Use-conditional meaning in Rational Speech Act models1
Ciyang QING — Stanford University
Reuben COHN-GORDON — Stanford University

Abstract. Motivated by shortcomings in the modeling of repeated utterances in Burnett’s Rational Speech Act (RSA) model of social meaning, we propose an alternative analysis in terms
of use-conditional meaning, which we implement in an extended RSA framework. We showthat it can not only model the production of a sequence of utterances throughout a discourse,
but also captures the similarities between social and expressive meaning.
Keywords: social meaning, use-conditional meaning, Rational Speech Act models.
1. Introduction
Since Labov (1963), variationist sociolinguistics has studied the subtle meaning differences
between linguistic variants (see Eckert, 2012 for an overview).
(1)

a.
b.

I am walking (velar -ing variant)
I am walkin’ (apical -in’ variant)For example, (1a) and (1b) have the same truth conditions, but after hearing them, listeners
tend to infer different properties of the speaker: (1a) is associated with education, intelligence,
articulateness (clustered as competent), and formality and distance (clustered as aloof) whereas(1b) is associated with the opposite properties (Campbell-Kibler, 2006, 2007, 2008, 2009). To
the extent that the inference patterns are different, we can say that the variants in (1) havedifferent social meanings. Moreover, people’s production of language is sensitive to such social
meanings and the context. For instance, Labov (2012) analyzes President Obama’s use of (ING)
in three recordings taken in three contexts with different levels of formality and finds 72% -in’at a barbecue, 33% at the press event that followed and 3% in his DNC acceptance speech.
These rich sociolinguistic phenomena have the potential to connect to semantics and pragmatics. Two fundamental research questions are (i) how to represent social meaning in thesemantics and (ii) how to integrate it into the pragmatics. Burnett (2017, 2019) pioneers theuse of Bayesian Rational Speech Act (RSA) models (Frank and Goodman, 2012; Goodman
and Frank, 2016) to address these questions. In this paper we explore the connections betweensocial meaning and semantics/pragmatics further. In particular, we address the following questions.
1. Empirically, what properties does social meaning have that resemble those studied in thesemantics/pragmatics literature?
2. Theoretically, how do we semantically represent social meaning to capture these properties and model people’s use of social meaning in production and comprehension?
The rest of the paper is organized as follows: in section 2, we list empirical properties thatsocial meaning shares with expressive meaning. In section 3, we review and assess Burnett’s
1 We would like to thank Heather Burnett, Judith Degen, Dan Lassiter, Chris Potts, Penny Eckert, the anonymous

reviewers and the participants of the SuB conference, for their very helpful comments and suggestions. All errors
are our own.
c 2019 Ciyang Qing and Reuben Cohn-Gordon. In: M.Teresa Espinal et al. (eds.)
Proceedings of Sinn und Bedeutung 23, vol. 2, pp. 253–265. Universitat Autònoma de Barcelona, Bellaterra (Cerdanyola del Vallès).

254

Ciyang Qing and Reuben Cohn-Gordon(2017, 2019) analysis of social meaning in the standard RSA framework, focusing on an issue
that it has in modeling the production of a sequence of utterances throughout a discourse. In
section 4, we propose an alternative analysis of social meaning in the spirit of Kaplan’s (1999)
use-conditional meaning, implement it in an extended RSA framework, and show that it can
not only model the production of a sequence of utterances throughout a discourse, but canalso capture the similarities between social and expressive meaning. We then discuss how thisenriched RSA framework can serve as a general paradigm for other use-conditional meanings
in section 5.
2. Social meaning and expressive meaning
Potts (2007) summarizes a list of empirical properties of expressive meanings (2).2(2)

Expressive meanings are• largely independent of the descriptive meanings• always about the utterance situation itself.

• not propositional and can be hard to pin down(Independence)(Nondisplaceability)(Descriptive ineffability)• performative in that the very act of utterance conveys the meaning• strengthened when repeated without redundancy(Immediacy)(Repeatability)

We note that social meaning also shares these properties. As a concrete example, consider thesocial meanings of the -in’ variant discussed in section 1.
(3)

John likes walkin’
The speaker is incompetent
The speaker is friendly

Let us check whether such social meanings also have the properties in (2):• Independence: The social meanings of (3), which are about its speaker, are indeed independent of its descriptive meaning (i.e., the proposition that John likes walking).
• Nondisplaceability: The social meanings of -in’ are about the speaker of the utterance,
and therefore about the utterance situation itself. For instance, the social meanings of (4)are about its speaker, even though the -in’ variant is embedded under past tense and said.
(4)

Mary said that John was walkin’.
The speaker is incompetent
The speaker is friendly• Descriptive ineffability: The social meaning of -in’ is hard to pin down. The propositionsin (3) are only approximations.
• Immediacy: Social meanings are performative. It is the very act of using the -in’ variant
that conveys its social meaning.

2 For simplicity, we do not discuss the property of perspective dependence in Potts’s list, but note that his treatmentof it can be similarly incorporated in our proposal.

Use-conditional meaning in Rational Speech Act models

255• Repeatability: the repeated use of the -in’ variant can strengthen its social meaning without redundancy. For instance, the inferences in (5) can be stronger than in (3).
(5)

John likes walkin’. Mary likes runnin’. Bob likes swimmin’.
The speaker is incompetent
The speaker is friendly

In sum, the empirical properties of expressive meanings in (2) are also shared by social meanings. These are properties that need to be accounted for by our analysis of social meaning.
3. Burnett’s (2017, 2019) analysis of social meaning in the standard RSA framework
3.1. The Rational Speech Act (RSA) framework
Burnett’s analysis is based on a Bayesian game-theoretic pragmatics framework, which provides a probabilistic formalization of Gricean reasoning (Frank and Goodman 2012; Goodman
and Frank 2016; see also Franke 2009). In this framework, listeners and speakers recursively
reason about each other (6).
(6)

a.
b.
c.

L0 (w | u) µ Pr(w) · JuK(w)S1 (u | w) µ Optimize(L0 (w | u))
L1 (w | u) µ Pr(w) · S1 (u | w)

Literal listener
Pragmatic speaker
Pragmatic listener

We will use a concrete example discussed by Burnett (2017) to illustrate the basics of thisframework. Suppose you left three cookies on the dinner table for your roommates. When you
come home, John, one of the roommates, tells you (7).
(7)

I ate some of the cookies.

You will likely infer from (7) that John ate one or two cookies but probably not all three. An
intuitive explanation is that if he had eaten all three cookies he would have told you (8), which ismore informative.3 How do we formalize this reasoning in the probabilistic framework above?
(8)

I ate all of the cookies.

First, we consider a literal listener (6a), who interprets an utterance u simply based on its truthconditional content JuK. This can be seen as a probabilistic generalization of a Stalnakerianmodel of conversation: instead of treating a context C as a set of possible worlds, a context is
now treated as a probability distribution P(·) over possible worlds. Updating an initial context(implemented as a prior distribution Pr(·)) with an utterance u results in a new context, i.e., theconditional probability L0 (· | u), obtained by probabilistic conditioning (9b) (cf. the traditional
contextual update via set intersection (9a)).
(9)

a.
b.

C + u = C \ JuK
L0 (w | u) µ Pr(w) · JuK(w)Concretely, in the cookie example, let wi be the possible world in which John ate exactly i
cookies (i = 0, 1, 2, 3). Just for illustration let us assume that the prior probabilities of w0 to w4
are 0.1, 0.4, 0.3, and 0.2, respectively (first row in (10)).
3 Assume that it is clear that eating all three cookies is totally acceptable, so John would have no reason to hide thefact if he did eat them all.

256

(10)

Ciyang Qing and Reuben Cohn-Gordon

Literal listener after hearing I ate some of the cookies

Pr(w)JsomeK(w)Pr(w) · JsomeK(w)L0 (w | some)

w0
.1
0
0
0

w1
.4
1
.4
4
9

w2
.3
1
.3
3
9

w3
.2
1
.2
2
9

The utterance I ate some of the cookies is true in w1 , w2 , and w3 , i.e., JsomeK(w0 ) = 0 andJsomeK(wi ) = 1 for i = 1, 2, 3 (second row in (10)). Based on the prior distribution Pr(·) andthe truth-conditional meaning JsomeK, we compute their product in the third row in (10). The
proportionality operator µ in (9b) means that its left term is obtained by multiplying a constantto the right term to ensure that the left term is a probability distribution (i.e., all the probabilities
sum up to 1). This is done by dividing each element in the third row of (10) by the sum of thatrow, and the resulting conditional probabilities L0 (w | some) are shown in the last row. Notethat L0 (w3 | some) = 2/9 ⇡ .22, which means that after hearing I ate some of the cookies, theliteral listener thinks it is roughly 22% likely that John ate all 3 cookies.
Similarly, the conditional probabilities L0 (w | all) are computed in (11).
(11)

Literal listener after hearing I ate all of the cookies

w0
Pr(w)
.1
JallK(w)0Pr(w) · JallK(w) 0
L0 (w | all)
0

w1
.4
0
0
0

w2
.3
0
0
0

w3
.2
1
.2
1

Note that L0 (w3 | all) = 1, which means that after hearing I ate all of the cookies, the literal
listener is completely sure that John ate all 3 cookies.
Now we will consider a pragmatic speaker, whose definition (6b) is repeated below as (12) toformalize the reasoning “if John had eaten all three cookies, he would have used all instead ofsome because all is more informative.”(12)

S1 (u | w) µ Optimize(L0 (w | u))

Pragmatic speaker4

What (12) says is that the probability of a pragmatic speaker choosing utterance u in world w isdetermined by optimizing (in some sense) the probability the literal listener assigns to w after
hearing u. For the purposes of the current paper we only require that Optimize satisfies (13),i.e., the pragmatic speaker would be more likely to choose u than u0 in world w iff the literal
listener would assign higher probability to world w after hearing u than u0 .5(13)

S1 (u | w) > S1 (u0 | w) iff L0 (w | u) > L0 (w | u0 )4 Here we make the simplifying assumption that all relevant utterances are equally likely a priori. A more realistic

speaker model that takes into account utterance priors would be S1 (u | w) µ Pr(u) · Optimize(L0 (w | u)). The
simplification made here does not affect the main points of this paper.
5 In many RSA models a priori preferences for utterances are represented as costs and the Optimize function issensitive to them. In such cases (13) does not hold in general, but it still holds when all relevant utterances are
assumed to be equally likely a priori.

Use-conditional meaning in Rational Speech Act models

257

In the cookie example, given that L0 (w3 | all) = 1 > L0 (w3 | some) = 2/9, from (10) we have
S1 (all | w3 ) > S1 (some | w3 ), i.e., the speaker would prefer to use all to some if he had eaten all
3 cookies.
Once we choose an exact definition of Optimize, we can make quantitative predictions about
the production probabilities and apply Bayes’ rule to make quantitative predictions about howa pragmatic listener would interpret an utterance (6c).
3.2. Personae and Eckert-Montague fields
In order to apply the RSA framework to analyze social meaning, we need to address two issues:(i) What do possible worlds represent? (ii) How do we represent social meaning?
Burnett (2019) uses Obama’s use of (ING) as a working example and assume two candidate
utterances u-ing and u-in’ that are different only in terms of the realization of (ING).
For (i), Burnett uses possible worlds to represent the speaker’s possible personae. A persona i
is a maximally compatible set of properties. In the Obama example, Burnett assumes that therelevant properties are competent and aloof and their opposites. The four possible personae
and their names are in the table below (14).
(14)

STERN LEADER{comp., aloof}

COOL GUYASSHOLEDOOFUS{comp., friendly} {incomp., aloof}{incomp., friendly}

For (ii), Burnett essentially treats an utterance u’s association with certain properties as a compatibility relation and uses type lifting to derive the set of personae that u is compatible with(i.e., treating personae as Montagovian individuals). A persona is compatible with u iff it contains a property that is compatible with u. Given that u-ing is compatible with both competentand aloof, the only persona incompatible with u-ing is DOOFUS. Similarly, since u-ing is compatible with both incompetent and friendly, the only persona incompatible with u-in’ is STERNLEADER . Burnett calls such compatibility relations between linguistic variants and personae
Eckert-Montague fields and uses them in the literal listener model as representations of social
meaning (15).
(15)

J-ingK
J-in’KSTERN LEADER

COOL GUYASSHOLEDOOFUS

1
0

1
1

1
1

0
1

As a concrete example, Burnett models Obama’s use of (ING) at the barbecue as follows. She
assumes that, because Obama is the president, the prior probability distribution slightly favors
personae that are aloof (i.e., STERN LEADER and ASSHOLE) than those that are friendly (i.e.,
COOL GUY and DOOFUS ) (first row in (16)). Given the Eckert-Montague field of the -ing
variant (second row in (16)), the probability that the literal listener assigns to each persona
after hearing the -ing variant can be calculated according to (6a) and is shown in the last row
in (16). In particular, L0 (COOL GUY | -ing) = 2/8 = .25. That is, after hearing the -ing variant,the literal listener thinks that it is 25% likely that Obama is a COOL GUY.
(16)

Literal listener after hearing -ing

258

Ciyang Qing and Reuben Cohn-Gordon

Persona iPr(i)J-ingK(i)L0 (i | -ing)

STERN LEADER

COOL GUYASSHOLEDOOFUS

.3
1

.2
1

.3
1

.2
0
0

3
8

2
8

3
8

Similarly, the probability that the literal listener assigns to each persona after hearing the -in’variant is calculated in (17). In particular, L0 (COOL GUY | -in’) = 2/7 ⇡ .286.
(17)

Literal listener after hearing -in’

Persona iPr(i)J-in’K(i)L0 (i | -in’)

STERN LEADER

COOL GUYASSHOLEDOOFUS

.3
0
0

.2
1

.3
1

.2
1

2
7

3
7

2
7

Given that L0 (COOL GUY | -in’) > L0 (COOL GUY | -ing), from (13) we can conclude that
S1 (-in’ | COOL GUY) > S1 (-ing | COOL GUY), i.e., assuming that Obama wants to convey the
COOL GUY persona, he would prefer the -in’ variant to the -ing variant. Recall that in this context Obama in fact uses -in’ 72% of the time. Therefore, it seems that Burnett’s model correctly
captures Obama’s use of (ING) in this case. (In fact, using a standard implementation of the
Optimize function, she is able to configure the model so that S1 (-in’ | COOL GUY) is predicted
to be around 69%.)
3.3. The issue with multiple utterances
However, when we examine more closely Burnett’s model’s prediction S1 (-in’ | COOL GUY), it
is not clear whether this truly captures Obama’s production rate of -in’.
Crucially, note that S1 (-in’ | COOL GUY) is implicitly relative to the literal listener’s prior probability distribution over personae. This gives rise to the important question of how such aprobability distribution should change over the entire discourse, which may consist of multiple
utterances in a sequence. To address this, recall that the literal listener model can be seen as aprobabilistic generalization of a Stalnakerian model (9), repeated below as (18).
(18)

a.
b.

C + u = C \ JuK
L0 (i | u) µ Pr(i) · JuK(i)If we have a second utterance u2 following the first u1 , in a Stalnakerian model we can take theoutput context C0 = C + u1 as the input context of u2 . By analogy, we can use the conditional
probability L0 (w | u1 ) as the new prior probability Pr0 (w) in the literal listener model (19).
(19)

L00 (i | u2 ) µ Pr0 (i) · Ju2 K(i)In general, for a sequence of utterances u1 , . . . , un+1 , we can define the literal listener modelrecursively as in (20).
(20)

(n)

L0 (i | u1 , . . . un+1 ) µ Pr(n) (i) · Jun+1 K(i),
(0)

(n)

Pr(n+1) (w) = L0 (i | u1 , . . . un+1 )(1)

As notational variants we will write L0 , Pr(0) simply as L0 , Pr, write L0 , Pr(1) as L00 , Pr0 , write(2)

L0 , Pr(2) as L000 , Pr00 , etc. Also, when the initial sequence u1 , . . . , un is clear from the context,

Use-conditional meaning in Rational Speech Act models

(n)

259

(n)

we will write L0 (i | un+1 ) instead of L0 (i | u1 , . . . un+1 )Once the literal listener is defined over a sequence of utterances, the pragmatic speaker model
can be similarly generalized (21).
(21)

(n)

(n)

S1 (un+1 | i) µ Optimize(L0 (i | un+1 ))Now let us consider what Burnett’s model predicts when the speaker needs to make multiple
utterances, again using Obama’s use of (ING) as a concrete example.
From the previous discussion we already know that S1 (-in’ | COOL GUY) > S1 (-ing | COOL GUY)and therefore let us assume that Obama first chooses the -in’ variant and see what the model
predicts about his second utterance.
In this case, the probability that the literal listener assigns to each persona after hearing -ing as
the second utterance is computed in (22). Note that the prior Pr0 (i) is by definition L0 (i | -in’),i.e., the last row in (17).
(22)

Literal listener after first hearing -in’ and then -ing

Persona i
Pr0 (i)J-ingK(i)L00 (i | -ing)

STERN LEADER

COOL GUYASSHOLEDOOFUS

0
1
0

1

1

0
0

2
7
2
5

3
7
3
5

2
7

Similarly, the probability that the literal listener assigns to each persona after hearing -in’ as
the second utterance is computed in (23). Note that the conditional probability L00 (i | -in’) is
identical to the prior Pr0 (i): Since all the personae with non-zero prior probabilities are alreadycompatible with the -in’ variant, no information is gained from hearing it.
(23)

Literal listener after first hearing -in’ and then -in’ again.

Persona i
Pr0 (i)J-in’K(i)L00 (i | -in’)

STERN LEADER

COOL GUYASSHOLEDOOFUS

0
0
0

1

1

1

2
7
2
7

3
7
3
7

2
7
2
7

Since we have L00 (COOL GUY | -ing) = 25 > L00 (COOL GUY | -in’) = 27 , from (13) we conclude
that S10 (-ing | COOL GUY) > S10 (-in’ | COOL GUY). That is, after using the -in’ variant once, it
is no longer preferred, because it is not informative anymore.
Finally, let us assume that Obama first uses -in’, and then -ing, and see what Burnett’s model
predicts about the third utterance.
In this case, the probability that the literal listener assigns to each persona after hearing -ing as
the third utterance is computed in (24). Note that the prior Pr00 (i) by definition comes from thelast row in (22). Also note that the conditional probability L000 (i | -ing) is identical to the prior
Pr00 (i), because all the persona with non-zero priors are already compatible with -ing.
(24)

Literal listener after first hearing -in’, followed by -ing, and then -ing

260

Ciyang Qing and Reuben Cohn-Gordon

Persona i
Pr00 (i)J-ingK(i)L000 (i | -ing)

STERN LEADER

COOL GUYASSHOLEDOOFUS

0
1
0

1

1

0
0
0

2
5
2
5

3
5
3
5

Similarly, the probability that the literal listener assigns to each persona after hearing -in’ as thethird utterance is computed in (25). Once again, note that the conditional probability L000 (i | -in’)is also identical to the prior Pr00 (i).
(25)

Literal listener after first hearing -in’, followed by -ing, and then -in’

Persona i
Pr00 (i)J-in’K(i)L000 (i | -in’)

STERN LEADER

000

COOL GUY
2
5

1
2
5

ASSHOLEDOOFUS

1

0
1
0

3
5
3
5

Since we have L000 (COOL GUY | -ing) = 25 = L000 (COOL GUY | -in’), from (13) we conclude that
S100 (-ing | COOL GUY) = S100 (-in’ | COOL GUY). That is, after using both -in’ and -ing variants
once, Burnett’s model predicts that the speaker should have no preference for either variant.
In sum, Burnett’s model predicts that at the barbecue (i) Obama would initially prefer the -in’variant, (ii) after he has produced one variant but not both, he would prefer the one he has notproduced, and (iii) after he has produced both variants, he would be indifferent. Together, thismeans that Obama’s production rate of -in’ is predicted to be around 50% when the speech
is sufficiently long (i.e., there are enough instances of (ING) after he produces both variants),
contrary to fact.
Note that the problem with multiple utterances does not crucially rely on the way the sequential
update of the prior distribution is defined in (20). For instance, after hearing the first -in’, we
can compute the pragmatic listener’s interpretation L1 (i | -in’) and use it as the new prior Pr0 (i),instead of using L0 (i | -in’) as Pr0 (i). However, the same problem will arise, because it is still
the case that every persona i whose new prior Pr0 (i) is greater than 0 is already compatible with-in’. This means that -in’ is totally uninformative (i.e., L00 (i | -in’) is identical to Pr0 (i)) andtherefore will never be preferred.
However, we note that this problem does depend on the simplifying assumption that the persona
intended by the speaker stays constant throughout the sequence of utterances in the discourse.
If we give up this assumption, and analyze the social meaning of a linguistic variant as a proposition relativized to the utterance time t (e.g., the meaning of -ing is “I am competent or aloofnow”), then the repeated use of a variant can be informative because two instances of use correspond to different propositions (e.g., “I am competent or aloof at t1 /t2 ”).
Although such an approach can potentially rescue Burnett’s analysis, many more complicatedissues need to be addressed to provide a realistic model. For instance, in order to calculate thespeaker’s production rate of a variant over a sequence of utterances in the discourse, we willneed to specify how the prior over personae is updated throughout the discourse, which is more
complicated because we need to take into account the potential change in persona.
Therefore, we conclude that Burnett’s analysis faces difficulties in modeling the production of asequence of utterances throughout the discourse. In the next section, we propose an alternativeUse-conditional meaning in Rational Speech Act models

261

analysis of social meaning in terms of use-conditional meaning, and show that it not only caneasily model the production of a sequence of utterances throughout the discourse, but also
captures the similarities between social meaning and expressive meaning very well.
4. Social meaning as use-conditional meaning
4.1. Use-conditional meaning
According to Kaplan (1999), the meanings of expressions such as ouch and oops are not captured by their truth conditions (since they do not have any), but rather by their conditions onuse, i.e., contexts in which they can be correctly/felicitously used. For instance, the use condition of oops can be roughly characterized as follows: oops is felicitously used iff the speakerobserves a minor mishap. Knowing this use condition, the listener of oops can infer that the
speaker observes a minor mishap, by virtue of knowing what it takes for the speaker to produce
this utterance.
In the case of social meaning on the one hand, the choice of variant is not totally constrained bylinguistic norms. For instance, anybody may use -ing and -in’ and using either variant would
be correct. On the other hand, we can still apply Kaplan’s insight to analyze social meaning,in that the hearer of a linguistic variant can gain information about the speaker, by virtue ofknowing (or more precisely, having an ideology about) what it takes for the speaker to producethat variant, which often has to do with the speaker’s social identity, or persona.
Therefore, we suggest that social meaning should be represented as the listener’s ideology
about how the speaker’s persona influences his/her choice of the linguistic variants. Below weformalize this idea in an extended RSA framework.
4.2. Implementing use-conditional meaning in an extended RSA framework
We generalize the literal listener to integrate both the truth-conditional (26a) and use-conditional(26b) meanings of an utterance.
(26)

L0 (w, i | u) = L0 (w | u) · L0 (i | u)a. L0 (w | u) µ Pr(w) · JuK(w)b. L0 (i | u) µ Pr(i) · S0 (u | i)where S0 (u | i) is a stereotypical speaker

JuK: truth-conditional meaning

S0 (u | i): use-conditional meaning

The literal listener updates their prior belief about the world w by conditioning on the truthof the utterance u (26a). Meanwhile, they update their prior belief about the speaker type iby reasoning about a hypothetical stereotypical speaker S0 .6 Crucially, this speaker is not a
production model of any real linguistic agent, but rather one that is based on ideological stereotypes. For instance, the stereotype that incompetent but friendly people tend to use the -in’variant corresponds to a high value for S0 (-in’ | DOOFUS), while the stereotype that competentbut aloof people tend to use the -ing variant corresponds to a low value of S0 (-in’ | DOOFUS).
Assuming that the production probabilities of the other two personae are in between, we take(27) as an example representation of the social meaning of -in’ and use it to model Obama’s
use of (ING) at the barbecue.
6 See Henderson and McCready’s (2017) analysis of dogwhistles for another case of using a speaker model S as0

the starting point of the iterative reasoning.

262

(27)

Ciyang Qing and Reuben Cohn-Gordoni
S0 (-in’ | i)

STERN LEADER

COOL GUYASSHOLEDOOFUS

0.1

0.7

0.2

0.9

4.3. Multiple utterancesFirst, we consider Obama’s first utterance. Assuming the same prior probability distribution
over personae as before, which slightly favors personae that are aloof, the probability that theliteral listener assigns to each persona after hearing -in’ is computed in (28).
(28)

Literal listener after hearing -in’iPr(i)S0 (-in’ | i)
Pr(i) · S0 (-in’ | i)
L0 (i | -in’)

STERN LEADER

COOL GUYASSHOLEDOOFUS

0.3
0.1
0.03
0.073

0.2
0.7
0.14
0.34

0.3
0.2
0.06
0.146

0.2
0.9
0.18
0.439

Similarly, the probability that the literal listener assigns to each persona after hearing -ing iscomputed in (29). Note that S0 (-ing | i) = 1 S0 (-in’ | i) for each persona i.
(29)

Literal listener after hearing -ingiPr(i)S0 (-ing | i)
Pr(i) · S0 (-ing | i)
L0 (i | -ing)

STERN LEADER

COOL GUYASSHOLEDOOFUS

0.3
0.9
0.27
0.458

0.2
0.3
0.06
0.102

0.3
0.8
0.24
0.407

0.2
0.1
0.02
0.034

Since L0 (COOL GUY | -in’) = 0.34 > 0.102 = L0 (COOL GUY | -ing), from (13) we conclude
that S1 (-in’ | COOL GUY) > S1 (-ing | COOL GUY). That is, Obama would initially prefer -in’ to-ing to construct the COOL GUY persona.
Now suppose Obama chooses -in’ as the first utterance. The probabilities that the literal listenerassigns to each persona after hearing -in’ or -ing as the second utterance are shown in (30).
(30)

Literal listener after hearing -in’ first, and then -in’ or -ingi
Pr0 (i)S0 (-in’ | i)
L00 (i | -in’)
L00 (i | -ing)

STERN LEADER

COOL GUYASSHOLEDOOFUS

0.073
0.1
0.011
0.2

0.34
0.7
0.356
0.311

0.146
0.2
0.044
0.356

0.439
0.9
0.589
0.133

(Pr0 (i) = L0 (i | -in’))Since L00 (COOL GUY | -in’) = 0.356 > 0.311 = L00 (COOL GUY | -ing), from (13) we conclude
that S10 (-in’ | COOL GUY) > S10 (-ing | COOL GUY). That is, after using the -in’ variant once,
Obama would still prefer it to -ing as the second utterance to construct the COOL GUY persona.
This prediction is in stark contrast with Burnett’s model’s, according to which Obama would
prefer -ing as the second utterance once he has used -in’ as the first utterance. The reason isthat in our model -in’ never completely rules out any persona and therefore its repeated use canstill be informative, whereas in Burnett’s model, repeated use of -in’ is never informative andtherefore the repeated use is never preferred.

Use-conditional meaning in Rational Speech Act models

263

Now suppose Obama chooses -in’ as the first and second utterances. The probabilities that theliteral listener assigns to each persona after hearing -in’ or -ing as the third utterance are shownin (31).
(31)(Pr00 (i) = L00 (i | -in’))

Literal listener after hearing -in’ twice, and then -in’ or -ingiPr00 (i)S0 (-in’ | i)
L000 (i | -in’)
L000 (i | -ing)

STERN LEADER

COOL GUYASSHOLEDOOFUS

0.011
0.1
0.001
0.047

0.356
0.7
0.316
0.508

0.044
0.2
0.011
0.166

0.589
0.9
0.672
0.28

Since L000 (COOL GUY | -in’) = 0.316 < 0.508 = L000 (COOL GUY | -ing), from (13) we conclude
that S100 (-in’ | COOL GUY) < S100 (-ing | COOL GUY). That is, after using -in’ twice, Obama would
prefer to use -ing as the third utterance to construct the COOL GUY persona.
This ensures that Obama will not use the -in’ variant indefinitely. Intuitively, this is because using the -in’ variant too much will make the listener assign too much probability to the DOOFUS
persona, since that persona corresponds to the highest production rate of -in’.
In general, the speaker’s best strategy to convey the intended persona i to the listener overmultiple utterances is to produce -in’ at the rate that conforms to the stereotype of that persona
i, i.e., S0 (-in’ | i). For example, Obama’s best strategy to convey the COOL GUY persona is to
produce the -in’ variant 70% of the time. We suggest that this captures the performative natureof social meaning: the speaker can succeed in conveying an intended persona iff the way he/she
produces the utterances conforms to the way the intended persona is supposed to produce thoseutterances. In other words, it is the very act of using linguistic variants in a particular way that
constructs and conveys the corresponding persona.
4.4. Capturing properties of expressive meanings
As discussed earlier, social meaning shares many properties of expressive meanings (2), repeated below as (32).
(32)

Expressive meanings are• largely independent of the descriptive meanings• always about the utterance situation itself.

• not propositional and can be hard to pin down(Independence)(Nondisplaceability)(Descriptive ineffability)• performative in that the very act of utterance conveys the meaning• strengthened when repeated without redundancy(Immediacy)(Repeatability)

We have discussed how our proposal captures Immediacy and Repeatability. The remaining
properties are discussed below.
• Independence holds due to our assumption that w and i are conditionally independent
given u, which is generally the case. However, sometimes this assumption might fail to264

Ciyang Qing and Reuben Cohn-Gordon
hold. Then we use the most general formula L0 (w, i | u) µ Pr(w, i)·JuK(w)·S0 (u | JuK, w, i),which allows for descriptive and indexical meanings to interact with each other.

• Nondisplaceability: Social meaning, represented as a production probability S0 (u | i), isalways about the utterance situation itself, since the persona i is always relative to the
speaker of the utterance.

• Descriptive ineffability: social meaning is represented as a production probability S0 (u |i), which is not propositional. It can be hard to pin down because it can be difficult to
describe the high likelihood region(s) of this production probability.
5. Further discussion
Representing use-conditional meanings in terms of the stereotypical speaker S0 is a naturalextension to previous multi-dimensional semantic systems (e.g., Potts, 2007; Gutzmann, 2015).
As a concrete example, consider the following simplified reformulation of Potts’s analysis of
the expression the damn dog. This expression has a multi-dimensional meaning. On the one
hand, it has a normal descriptive content d (a type e individual), which comes from Jthe dogK.
On the other, it also has an expressive content f , a function that updates/alters the context. Herethe context is represented by an expressive index of the form s I d, where I is an expressive interval, i.e., a subset of [ 1, 1] representing the set of possible attitudes of the speaker s towards
d. The effect of f is to shrink the expressive interval I and ensure that it is a subset of [ 1, 0],i.e., the speaker s holds negative attitudes towards the dog d.
Generalizing the expressive interval I to a probability distribution p(i) over the speaker’s possible attitude i towards the dog d, we can derive a probabilistic literal listener model based on(26b), as shown in (33).
(33)

L0 (i | damn) µ Pr(i) · S0 (damn | i)

We can see that, once S0 (damn | i) is specified, (33) will implicitly define a mapping fromthe input context Pr(i) to an updated context L0 (i | damn), i.e., the expressive content of thedamn dog. In other words, the expressive meaning of the damn dog can be represented as
S0 (damn | i), a probabilistic use-conditional meaning.

Note that this example can be generalized to a fully compositional analysis of damn: its
descriptive content is the identity function id, and its expressive meaning is represented asl k.S0 (damn | i[kd (id)]). This expressive meaning has two main components. The first isl x.S0 (damn | i[x]), the probabilistic use-conditional meaning in (33) relativized to x, i.e., howlikely a speaker will use damn, given that his/her attitude towards x is i[x]. Here x can be an individual (e.g., the dog d in the above example), a proposition (e.g., the fact that the speaker lostthe key in I lost the damn key), etc. The second component specifies that x is determined by thescope of damn. Concretely, x is the result of feeding the descriptive content of the expressionthat damn takes scope over with the identity function as its argument, i.e., kd (id). For instance,
when damn takes scope over the rest of the DP in the damn dog, i.e., the descriptive content
of the expression that damn takes scope over would be l f .the( f (dog), feeding it with id will
make x be the(dog) (i.e., the dog d). When damn takes scope over the rest of the sentence inI lost the damn key (schematically, damn(l f . I lost the ( f key)), applying the same proceduremakes x be the proposition that the speaker lost the key.

Use-conditional meaning in Rational Speech Act models

265This probabilistic approach provides a principled way to concretely specify expressive meanings and explain their properties. For instance, when the expressive meaning of damn is represented as a function that shrinks expressive intervals, it can be hard and arbitrary to specify
how much the function should shrink each interval. In contrast, when the expressive meaning
is represented a production probability S0 (damn | i), it is much easier to specify an intuitively
plausible production probability or learn it from empirical data.
6. Conclusion
In this paper, we analyze social meaning as use-conditional meaning, and provide a formal
analysis by extending the RSA framework. We show that such an analysis can well capture
the properties social meaning shares with expressive meanings, and discuss how the extended
probabilistic framework could model use-conditional meanings in general.
References
Burnett, H. (2017). Sociolinguistic interaction and identity construction: The view from gametheoretic pragmatics. Journal of Sociolinguistics 21(2), 238–271.
Burnett, H. (2019). Signalling games, sociolinguistic variation and the construction of style.
Linguistics and Philosophy, 1–32.
Campbell-Kibler, K. (2006). Listener perceptions of sociolinguistic variables: The case of(ING). Ph. D. thesis, Stanford University.
Campbell-Kibler, K. (2007). Accent, (ING), and the social logic of litsner perceptions. American Speech 82(1), 32–64.
Campbell-Kibler, K. (2008). I’ll be the judge of that: Diversity in social perceptions of (ING).
Language in Society 37(5), 637–659.
Campbell-Kibler, K. (2009). The nature of sociolinguistic perception. Language Variation andChange 21(1), 135–156.
Eckert, P. (2012). Three waves of variation study: The emergence of meaning in the study ofsociolinguistic variation. Annual review of Anthropology 41, 87–100.
Frank, M. C. and N. D. Goodman (2012). Predicting pragmatic reasoning in language games.
Science 336(6084), 998–998.
Franke, M. (2009). Signal to Act: Game Theory in Pragmatics. Ph. D. thesis, Institute for
Logic, Language and Computation, Universiteit van Amsterdam.
Goodman, N. D. and M. C. Frank (2016). Pragmatic language interpretation as probabilistic
inference. Trends in Cognitive Sciences 20(11), 818–829.
Gutzmann, D. (2015). Use-conditional meaning: Studies in Semantics and Pragmatics. Oxford: Oxford University Press.
Henderson, R. and E. McCready (2017). Dog-whistles and the at-issue/not-at-issue distinction.
Presentation at the DGfS Workshop: Secondary Information & Lingustic Encoding.
Kaplan, D. (1999). The meaning of ouch and oops: Explorations in the theory of meaning asuse. Unpublished manuscript, University of California, Los Angeles.
Labov, W. (1963). The social motivation of a sound change. Word 19(3), 273–309.
Labov, W. (2012). Dialect diversity in America: The politics of language change. Charlottesville, VA: University of Virginia Press.
Potts, C. (2007). The expressive dimension. Theoretical Linguistics 33(2), 165–197.