department of Psychology, Stanford University, 450 Serra Mall, Stanford, CA 94305

Abstract
Understanding language is more than the use of fixed conventions and more than
decoding combinatorial structure. Instead, comprehenders make exquisitely
sensitive inferences about what utterances mean given their knowledge of the
speaker, the language, and the context. Building on developments in gametheory and probabilistic modeling, we describe the rational speech act (RSA)
framework for pragmatic reasoning. RSA models provide a principled way toformalize inferences about meaning in context; they have been used to makesuccessful quantitative predictions about human behavior in a wide variety ofdifferent tasks and situations, and they explain why complex phenomena like
hyperbole and vagueness occur. More generally, they provide a computationalframework for integrating linguistic structure, world knowledge, and context inpragmatic language understanding.

... one of my avowed aims is tosee talking as a special case orvariety of purposive, indeed
rational, behavior ...
Grice (1975), p. 47

1. Understanding language
Language is central to the successes of our species; with language we can coordinate our actions, learn from each other, and convey our innermost thoughts.
From sounds to syntax, natural languages provide structured methods of combining discrete materials to generate an infinite variety of sentences. Yet this
∗ Corresponding author, please send correspondence to ngoodman@stanford.edu.

Manuscript submitted to Elsevier

August 8, 2016

discrete combinatorics does not fully explain how speakers can use language so
flexibly to achieve social goals. The interpretation of a particular utterance canitself be almost infinitely variable, depending on factors such as the identity ofthe speaker, the physical context of its use, and the previous discourse. While
the systematization of structural features of language is one of the proudest
accomplishments of cognitive science [e.g., 15, 40, 30], its contextual flexibility– its pragmatics – has been stubbornly difficult to formalize.
Grice [34] presented an initial framework theory for pragmatic reasoning, positing that speakers are taken to be cooperative, choosing their utterances to convey particular meanings. Gricean listeners then attempt to infer the speaker’s
intended communicative goal, working backwards from the form of the utterance. This goal inference framework for communication has been immensely
influential [e.g., 37, 71, 17, 53]. But attempts to build on these ideas by providing a specific set of formal principles that allow the derivation of pragmatic
inferences have met with difficulty.
For example, the core of Grice’s proposal was a set of conversational maxims(see Glossary). Inferences about speakers’ behavior relative to these maxims (betruthful, relevant, informative, and perspicuous) could lead to implicatures –inferences about their intended meaning. Formalization of the Gricean notionof implicature using the maxims is difficult, however, and many post-Gricean
theories have instead proposed alternative sets of principles [71, 53]. An important test of the difficulty of this theoretical project is that the burgeoning
experimental psycholinguistic literature attempting to measure pragmatic inference has found these principles only modestly useful [11, 39, 60]. In addition,
this sort of informal theory of pragmatics can make only directional, qualitative predictions with respect to experimental data that are typically graded andquantitative.
An alternative strand of Gricean thought has had more success in making contact with data. Grice’s core insight was that language use is a form of rational
action; thus, technical tools for reasoning about rational action should elucidate
linguistic phenomena. Such a goal-directed view of language production has
led to the development of engineering systems for natural language generation[18] that have in turn been applied as theories of human language production[e.g., 75]. Concurrently, the tools of game-theory – which allow for the characterization of rational actions with respect to defined utilities – have provided a
vocabulary for formal descriptions of pragmatic phenomena [e.g., 6, 41]. The
recent work we focus on here builds on these developments, combining themwith a more detailed view of cognition that arises from the Bayesian cognitivemodeling tradition.
Probabilistic, or Bayesian, models have been at the core of a set of recent attempts to understanding the interplay between structured representations andgraded or statistical information [74]. These models have been an important
tool for understanding non-linguistic varieties of rational action, integrating belief understanding with action planning [2]. A critical feature of these models
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is that they use the probability calculus to describe inferences under uncertainty. Within formal models of pragmatics, this uncertainty stems from avariety of sources, including uncertainty about speakers’ goals and beliefs, uncertainty about the discourse and broader context, and even uncertainty about
the meanings of words.
In the remainder of this paper we describe the probabilistic approach to pragmatics. We begin by presenting the rational speech act (RSA) model, andthe growing body of empirical data supporting its utility in explaining pragmatic reasoning. We next discuss extensions to RSA that allow it to be applied
to non-literal uses of language like hyperbole, irony and metaphor, to cases ofvagueness and ambiguity, and to complex interactions between pragmatics andcompositional syntax/semantics. We close by considering the broader applications of – and challenges for – probabilistic pragmatics models.

2. A “rational speech act” model
The “rational speech act” (RSA) model implements a social cognition approach
to utterance understanding. At its core, it captures the idea (due to Grice,David Lewis, and others) that speakers are assumed to produce utterances tobe helpful yet parsimonious, relative to some particular topic or goal. Listeners
then understand utterances by inferring what such a helpful speaker must havemeant, given what she said.1 The first of these basic assumptions is formalizedby viewing the speaker as a utility-maximizing agent (where the effort of language production is costly, but communicating information is beneficial). The
listener then updates his beliefs via Bayesian inference.
The pragmatic listener infers the state of the world, w, using Bayes’ rule, given
the observation that the speaker chose a particular utterance, u:
PL (w | u) ∝ PS (u | w)P (w)The key assumption he must make is that the speaker is approximately rational,
that is, that she has chosen her utterances in proportion to the utility she expects
to gain.
PS (u | w) ∝ exp(αU (u; w))
The speaker chooses u from a set of alternative utterances (see Outstanding
Questions). The parameter α captures the extent to which the speaker maximizes her utility – how rational she will be. The basic speaker utility used in
RSA captures the social benefit of providing epistemic help to a listener:
1 For clarity throughout, we use a female pronoun for Alice, the speaker, and a male pronoun
for Bob, the listener.

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U (u; w) = log PLit (w | u)This expression measures how certain the listener becomes about the intended
world, after hearing the utterance; in order to avoid an infinite recursion andprovide an entry point for conventional (semantic) meaning, the speaker is assumed to consider a simpler listener, the literal listener PLit . The literal listener
again updates his beliefs in accord with Bayesian inference, under the assumption that the literal meaning of the utterance is true:
PLit (w | u) ∝ δ [[u]](w) P (w)This definition of the literal listener requires a semantic denotation for eachsentence, [[u]], in which a sentence has the value true or false when applied to aparticular state of affairs, w (the “world”). This denotation is how conventional
meaning enters the pragmatic reasoning process, and, as we describe briefly
below, it connects RSA to work in lexical and compositional semantics [36, 22].
Consider the scenario in Figure 1, in which speaker and listener share a worldof three faces – one with hat and glasses (hg), one with glasses only (g), andone with neither (n); one of these (known to the speaker but not the listener)
is the “friend.” The speaker says “my friend has glasses,” presupposing that
there is a single friend. Experimental participants, who know that the only
alternative utterance was “my friend has a hat,” tend to share the intuition that
this sentence refers to g and not hg or n [72, 73]. While real-world language
has many more utterances available (e.g., “my friend has glasses, but no hat”),
this restricted scenario serves to illustrate the underlying dynamics of pragmatic
reasoning.
Under RSA, listener L reasons about S (a simplified internal representationof the speaker), who in turn reasons about Lit (a yet more simplified internal model of the listener). Lit updates his beliefs based on a straightforward
denotation: “glasses” applies to both g and hg, while “hat” applies only to
hg. Thus PLit (w | “hat”) places all probability on the friend being hg, while
PLit (w | “glasses”) places equal probability on g and hg (see innermost thought
bubbles in Figure 1). The speaker S who intends to communicate that hg is
the friend will thus tend to choose the more informative “hat”; but if she intends to communicate that g is the friend, she will use “glasses.” Finally, uponhearing “glasses,” the listener L infers that this likely refers to g (reflecting thecounterfactual that if S had been talking about hg, she would have said “hat”
instead).
In the simplest RSA model, as illustrated above, the speaker values providing
epistemic help – information – to the listener. But the model can also be extended to create a more sophisticated speaker who is uncertain about the worldstate, who avoids costly utterances, or who aims to provide relevant information.

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Figure 1: Application of RSA-style reasoning to a signaling game (shown by the three faces
along the bottom). Agents are depicted as reasoning recursively about one another’s beliefs:
listener L reasons about an internal representation of a speaker S, who in turn is modeled asreasoning about a simplified literal listener, Lit. Boxes around targets in the reference gamedenote interpretations available to a particular agent.

Connections to other theoretical approaches and aspects of language then become straightforward. For instance, by modifying the speaker’s utility function,
we can model the notion of topic-relevant information, which connects to linguistic ideas about the “question under discussion” [68]. As a second example,
RSA can be combined with the noisy channel approach to language comprehension [54], in order to explain the communicative use of sentence fragments andprosodic stress [7].
In sum, RSA models replace Grice’s maxims with a single, utility-theoretic
version of the cooperative principle [27]. This formulation is based on utilities
that can reflect the communicative and social priorities of a complex, real-worldagent.

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3. Empirical support for RSA
The example shown above in Figure 1 is an instance of a signaling game of
the type initially introduced by Lewis [55]. Such games are a valuable toolfor exploring pragmatic inferences in context, and experiments testing the RSA
framework have used games of this type to make quantitative measurements ofa variety of different inferences. For example, one study [24] used a one-shot,
web-based paradigm to present participants with geometric shapes in a variety
of different configurations. Using a betting paradigm (participants were asked
to distribute $100 between response options), these experiments collected separate judgments about what a speaker would say, a listener would interpret, andabout baseline expectations for reference (corresponding to the prior P (w)).
The RSA model showed a tight fit to listeners’ aggregate judgments when combined with empirical measurements of the prior distribution: PS and PL models
correlated very strongly with participants’ average bets on what to say and how
to interpret, respectively.
Although in this initial work RSA was used to simulate the behavior of bothspeakers and listeners, most subsequent work has focused on the behavior of
listeners alone. This work follows the idea that RSA captures listeners’ (perhaps
optimistic) assumptions about the rational behavior of speakers. Thus, RSA is‘rational’ in the sense of assuming that speakers are rational; a separate questionis how rational speakers actually are (see Box 11). In addition, though mostresearch using RSA models has focused on mature language comprehenders,these models have also been the inspiration for a variety of developmental work(see Box 10).
A variety of other work has replicated and extended the initial findings using
similar signaling-game paradigms. A tight replication of the initial results [66]reproduced the basic findings and explored a set of variants to the initial RSA
utility function. Other studies [13] found that RSA predicted judgments in acommunication game using much more complex spatial language stimuli, albeit
with somewhat noisier fits. Thus, RSA with an epistemic utility can predict
judgments in simple signaling games across variations in both participant sample
and stimulus.
One question raised by this initial work was the level of social recursion(see Glossary) that best fit human performance. The presentation of RSA given
above is stated in terms of a minimal recursion (a listener reasons about speaker,
who in turn reasons about a literal listener) but much greater depths of reasoning are in principle possible. The evidence is mixed on whether deeper levels ofrecursion are commonly seen in language comprehension. In a variety of experiments exploring this issue, participants tended to show chance-level performancefor signaling systems that required deeper levels of recursion to find unique interpretations [72, 19, 77]. More recent studies [26], however, showed some evidence
of deeper recursion for a subpopulation of participants (approx. 15%) in a more
complex paradigm, consistent with work on competitive economic games where
6deeper recursions are sometimes found [12]. This heterogeneity – and its dependence on individual and contextual differences – is an interesting topic for
future work.
A number of other studies have tested RSA with more elaborated utility functions (see Box on Refinements to the speakers utility). For instance, a
speaker might be expected to produce a less informative utterance when the
more informative one is much harder to say. This tendency can be formalized
by including a cost term in the speaker’s utility; with this modification, RSA
predicts the impact of production costs on interpretations of the listener. Work
exploring this extension [8] showed that participants in a reference game areindeed sensitive to the cost of message choices: the effect of alternative possible messages on a listener’s inferences is modulated by their cost, in dollars.
Related studies [20] tested the effect of production difficulty by manipulating
how quickly the speaker could type on an on-screen keyboard; participants’ interpretations reflected this difficulty as predicted. Additional work has used
proxies for production cost such as number of words and their frequencies in
explorations of phenomena such as negation [58] and the choice of noun used torefer to an object [33].
Finally, in addition to ad-hoc signaling systems, RSA provides a way to describe reasoning about classic linguistic implicatures. Perhaps the best-studiedof these is the scalar implicature that “some of the letters had checks inside”
implicates that not all did. One study [32] measured participants’ judgments
about the interpretations of quantifiers and number words in exactly this situation and found that these judgments were well-predicted by RSA. In addition,a critical feature of this study was the inclusion of an epistemic manipulation(e.g., whether all of the letters had already been opened). By using expected
informativity (see Box) to account for the speaker’s limited perceptual access,the model was able to predict differing patterns of listener judgments based on
different levels of speaker uncertainty. These empirical findings are congruent
with other recent demonstrations of the importance of epistemic reasoning inpragmatic implicature [8, 10], and the theoretical account accords with otherprobabilistic treatments of scalar implicature [69]. They also highlight the way
the RSA framework provides a (non-modular) theory for interactions between
language and non-linguistic cognition. We next turn to a variety of other extensions to the basic RSA model that explore additional interactions.

4. Uncertainty about the speaker: Joint reasoning
In the basic RSA model, the listener has a specific model in mind of how aspeaker will behave. But what should a listener do if he is not sure what
speaker model is appropriate? Speakers can differ in knowledge, communicative
goals, and many other aspects; these differences can lead a listener to arrive at
different interpretations of the same utterance. Recent work has addressed thisissue by positing a joint inference: What type of speaker am I interacting with7

and what is the world like, given the utterance I heard? Formally this uncertain
RSA (or uRSA) framework requires only a small change:
PL (w, s | u) ∝ PS (u | w, s)P (s)P (w)where the new variable s parametrizes different speaker types. In practice, s
can refer to any factor that might influence the speaker’s behavior, including
uncertainty about conversational topic, word meanings, background knowledge,or general discourse context. This modification allows uRSA to capture a muchwider variety of linguistic phenomena; intuitively, an uRSA listener is a more realistic cognitive agent than the RSA listener, who was restricted to the specifics
of a very particular context and goal. To illustrate this intuition, we provide
three examples of phenomena captured by uRSA (but not by basic RSA): nonliteral language, vagueness, and embedded implicatures.
Non-literal or figurative language – utterances that are easily interpreted but
not “actually true” – poses a problem for nearly all formal models of language
understanding. How can tropes like hyperbole, sarcasm, and metaphor be interpreted, and why are they used? Under uRSA, these uses can be described
as arising from uncertainty about the topic of conversation. If the speaker is
expected to provide information relevant for a particular topic, the pragmatic
listener will only update his beliefs along this topical dimension. Within uRSA,
the interaction between uncertainty about the speaker’s intended topic and her
intended meaning about that topic can drive complex interpretations.
Hyperbolic utterances such as “the electric kettle cost $1,000” are a key casestudy [45]. In this example, the number $1,000 can be interpreted as conveying
information about the speaker’s affect, not the actual price, in part because one
thousand dollars is an implausibly high price for a kettle. As shown in Figure
2, the uRSA model captures this intuition by positing that the topic of the
speaker’s utterance may be the actual price of the kettle, the speaker’s opinion
about the price, or some combination of the two. Since the listener does notknow the topic, he jointly infers it together with the likely true price of the kettle
and the speaker’s affect. When the uttered price is implausible it becomes more
likely that the speaker is aiming to convey her opinion, and using $1,000 (a pricewhich most people would find too high) to do so. In this way, the listener’s joint
inference can yield a non-standard topic and hence a non-literal interpretation.
By extending the space of affect to include both valence and arousal, the samemodel predicts verbal irony [44]. And a similar approach has been suggested
for simple metaphors [43], such as “John is a shark.” Here the potential topics
include not affect, but features of the target, such as how vicious John is and how
likely he is to swim underwater. In each of these cases of figurative language,
the uRSA model accounts for almost all of the explainable variance in humaninterpretations, a striking result considering the complexity and subtlety of these
phenomena.

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Figure 2: Uncertain RSA-style reasoning applied to hyperbole. Listener L reasons jointly
about the price of the item and the speaker’s affect. In doing so he considers two speakers,
one who is primarily interested in conveying her affective response to the kettle, and one who
is primarily interested in conveying the actual price. (The full model also considers speakers,
not pictured, that wish to convey approximate price and combinations of these goals.) Eachof these speakers is modeled as reasoning about a literal listener who interprets the utterance
literally (indicated by the box selecting the “$1000” state), but focus on different aspects ofthe situation (price on the left and affect on the right).

Many linguistic descriptions, especially adjectives, are both context-sensitiveand vague. Providing precise definitions for words like expensive or tall has
been a persistent challenge for philosophers and semanticists [79]. uRSA models address this challenge by assuming that word meanings can differ between
speakers and contexts, and and that these meanings themselves can be a subject for inference. In the case of scalar adjectives like tall, the uncertainty isover the threshold required: what height is required before an object counts as
tall? Under the uRSA model, judgments about meaning take into account two
conflicting pressures: On one hand, a stricter threshold for tallness makes theterm tall more informative. For instance “Bob is tall” tells us a great deal if
tall requires a height greater than eight feet. But, on the other hand, a stricter
threshold makes such a sentence quite unlikely to be true a priori. By negotiating this balance between informativity and plausibility, uRSA accounts forthree key phenomena of vague adjectives [51]: the inferred meaning depends on9the class (tall for a tree vs. tall for a person), there are borderline cases, and theinterpretations are subject to a sorites paradox (no single minimal increment inheight will make you tall, but enough increments will). The process of reasoning
about meaning that are modeled by uRSA might even interact with learning
processes to produce more long-lasting inferences about word meaning, leading
to language change (see Box on Language use and language change).
Finally, this uRSA approach allows for progress on an important puzzle in recent discussions of pragmatic inference: embedded implicature [29, 14]. Embedded implicatures occur when quantifiers are nested within one another, as
in sentences like “Exactly one letter is connected with some of its circles.” Inthese cases, some experimental evidence suggests that participants access theinterpretation that one letter is connected with some but not all of its circles, aninterpretation that standard Gricean theories cannot generate [14]. Recent work[65] has replicated these interpretations in a series of large-scale experiments andconfirmed that basic RSA models could not capture them. An implementationof uRSA that jointly infers word meanings and world state [9, 65] showed a good
fit to the overall pattern of data. Sentence meanings in this model are built bycomposing uncertain word meanings, showing how uRSA is a fruitful way toincorporate pragmatic reasoning into compositional semantic systems.
5. Concluding remarks and future directions
Context-dependence is one of the core features of natural language. Yet becauseof the informal nature of theorizing about this context-dependence, pragmatics
has often been treated as a theoretical “wastebasket,” in which unexplained
phenomena are hidden [3]. Countering this trend, new formal theories of pragmatics make quantitative predictions about a wide variety of phenomena thathave previously been considered too difficult to operationalize. These include
implicature, vagueness, non-literal language, and the myriad other cases where
linguistic meaning is changed by context.
The key tool in this work is the Rational Speech Act framework, which builds
upon and synthesizes a number of formal traditions in the study of human inference, from game theory to models of human reasoning. The RSA approachalso builds on existing work on semantic representation – using a compositionalsemantics a la Montague [22] – and contributes back to semantics, providing a
specific mechanism by which underspecified meanings become precise, in context. Rather than formalizing only a single hypothesis about pragmatic language understanding, RSA provides a framework in which many variations canbe explored. Varying assumptions about the speaker’s utility (see Box: Refinements to the speaker’s utility) and listener’s uncertainty (see Section4), for instance, yields a spectrum of hypotheses that can be evaluated against
quantitative experimental data.
While it has been successful in many recent cases, it may emerge that the
RSA approach is not able to capture some aspects of language understanding,10either because the foundational, Bayesian, tools it relies on are inadequate [42],or because pragmatic effects arise from sources not easily incorporated into
RSA. Optimistically, however, RSA can be combined with other approaches
when needed. For instance, the alternative utterances in RSA can be restricted[65] using previously-proposed grammatical mechanisms [23]. And increasingly,
methods in machine learning have been used to supplement RSA with powerfullearning mechanisms [57]. Indeed, this cross-fertilization is among the mostencouraging outcomes of work on RSA.
The RSA framework is a computational level description of the language user’scompetence, in Marr’s sense [56]. There are many possible ways a cognitive
agent could implement RSA at the algorithmic level, and it is unclear whichmight match the speed and competence of human language understanding andproduction. These alternatives must further be evaluated for their ability to
explain the processing signatures of language comprehension such as reaction
times and eye gaze [21, 58]. Yet even as a computational-level framework, RSA
inspires different intuitions about processing than previous theories. For example, RSA-style reasoning makes pragmatic inferences a fundamental part oflanguage comprehension, in which the ultimate goal of all interpretation is tosettle on the intended meaning, given both the literal semantics of the utterance and the broader pragmatic context. This framing contrasts with Gricean
analyses, in which pragmatics enters when the violation of a maxim leads toreasoning to “repair” the interpretation, and correspondingly slower processing,a view that has been challenged both theoretically and empirically [e.g., 53, 35].
Future extensions of RSA will likely include worlds with more and richer structure; a thorough and practical theory of pragmatic alternatives; more sophisticated discourses that unfold over many utterances; and utility structures that
better take into account the complexities of social interaction. On the practicalside, computing the predictions of RSA models can become prohibitive when
the number of world states or utterances grows large. Further development ofalgorithms to implement RSA is needed. These developments may go together
with new algorithms for learning aspects of the underlying semantics, which will
open up new applications for the RSA approach in computational linguistics andartificial intelligence [31, 76, 57, 1, 61].
The work outlined in this review represents steps towards a comprehensive,
formal theory of language understanding in context. Although much further
work will be required, RSA models and their uRSA extensions have proven to
be useful tools for explaining both qualitative and quantitative empirical data
across a wide range of tasks and contexts. Language is central to the humanexperience. We hope our work sheds light on how its structure and systematicity
can still give rise to such an astonishingly flexible communication system.

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6. Acknowledgements
We gratefully acknowledge funding from a James S. McDonnell Foundation
Scholar Award to Goodman, ONR Grants N00014-13-1-0788 and N00014-13-10287 to Goodman and Frank, and NSF BCS Grant 1456077 to Frank.

7. Trends• Rational speech act (RSA) models provide a quantitative framework to
capture intuitions about pragmatic reasoning in language understanding.
• Extensions to RSA that allow for reasoning about the speaker – for instance, her goals and word usage – can capture many otherwise puzzling
phenomena including vagueness, embedded implicatures, hyperbole, irony,and metaphor.
• The RSA framework can inform psycholinguistic processing experiments,
linguistic theory, and scalable natural language processing models.

8. Box: Outstanding questions• Social recursion. How deeply do human comprehenders reason about others’ intentions? Is depth of recursion – “I think that you think that...” –constant, or does it vary across situations?
• Alternatives. How are alternative utterances computed? Do they dependon the language grammar? On situational factors?
• Linguistic goals. How do “Gricean” utilities – the drive to be informative
yet succinct – relate to other social goals like conveying affect, or establishing relationships? How do cooperative and competitive goals mix inlanguage use?
• Dialogue. How can RSA be used to model the evolution over the courseof a conversation of a partners’ utilities, possible goals, and the context
more broadly?
• Learning and language change. How do pragmatic language understanding
and language learning interact? How and when does pragmatic language
use lead to language change?
• Algorithmic challenges. Given the potential complexity of recursive pragmatic computations, how is language processed so quickly? How can RSA
models be “scaled up” for natural language processing tasks?

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9. Box: Refinements to the speaker’s utility
The notion of the speaker’s utility – what is rewarding for a speaker – is central
to the RSA approach. The basic RSA model captures the speaker’s need to be
informative to a listener: U (u; w) = log PLit (w | u). Different utilities lead todifferent kinds of speakers, which in turn lead to different interpretations by thepragmatic listener. Several utility refinements (and their combinations) havebeen considered in recent work:• Utterance cost: In order to capture a tendency of speakers to be parsimonious we can simply add a cost term: U (u; w) = log PLit (w | u) + cost(u).
The cost may reflect actual production cost (such as number of words)
or proxies such as word frequency. This extension yields effects similar to
Grice’s maxim of manner [9].
• Speaker uncertainty: When the speaker does not have full knowledge of
the world she should choose an utterance according to expected utility:
U (u; k) = EP (w|k) [U (u; w)], where k summarizes the speaker’s knowledge
or observations. This extension correctly predicts interactions between aspeaker’s knowledge and a listener’s interpretations [32].
• Topic relevance: Although it may be highly informative to provide detailed
descriptions, such detail is not always relevant. Relevance can be captured
by introducing a topic of conversation [sometimes known as a Question
Under Discussion, 68] and adjusting the epistemic
P utility to reflect only
information about this topic: U (u; w, t) = log w0 s.t. t(w0 )=t(w) PLit (w0 |u). Here the topic is encoded in a function t that takes a complete worldand yields some subset or summary; for instance, in the case of hyperbole[45], t can pick out only the speaker’s affect, dropping objective states.
• Other social goals: Language is often used not just to inform, but also to
flirt, insult, comfort, and to pursue myriad other social goals. For example, non-informational utilities, e.g. utility directed towards kindness, canproduce behaviors that appear polite [81].

10. Box: RSA and children’s developing pragmatic competence
From a very early age, children are oriented towards communication, understanding the function of language for information transfer and repurposing theirlimited linguistic means to achieve a wide variety of ends [78, 16]. In light of thisgeneral early orientation, the literature on pragmatic development specificallyhas been puzzling: older children very reliably fail to make scalar implicatures
under a range of circumstances [59]. In one striking example, five-year-oldsendorsed the statement that “some of the horses jumped over the fence” evenwhen three out of three of a set of horses had made the jump [62]. RSA-style13

models can provide a framework for thinking about this disconnect between
early communicative successes and later pragmatic failures.
Recently, theorists have proposed that children’s apparent difficulties with pragmatic implicatures may have resulted from their inadequate knowledge of relationships between lexical alternatives rather than difficulty with pragmaticcomputations more generally [4]. Congruent with this idea, three-year-old children show signs of successful implicature computations in the kinds of signalinggames shown in Figure 1, where the referential alternatives are all simple objects that are visible in the scene [73]. And children in the same age range wereable to use an implicature to guess the meaning of a novel word [25] or a novel
context [38], showing the kind of inferential flexibility posited in RSA accounts.
These findings support the idea that even young children are able to make flexible pragmatic inferences, and are consistent with the application of RSA-stylereasoning, albeit with limits on the available semantic alternatives. Future research will be required, however, to test whether RSA (or some capacity-limited
modification) could make quantitative predictions about pragmatic development.

11. Box: Producing referring expressions
RSA stands for the “rational speech act” model, indicating that listeners idealize
speakers as rational. Are speakers in fact rational in a meaningful way? And
if so, how can this conclusion be integrated with the large body of evidence
indicating that speakers are egocentric, error prone, and subject to idiosyncratic
production preferences [47, 50, 28]?
Although our initial studies collected judgments about language production in
extremely restricted tasks [24], most recent work using the RSA model has focused on modeling listeners’ judgments, rather than speakers’ productions. One
reason for this choice is that often the most interesting pragmatic inferences
come about when speakers are not maximally informative. For example, in thesignaling game shown in Figure 1, helpful speakers will often overspecify andsay “glasses and no hat” [5]. But this unnecessarily redundant utterance may
in fact be a reasonable response to uncertainty about whether a conversational
partner will in fact draw the desired implicature. More generally, speakers’ production choices are a promising area for future research using RSA models witha broader range of utility functions (see Box) and various sources of potential
miscommunication (a topic of ongoing research).
Nevertheless, it is clear that in their natural behavior, speakers make production
decisions under time pressure and a variety of cognitive demands [52]. Integrating these demands with the predictions of utility-theoretic models should be an
important challenge for future work.

1412. Box: Language use and language change
The pragmatic processes described by RSA models occur in the moment ofcommunication, but can have a set of effects that ripple out through language
as a whole. The construal of an individual communication event can influencelearning processes, which in turn can lead to systematic changes in word meanings [70]. Words that are too narrow in their denotation can be pragmaticallyextended [45], while words that are too broad can be narrowed via implicature.
Over time, word meanings may converge to the appropriate level of ambiguity
to enable efficient communication [64]. In this sense, in-the-moment pragmaticinterpretation may bootstrap long term language change.
The processes of change that promote efficient communication have been explored extensively within the iterated learning paradigm [48]. This framework
can also be used to express the competing pressures of learnability and communication. When languages are selected only to be learnable, they often become
degenerate, including only a single word [63]. But when they include a countervailing pragmatic pressure, which can be modeled via RSA, expressive andcompositional languages can emerge [49].
If pressures for efficient communication lead to language change, then thesepressures should be visible in the lexicons of human languages. Indeed, a recent body of evidence suggests that the typological distribution of languages inparticular semantic domains reflects the range of optimal communication systems [e.g., 67, 46, 80]. An important future direction is to understand whether
this typological distribution is predicted to arise from iterated learning with apopulation of RSA-like language users.

13. Glossary• Rational speech act model (RSA). A class of probabilistic model thatassumes that language comprehension in context arises via a process ofrecursive reasoning about what speakers would have said, given a set ofcommunicative goals.
• Uncertain RSA models (uRSA). A specific extension of RSA models
that allow for joint inferences about both the speaker’s intended meaningand other aspects of the interaction, such as the topic, the context, oreven the meanings of particular words.
• Implicature. An inference about the meaning of an utterance in context that goes beyond its literal semantics. Implicatures are typicallycancellable in that they can be contradicted, as in “Some of the students
passed the exam; indeed, all of them did.”15

• Scalar implicature. An implicature that arises when a speaker didn’t
use a stronger alternative term, leading to narrowing of the interpretation.
For instance, hearing “some” usually leads to a scalar implicature that“not all.”• Conversational maxims. A set of principles described by Grice [34]as a theory of how listeners reason about speakers’ intended meaning toarrive at pragmatic implicatures.
• Social recursion. Reasoning that involves two people, such as listenerand speaker, thinking about each other: “I think that you think that I
think that....” This may proceed to a finite depth, or continue ad infinitum.

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