1. Introduction
In natural language communication, hearers regularly infer messages beyond what is literally and explicitly said by the speaker. In doing so, they rely not only on what is said, but also on what is not said. One well-studied instantiation of this phenomenon is (the family of) implicatures, exemplified in (1) by scalar inference.
To derive the inference-enriched reading of the sentence in (1), hearers consider and reason about the informationally stronger alternative that could have been uttered in place of what has actually been uttered. In particular, hearers are taken to reason that the stronger statement (Mary ate all of the cookies) was also available to the speaker, but because she chose not to utter it, its negation can be inferred. This process can be viewed as an interaction of the Quality and Quantity maxims (Grice Reference Grice and Grice1967).
A central question that has been asked about pragmatic inferences, such as scalar inference, concerns their processing: does generating them incur processing cost? A large body of research has shown that implicature generation is indeed costly, as evidenced by increased reaction times (Bott & Noveck Reference Bott and Noveck2004), ERP data (Noveck & Posada Reference Noveck and Posada2003), and delays in eye-tracking (Huang & Snedeker Reference Huang and Snedeker2009). These results support a literal-first model of implicature processing (Huang & Snedeker Reference Huang and Snedeker2009). At the same time, however, some studies found evidence for a speedy implicature calculation process (Grodner et al. Reference Grodner, Klein, Carbary and Tanenhaus2010) – a finding compatible with the default hypothesis about implicature processing (Levinson Reference Levinson2000). On the other hand, instead of making a categorical distinction between ‘costly’ vs. ‘cost-free’ processing, a constraint-based approach views implicature calculation and processing as resulting from the interaction of multiple cues and constraints (Degen & Tanenhaus Reference Degen and Tanenhaus2015). Such a model privileges neither semantics nor pragmatics, and the research program is instead to identify and quantify the cues that modulate processing. In this paper we focus on one such cue: the Question Under Discussion (QUD).
In particular, we build on earlier work in the constraint-based framework by Degen (Reference Degen2013) and Degen & Tanenhaus (Reference Degen and Tanenhaus2015), which put forward the hypothesis that processing cost tracks the QUD. This predicts no uniform cost or lack of cost for calculating conversational implicatures per se. Instead, it attributes particular importance to supportive vs. non-supportive contexts and predicts that the likelihood of inference calculation, and crucially also whether this calculation causes a delay in reaction times, is a function of how much the target inference is supported by the QUD. When a target inference is congruent with the QUD, an increased rate of inference generation is predicted, as well as decreased reaction times. When the target inference is not supported by the QUD, the opposite pattern is predicted. Our empirical findings confirm these predictions. Specifically, in Experiment 2 we show that under a QUD that makes the target inference likely to arise, inference computation does not cause a delay in reaction times. On the contrary, under a QUD that makes inference calculation unlikely, that calculation is time-consuming. Crucially, our QUD manipulation is grounded in an elicitation study (Experiment 1), which goes beyond earlier work by relying on experimental production data to establish likely QUDs, and thus constitutes a first attempt to address the problem of systematically identifying QUDs relevant to a given context.
The empirical case study for testing the QUD-sensitivity of conversational implicatures is first scalar inference, as exemplified in (1). Our finding that QUDs modulate the calculation rate and reaction time cost of scalar inference is in line with existing work, successfully replicating previous results in a different experimental paradigm. We also extend these findings to a different kind of pragmatic inference, it-cleft exhaustivity (2):
In the case of (2), just like in (1), hearers regularly go beyond the literal meaning of the sentence and calculate the inference-enriched meaning. This suggests that, at least on a descriptive level, it-cleft exhaustivity is similar to scalar inference. Our motivation for including it-cleft exhaustivity in our empirical scope is to probe whether the hypothesis that pragmatic inferences are QUD-sensitive is more widely applicable than just to some but not all inferences. There has also been recent interest in probing the extent to which different conversational implicatures, in our case scalar inference and it-cleft exhaustivity, pattern alike (see e.g. Chemla & Bott Reference Chemla and Bott2014; van Tiel & Schaeken Reference van Tiel and Schaeken2017).Footnote 2
We are aware that the question might be raised whether these two types of inference have the same theoretical status. For example, there exist different proposals in the literature about whether the exhaustivity effect in it-clefts arises as a conversational implicature (Horn Reference Horn, Burke and Pustejovsky1981; Drenhaus, Zimmermann & Vasishth Reference Drenhaus, Zimmermann and Vasishth2011; Onea & Beaver Reference Onea, Beaver, Cormany, Ito and Lutz2011; Byram Washburn, Kaiser & Zubizarreta Reference Washburn, Mary, Zubizarreta, von Heusinger, Zimmermann and Onea2019), as a presupposition (Percus Reference Percus1997; Büring & Križ Reference Büring and Križ2013), or as part of the truth-conditional semantics (Atlas & Levinson Reference Atlas, Levinson and Cole1981; É. Kiss Reference É. Kiss1998). Similarly, it has been argued that scalar inference is located in the grammar (and is computed locally, see e.g. Chierchia Reference Chierchia and Belletti2004; Fox Reference Fox, Sauerland and Stateva2007), or on the contrary, that it is in fact pragmatic and computed globally (Horn Reference Horn1972; Gazdar Reference Gazdar1979; Atlas & Levinson Reference Atlas, Levinson and Cole1981; Sauerland Reference Sauerland2004). Regardless of one’s particular commitment about the status of these alternative-sensitive inferences, it is an empirical question whether computing inferences from these constructions is QUD-sensitive. In the current paper, we will thus sidestep the debate above and use the term implicature more broadly to refer to scalar inference and it-cleft exhaustivity. Our empirical findings showing that both scalar inference and it-cleft exhaustivity track QUDs can potentially inform that debate, but we leave that question for future work.
The rest of the paper is structured as follows. In Section 2.1, we discuss different hypotheses about the processing cost of implicatures and, in Section 2.2, the theoretical and experimental arguments for the importance of context. Section 2.3 outlines the goals and contributions of the present study. Section 3 reports on the QUD elicitation experiment that we conducted, and Section 4 presents the findings of the QUD manipulation experiment. Section 5 discusses the broader implications of our findings. Section 6 concludes.
2. Background
In this section we first review different accounts of the processing of implicatures (Section 2.1), followed by a discussion of previous work that investigated the influence of context and QUDs on the rate and cost of implicature calculation (Section 2.2). Finally, we outline the contributions of the present paper: (i) an experimental elicitation paradigm probing what QUDs are relevant in a given context, and (ii) testing the robustness of the QUD hypothesis using sentence-picture verification, extending its predictions to a previously untested pragmatic inference (Section 2.3).
2.1 The cost of implicature processing
One of the major questions in psycholinguistic studies of semantics and pragmatics is how fast implicatures are processed: are they processed on par with other inferences, i.e. does generating them incur a cost? This is meant to inform our understanding of the relations between semantic and pragmatic processes during language comprehension. In the following we review three different approaches to this question.
2.1.1 Default hypothesis
Levinson’s (Reference Levinson2000) default hypothesis takes implicatures to be default inferences, derived automatically and regardless of context. This predicts implicature calculation to be immediate and effortless, where inference-enriched interpretations will always precede and be accessed faster than literal interpretations. On the contrary, it is canceling a conversational implicature that requires processing resources, and therefore time. This is offered as a solution to the puzzle of the communicative bottleneck: communication proceeds remarkably quickly despite physical limits on the rate of speech production. Experimental evidence for the default hypothesis comes, among others, from Grodner et al. (Reference Grodner, Klein, Carbary and Tanenhaus2010), who found eye-tracking evidence for a rapid interpretation of the inference-enriched meaning of some. Nonetheless, though Grodner et al. (Reference Grodner, Klein, Carbary and Tanenhaus2010) showed that scalar inferences are derived without processing delay, a further prediction of the default hypothesis, namely that the derivation of the literal interpretation (some and possibly all) should be associated with a processing delay, has not been confirmed.
2.1.2 Literal-first hypothesis
The literal-first hypothesis (put forward by, among others Huang & Snedeker Reference Huang and Snedeker2009), assumes a two-stage processing sequence: literal interpretations are necessarily computed before, and therefore accessed faster than inference-enriched ones. Though scalar implicature processing may be rapid, it has to be preceded by some semantic analysis – in line with a model of linguistic architecture that takes semantic representations to serve as a mediator between phonology and pragmatics. A large body of research has indeed shown that implicature generation is costly, as evidenced by increased reaction times (Bott & Noveck Reference Bott and Noveck2004), ERP patterns (Noveck & Posada Reference Noveck and Posada2003), and delays in eye-tracking (Huang & Snedeker Reference Huang and Snedeker2009).
2.1.3 Probabilistic frameworks
Under the default and literal-first hypotheses, semantics and pragmatics are clearly separated in the grammar and processing. Probabilistic frameworks, on the other hand, do not posit such a sharp boundary; rather, semantic and pragmatic processes are taken to be intertwined. Degen & Tanenhaus’s (Reference Degen and Tanenhaus2015) constraint-based framework (see also Degen & Tanenhaus Reference Degen, Tanenhaus, Cummins and Katsos2019 for an overview), for example, does not assign a privileged status to either literal or inference-enriched readings – neither reading is taken to always require more/less processing resources or time than the other. Instead, it assumed that how fast a scalar implicature is computed is in large part determined by context. Robustness of inference calculation, as well as speed and ease of processing, depend on the strength of cues available. The more probabilistic support there is from such cues, the faster comprehenders will arrive at the inference, and the less easily cancelable that inference will be.
The primary goal of these probabilistic models is not to test whether implicatures are calculated by default or at a cost, but rather to identify and quantify the cues that hearers rely on when generating inference-enriched meanings. Cues that have been shown to have an effect on the rate or cost of implicature calculation are, e.g. the syntactic partitive or the availability of lexical alternatives (Degen & Tanenhaus Reference Degen and Tanenhaus2015); the relevance of the stronger alternative proposition (Breheny, Katsos & Williams Reference Breheny, Katsos and Williams2006; Politzer-Ahles & Fiorentino Reference Politzer-Ahles and Fiorentino2013); cognitive load (De Neys & Schaeken Reference De Neys and Schaeken2007); the speaker’s knowledge state (Goodman & Stuhlmüller Reference Goodman and Stuhlmüller2013); or face threat (Bonnefon, Feeney & Villejoubert Reference Bonnefon, Feeney and Villejoubert2009). QUDs are also taken to be such a probabilistic cue and have thus been predicted to influence implicature calculation and processing (Degen Reference Degen2013; Degen & Tanenhaus Reference Degen and Tanenhaus2015). In the following, we turn to previous work on the role of context and QUDs.
2.2 The relevance of context
It has long been noted that, depending on the discourse context, otherwise predicted implicatures can fail to arise (see e.g. van Kuppevelt Reference van Kuppevelt1996). Following Roberts ([Reference Roberts1996] 2012), we formalize context using the notion of Questions Under Discussion (QUDs), defined as the immediate topic of discussion, which proffer a set of relevant alternatives. Discourse is construed as giving rise to a stack of QUDs and the ultimate discourse purpose is to answer all of these QUDs. An assertion is felicitous, then, if it chooses among the proffered alternatives and thereby bears upon the QUD. To see how QUDs could modulate implicature calculation, let’s consider the example in (3):
Assuming the QUD How many cookies did Mary eat?, Mary ate some of the cookies and Mary ate all of the cookies are both in the set of proffered alternatives. That is, both (3a) and (3b) would be felicitous responses to the QUD. The hearer of (3a) is therefore predicted to identify (3b) as a felicitous alternative, leading them to realize that the speaker’s choice to utter (3a) implicates the negation of (3b), ultimately deriving the inference in (3c).
As the below example from Levinson (Reference Levinson2000) shows, QUDs can also discourage the calculation of an implicature:
The potentially available but dispreferred implicature in (4) would be consistent with the common ground and B’s utterance; however, it is less likely to arise than the implicature in (3), because A’s question suggests that they are only interested in whether there is at least some evidence against the criminals. Thus there is no particular reason to consider All of their identity documents are forgeries as an alternative that B could have said. We can thus see that QUDs offer a way to capture whether an implicature is more or less likely to arise.Footnote 3
As mentioned, under a probabilistic constraint-based model, QUD is one of many cues that is predicted to influence how likely an implicature is to be calculated. Predictions regarding the effect of QUDs on implicature calculation are supported by ample empirical data in experiments with both adults and children. It has long been observed that children are not adult-like in how they interpret structures that give rise to two or more competing readings, and are therefore more reluctant to calculate implicatures than adults (see e.g. Chierchia et al. Reference Chierchia, Crain, Guasti, Gualmini, Meroni, Do, Domínguez and Johansen2001; Noveck Reference Noveck2001). However, Papafragou & Tantalou (Reference Papafragou and Tantalou2004) showed that in contexts approximating naturalistic conversations, children can and do calculate implicatures. Investigating well-known lexical (some-all) as well as more context-dependent and ad hoc implicatures, the authors found that children exhibit robust rates of implicature calculation. Similar effects have been observed in the domain of scope ambiguities, where children are known to resort to surface (as opposed to inverse) scope interpretation more than adults (Musolino Reference Musolino1998, Reference Musolino, de Villiers and Roeper2011), but actually show adult-like behavior given the right context (Gualmini et al. Reference Gualmini, Hulsey, Hacquard and Fox2008).
QUDs have also been shown to induce variation in calculation rates in adult interpretations. Experiments have been carried out either using an explicit QUD (Zondervan, Meroni & Gualmini Reference Zondervan, Meroni, Gualmini, Friedman and Ito2008; Yang, Minai & Fiorentino Reference Yang, Minai and Fiorentino2018) or promoting one implicitly via a background story (Degen Reference Degen2013) or via focus intonation (Cummins & Rohde Reference Cummins and Rohde2015). Zondervan et al. (Reference Zondervan, Meroni, Gualmini, Friedman and Ito2008), Degen (Reference Degen2013), and Yang et al. (Reference Yang, Minai and Fiorentino2018) investigated some but not all scalar inferences, placing them under QUDs containing some vs. all, none vs. all and any vs. all, respectively. They found that reliably more inferences were calculated when an all-QUD is promoted. For example, Zondervan et al. (Reference Zondervan, Meroni, Gualmini, Friedman and Ito2008) presented participants with the sentence Some pizzas were delivered, which had to be evaluated with respect to either a question containing some (5), or one containing all (6).
The study found a 7% calculation rate of the some but not all inference in (5), but a 43% calculation rate in (6). Cummins & Rohde (Reference Cummins and Rohde2015) found comparable results testing a wider variety of scalar inferences, e.g. warm-not hot, which is especially important in light of recent findings that there is substantial variability among scales such as some-all vs. warm-hot with regard to the availability of the corresponding implicature (i.e. scalar diversity; van Tiel et al. Reference Tiel, Bob, Zevakhina and Geurts2016). This constitutes empirical confirmation that hearers do not always calculate scalar inference; rather, they are more or less likely to do so depending on context.
Constraint-based models predict QUDs to influence not only the likelihood of implicature calculation, but also the processing cost associated with this calculation. Indeed, Degen (Reference Degen2013) and Degen & Tanenhaus (Reference Degen and Tanenhaus2015) put forward the prediction that a QUD that makes the alternative all more relevant should lead to faster calculation of scalar inference than one that makes none salient. Degen (Reference Degen2013) explicitly manipulated the QUDs to test these predictions, and found that calculating the scalar inference is numerically faster under an all-QUD than under an any-QUD (Experiment 2a). Moreover, Degen (Reference Degen2013) and Degen & Tanenhaus (Reference Degen and Tanenhaus2015) also observed individual differences for scalar inference calculation, such that some participants consistently calculated the inference, some consistently did not, while a third group was inconsistent. The authors argued that participants’ response consistency is indicative of how much uncertainty they had about the QUD. Inconsistent participants were argued to have more uncertainty, leading to a higher cost for generating the inference. Similarly, Kursat & Degen (Reference Kursat, Degen, Denison, Mack, Xu and Armstrong2020) have found that reaction times are influenced by an interaction between the QUD and ‘participant type’ (i.e. whether or not a participant tends to calculate the inference), though their results did not reveal an overall modulating effect of QUDs.
2.3 Contributions of the present study
Existing work has thus hypothesized that the rate and speed of implicature calculation is not always uniform; rather, it depends on the QUD. Indeed, context has been shown to serve an important role in implicature calculation, modulating how likely an inference is to arise, as well as having an impact on response times. In this paper, our goal is twofold. First, we acknowledge the known problem that there exists no explicit mechanism for identifying the QUDs relevant for a given context. We make the first step to address this problem, and go beyond previous studies by establishing the relevant QUDs for a given utterance in a more empirically grounded manner, namely, by relying on experimental production data. The assumption that has often been made is that the relevant questions are the ones that contain a member of the given lexical scale, i.e. for the target sentence Mary ate some of the cookies, the possible questions would be Did Mary eat some/none/all of the cookies? Although the assumption that these are the relevant QUDs is informed by theory, there has not been systematic empirical work probing the possible range of QUDs.
Second, we further test the hypothesis that pragmatic inference generation is QUD-sensitive (Degen Reference Degen2013; Degen & Tanenhaus Reference Degen and Tanenhaus2015). Specifically, we test two predictions of the QUD hypothesis. Our first prediction is that the effect of QUDs on calculation rates extends beyond the case of scalar inference to other types of quantity implicatures, specifically it-cleft exhaustivity. Second, and more importantly, we explore the prediction that QUDs modulate not only the calculation rates of implicatures, but also the reaction time cost of that calculation. The QUD hypothesis predicts that for both scalar inference and it-cleft exhaustivity, whether cost is incurred depends on the type of question that the target sentence addresses. If a QUD supports the derivation of the inference (Inference-biasing), then there should be no increase in reaction times, but if the QUD biases against deriving the inference (Literal-biasing), processing cost is predicted.
Experiment 1 is the elicitation experiment aimed to empirically identify potential QUDs for a given context. Experiment 2 uses the elicited QUDs in a sentence-picture verification task, and shows that they modulate calculation rates and processing cost for both scalar inference and it-cleft exhaustivity. Additionally, we explore whether our findings might be informative not just regarding the presence or absence of processing cost for implicature calculation, but also regarding the exact source of this cost – especially as compared to the recent alternative-based Lexical Access account of van Tiel & Schaeken (Reference van Tiel and Schaeken2017) (Section 5.1).
3. Experiment 1: QUD elicitation
In this section we present an elicitation experiment, which established the likely QUDs for a given context for two types of quantity implicatures: scalar inference (SI) and it-cleft exhaustivity (EXH).
3.1 Participants
Forty monolingual speakers of American English participated in an online elicitation experiment, administered on the Ibex platform (Drummond Reference Drummond2007). Participants were recruited on Amazon Mechanical Turk. Native speaker status was established via a language background questionnaire, where payment was not conditioned on the participant’s response. Participants were compensated $2.00.
3.2 Task, materials, and procedure
The task was a modified sentence-picture verification task used for elicitation. Participants were provided with a background story that two people, Anne and Bob, are discussing pictures about shapes. Anne cannot see these pictures, so she is always asking Bob about what he sees. The instructions also emphasized that Bob always answers truthfully. Example (7) shows the instructions given to participants before the start of the experiment.
Participants then saw written SI and EXH target sentences paired with pictures, and were told that the sentences were Bob’s answers to Anne’s questions. Target sentences and pictures were adapted from the materials used by van Tiel & Schaeken (Reference van Tiel and Schaeken2017), with the addition of the context manipulation. The target sentences investigated were of the following form: SI: Some of the shapes are blue and EXH: It is the square that is blue. In place of Anne’s question participants saw a blank line. We present an example of a trial screen in (8).
The task was question elicitation: participants were instructed to guess what Anne’s question could have been, based on Bob’s answer and the picture, and had to provide their response in writing. We are aware that linguistically overt questions and the QUDs they evoke are different notions (see e.g. Hawkins et al. Reference Hawkins, Stuhlmüller, Degen, Goodman, Noelle, Dale, Warlaumont, Yoshimi, Matlock, Jennings and Maglio2015 and references therein). Nevertheless, this task still gathers a measure of what participants think the target sentence is in response to, and is therefore a good proxy for tracking QUDs. For ease of explication, we will refer to the stimulus questions throughout as ‘QUDs’, which strictly speaking are the conversational topics tracked by the overt questions.
There were two types of pictures: Bob’s answers were unambiguously good descriptions of Good Control pictures. For Target pictures, they were good descriptions on their literal (SI: Some and possibly all of the shapes are blue, EXH: The square is blue), but not on their inference-enriched reading (SI: Some but not all of the shapes are blue, EXH: Only the square is blue). Examples of the pictures can be seen in Figures 1 and 2 for SI and EXH respectively.
Figure 1 SI
Figure 2 EXH
SI Good Control pictures always contained five shapes, three of which matched the color mentioned in Bob’s sentence (here, blue), while two were a different color (here, yellow). SI Target pictures contained five shapes of the same color, the one mentioned in the sentence. EXH Good Control pictures depicted the shape with the color that was mentioned (here, blue square), as well as a different shape with a different color (here, red triangle). EXH Target pictures depicted two shapes of the mentioned color. Shapes were varied between triangle, circle, and square (with SI pictures containing either a mix of shapes or the same shape five times), and colors were varied between blue, yellow, red, green, orange, and black.
The experimental design included the two-level factor of Picture type as a between-participants manipulation: 20 participants saw only Good Control, and 20 other participants only Target pictures. A previous pilot with a within-participants design produced qualitatively the same results. Each participant saw 15 SI trials and 15 EXH trials. The experiment was administered in a Latin Square design.
3.3 Results and discussion
Results were coded in the following way. Whenever two responses only differed from each other in the mentioned color or shape, they were coded as the same type of question. For example, Are any of the triangles yellow? and Are any of the shapes red? were both coded as any. Under each question type, we collapsed across closely related linguistic variants, for example, any of the shapes and any shapes were both coded as any. In (9)–(10), we demonstrate the most commonly offered QUD types.
Though both SI and EXH elicited 13 distinct types of questions each, the majority of answers came from a much smaller set for both constructions. Table 1 shows the frequencies of the most frequent types of questions in the data. The question types not included here occurred with less than 5% frequency.Footnote 4
Table 1 Frequencies of elicited question types.
We can see that a small number of questions dominated in the elicitation task for each construction. But for SI, two types seem roughly equally frequent (any-and what-questions), whereas for EXH one type of question (which-questions) is clearly favored over all others.
Another observation to be made about the data is that for both Good Control and Target pictures, the same type of questions were elicited and in largely the same frequencies. This is somewhat puzzling, considering that several of the elicited questions were previously thought to bias toward one or the other interpretation. For example, all-QUDs have been argued to bias toward the enriched reading, and any-QUDs toward the literal reading. Based on this argument, we might predict that only Good Control pictures, which are compatible with the inference-enriched meaning of SI, would have elicited e.g. all-questions. Conversely, we might not have predicted Target pictures, which are not compatible with the enriched reading, to elicit all-questions. One thing to keep in mind, however, is that in this experiment we do not obtain information about what interpretation participants actually assigned to the target sentences. As many studies (including our Experiment 2) have found, some participants do judge Some of the shapes are blue to be a good description of both Good Control and Target pictures – in these cases, it is perhaps unsurprising that both pictures elicited the same type of questions. Another explanation might be that when participants provided all-questions in the Target condition, this was driven by the salience of the picture (where all shapes were blue), and not by question–answer congruence considerations. Future research should further probe these issues about the interplay of production and interpretation.
We also observe some differences between what kinds of questions the two construction types elicited, and in what frequency. As a reviewer points out, some of these differences may be due to the presuppositional difference between the SI and EXH constructions. We can see that SI sentences elicited more what-questions than EXH sentences, which in turn predominantly elicited which-questions. Which shape is blue? presupposes that there is a blue shape, but What color are the shapes? does not. The EXH construction similarly presupposes that there is something that is blue, while the SI construction asserts it. Therefore, participants may have supplied questions with the same presuppositional status as the target sentence, i.e. the answer: which-questions for EXH sentences and what-questions for SI sentences. The finding that any-questions were more frequent with SI than with EXH may also receive an explanation along these lines: any-questions are not presuppositional, but the EXH construction is. But although we recognize the appeal of this argument, the claim that question–answer pairs should be congruent in presuppositional status cannot account for the full set of data. In particular, according to such an argument, it is surprising that any-questions were elicited at all with EXH sentences: as we noted, the EXH construction carries a presupposition not present in the any-question; and given that the question-asker is stipulated to be ignorant, this presupposition should not already be in the common ground. But any-questions were in fact the second most frequent question type elicited given an EXH answer.
The primary aim of Experiment 1 was to test in a more systematic and empirically grounded manner what the likely QUDs are for a given dialogue context, where the dialogue includes either a some or an it-cleft sentence. Previous work on the role of context in SI calculation has largely assumed questions that contain members of the relevant lexical scale, while no investigation to our knowledge has been conducted about EXH in this respect. We can see that our elicitation study has indeed uncovered questions that have not been discussed in existing literature as relevant to implicature derivation or the particular target sentences, e.g. the what- and which-QUDs. On the other hand, some questions previously discussed in theoretical or experimental contexts did in fact show up in our elicitation data, e.g. any-, some-, and all-QUDs.
Experiment 1 established likely QUDs whose effects on SI and EXH computation we can then investigate. We therefore took the most frequent questions for each construction from Experiment 1 and used them in Experiment 2 to see if they modulate implicature calculation rates and processing cost.
4. Experiment 2: QUDs modulate calculation rates and processing cost
We present a sentence-picture verification experiment, where we embedded scalar inference and it-cleft exhaustivity sentences under the most frequent QUDs elicited in Experiment 1. Our results showed that the probability of inference calculation, as well as whether there is an increase in reaction times, is conditioned on the QUD.
4.1 Participants
Ninety (30 in each QUD condition, different from those in Experiment 1) native monolingual speakers of American English participated in the experiment, administered on the Ibex platform (Drummond Reference Drummond2007). Participants were recruited on Amazon Mechanical Turk. Native speaker status was established via a language background questionnaire, where payment was not conditioned on the participant’s response. Participants with a mistake rate exceeding 25% on filler items were removed from the analysis. This resulted in the removal of one participant from the wh-word experiment and four participants from the quantifier-experiment. Participants were compensated $1.50.
4.2 Task, materials, and procedure
Experiment 2 employed the sentence-picture verification paradigm, with target sentences embedded in a dialogue context. Participants were given the same background story as in Experiment 1: Anne is asking questions from Bob, about pictures that only Bob can see. On the first screen, participants saw Anne’s question, and they were instructed to press a key after they have read it. On the following screen, they saw Bob’s answer to Anne’s question, as well as the picture they were discussing. Participants were instructed to make a binary judgment (by clicking on a button) about whether Bob gave a good answer to Anne’s question, given the picture he saw. The two buttons said ‘Good’ and ‘Not Good’. Participants’ choices were recorded, as well as reaction times from the onset of the second screen (displaying Bob’s utterance and the picture) until the participant pressed one of the buttons.
The experiment featured a three-by-three design: crossing Picture (within participants: Good Control, Bad Control, Target) and QUD (between participants: wh-word, indefinite, quantifier). Similarly to Experiment 1, there were two types of pictures: Control, of which Bob’s sentence was an unambiguously good/bad description, and Target, where the judgment depends on whether the inference has been derived – see Figures 3 and 4. Bob’s answers are good descriptions of the Target pictures on their literal, but not on their inference-enriched reading. Good Control and Target pictures were identical to those used in the elicitation experiment. Note that for Experiment 2, Bad Controls were also added. SI Bad Control pictures contained five shapes, none of which has the color (here, blue) mentioned in the sentence. EXH Bad Controls contained the shape mentioned in the sentence, but in a color different from the one in the sentence (here, black square), while the mentioned color showed up on a different shape (here, blue circle).
Figure 3 SI
Figure 4 EXH
The QUD condition (i.e. Anne’s questions) was also a three-level manipulation: wh-word, indefinite, and quantifier questions. These questions were the most frequent elicited questions in Experiment 1 (see Table 1), with the exception of the both-question (in EXH), which we added as a counterpart to the all-question (in SI). Examples (11)–(12) provide examples of the question manipulation for each construction. (Wherever there are two questions listed, half the participants saw one variant, and half the other variant.)
QUD was manipulated between participants, placing each participant in either the wh-word, the indefinite, or the quantifier QUD condition. To prevent fatigue effects due to only encountering the same type of question, experimental items were intermixed with filler items, which included different shapes and questions unrelated to either inference, or QUD type. Each participant saw 12 SI, 12 EXH and 12 filler trials. The experiment was administered in a Latin Square design.
4.3 Predictions
Existing experimental work has shown that QUDs affect how likely an implicature is to be calculated (Section 2.2) – an effect we predict to extend to the previously untested it-cleft exhaustivity. Based both on previous empirical results (Zondervan et al. Reference Zondervan, Meroni, Gualmini, Friedman and Ito2008; Degen Reference Degen2013) and theoretical proposals (Hulsey et al. Reference Hulsey, Hacquard, Fox and Gualmini2004), we can make the prediction that for SI, all-QUDs would result in the highest rate of implicature calculation. Any-QUDs, on the other hand (see e.g. (4)), are predicted to bias against deriving the implicature and lead to lower calculation rates. For EXH, parallel predictions can be made for the corresponding quantifier and indefinite: both-QUDs are predicted to lead to higher rates of implicature calculation than any-QUDs. The predictions for wh-question QUDs (SI what-QUD, EXH which-QUD) are less clear, in part because they have previously not been treated as relevant QUDs in these contexts, and it is less obvious what existing theoretical frameworks would predict about them (we discuss this in more detail in Section 5). We therefore treat their biasing behavior as an empirical question. When analyzing the results, our primary focus will be on the two other QUDs (any and all for SI; any and both for EXH), and our analysis of the wh-questions will be more exploratory.
Implicature calculation rates are indexed by the proportion of ‘Not Good’ responses to Target pictures: if a participant says that Bob gave a ‘Not Good’ description of a Target picture, they have calculated the SI/EXH inference. We thus predict variation across QUDs in the percentage of ‘Not Good’ responses to Target. For example, any-QUDs are predicted to result in lower rates of calculation and therefore lower ‘Not Good’ percentages for Target pictures. In what follows, we make a distinction between Literal-biasing QUDs, which lead to lower rates of inference generation (the prediction for, e.g. any) and Inference-biasing QUDs, which lead to higher rates of inference generation (the prediction for, e.g. all, both).
We consider longer RT when responding ‘Not Good’ to Target, relative to the RT when responding ‘Not Good’ to (Bad) Control, to be what indexes the cost of implicature calculation. This is because Bad Controls can be rejected based on literal, semantic meaning, but the rejection of a Target picture suggests that the participant has gone through the inference calculation process. In conducting such an analysis, we depart from Chemla & Bott (Reference Chemla and Bott2014) and van Tiel & Schaeken (Reference van Tiel and Schaeken2017), who additionally analyzed ‘Good’ responses and focused on the interaction of Condition and Response. Our reason for doing so is that responding ‘Good’ to Target pictures might indicate implicature non-calculation and reasoning only with the literal meaning, but it is also consistent with participants calculating, and then canceling the implicature. Thus it is possible that for at least some participants or trials, responding ‘Good’ to Target may have included going through the inference calculation process. This would have led to increased RTs, introducing a confound for the interpretation. For this reason, in our analysis we focus on the Target vs. Control difference when responding ‘Not Good’, and disregard ‘Good’ responses to Targets.
Our predictions, then, are that under Inference-biasing QUDs (i.e. those that bias toward deriving an implicature) implicature derivation will not incur a cost. That is, we should not see a difference in ‘Not Good’ to Target as compared to ‘Not Good’ to Control RTs in Inference-biasing QUD conditions. On the other hand, Literal-biasing QUDs (i.e. those that bias against deriving an implicature) will have the effect that when the implicature is derived, its calculation is a costly and therefore slower process. Under Literal-biasing QUDs, therefore, we predict an increase in the time it takes to respond ‘Not Good’ to Target as compared to ‘Not Good’ to Control.
4.4 Results and analysis: rate of inference calculation
Prior to data analysis, we removed trials with extremely short or long response times by excluding the top and bottom 2.5% of the data based on reaction times.
Figures 5 and 6 plot the proportions of ‘Not Good’ responses for SI and EXH respectively. The primary purpose of Good and Bad Control pictures was to make sure participants are adequately doing the task, which we can see from responses being largely at floor and ceiling, respectively. Therefore, in the following, we focus on the analysis of the more informative Target pictures, which constitute our critical manipulation. Recall that for Target pictures, a ‘Not Good’ answer indicates implicature calculation. For the statistical analysis, a logistic regression model (glm function in R) was fit (mixed effects models did not converge), predicting Response (Good vs. Not Good) by QUD. Because our main prediction concerns the any-all/both difference, levels within the QUD variable were treatment coded, with any serving as the reference level. In SI, the statistical analysis revealed that the difference between all vs. any (
$ p<0.001 $
) is significant, while what resulted in responses somewhere in between the two other QUDs, with the any vs. what (
$ p<0.06 $
) difference being only marginally significant (see Figure 5 and Table 2). An additional pair comparison between all and what revealed a marginally significant difference (
$ \beta =-0.58 $
,
$ z=-1.93 $
,
$ p<0.06 $
). In EXH, any vs. both (
$ p<0.001 $
) was revealed to be significantly different, but the any vs. which difference is not significant (
$ p=0.7 $
) (see Figure 6 and Table 3). An additional pair comparison between both and which revealed a significant difference (
$ \beta =-1.64 $
,
$ z=-4.64 $
,
$ p<0.001 $
).
Figure 5 Proportion of participants’ ‘Not Good’ (as opposed to ‘Good’) responses by Picture condition for scalar inference. Different colors denote the different QUD conditions. Error bars represent standard error.
Figure 6 Proportion of participants’ ‘Not Good’ (as opposed to ‘Good’) responses by Picture condition for it-cleft exhaustivity. Different colors denote the different QUD conditions. Error bars represent standard error.
Table 2 Scalar inference: Parameter estimates, standard errors, z values and p values from a logistic regression model of the ‘Not Good’ vs. ‘Good’ responses to Target, predicted by QUD.
Table 3 It-cleft exhaustivity: Parameter estimates, standard errors, z values and p values from a logistic regression model of the ‘Not Good’ vs. ‘Good’ responses to Target, predicted by QUD.
Our prediction was that QUDs would modulate the rate of deriving pragmatic inferences, as indexed by rates of judging Bob’s answer (as a description of the Target picture) ‘Good’ vs. ‘Not Good’. Our findings are in line with these predictions. For SI, we found significantly fewer implicatures calculated under any-QUDs than under all-QUDs: that is, any is a Literal-biasing, while all is an Inference-biasing QUD. What-QUDs fall in the middle, making it unclear whether they can be categorized as either Literal- or Inference-biasing. In EXH, we also found significant differences in rate of implicature calculation, successfully extending earlier findings to a different kind of inference. Specifically, significantly fewer implicatures were calculated under any- and which-QUDs than under both-QUDs. In other words, for EXH, any and which are Literal-biasing, while both is an Inference-biasing QUD.
It is worth noting that under any-QUDs, there is a presuppositional mismatch between the EXH target sentence and the question: the EXH construction carries the existential presupposition that something is blue, while any-questions are not presuppositional. But it is instructive to note that in the Good Control condition, the rate of ‘Good’ responses was at ceiling. That is, participants almost always deemed the EXH sentence a ‘Good’ answer to an any-question, given a picture compatible with the exhaustivity inference. This suggests that participants were able to accommodate the existential presupposition and generate the exhaustivity inference, which is the phenomenon of interest to us.
Now that we have established that for both SI and EXH, some QUDs bias toward deriving the inference, while other QUDs bias against it, we turn to our main hypothesis. We show that these differences among QUDs are reflected in reaction time cost: the implicature calculation process will incur more or less reaction time cost depending on whether the target sentence is in a supportive context (i.e. under Inference-biasing QUDs) or a non-supportive context (i.e. under Literal-biasing QUDs). We analyze reaction time results in the next section.
4.5 Results and analysis: reaction times
Figures 7 and 8 plot reaction times broken down by QUD. Because our predictions concern the difference in RT when responding ‘Not Good’ to Target, as compared to Control (see Section 4.3), and we do not have specific hypotheses about differences in RTs when responding ‘Good’, we restrict the statistical analysis to ‘Not Good’ responses. Nevertheless, the full data set is plotted in Figures 7–8. For the statistical analysis, a linear mixed effects model (lmer from the lme4 package in R; Bates et al. Reference Bates, Mächler, Bolker and Walker2015) was fitted, predicting RT by Condition (Target vs. Control). Levels within Condition were treatment coded, with Control serving as the reference level. Random slopes and intercepts were included for participants and items. Whenever the full model did not converge, the random effects structure was simplified following the recommendations of Barr et al. (Reference Barr, Levy, Scheepers and Tily2013). The p values reported below were estimated using the Satterthwaite procedure, as implemented in the lmerTest package in R (Kuznetsova, Brockhoff & Christensen Reference Kuznetsova, Brockhoff and Christensen2017). In the following we analyze RT data question-by-question, following the predictions that we have made.
Figure 7 Mean reaction times (RT) in milliseconds (ms) for judging Bob’s answer as ‘Good’ or ‘Not Good’ in scalar inference. Different QUD conditions are displayed on separate plots. Colors denote Control (Good and Bad) vs. Target pictures. Error bars represent standard error.
Figure 8 Mean reaction times (RT) in milliseconds (ms) for judging Bob’s answer as ‘Good’ or ‘Not Good’ in it-cleft exhaustivity. Different QUD conditions are displayed on separate plots. Colors denote Control (Good and Bad) vs. Target pictures. Error bars represent standard error.
4.5.1 Any-QUDs
Recall that any-QUDs were predicted to bias toward the literal meaning based on earlier theoretical and experimental work, and that is indeed what we found in our inference calculation rate data. Thus any-QUDs are predicted to make calculating an SI/EXH inference a costly process, manifested in longer RTs when responding ‘Not Good’ to Target as compared to Control. For the SI any-QUD, we found a significant difference in RT between responding ‘Not Good’ to Target vs. Control (
$ \beta =391.47 $
,
$ t=2.6 $
,
$ p<0.05 $
). Similarly, for the EXH any-QUD, we found a significant difference in RT between responding ‘Not Good’ to Target vs. Control (
$ \beta =539.01 $
,
$ t=3.3 $
,
$ p<0.01 $
). Importantly, both patterns (see middle panels in Figures 7 and 8) show increased RT for the Target picture, as compared to the Control picture when responding ‘Not Good’. This is thus in line with our prediction that any-QUDs make inference computation time-consuming.
4.5.2 All- and both-QUDs
The predictions made for the all- and both-QUDs are the opposite of the prediction about the any-QUDs. All- and both-QUDs are Inference-biasing, and should therefore not lead to increased RTs when responding ‘Not Good’ to Target. For the SI all-QUD, there was no significant difference in RT between responding ‘Not Good’ to Target vs. Control (
$ \beta =5.06 $
,
$ t=0.04 $
,
$ p=0.97 $
). For the EXH both-QUD, we found a significant difference in RT between responding ‘Not Good’ to the two types of pictures (
$ \beta =-478.01 $
,
$ t=-2.82 $
,
$ p<0.01 $
), such that responding to Control resulted in longer RTs than responding to Target. That is (see the rightmost panel in Figure 8), while there was no reaction time cost for calculating the inference (i.e. no increased RTs for Target), we found an unexpected cost for responding ‘Not Good’ to the Control picture.
We argue that this unexpected cost is a side effect of the picture stimuli. In particular, the verification process involved in rejecting a Bad Control involves two steps for EXH, but not for SI. For EXH (see Figure 10), given Bob’s utterance, It is the square that is blue, both the color and identity of each shape needs to be checked. This is because there is in fact only one blue shape (cf. exhaustive meaning) in the Bad Control picture, but that blue shape is not the correct one (i.e. the square). Note that all EXH stimuli necessarily have to include a blue shape, because the it-cleft sentence also carries an existential presupposition that something is blue. In contrast, for SI (see Figure 9), Bob’s utterance Some of the shapes are blue can be rejected in one step, because no shapes in that display are blue.
Figure 9 SI
Figure 10 EXH
Nevertheless, our findings are generally in line with the predictions of the QUD hypothesis in that the Inference-biasing all- and both-QUDs did not lead to a delay in reaction times for deriving the SI/EXH inference.
Based on the above, we see a difference between any-QUDs, which led to processing cost, and all- and both-QUDs, which did not. To confirm that RT patterns vary across QUDs, we conducted an additional analysis focusing on the interaction of Condition with QUD. A linear mixed effects model (lmer) was fit, predicting RT by Condition (Target vs. Control), QUD (SI: any vs. all; EXH: any vs. both) and their interaction. Both variables were sum-coded, and models included random effects as described at the beginning of Section 4.5. For SI, we found a significant interaction of Condition with QUD (
$ \beta =96 $
,
$ t=2.1 $
,
$ p<0.05 $
). Similarly, for EXH, we found a significant interaction of Condition with QUD (
$ \beta =251.21 $
,
$ t=4.62 $
,
$ p<0.001 $
). That is, for both SI and EXH sentences, the RT patterns signaling processing cost were found to vary according to the preceding QUD.
4.5.3 What- and which-QUDs
Recall that we were not able to make clear predictions about what- and which-QUDs (Section 4.3), despite their frequency in the elicitation experiment. For the SI what-QUD, we found no significant difference in RT between responding ‘Not Good’ to Target vs. Control (
$ \beta =194.91 $
,
$ t=1.74 $
,
$ p=0.1 $
). That is, the what-QUD parallels the all-QUD in resulting in no difference in RTs when responding ‘Not Good’ to Control vs. Target. This suggests that despite the mixed results in terms of SI calculation rate, the what-QUD is Inference-biasing based on reaction time measures. As for the EXH which-QUD, there was no significant difference in RT between responding ‘Not Good’ to Target vs. Control (
$ \beta =266.6 $
,
$ t=1.61 $
,
$ p=0.11 $
). Qualitatively the which-QUD shows a somewhat similar pattern to the any-QUDs, but the results are much less clear.
In sum, our predictions are largely borne out in the data: the questions which we could unambiguously classify as Literal- (any) vs. Inference-biasing (all, both) show divergent behavior in terms of reaction time cost. Any-QUDs resulted in SI and EXH calculation being time-consuming, while the SI all-QUD and EXH both-QUD facilitated reaction times. The SI what-QUD patterned with Inference-biasing QUDs in that it did not lead to increased reaction times, while the EXH which-QUD was qualitatively similar to Literal-biasing any-QUDs. We discuss the implications of these results in the next section, along with the calculation rate results.
5. General discussion
In this paper we tested the hypothesis that the likelihood of calculating SI and EXH pragmatic inferences, as well as the processing cost of that calculation, tracks the QUD – a prediction of constraint-based models of implicature calculation. Under such a model, the more probabilistic support there is from multiple cues, the more quickly and robustly listeners will compute pragmatic inferences, with the QUD being one of the relevant cues. We elicited explicit questions to approximate the relevant QUDs (Experiment 1). Using these QUDs in Experiment 2, we found that they fall into one of two classes: under Literal-biasing QUDs, the rate at which participants drew inferences was lower, and under Inference-biasing QUDs, the rate at which they drew inferences was higher. Differences among QUDs also predicted processing cost. Under the Literal-biasing QUDs, making an inference-enriched judgment took longer than responding to the relevant literal control, whereas a facilitation of reaction time for such inferences was observed under Inference-biasing QUDs. By and large, these patterns hold for the majority of the questions that we examined, although it is also worth noting that there appeared to be more nuanced patterns with wh-questions (see more discussion below). In general, we did not observe across-the-board processing cost for deriving implicatures, nor did we observe that computing inferences is always cost-free. Instead, our results strongly suggest that the cost of computing SI and EXH inferences is context-dependent – it is costly when the target expression was preceded by non-supportive QUDs. Such a context-dependent cost imposes a significant constraint on our hypothesis space. For example, these results would be challenging for the default hypothesis and the literal-first hypothesis introduced in Section 2.1, since both would predict categorical behavior that is QUD-independent.
Our findings contribute to the empirical landscape in a number of ways. First, we probed the robustness of earlier work on the QUD-sensitivity of scalar inference calculation and processing. Using a different experimental paradigm (sentence-picture verification) than existing work on QUDs, our findings successfully replicate the results of, among others, Zondervan et al. (Reference Zondervan, Meroni, Gualmini, Friedman and Ito2008), Degen (Reference Degen2013), and Cummins & Rohde (Reference Cummins and Rohde2015) (for calculation rates) and are in line with trends observed by Degen (Reference Degen2013) and Degen & Tanenhaus (Reference Degen and Tanenhaus2015) (for reaction time). Moreover, this was done by manipulating the QUD directly via explicit questions, rather than implicitly via background stories – which the earlier processing experiments utilized. Crucially, we also found that QUD-sensitivity extends beyond the well-known case of scalar inference, to a previously untested pragmatic inference: it-cleft exhaustivity. Lastly, we took an important step toward better understanding how to empirically probe relevant QUDs, which we return to at the end of this section.
The specific role of QUDs observed in our study could be formalized under the Question–Answer Requirement (QAR; Hulsey et al. Reference Hulsey, Hacquard, Fox and Gualmini2004) approach:
In other words, any sentence is to be understood as an answer to a question, this question being the QUD (Hulsey et al. Reference Hulsey, Hacquard, Fox and Gualmini2004; Gualmini et al. Reference Gualmini, Hulsey, Hacquard and Fox2008). The QAR posits that the selected interpretation of an ambiguous sentence is required to be a good answer to the QUD. The two interpretations that SI target sentences allow for are repeated in (14) below.
Using a standard Hamblin semantics for questions (Hamblin Reference Hamblin and Partee1976), the SI results can be accommodated under the QAR as follows. On such a semantics, the meaning of a question, including the meaning of a QUD, is a partition of the set of possible worlds. The meaning of the QUD Are there any blue shapes? is a partition of worlds into the two sets (15a) and (15b):
Here, it is not necessary to derive the SI inference from Some of the shapes are blue in order to provide a good answer in the sense of the QAR, because the literal interpretation Some and possibly all of the shapes are blue corresponds to (15a). Deriving the inference also results in a good answer, because the inference-enriched interpretation (Some but not all of the shapes are blue) entails (15a). Therefore, under the any-QUD, the target sentence is a good response whether or not the inference is derived.
However, the picture changes for the some but not all SI target sentence under the QUD Are all shapes blue?, which partitions the set of worlds into the following two sets (assuming a five-shape display):
In this case, only if the inference is derived is the dialogue QAR-compliant, because the literal reading does not address the QUD. However, the enriched reading Some but not all of the shapes are blue entails (16b). Thus, the SI target sentence is only a good response to the all-question on the inference-enriched reading. This is reflected in our finding that participants derived significantly more implicatures with the all- than with the any-QUD, and that SI calculation led to a reaction time cost under the any-, but not under the all-QUD.
As for EXH, the two potential interpretation of the target sentence are repeated in (17).
Assuming a two-shape display, the QAR captures the EXH findings in a way parallel to the SI findings. The EXH any- and both-QUDs result in the same partitioning of the set of worlds as the SI any- and all-QUDs respectively. The only difference is that the domain of quantification is now two instead of five, given the experimental pictures – as is reflected in the English paraphrases below.
Under the any-QUD, both the literal (The square is blue) and the inference-enriched (Only the square is blue) readings entail (18a). Therefore, both constitute good answers according to the QAR. However, under the both-QUD, only the inference-enriched reading answers the question by entailing (19b); the literal reading does not bear on the QUD. This difference is reflected in the empirical data: significantly more implicatures were derived under the both- than under the any-QUD, and only under the any-QUD was the computation time-consuming.
Additional to our main finding that context modulates the calculation and processing of SI and EXH, there remain some empirical puzzles regarding the interplay of production and interpretation of QUDs. In Experiment 1, we took a first step in addressing the problem of narrowing down potential QUDs for a given context and conducted an elicitation study, the results of which fed into our QUD manipulation experiment. In doing so, we went beyond previous work that relied only on theoretically informed introspection to identify what may serve as a relevant QUD, and instead we treated this issue as an empirical question. Based on the results of the elicitation experiment, we focused on three types of questions: any-, all/both- and wh-QUDs. While the quantifier-QUDs have been discussed in existing literature as being relevant QUDs to the SI and EXH target sentences, the wh-QUDs (SI what-QUD, EXH which-QUD) have not. Yet it is interesting to observe that the novel wh-QUDs were the ones that proved most frequent in the elicitation experiment.
In addition to their novelty, the wh-QUDs also have some other puzzling properties. For instance, the focus structures of the what-QUD and the SI answer are potentially incongruent. The what-QUD focuses colors, yielding a set of alternatives of the form
$ \Big\{ $
The shapes are red, The shapes are blue,
$ \dots \Big\} $
; but one might think that the inference from the SI target sentence is most natural with focus on the quantifier some in Some of the shapes are blue, with an attendant set of focus alternatives
$ \Big\{ $
None of the shapes are blue, Some of the shapes are blue, All of the shapes are blue
$ \Big\} $
. The wh-QUDs also showed more nuanced results in Experiment 2. The SI what-QUD did not fall neatly into the Literal- or Inference-biasing category based on the rate of inference calculation, though in RT results it qualitatively patterned with the SI all-QUD. As for the EXH which-QUD, while it showed distinct Inference-biasing behavior in terms of likelihood of inference calculation, it resulted in mixed RT patterns. On the other hand, the QUDs that showed the clearest patterns (any-, all-QUDs) are in fact the ones with the closest link to existing theoretical work. Future work should thus address this tension between the observed mixed biasing and processing behavior of what- and which-QUDs, and their apparent popularity with naive participants in an elicitation task.
The fact that elicitation resulted in somewhat surprising QUDs raises the issue of how to successfully probe theoretical constructs in an empirically grounded manner. One thing lacking in the current empirical picture is a measure of whether participants calculated the SI and EXH inferences in the elicitation experiment. Gathering such a measure could help address open questions regarding why the Target and Good Control conditions elicited very similar questions, as well as the surprising finding that wh-questions, which are not fully congruent with the target sentences in their presuppositions or focus structure, were also elicited. Conducting an elicitation experiment that also targets interpretation would thus be a valuable avenue for future work. Our study constitutes only a first step in understanding how QUDs can be elicited experimentally.
5.1 Lexical Access: Alternative construction as the source of cost
Our findings highlight the role of QUDs as one source of the processing cost associated with implicature calculation. There are potentially other sources as well. Making reference to Katzir’s (Reference Katzir2007) structurally based theory of alternative construction and complexity (see also Fox & Katzir Reference Fox and Katzir2011), van Tiel & Schaeken (Reference van Tiel and Schaeken2017) (following Chemla & Bott Reference Chemla and Bott2014) propose that the aspect of implicature calculation that causes a delay is lexical retrieval during alternative construction (Lexical Access hypothesisFootnote 5). For example, in scalar inference, to construct the alternative All of the shapes are blue for Some of the shapes are blue, the lexical item all needs to be retrieved. The calculation of it-cleft exhaustivity, on the other hand, is argued to proceed without recourse to lexical alternatives. Van Tiel and Schaeken’s (Reference van Tiel and Schaeken2017) empirical findings were in line with the Lexical Access hypothesis: it is only scalar inference (some-all) that resulted in processing effort, it-cleft exhaustivity did not.
The current findings pose an empirical challenge for the Lexical Access account. While evidence for Lexical Access comes from studies that presented target sentences in the absence of any context, our experiments varied the QUD. Our results do not support the prediction that the calculation of SI inferences, but not the calculation of EXH inferences, would lead to processing cost. Instead, we found that depending on context, both inferences can lead to a reaction time delay (or the lack of a delay). This effect of context-dependence is unexpected if the cost of calculating pragmatic inferences is directly and uniquely tied to the construction and complexity of the relevant alternatives.
Particularly informative in this respect are our findings about EXH, as well as SI what-QUDs. The predictions of Lexical Access converge with that of a QUD-based hypothesis about processing cost in the case of questions that explicitly mention alternatives, e.g. all-QUDs. Following a context (in our study: an explicit question) where the alternative all has been made salient, lexical retrieval of all will likely be a faster process. However, it is less clear how the Lexical Access hypothesis would capture our findings about questions that do not explicitly mention relevant lexical alternatives: the what-QUD, which showed reaction time patterns similar to the all-QUD, or the findings about EXH, where no lexical alternatives are relevant.
It is possible that both lexical retrieval and context-dependence contribute to the complexity of generating pragmatic inferences. Our results do not necessarily rule out that lexical access plays a role. Future research should probe further whether these diverse sources of complexity could selectively target different aspects of the processing cost generated during the inferential process.
6. Conclusion
How people generate pragmatic implicatures has been a central question in linguistics, as it serves as a window into the process that integrates semantic and pragmatic information. The current study found that QUDs affect the likelihood of inference calculation. Our empirical case studies included both scalar inferences and it-cleft exhaustivity. Also importantly, for both kinds of pragmatic inferences, QUDs also predicted the amplitude of the processing cost (measured by reaction time). Altogether, our findings provide support for the constraint-based framework, and also open up questions about the precise source(s) of the complexity associated with computing pragmatic inferences.
