A rational speech-act model of projective content
Ciyang Qing, Noah D. Goodman, Daniel Lassiter{qciyang, ngoodman, danlassiter}@stanford.edu
Stanford University
Abstract
Certain content of a linguistic construction can project when
the construction is embedded in entailment-canceling environments. For example, the conclusion that John smoked in thepast from the utterance John stopped smoking still holds forJohn didn’t stop smoking, in which the original utterance isembedded under negation. There are two main approaches toaccount for projection phenomena. The semantic approach adds
restrictions of the common ground to the conventional meaning.
The pragmatic approach tries to derive projection from generalconversational principles. In this paper we build a probabilistic
model of language understanding in which the listener jointlyinfers the world state and what common ground the speakerhas assumed. We take change-of-state verbs as an example
and model its projective content under negation. Under certain
assumptions, the model predicts the projective behavior and its
interaction with the question under discussion (QUD), without
any special semantic treatment of projective content.
Keywords: Presupposition; projection; Bayesian pragmatics

Introduction“How am I to get in?” asked Alice again, in a louder tone.
“Are you to get in at all?” said the Footman. “That’s thefirst question, you know.”— Carroll (1866), ch. VI
Courtroom drama, political misinformation, and ordinary
misunderstandings often revolve around presupposition, abackgrounded aspect of meaning with a complex logic andcommunicative function. Famously, presuppositions can beused manipulatively, as in the classic loaded question “Haveyou stopped beating your wife?”, or the sly reporter’s “Whendid you become aware that this policy was a failure?”. At thesame time, presuppositions serve to streamline conversationby allowing interlocutors to convey multiple pieces of information simultaneously. Alice’s question “How am I to get in?”efficiently indicates both Alice’s assumption that she will get
in, and her wish to know how to enter.
In addition to their important communicative role, presuppositions are interesting because they seem to flout some of themost basic rules of logic. For example, from John danced we
can infer John moved, but we cannot infer this from John didn’t
dance—the inference that John moved is canceled by negation.
In contrast, from both John stopped smoking and John didn’t
stop smoking we are likely to infer that John used to smoke—this inference is said to project over negation. In natural
language semantics and pragmatics, an inference that survives
an operator that usually cancels inferences is called projective
content of the sentence under that operator. Change-of-stateverbs can have information about the past as projective content
under negation: John used to smoke is projective content undernegation of “John stopped smoking.” There are many othertypes of projective contents (e.g., the complement of know)
under different operators (e.g., questions, modals) identified

and discussed in the literature. The problem of explaining how
certain inferences can survive entailment-canceling operators
is called the projection problem.
There are two main approaches to the projection problem.
According to the semantic approach, projective contents areconventional properties of lexical items (e.g., Frege, 1948;
Heim & Kratzer, 1998). According to the pragmatic approach,projection can be derived from general conversational principles (e.g., Stalnaker, 1974; Simons, 2001, 2006). How could
we capture projection patterns using general conversational
principles? To illustrate the reasoning, let us expand the example scenario: Alice and Bob are talking about John, an oldfriend of Alice’s who is visiting her. Bob has never met John
before so he knows nothing about him. Bob asks Alice, “DoesJohn smoke?” Alice replies, “John did not stop smoking.”1
Taken literally, Alice’s utterance seems under-informative: itcan be literally true, regardless of whether or not John smokes.
If Alice knows whether John smokes and is cooperative, shewould not have said something under-informative. So perhaps
her answer is informative after all, but how? Maybe she hastaken some additional information for granted, assuming that
it is in the common ground with Bob. Indeed, if Alice took
for granted that John smoked in the past, then, together with“John did not stop smoking,” this information would mean thatJohn still smokes, which fully answers the question of whether
John smokes now. In other words, assuming that Alice took
for granted that John smoked in the past best explains Alice’s
utterance. If Bob further assumes that if Alice took it for
granted then it must be true, then he will arrive at the projected
content: John used to smoke.
There are different types of projective content (Tonhauser,
Beaver, Roberts, & Simons, 2013). It is possible that they
project for different reasons. For change-of-state verbs, there
are several reasons why one might prefer a pragmatic approachto projection to a semantic one. First, they systematicallyshow projective behavior. Therefore, a generalization would
be missing if their projective contents are lexically-encoded
properties that could vary arbitrarily from verb to verb. In
contrast, a pragmatic approach could in principle explain why
a class of verbs with a similar basic meaning would also havethe same projection behavior. Second, projection interacts
with the contextual question under discussion, as can be seenfrom the following example (Geurts, 1995). Imagine thatBob asked Alice: “I notice that John keeps chewing on his
pencil. Did he recently stop smoking?” In this context Bob
is not interested in whether John is currently a smoker, but
1 Alice’s answer is indirect and complex, and hence would be infelicitous without additional contextual justification. This is predictedby our model.

in whether there was a change from smoking to non-smoking
which could explain John’s odd behavior. As a result, if Alicewere to answer “no (it’s just an nervous habit)”, Bob would
not infer that John used to smoke. Similarly, if a customer
asks whether an item on sale has been used by anyone before,a reply “it is not refurbished” would imply that it is brandnew. Third, projection is sensitive to prosodic focus: “John
did not stop smoking” seems to suggest he never smoked. Yet
a major obstacle to adopting the pragmatic approach has been
the difficulty in formalizing the reasoning and showing that it
emerges naturally from conversational principles.
In this paper, we build on and formalize previous ideas ofthe pragmatic approach. We do so within the Rational SpeechActs (RSA) framework (Frank & Goodman, 2012; Goodman& Stuhlmüller, 2013): a Bayesian approach to language understanding. We extend the previous models by allowing thelistener to reason about the facts that the speaker took to be incommon ground (along similar lines to Degen, Tessler, andGoodman (2015)). We find that to account for the example
scenario we must also make certain assumptions about whichfacts are plausible common ground and which question is under discussion. With these assumptions and extensions, themodel accounts for projection phenomena of change-of-stateverbs under negation. It further predicts an interaction between
projective behavior and the question under discussion (QUD)(Roberts, 2012), suggesting further experimental research to
the growing body of literature (e.g., Cummins, Amaral, &Katsos, 2013; Schwarz, 2015)

A Rational Speech-Act (RSA) model
In this section we introduce an extension to Rational SpeechAct (RSA) model (Frank & Goodman, 2012; Goodman &Stuhlmüller, 2013) to account for the projection phenomenonof change-of-state verbs under negation, by formalizing theideas introduced in the previous section. We will continue to
use our working example of the conversation between Aliceand Bob regarding John’s smoking habit.
We consider the following relevant utterances: “Johnsmokes,” “John smoked,” “John has always smoked,” “John
stopped smoking,” “John started smoking,” “John has neversmoked,” and their negations. In addition, we introduce thenull utterance “” (say nothing). The prior probability of anutterance depends on the number of content words (i.e., negation and auxiliaries are excluded) that it has. The shorter anutterance, the higher its prior probability is, as defined in (1).
Pr(u) ∝ 2−#content-words(u)(1)

The meaning/denotation of an utterance is standardly defined as the set of worlds where the utterance is true. We define
a world w as a pair. Its first element is whether John smokedin the past and its second element is whether John smokes
now. This gives us a set of four possible worlds (the universe
U = {(T, T ), (T, F), (F, T ), (F, F)}). All positive utterances
and their denotations are listed in Table 1. In addition, we define that saying nothing is always true, and that the denotationof the negation of an utterance u is U − JuK.

u“John smokes”“John smoked”“John has always smoked”“John stopped smoking”“John started smoking”“John has never smoked”

JuK{(T, T ), (F, T )}{(T, T ), (T, F)}{(T, T )}{(T, F)}{(F, T )}{(F, F)}

Table 1: Positive utterances and their denotations
A Question Under Discussion (QUD) is a function Q thattakes a possible world as its argument and returns the answer
to the question in this world. For example, QUDnow is thequestion “Does John smoke now?” It takes a world and returns
its second element, which answers whether John smokes now.
Another example is the maximal QUDmax , which is the identity
function. Intuitively, QUDmax is asking which is the actual
world. It is maximal in the sense that knowing its answer
means knowing the answer to any QUD.
To account for projective behavior, we propose additional
components and assumptions to the standard RSA model in theliterature (Frank & Goodman, 2012; Goodman & Stuhlmüller,
2013; Goodman & Lassiter, 2015). To better illustrate why
each of them is necessary and how they contribute to themodel’s prediction, we will present the model incrementally.
We will start with the standard RSA model, point out its
problems, motivate a modification, explain the problem it
addresses, review the remaining issues, motivate another modification, and so on, until we reach the final model.
Standard RSA model
In the standard RSA model (augmented with QUD as inGoodman and Lassiter (2015)), the literal listener, given anutterance and a QUD, randomly samples a world that is consistent with the utterance, and returns the value of the QUD inthat world, as in (2). In this paper we always assume that all
worlds are equally likely a priori, i.e. Pr(w) = 1/4 for each w.
L0 (Q(w) | u, Q) ∝∑ δQ(w)=Q(w0 ) · Pr(w0 )(2)

w0 ∈JuK

Here δ subscripted with a statement is defined to be 1 if
the statement is true and 0 otherwise. For example, if Q
is QUDmax , which asks for a complete specification of thestate of the world, after hearing “John didn’t stop smoking,”
the literal listener will rule out world (T, F), and return theremaining 3 worlds with equal probability.
Given the actual world and the QUD, the probability of the
speaker’s utterance u depends on two factors: the utterance
prior and the probability that the utterance will make the literal
listener return the correct answer to the QUD, as in (3).
S(u|w, Q) ∝ Pr(u) · L0 (Q(w) | u, Q)α(3)Here α is a rationality parameter controlling the extent towhich the speaker optimizes her utterance to induce the correct
answer from the literal listener. When α → ∞, the speaker will
always choose utterances that strictly maximize the probabilityof inducing the right answer. In this paper we set α = 6, but
the qualitative predictions do not hinge on this specific value.

literalspeaker
listener
CG prior
QUD

Standard (no CG + QUDmax )L0 (Q(w) | u, Q) ∝ ∑w0 ∈JuK δQ(w)=Q(w0 ) · Pr(w0 )S(u|w, Q) ∝ Pr(u) · L0 (Q(w) | u, Q)αL(w | u, Q) ∝ Pr(w) · S(u | w, Q)–
QUDmax (w) = w

Uniform CS + QUDmax CG prior + QUDmax CG prior + QUDnow
L0 (Q(w) | u,C, Q) ∝ ∑w0 ∈C∩JuK δQ(w)=Q(w0 ) · Pr(w0 )S(u|w,C, Q) ∝ Pr(u) · L0 (Q(w) | u,C, Q)α
L(w,C | u, Q) ∝ Pr(w) · Pr(C) · S(u | w,C, Q)
Pr(C) ∝ 1
Pr(C) ∝ ∑CG⊆Obs P(CG) · δC=∩CG
QUDmax (w) = w
QUDmax (w) = w
QUDnow ((x, y)) = y

Table 2: Specifications of four RSA models , with Pr(w) ∝ 1 and Pr(u) ∝ 2−#content-words(u) for all four models(T, F)(T, F)(T, F)(T, F)

world(T, T)

world(T, T)

world(T, T)

world(T, T)(F, T)(F, T)(F, T)(F, T)(F, F)(F, F)(F, F)(F, F)

0.00

0.25

0.50

probability

0.75(a) No CG + QUDmax

1.00

0.00

0.25

0.50

probability

0.75

1.00

(b) Uniform CS + QUDmax

0.00

0.25

0.50

probability

0.75

1.00

(c) CG prior + QUDmax

0.00

0.25

0.50

probability

0.75

1.00

(d) CG prior + QUDnow

Figure 1: Pragmatic listener after hearing “John did not stop smoking” for each model, with α = 6
The pragmatic listener, given the QUD, infers the actual
world given the speaker’s utterance, using Bayes’ rule (4).
L(w | u, Q) ∝ Pr(w) · S(u | w, Q)(4)
The standard RSA model is summarized in the first columnof Table 2, and the predicted pragmatic listener’s distribution
over worlds is shown in Figure 1(a). As we can see, thestandard RSA model predicts a uniform distribution over thethree worlds that are consistent with the literal meaning of“John did not stop smoking”. It therefore fails to capture theprojective content — the inference that John used to smoke.
The reason for this failure is that “John did not stop smoking” is equally under-informative in any of the three worlds
compatible with its literal meaning. For example, suppose theactual world is (T, T ). Since the literal listener will return thisworld with probability only 1/3 after hearing “John did notstop smoking,” the speaker is unlikely to choose this utterance.
She is more likely to say “John has always smoked” instead,which will always induce the correct answer. The same holds
for the other two worlds (F, T ) and (F, F) and therefore thepragmatic listener in the standard RSA model will infer thatthe three worlds are equally likely.
RSA with common groundWe have seen that one important reason that the standard
RSA model fails to capture the projective content of “John
did not stop smoking” is that its literal meaning is underinformative when considered in the entire universe U. However, as discussed before, there can be information taken for
granted by the speaker and the listener, i.e., the common
ground, and an utterance that is under-informative when considered in the entire universe U may nevertheless be informative when evaluated in the common ground. To formalize thisobservation, we now add common ground to the RSA model.
We first define a related notion. A context set C is a non-empty subset of the universe (Stalnaker, 1974). Since we have
4 possible worlds, there are 24 − 1 = 15 different context sets.
These context sets are intuitively named. For example, +past
is the context set that contains (T, T ) and (T, F), +past+now
contains only (T, T ), ∼+past+now contains all the worlds except (T, T ) (∼ A is defined to be U − A, i.e., A’s complement),
and change is the context set that contains (T, F) and (F, T ).
A literal listener, given an utterance, the current context set
and QUD, randomly samples a world that is consistent withboth the utterance and the context set, and returns the value ofthe QUD in that world, as in (5).
L0 (Q(w) | u,C, Q) ∝∑

δQ(w)=Q(w0 ) · Pr(w0 )(5)

w0 ∈C∩JuK

For example, given context set +past and QUDmax , after
hearing “John did not stop smoking,” the literal listener willrule out (T, F) because of the utterance’s literal meaning, and(F, T ) and (F, F) because they are incompatible with the context set. Therefore he will always return (T, T ). We can see
from this example that an utterance that is under-informative
when the entire universe is considered can be informative insome other context sets.
The new speaker model is almost the same as (3), exceptthat it is relativized to the current context set, as in (6).
S(u|w,C, Q) ∝ Pr(u) · L0 (Q(w) | u,C, Q)α(6)Finally, given an utterance and the QUD, the pragmatic
listener now jointly infers the real world and the context set
the speaker assumes when she produces the utterance.
L(w,C | u, Q) ∝ Pr(w) · Pr(C) · S(u | w,C, Q)(7)

We need to specify a prior distribution Pr(C) over context
sets in (7). We consider two possibilities. First, we consider
a uniform distribution over all context sets, i.e., Pr(C) ∝ 1.

world, context set(T, T), U(T, T), +past+now(T, T), ~+past−now(T, T), ~−past+now(T, T), ~−past−now(T, T), +past(T, T), +now
(T, T), ~change(F, T), U(F, T), −past+now(F, T), ~+past+now(F, T), ~+past−now(F, T), ~−past−now(F, T), −past(F, T), +now
(F, T), change(F, F), U(F, F), −past−now(F, F), ~+past+now(F, F), ~+past−now(F, F), ~−past+now(F, F), −past(F, F), −now
(F, F), ~change

world, context set(T, T), U(T, T), +past+now(T, T), ~+past−now(T, T), ~−past+now(T, T), ~−past−now(T, T), +past(T, T), +now
(T, T), ~change(F, T), U(F, T), −past+now(F, T), ~+past+now(F, T), ~+past−now(F, T), ~−past−now(F, T), −past(F, T), +now
(F, T), change(F, F), U(F, F), −past−now(F, F), ~+past+now(F, F), ~+past−now(F, F), ~−past+now(F, F), −past(F, F), −now
(F, F), ~change
0.00

0.25

0.50

0.75

probability

1.00(a) Uniform CS + QUDmax

0.00

0.25

0.50

0.75

probability

1.00(b) CG prior + QUDmax

Figure 2: Pragmatic listener after hearing “John did not stop smoking,” with α = 6Assuming the maximal QUD, the model is summarized in
the second column of Table 2 and the pragmatic listener’s
marginal distribution over worlds is shown in Figure 1(b). We
can see that this model predicts that (F, T ) is slightly less likely
than (T, T ) and (F, F), and (T, T ) has the same probability as(F, F). This does not capture projection.
The second possibility makes use of the notion of a common ground (CG) in the pragmatic approach to derive a priorover context sets (Stalnaker, 1974). Intuitively, a common
ground represents everything that is taken for granted for conversational purposes. Formally it is a set of propositions (aproposition is a set of worlds), all of which are taken for
granted. The context set C, as defined above, can be thoughtof as the conjunction ofTall of the propositions that are being
taken for granted: C = CG.
In our example scenario, Alice (the speaker) could reasonably take for granted certain propositions representing plausible observations about John’s smoking habits — whether hesmoked in the past, and whether he does now. Therefore, assuming that the propositions in the common ground come fromobservations about John’s past and present smoking habits,
we can use (8) to naturally define a prior over context sets(henceforth the CG prior).
Pr(C) ∝∑ P(CG) · δC=∩CG(8)CG⊆ObsConcretely, we assume that each of the observations enters
the common ground independently, with probability .4 (meaning that the speaker does not tend to take things for granted).
In addition, we add a small amount (5%) of noise to (8), sothat every non-empty C has a nonzero prior probability. Thismodel assigns low prior probability to those context sets thatcannot be built up via conjunctions of natural observations.
One example of such a context set is change, the rather complex assumption that John has either switched from smoking
to not, or switched from not smoking to smoking — but we do
not know which. In contrast, context sets such as +past (i.e.,taking for granted that John used to smoke) and -past-now(i.e., John did not smoke and does not smoke now) receive
higher probabilities because they correspond to observations
that the speaker could plausibly have made.
Using the CG prior (the model is summarized in the thirdcolumn of Table 2), the pragmatic listener’s marginal distribution over worlds is shown in Figure 1(c). We can see that thismodel predicts that world (F, T ) is very unlikely, and world(T, T ) has the same probability as world (F, F). Although it
still does not capture projection because (T, T ) is predicted to
be as likely as (F, F), the model correctly predicts that (F, T )is unlikely. Therefore we have made some progress.
To better understand how the CG prior improves the modeland what the remaining problem is, we plot the pragmatic
listener’s joint distribution of world and context set in Figure 2.
In Figure 2(a), with a uniform prior over context sets, thepragmatic listener has 3 most likely outcomes: world (T, T )with context set +past, world (F, F) with context set -now,
and world (F, T ) with context set change (this last outcome isslightly less likely than the first two). This is because in theseoutcomes, “John did not stop smoking” can fully identify theworld given the context set, and hence these outcomes best
explain the speaker’s utterance. As a result, the marginal
distribution over worlds is almost uniform over the 3 worlds.

world, context set(T, T), U(T, T), +past+now(T, T), ~+past−now(T, T), ~−past+now(T, T), ~−past−now(T, T), +past(T, T), +now
(T, T), ~change(F, T), U(F, T), −past+now(F, T), ~+past+now(F, T), ~+past−now(F, T), ~−past−now(F, T), −past(F, T), +now
(F, T), change(F, F), U(F, F), −past−now(F, F), ~+past+now(F, F), ~+past−now(F, F), ~−past+now(F, F), −past(F, F), −now
(F, F), ~change
0.00

0.25

0.50

0.75

probability

1.00

Figure 3: Pragmatic listener after hearing “John did not stopsmoking,” with α = 6, CG prior + QUDnow
In contrast, in Figure 2(b), with the CG prior, world (F, T )with context set change is no longer a likely outcome, because as noted earlier, the context set change is assigned avery low prior. This is why world (F, T ) is correctly predicted
to be unlikely. Although the CG prior we introduce above is
probably over-simplified, the crucial assumption we need isjust that not all context sets are equally likely a priori, and inparticular change is a fairly unusual context set and should be
assigned a low prior probability, which seems intuitively plausible. As long as this assumption is satisfied, there could bealternative ways to motivate a more realistic prior over context
sets without affecting the model’s qualitative prediction.
Nevertheless, we can see that world (F, F) with common
ground -now is still one of the most likely outcomes in Figure 2(b), and hence the marginal probability of (F, F) is thesame as (T, T ) in Figure 1(c). This is not desirable, but is
totally expected from the model: the prior for context set -nowis the same as for context set +past. Therefore, to fully capture projective behavior, we need to further explain why (F, F)
with context set -now is dispreferred.
Non-maximal QUDs So far, we have been assuming that
the QUD is maximal, i.e., the utterance “John did not stopsmoking” is chosen to address the question of whether Johnsmoked in the past and whether John smokes now. For this
QUD, the RSA model with common ground prior predictsa tie between (T, T ) with context set +past and (F, F) with
context set -now.
The maximal QUD is often assumed in applications of RSA
models (though see Kao, Bergen, and Goodman (2014)), but
in this case there are good reasons to consider non-maximal
QUDs. Empirically, as noted in the beginning, projection
is sensitive to the QUD. Theoretically, there has been a lotof discussion in the previous literature on the relation between at-issueness and projection (Beaver, 2010; Simons, Tonhauser, Beaver, & Roberts, 2010). Their notion of at-issuenessroughly corresponds to QUDs in our model, which may be
non-maximal.
In our running example, Bob explicitly asked about whether
John smokes, which means that the QUD is presumably
QUDnow (i.e., “Does John smoke?”). When we use the previous RSA model with the common ground prior, but replace
QUDmax with QUDnow (summarized in the last column ofTable 2), the pragmatic listener’s marginal distribution overworlds is shown in Figure 1(d) and the joint distribution ofworld and context set is in Figure 3. We can see from Figure 3
that (T, T ) with context set +past is the only most likely outcome, and the world (T, T ) is the only most likely world (andits probability increases with a higher α). This is exactly the
projection pattern we aim to capture.
To understand why we obtain this result, we note that when
the QUD is QUDnow , (F, F) with context set -now is dispreferred because the context set -now already entails the answer
to the QUD. That is, it is already known from the context
set -now that John does not smoke now. This means thatthe speaker would be maximally informative even if he says
nothing. As a result, the speaker would be unlikely to say“John did not stop smoking” when the context set is -now, andthe pragmatic listener could therefore infer that the context
set -now is unlikely, which means that (T, T ) with context set+past is the only winner.
Hence the current model predicts the projective behavior for“John did not stop smoking” in the example scenario, where
the QUD is explicitly given by Bob’s question. Assumingthat people generally care about information about now rather
than the past, i.e., the default or most salient QUD is QUDnow ,the model predicts that the preferred projective content of“John did not stop smoking” without explicit QUD is that Johnsmoked in the past. Note that our speaker model predicts
that “John did not stop smoking” is very unlikely to be used
to answer QUDnow , as there exist simpler utterances “Johnsmokes/does not smoke.” This explains the perceived weirdness of Alice’s indirect answer to Bob’s explicit question.
Other QUDs We have introduced a RSA model with
common ground and shown its predictions for QUDnow and
QUDmax . The prediction is sensitive to the QUD—in Figure 4
we show predictions for eight different QUDs. In general, it
seems that the model is making plausible predictions. The
utterance “John did not stop smoking” implies that John has always smoked if the QUD is whether John has always smoked(Figure 4(e)).2 It implies that John has never smoked when the
QUD is whether John has never smoked (Figure 4(h)). When
the QUD is about whether John stopped smoking (Figure 4(f))
or there is a change (Figure 4(d)), the listener will believe thatJohn smoking in the past is about 50% likely (recall Geurts’
example described earlier). These results are compatible with
Simons et al.’s generalization that only non-at-issue content
projects. But further experimental data will be needed toassess whether they are borne out.
2 Note that QUDs are just partitions and not presuppositional. We
use, e.g., always to describe the QUDs only as a mnemonic device.

(T, F)(T, F)(T, F)(T, F)

world(T, T)

world(T, T)

world(T, T)

world(T, T)(F, T)(F, T)(F, T)(F, T)(F, F)(F, F)(F, F)(F, F)

0.00

0.25

0.50

probability

0.75

1.00

0.00

(a) QUDmax

0.25

0.50

probability

0.75

1.00

0.00

(b) QUDnow

0.25

0.50

probability

0.75

1.00

0.00

(c) QUDpast(T, F)(T, F)(T, F)(F, T)(F, T)(F, T)(F, T)(F, F)(F, F)(F, F)(F, F)

0.50

probability

0.75

1.00

(e) QUDalways

0.00

0.25

0.50

probability

0.75

1.00

(f) QUDstop

0.75

1.00

world

(T, F)

world(T, T)

world(T, T)

world(T, T)

0.25

0.50

probability(d) QUDchange(T, T)

0.00

0.25

0.00

0.25

0.50

probability(g) QUDstart

0.75

1.00

0.00

0.25

0.50

probability

0.75

1.00

(h) QUDneverFigure 4: Pragmatic listener after hearing “John did not stop smoking” for different QUDs, with α = 6 and CG priorConclusion and future directions
In this paper, we introduced a probabilistic model in the RSA
framework, which analyzes the projective content of changeof-state verbs under negation as the result of the listener using
general conversational principles to jointly infer the actual
world and the context set that the speaker assumes The model
predicts an interaction between projection and the question
under discussion, formalizing insights of previous pragmatic
approach to projection and providing concrete quantitative
predictions that we plan to test experimentally.
Our model is a first step towards a full integration of pragmatic approach to the projection problem into a general probabilistic model of language understanding. We plan to further
explore the model and see to what extent it can be generalized to other types of projective content and other entailmentcanceling operators, which will help us further understandthe division of labor between semantics and pragmatics in the
projection phenomena.

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