报告
Prior Beliefs Modulate Projection
Judith Degen1 and Judith Tonhauser2
1语言学系, 斯坦福大学
2Department of English Linguistics, University of Stuttgart
关键词: experimental semantics, experimental pragmatics, 投影
开放访问
杂志
抽象的
Beliefs about the world affect language processing and interpretation in several empirical
域. In two experiments, we tested whether subjective prior beliefs about the probability
of utterance content modulate projection, 那是, listeners’ inferences about speaker
commitment to that content. We find that prior beliefs predict projection at both the group and
the participant level: the higher the prior belief in a content, the more speakers are taken to be
committed to it. This result motivates the integration of formal analyses of projection with
cognitive theories of language understanding.
介绍
Psycholinguistic work has documented several ways in which probabilistic beliefs about the
世界, often termed world knowledge, affect language processing (例如, Chambers et al., 2002;
Hagoort et al., 2004; Hald et al., 2007; Warren & McConnell, 2007), including syntactic am-
biguity resolution (例如, 比克内尔 & Rohde, 2014; Chambers et al., 2004), reference resolution
(例如, Hanna & Tanenhaus, 2004; 维诺格勒, 1972), genericity (例如, Tessler & 古德曼,
2019), scalar implicature (例如, Degen et al., 2015), underinformativity implicatures
(Kravtchenko & 登贝格, 2015), and the production of redundant referring expressions
(Degen et al., 2020; 米切尔等人。, 2013; Rubio-Fernández, 2016; Sedivy, 2003;
Westerbeek et al., 2015). 相比之下, formal linguistic research on meaning in the tradition of
Montague (1973), which is devoted to specifying how meanings of expressions are computed
from the meanings of the parts of the expressions, the way the parts are combined, and the con-
texts in which the expressions are used, has often sidelined world knowledge as nonlinguistic,
encyclopedic knowledge that must enter into the meaning computation, but whose effect has
eluded systematic investigation and formalization (for relevant discussion see, 例如, Beaver,
2001; Dowty, 1986; Hobbs, 2019; Peeters, 2000).1 在本文中, we provide empirical evi-
dence from English that projection, a key topic in linguistic research on meaning, is systemati-
cally modulated by listeners’2 subjective beliefs about the world. This provides further impetus
1 Because knowledge implies justified true belief but subjective beliefs need not be accurate to affect language
processing in systematic ways, we henceforth avoid the term world knowledge and instead refer to (subjective
prior) beliefs about the world.
2 We include readers, writers, and signers in the terms listener and speaker.
引文: Degen, J。, & Tonhauser, J.
(2021). Prior Beliefs Modulate
Projection. 开放的心态: Discoveries in
认知科学, 5, 59–70. https://土井
.org/10.1162/opmi_a_00042
DOI:
https://doi.org/10.1162/opmi_a_00042
补充材料:
https://doi.org/10.1162/opmi_a_00042
已收到: 19 二月 2021
公认: 29 六月 2021
利益争夺: 作者
declare that no conflict of interest.
通讯作者:
Judith Degen
jdegen@stanford.edu
版权: © 2021
麻省理工学院
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Prior Beliefs Modulate Projection Degen and Tonhauser
for accounts of meaning computation to include a mechanism for integrating subjective prior
信仰. We provide a sketch of such an account at the end of this article.
To introduce projection, consider first that speakers can present themselves, through their
utterances, as believing that a particular content is true, 那是, as committed to that content.
Listeners, 反过来, regularly draw inferences about which content speakers present themselves
as committed to. 例如, if a speaker utters Sam knows that it’s raining, listeners typically
infer that the speaker is committed to the following two contents: (我) the content of the com-
补充 (CC) of know, that it’s raining; 和 (二) the content of the matrix clause, that Sam
knows (我). In formal research on meaning, the inference to (二) is attributed to the speaker having
uttered the sentence, and the inference to (我) is attributed to a particular aspect of the lexical
meaning of know, 具体来说, that if an individual knows some content p, then p is true (例如,
Chierchia & McConnell-Ginet, 1990). The puzzle is that the inference to (我) may persist even
when the speaker inquires about what Sam knows, as in Does Sam know that it’s raining?, or when
the speaker denies Sam’s knowledge, as in Sam doesn’t know that it’s raining. Because Sam’s
knowledge is questioned or even denied in these variants, 那是, the inference to (二) 不
persist, these inferences to (我) cannot be attributed to the aforementioned lexical meaning of
知道. This phenomenon of speaker commitment to utterance content that occurs in negated
sentences or questions is termed projection. Decades of research in formal semantics have
aimed to explain why content projects (例如, Beaver & Geurts, 2014; Langendoen & Savin,
1971).
While content is standardly taken to either project or not (Beaver & Geurts, 2014), 最近的
experimental work suggests that projection is gradient: listeners’ inferences about speaker
commitment to utterance content vary in strength. This experimental work suggests that sev-
eral factors modulate the strength of the inference, including the expression (例如, know vs.
discover vs. announce), the discourse status of the content, and the prosody of the utterance
(for an overview see Tonhauser, Beaver, & Degen, 2018). The hypothesis that listeners’ prior
beliefs modulate projection was initially put forth by Stevens et al. (2017) and Tonhauser et al.
(2018), who observed by-item projection variability for different CCs of clause-embedding
predicates like know and discover. They argued that one source of the observed variability
may be that more a priori likely content (Kim flew to New York) projects more strongly than
less a priori likely content (Kim flew to the moon) when realized as the CC of a clause-
embedding predicate (as in Did John discover that Kim flew to New York/the moon?). 这
idea can straightforwardly be made sense of under recent Bayesian accounts that treat prag-
matic utterance interpretation as a matter of combining uncertain prior beliefs about the world
with uncertain beliefs about likely speaker production choices via Bayes’ rule (Degen et al.,
2015; 古德曼 & Frank, 2016): a CC that is more likely a priori (before observing an utter-
安斯) is also more likely a posteriori (after observing an utterance).
There is conflicting evidence for the hypothesis that prior beliefs modulate projection.
Support for the hypothesis comes from Mahler (2020), who investigated the projection of po-
litically charged CCs of English clause-embedding predicates. 例如, the politically
charged content in (1) is that Obama improved/damaged the American economy. The prior
probability of the content was manipulated by the speaker (Cindy in [1]) speaking at the club
meeting of either the College Republicans or Democrats.
(1) Cindy, at the College Republicans/Democrats club meeting: Ben doesn’t know that …
A. … Obama improved the American economy.
乙. … Obama damaged the American economy.
(Mahler, 2020, PP. 784–785)
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Prior Beliefs Modulate Projection Degen and Tonhauser
Higher prior probability content (例如, a liberal content like [1A] uttered by a Democrat) 曾是
more projective than lower prior probability content (例如, a liberal content uttered by a
Republican).
相比之下, Lorson (2018) did not find empirical support for the hypothesis that listeners’
prior beliefs modulate projection in a study of the projection of the prestate content of the
English change of state verb stop. Prior probability was manipulated through gender stereo-
types reported in Boyce, 从 马尔斯堡, Poppels, and Levy (2018). 例如, 因为
men are more likely than women to be plumbers, the prestate content of (2A), that James has
worked as a plumber, was hypothesized to be more projective than the prestate content of
(2乙), that Linda has worked as a plumber.
(2)
A. Did James stop working as a plumber?
乙. Did Linda stop working as a plumber?
(Lorson, 2018, p. 38)
Several differences between Mahler (2020) and Lorson (2018) could be implicated in the
differential support for the hypothesis: (A) the projective content investigated (CCs vs. prestate
content of stop); (乙) stimulus type (negated sentences vs. 问题); (C) the manipulation of
prior beliefs (political party affiliation vs. gender stereotypes); 和 (d) how explicitly the
prior-manipulating information was provided to participants (statement of political party affil-
iation vs. use of a male or female name to indicate gender). The two experiments reported on
in this article provide additional support for the hypothesis that prior beliefs modulate projec-
的. The experiments included 20 clause-embedding predicates (rather than just 7, 如
Mahler, 2020) and the prior belief manipulation involved 20 properties of individuals, 相当
than just political party affiliation (as in Mahler, 2020), or gender (as in Lorson, 2018).
此外, we tested the hypothesis both at the level of the individual and of the group:
实验 1 investigated the effect of prior beliefs on projection by measuring prior probability
and projection in a within-participant design. In Experiments 2a and 2b, prior probability and
projection were measured in separate groups, as in Mahler (2020) and Lorson (2018).
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EXPERIMENT 1
This experiment tested whether higher prior probability content is more likely to project than
lower probability content. Prior probability and projection ratings were collected for the con-
tents of 20 clauses that realized the complements of 20 clause-embedding predicates.3
方法
Participants Three hundred participants with U.S. IP addresses and at least 99% of previous
human intelligence tasks (HITs) approved were recruited on Amazon’s Mechanical Turk plat-
形式 (年龄: 18–82, median: 35.5; 119 女性, 179 male, 1 其他, 1 undeclared). They were
paid $1.80 and took 9.1 minutes on average to complete the experiment.
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3 The experiments, data and R code for generating the figures and analyses of the experiments reported on in
this article are available at https://github.com/judith-tonhauser/projective-probability. 实验 1 was prere-
gistered: https://osf.io/vd9ru/. All experiments were conducted with approval from the institutional review board
of The Ohio State University and informed consent was obtained.
开放的心态: 认知科学的发现
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Prior Beliefs Modulate Projection Degen and Tonhauser
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数字 1. Example trials and 20 clause-embedding predicates. A. Example target trial in prior block. 乙. Example target trial in projection
block. C. 这 20 clause-embedding predicates. D. Example filler trial in prior block. 乙. Example control trial in projection block.
Materials and Procedure The prior probability and projection of the contents of 20 条款
were measured in separate blocks. Each clause (例如, Julian dances salsa) was paired with
two facts between participants: The content of the clause was expected to have a higher prior
probability in the presence of one fact (例如, Julian is Cuban) than of the other (例如, Julian is
德语). See the Supplemental Materials for the full set of clauses and facts.
In the prior block, 这 20 clauses were realized as the complements of How likely is it
that … ? 问题. As shown in Figure 1A, each target stimulus consisted of one of the two
facts for that clause and the How likely is it that … ? 问题. Participants read the fact and
assessed the likelihood of the content, given the fact. They gave their responses on a slider
marked “impossible” at one end (coded as 0) and “definitely” at the other (coded as 1).
In the projection block, target stimuli consisted of a fact and a polar question that was ut-
tered by a named speaker, as shown in Figure 1B. The polar questions were formed by real-
izing the 20 clauses as the complements of the 20 clause-embedding predicates in Figure 1C.
Participants were told to imagine that they are at a party and that, on walking into the kitchen,
they overhear somebody ask somebody else a question. Projection was measured using the
“certain that” diagnostic (Djärv & Bacovcin, 2017; Lorson, 2018; Mahler, 2020; Tonhauser
等人。, 2018): participants were asked to rate whether the speaker was certain of the CC, 采取
into consideration the fact. They gave their responses on a slider marked “no” at one end
(coded as 0) and “yes” at the other (coded as 1). Greater speaker commitment to the CC should
result in higher slider ratings.
The projection block also included six control trials, which functioned as attention checks.
The content of these stimuli was expected not to project: 例如, in Figure 1E, 这
开放的心态: 认知科学的发现
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Prior Beliefs Modulate Projection Degen and Tonhauser
数字 2. Mean prior probability by content and fact in Experiment 1. Error bars indicate 95% bootstrapped confidence intervals.
Transparent dots indicate individual participant ratings.
speaker is not committed to the main clause content, that Samantha has a new hat. 相同
six main clauses were also used to form 6 filler trials in the prior block; a sample stimulus is
given in Figure 1D. These filler stimuli were not used to assess participants’ attention. 为了
full set of stimuli see the Supplemental Materials.
Each participant’s stimulus set was semi-randomly generated by first randomly pairing up
这 20 predicates and clauses. Half of the stimuli were then randomly assigned the respective
clause’s higher-probability fact, and half its lower-probability fact. Participants completed a
total of 52 试验: 20 target trials in each block, six control trials in the projection block, 和
six filler trials in the prior block. Each participant completed the same six filler and control
试验. Block order and within-block trial order were randomized.
After completing the experiment, participants filled out a short optional demographic sur-
vey. To encourage truthful responses, participants were told that they would be paid no matter
what answers they gave in the survey.
Data Exclusion Data were excluded based on self-declared non-native speaker status and other
criteria given in the Supplemental Materials, 离开 5,720 data points from 286 participants to
be analyzed (ages 18–82; median: 35.5; 116 女性, 186 male, 1 其他, 1 undeclared).
Results and Discussion
Prior Beliefs Figure 2 shows the mean prior probabilities of the 20 contents by fact. 我们骗-
ducted a mixed-effects linear regression predicting slider rating from dummy-coded fact type
(reference level: “lower probability”) and random by-item and by-participant intercepts and
slopes for fact type.4 Each content’s mean prior probability was rated as higher when it was
presented with its higher probability fact than when it was presented with its lower probability
4 All analyses were conducted in R (R核心团队, 2016) using the lme4 package (Bates et al., 2015).
开放的心态: 认知科学的发现
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Prior Beliefs Modulate Projection Degen and Tonhauser
数字 3. Mean certainty ratings by predicate and prior probability of the content of the com-
plement in Experiment 1. Error bars indicate 95% bootstrapped confidence intervals. Light dots
indicate participants’ ratings.
事实 (β = 0.45, SE = 0.01, t = 31.12, p < .0001). This suggests that the manipulation of the prior
probability of the 20 contents was successful.
Do Prior Beliefs Modulate Projection? Figure 3 shows the mean certainty ratings for the CCs by
predicate and by fact, as well as the mean certainty rating for the main clause controls (abbre-
viated MC). Each predicate/clause combination was rated 5–25 times (mean 14.3). We con-
ducted a mixed effects linear regression predicting certainty ratings from dummy-coded fact
type (reference level: “lower probability”) and random by-item and by-participant intercepts
and slopes for fact type. The mean certainty ratings were higher for contents presented with
higher probability facts than for contents presented with lower probability facts ( β = 0.14, SE =
0.01, t = 12.24, p < .0001). The same was true when using the group-level by-item mean prior
belief as a predictor ( β = 0.31, SE = 0.02, t = 12.58, p < .0001). This suggests that participants’
prior beliefs about content probability systematically modulated the extent to which they take
the speaker to be committed to that content.
We also replicated the by-predicate variability in the projection of the CC observed by
Tonhauser and Degen (2020): for instance, the CC of be annoyed was more projective than
that of discover, which in turn was more projective than that of announce. The Spearman rank
correlation between the mean certainty ratings in Experiment 1 (collapsing over facts) and
Experiment 1a of Tonhauser and Degen (2020) is .991; see the Supplemental Materials for
a visualization. Experiment 1 thereby also provides further evidence for the systematic influ-
ence of the predicate on projection. Crucially, the effect of the prior was observable indepen-
dently of the predicate.
Closer inspection of Figure 2 reveals by-participant variability in prior probability ratings,
suggesting that individual participants’ prior beliefs may not align with the prior probability
classification assumed in Figure 3. For example, given a particular content ( Julian dances
OPEN MIND: Discoveries in Cognitive Science
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Prior Beliefs Modulate Projection Degen and Tonhauser
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Figure 4. Certainty ratings against individual prior probability ratings for each predicate in Experiment 1. Linear smoothers with 95%
confidence intervals are overlaid.
salsa), it is possible that one participant’s prior probability rating was lower than that of another
participant, even though the first participant was presented with the higher probability fact
( Julian is Cuban) and the second one with the lower probability fact ( Julian is German).
Figure 4 shows participants’ certainty ratings by their individual prior probability ratings. To
investigate whether prior beliefs modulate projection at the by-participant level, we conducted
the same mixed-effects analysis reported above, but used participants’ individual, continuous
prior probability ratings as the fixed effect prior predictor. Again, higher prior–probability CCs
were more likely to project ( β = 0.28, SE = 0.02, t = 13.85, p < .0001). This suggests that prior
beliefs modulate projection even at the by-participant level. A Bayesian information criterion
(BIC) model comparison revealed that the individual-level model better captured the variance
in the data (categorical model BIC: 2654; group-level model BIC: 2586; individual-level model
BIC: 2291),5 suggesting that individual listeners’ prior beliefs systematically modulate the
5 The BIC model comparisons were not preregistered, so we also ran Akaike information criterion (AIC) model
comparisons as a robustness check. The results were qualitatively identical (categorical model AIC: 2607;
group-level model AIC: 2539; individual-level model AIC: 2244).
OPEN MIND: Discoveries in Cognitive Science
65
Prior Beliefs Modulate Projection Degen and Tonhauser
extent to which they take the speaker to be committed to a content: the more they believe it,
the more they take the speaker to believe it.
The results of Experiment 1 provide empirical support for the hypothesis that higher prior
probability content is more likely to project. It is possible, however, that the within-participant
design resulted in participants’ responses on either block influencing their responses on the
other block. To guard against this possibility, we replicated Experiment 1 by collecting prior
probability and projection ratings from different groups.
EXPERIMENT 2
Experiments 2a and 2b measured the prior probability and the projection of the 20 contents of
Experiment 1, respectively.
Methods
Participants Participants with U.S. IP addresses and at least 99% of previous HITs approved
were recruited on Amazon’s Mechanical Turk platform. The 95 participants in Experiment 2a
(ages: 21–75, median: 33; 45 female, 50 male) were paid 55 cents and took 3.9 minutes on
average to complete the experiment. The 300 participants in Experiment 2b (ages: 21–72, me-
dian: 36; 145 female, 154 male, 1 undeclared) were paid 85 cents and took 7.1 minutes on
average.
Materials and Procedures The target stimuli of Experiment 2a were identical to those of the
prior block of Experiment 1. Each participant saw two control stimuli as attention checks
(see the Supplemental Materials). The materials of Experiment 2b were identical to those of
the projection block of Experiment 1. Trial order in both experiments was random. The pro-
cedures of Experiments 2a and 2b were identical to those of the prior and projection blocks of
Experiment 1, respectively.
Data Exclusion We excluded data based on the criteria given in the Supplemental Materials,
leaving data from 75 participants to be analyzed in Experiment 2a (1,500 data points; ages 21–
75; median: 35; 34 female, 41 male) and from 266 participants in Experiment 2b (5,320 data
points; ages 21–72; median: 36; 129 female, 136 male, 1 undeclared).
Results and Discussion
Prior Beliefs Experiment 2a successfully replicated the prior probability manipulation of
Experiment 1: contents were rated as more likely when presented with a higher probability
fact ( β = 0.54, SE = 0.04, t = 15.07, p < .0001). Figure 5 shows contents’ mean prior proba-
bility ratings in Experiment 2a against those of Experiment 1. The Spearman rank correlation
was very high, at r = .977. For a visualization of the by-content prior ratings see the
Supplemental Materials.
Do Prior Beliefs Modulate Projection? Each predicate/clause combination was rated 4–27 times
(mean 13.3). Mean certainty ratings were higher for contents presented with higher prior prob-
ability facts than for contents presented with lower prior probability facts (see Figure 6). This
was true when the prior predictor was entered as a categorical predictor (reference level: “lower
probability”; β = 0.18, SE = 0.01, t = 12.81, p < .0001) and when it was entered as a continuous
predictor representing group-level prior means ( β = 0.34, SE = 0.03, t = 13.27, p < .0001).
Thus, Experiment 2b replicates the critical result of Experiment 1 that prior content probability
OPEN MIND: Discoveries in Cognitive Science
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Prior Beliefs Modulate Projection Degen and Tonhauser
Figure 5. Mean prior probability ratings in Experiment 2a against those of Experiment 1. Error
bars indicate 95% bootstrapped confidence intervals.
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Figure 6. Mean certainty ratings by predicate and prior probability of the content of the com-
plement in Experiment 2b. Error bars indicate 95% bootstrapped confidence intervals. Light dots
indicate participants’ ratings.
OPEN MIND: Discoveries in Cognitive Science
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Prior Beliefs Modulate Projection Degen and Tonhauser
modulates its projection.6 The replication suggests that the result of Experiment 1 is not an
artifact of the within-participant design of Experiment 1.
GENERAL DISCUSSION AND CONCLUDING REMARKS
We tested whether listeners’ prior beliefs modulate projection. While previous research on this
question has yielded conflicting results (Lorson, 2018; Mahler, 2020), we showed in two ex-
periments that content is more likely to project the more a priori likely it is, thus confirming the
results of Mahler (2020) and expanding on them in several ways. First, while Mahler (2020)
manipulated only the political party affiliation of the speaker, the manipulation in Experiments
1 and 2 relied on 20 distinct properties of individuals (e.g., whether Julian is more likely to
dance salsa if he is German or Cuban). Thus, the results of Experiments 1 and 2 suggest a
general effect of prior beliefs on projection. Second, our experiments show that prior beliefs
modulate projection for a wider cross-section of clause-embedding predicates, including cog-
nitive (e.g., know), emotive (e.g., be annoyed ), communication (e.g., announce), and inferen-
tial (e.g., prove) predicates. Thus, projection joins the many linguistic phenomena that are
systematically modulated by prior beliefs (Bicknell & Rohde, 2014; Chambers et al., 2004;
Degen et al., 2015; Hagoort et al., 2004; Hald et al., 2007; Kravtchenko & Demberg, 2015;
Sedivy, 2003; Tessler & Goodman, 2019; Warren & McConnell, 2007; Westerbeek et al.,
2015). Finally, the within-participant design of Experiment 1 shows that individuals’ gradient
prior beliefs better predict projection than gradient group-level beliefs,which in tum better pre-
dict projection than binary, categorical group-level beliefs (as investigated by Mahler, 2020).
This suggests that at least some by-participant variability observed in previous projection ex-
periments (see, e.g., Tonhauser et al., 2018; Tonhauser & Degen, 2020) may be due to par-
ticipants assigning different prior probabilities to investigated content.
Does our work help explain the discrepancy in findings between the work of Mahler (2020)
and Lorson (2018)? In the introduction, we raised four possibilities for the observed differ-
ences: (a) the projective content investigated (CCs vs. prestate content of stop); (b) stimulus type
(negated sentences vs. questions); (c) the manipulation of prior beliefs (political party affiliation
vs. gender stereotypes); and (d) how explicitly the prior-manipulating information was provided
to participants (statement of political party affiliation vs. use of a male or female name to in-
dicate gender). Our work used (a) CCs; (b) questions; (c) introduced novel properties of indi-
viduals; and (d) introduced prior-manipulating information via explicit statement of facts. Thus,
our work rules out option (b)—that prior beliefs don’t affect projection out of questions—but
not the other possibilities, which should be investigated in future work.
Our results have two broader implications. First, they suggest that the purview of projection
analyses is wider than assumed by current analyses, which typically limit their attention to a
narrow subset of clause-embedding predicates, like factive ones (e.g., Abrusán, 2011, 2016;
Heim, 1983; Romoli, 2015; Simons et al., 2017; van der Sandt, 1992). Rather than being cat-
egorical and limited to factive predicates, projection inferences are systematically drawn to
varying degrees as a function of at least predicate identity and prior beliefs about content.
Second, the results motivate the development of projection analyses that consider listeners’
variable subjective beliefs about the world. Given the gradient nature of the measured (prior
and posterior) beliefs and the uncertainty inherent in the different factors that have been shown
to modulate projection (e.g., at-issueness, prosody), probability theory suggests itself as a
6 28 participants took Experiment 2b after taking Experiment 2a two weeks before. Analyses that excluded
these participants’ data did not change the results. Experiment 2b also replicated the result of Tonhauser and
Degen (2020) that there is by-predicate variability in the projection of the CC; see the Supplemental Materials.
OPEN MIND: Discoveries in Cognitive Science
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Prior Beliefs Modulate Projection Degen and Tonhauser
representational framework within which to model projection. To date, only few probabilistic
models of projection have been developed (Qing, Goodman, & Lassiter, 2016; Stevens et al.,
2017). In these models, projection is the result of listeners’ reasoning about the common
ground that the speaker is assuming and the likely question that was being addressed, respec-
tively. While neither investigated the effect of prior beliefs explicitly, both models are couched
within the Rational Speech Act (RSA) framework (Franke & Jäger, 2016; Goodman & Frank,
2016), which standardly assumes that utterance interpretation is modulated by listeners’ prior
beliefs. The RSA framework is thus equipped to capture the effects reported here. We see the
implementation of projection analyses within RSA as a promising avenue for formalizing the
intricate interplay of semantic and pragmatic factors in the projection of contents of comple-
ments of clause-embedding predicates, including the conventional contribution of predicates,
content at-issueness, and subjective prior beliefs about content.
ACKNOWLEDGMENTS
For helpful comments on the research presented here, we thank the audiences at the 2018
Annual Meeting of XPRAG.de and at the University of Tübingen.
FUNDING INFORMATION
JT, National Science Foundation (https://dx.doi.org/10.13039/100000001), Award ID: BCS-
1452674.
AUTHOR CONTRIBUTIONS
JD: Conceptualization: Equal; Formal analysis: Lead; Methodology: Equal; Visualization: Lead;
Writing - Original Draft: Equal; Writing - Review & Editing: Equal. JT: Conceptualization:
Equal; Formal analysis: Supporting; Methodology: Equal; Visualization: Supporting; Writing -
Original Draft: Equal; Writing - Review & Editing: Equal.
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