Glossa Psycholinguistics

2.1 Scalar inference and scalar diversity

SI represents one of the classic examples of pragmatic enrichment. An utterance containing the quantifier some (1), for example, is often enriched from its lower-bounded meaning (1a) to the upper-bounded meaning some but not all (1b).

While there are many different theoretical proposals as to how SIs arise, a standard (neo-)Gricean account posits the following. Hearers assume that speakers are following the Maxim of Quantity (Grice, 1967), and are therefore trying to be as informative as is required in the context. A more informative alternative utterance to (1) would have been Miriam caught all of the mice. Informativity can be defined as asymmetric entailment: Miriam caught all of the mice entails Miriam caught some of the mice, but not vice versa, hence, the former is more informative (Horn, 1972). Therefore, when a comprehender encounters an utterance like (1), they reason about the speaker’s intention behind not uttering the more informative, stronger alternative statement. This may have happened because the stronger alternative is false, and the speaker chose not to utter it in order to avoid violating the Maxim of Quality. This reasoning process leads hearers to derive the negation of the unsaid alternative (Miriam didn’t catch all of the mice) which, combined with the original utterance’s literal meaning (1a), results in the SI-enriched meaning (1b).

While the some but not all SI, based on the <some, all> lexical scale, is the most widely discussed example, SI can also arise from other pairs of lexical items that form a scale. The example in (2), for instance, is based on the <happy, ecstatic> scale.

Given (neo-)Gricean assumptions, the happy but not ecstatic SI can be derived in the same way as some but not all. Hearers of the weaker utterance in (2) can reason that the speaker did not utter the more informative alternative The winner is ecstatic, because it would not have been true. The weaker utterance’s literal meaning (2a) and the negation of the stronger alternative, then, together give rise to the SI-enriched meaning (2b). But while the mechanism underlying these two different SIs is posited to be the same, they do not arise equally robustly: hearers are much more likely to enrich some to mean not all than happy to mean not ecstatic (Ronai & Xiang, 2024). In fact, scalar diversity is now a well-replicated finding. This term refers to the substantial variation across different lexical scales in the likelihood that they would lead to SI. In van Tiel et al.’s (2016) highly influential study, for instance, the rate at which participants calculated SIs ranged from 4% to 100%, with the 43 scales tested spanning that full range (see also earlier work by Baker et al., 2009; Beltrama & Xiang, 2013; Doran et al., 2012).

Existing experimental studies of scalar diversity have concentrated on answering the question of what can explain the observed inter-scale variation in SI calculation. How likely a scale is to lead to SI has been related to various properties of the stronger alternative (e.g., all, ecstatic), or of the relationship between the weaker scalar term (e.g., some, happy) and that alternative. For example, van Tiel et al. (2016) have shown that the more distinct the weaker and the stronger term are, the more likely they are to lead to SI. This is because the stronger alternative needs to be sufficiently distinct from the weaker term for SI to arise; if the two terms are not distinct enough, the speaker’s non-utterance of the stronger term is not necessarily due to its falsity. Here, distinctness was operationalized as semantic distance (as measured in a rating task) and boundedness (whether the stronger alternative is endpoint-denoting). Westera and Boleda (2020) have proposed that semantic relatedness, based on distributional semantics, is another component of distinctness, which they indeed found to be negatively correlated with SI rates. A property of stronger alternatives that has been shown to predict scalar diversity is how expected they are or, in other words, how (un)certain hearers are about the identity of the relevant stronger alternative, given the weaker term uttered – the greater the uncertainty, the less likely SI is to arise (Hu et al., 2022, 2023; see also Ronai & Xiang, 2022). Concentrating on SIs arising from adjectival scales in particular, Gotzner et al. (2018) have related scalar diversity to the underlying scalar semantics of adjectives. Polarity was one relevant predictor, with the authors’ results revealing higher SI rates for negative adjectives (e.g., <bad, awful>) than positive ones (e.g., <good, great>); see also Pankratz and van Tiel (2021) for a replication using different diagnostics for polarity. Another factor from adjectival semantics is extremeness: extreme adjectives (e.g., excellent, huge) have been shown to lead to lower SI rates (Beltrama & Xiang, 2013; Gotzner et al., 2018). Aside from deriving across-scale variation from properties of the weaker term and its stronger alternative, studies have also suggested that the propensity for SI is linked to another type of semantic process or pragmatic inference that is variable across scales (Gotzner et al., 2018; Sun et al., 2018). Last but not least, the role of context and contextual relevance in explaining scalar diversity has also been investigated, focusing either on discourse or on sentential context (Pankratz & van Tiel, 2021; Ronai & Xiang, 2021a; Simons & Warren, 2018; Sun et al., 2023).

One limitation of this existing body of work that we would like to highlight is that all prior studies of scalar diversity have used exclusively written experimental stimuli, or modeled data from other studies that have done so. This presents a potential issue in light of the fact that – as we will review below in 2.2 – intonation is known to affect SI calculation. Most crucially for our purposes, certain intonational contours are also sensitive to the same factors that have been identified as predicting scalar diversity. As mentioned in Section 1 and further discussed in 2.3, one contour of interest is the RFR, which is predicted to affect the likelihood of drawing an SI. Additionally, the RFR has been argued to be felicitous with positive, but not negative, statements (in negative and positive contexts, respectively; see Göbel, 2019; Göbel & Wagner, 2023). These two factors could, then, conspire to give the appearance that adjective polarity affects SI rates directly. As mentioned, negative scales have been found to lead to SI more robustly than positive ones (Gotzner et al., 2018). Such a finding, however, could in principle be an epiphenomenon arising from the RFR decreasing SI rates and negative adjectives being less likely to be silently read with an RFR. Notably, adjective polarity may be just one factor with the potential to conspire in this way, given that many aspects that constrain the use of the RFR are not yet fully understood. As a result, there is reason to believe that using auditory stimuli, carefully controlling and manipulating the intonation with which SI-triggering utterances are produced, could uncover interesting patterns that written studies on scalar diversity have obscured.

2.2 The role of intonation for SI

As mentioned, there are robust findings in the literature showing that intonation affects how likely SI is to arise for intonation languages like English, French, Dutch and German.² We start by reviewing work that has examined the effect of pitch accent placement. Schwarz et al. (2007) investigated SI arising from the <or, and> lexical scale, via sentences such as (3). They varied the placement of the L+H* accent,³ which was assumed to mark prosodic focus; it occurred either on the disjunction (3a) or the auxiliary (3b).

Having been presented with one of the above sentences, participants had to choose between two alternative interpretations: the literal meaning She will invite Fred or Sam or possibly both and the SI-enriched meaning She will invite Fred or Sam but not both. The authors found a higher rate of SI-enriched, exclusive not both interpretations when the L+H* accent was placed on or (3a). Using a truth value judgement task, Chevallier et al. (2008) found converging results for French, namely, that prosodic stress on or leads to an increase in the exclusive not both interpretation. Lastly, Zondervan (2010) conducted a similar manipulation in Dutch, contrasting sentences like those in (4). In (4a), the entire NP containing the disjunction received two H* accents (one on each disjunct), whereas in (4b), the subject received one H* accent.

Participants were asked to judge the target sentence – (4a) or (4b) – as true or false, in the context of a story that made it clear that Paola had, in fact, taken both an apple and a pear. If a hearer has calculated the not both SI from the disjunction, they would, therefore, judge the target sentence to be false. In line with the other studies discussed, Zondervan (2010) found a significant effect such that more SIs were calculated when or was in the accented part of the sentence (4a).

There also exists work manipulating not the placement of the accent, but its type. Several studies in this domain have focused on ad hoc scales (Hirschberg, 1985) giving rise to exhaustive inferences. Gotzner (2019), for instance, tested sentences like (5) in German.

Participants were presented with the context sentence, followed by the critical sentence, and then had to make a truth value judgment on the alternative statement. If a participant has calculated the ad hoc inference The judge, but not the witness, believed the defendant, then they would judge the alternative statement to be false. Crucially, Gotzner (2019) manipulated the intonation of the critical sentence, which occurred either with an L+H* or an H* accent on the target word (judge). The findings revealed that participants computed more exhaustive inferences with an L+H* accent, as indicated by a lower % of True responses.

Using mouse-tracking to investigate online processing, Tomlinson et al. (2017) also compared what effect an L+H* vs. H* pitch accent has on ad hoc SIs in English, and found that the inference is processed earlier under the former contour. Tomlinson and Ronderos (2021), in turn, compared the effect of the L+H* and L*+H contours on the exhaustive interpretation arising from dialogues such as (6).

The authors were interested in the derivation of the inference that Speaker B believes that Manu was there at the party, but Moni was not (=Speaker B believes that (¬Moni, Manu)). They compared B’s utterance when pronounced with the L+H* vs. L*+H contour and found that SIs were more delayed and derived at lower rates with the L+H* contour. Altogether, the studies discussed thus far provide convincing evidence that intonation affects both the likelihood and processing of SIs.

As mentioned above, though the effects of intonation on SI calculation are well established, work on scalar diversity has tended to use written stimuli. Nonetheless, there are two notable exceptions, that is, two studies that manipulated intonation while testing multiple different lexical scales. Cummins and Rohde (2015) tested 20 different English adjectival scales, and presented participants with sentences such as The view from the hotel room is pretty in two intonation conditions: neutral vs. with prosodic focus placement on the scalar adjective (here, pretty). The authors take the focus manipulation to be a manipulation of the question under discussion (QUD; Roberts, 2012), which they predict would influence SI rates. Indeed, they found that participants were more likely to calculate the SI (e.g., not gorgeous) in the focus condition. However, as their by-item results show (Cummins & Rohde, 2015, p. 7, Figure 1), scalar terms differ in how susceptible they were to the intonation manipulation. There is substantial variation in effect size – i.e., in how much more likely the SI was to be calculated in the focus condition than in the neutral condition – and 6 scales, in fact, show the opposite pattern to the overall effect. This suggests that it is indeed important to study the effects of intonation on SI calculation across many scales, and to study scalar diversity with auditory stimuli. Crucially, one way in which our study differs from Cummins and Rohde (2015) is that we are interested in more complex intonational contours over the whole SI-triggering utterance (e.g., the RFR), rather than just manipulating whether the weaker scalar term is focused.

An even more relevant study for the present purposes, de Marneffe and Tonhauser (2019), tested the effect of the RFR on multiple scales. Before discussing this study in more detail, however, we first want to provide sufficient background on prior research on the RFR.

2.3 The rise-fall-rise contour

The use of the RFR is illustrated in the naturally occurring example in (7) on the underlined sentences.

An early influential account of the RFR comes from Ward and Hirschberg (1985), who propose that it conveys speaker uncertainty with respect to a scale. The authors primarily focus on the RFR in replies to questions as in (8), where its contribution can be intuitively described as a polite hedge. Ward and Hirschberg (1985) capture data like this by proposing that the RFR conveys uncertainty either about whether it is appropriate to evoke a scale (8a), what scale is being evoked (8b), or where a particular value falls on a given scale (8c).

As an alternative but related proposal, Constant (2012) draws a connection between the RFR and focus particles like only. On this view, the RFR quantifies over alternative propositions and indicates that they cannot be safely claimed by the speaker. One – highly relevant – pattern that motivates this account is that the RFR can only occur when the alternatives to the accented element do not resolve all other alternatives (are not “alternative dispelling”, in Constant’s terms), illustrated in (9). Both maximal scale elements, which either entail the falsity of all stronger alternatives (no one) or entail the truth of all weaker alternatives (all), are infelicitous, while the element that leaves alternatives open (most) is not. This pattern is captured by the assumption that in the cases of no one and all, the domain of alternatives to the asserted proposition that the RFR quantifies over is empty, and that there is a general ban on this vacuous quantification. Additionally, the contribution of the RFR is treated as a conventional implicature, by virtue of it being speaker-oriented and independent of at-issue content.

Further related accounts come from Wagner (2012) and Wagner et al. (2013). Wagner differs from Constant in assuming that the RFR operates over alternative speech acts rather than propositions, and that it contributes a presupposition rather than a conventional implicature. That is, the alternatives assumed to be evoked by the RFR are not calculated relative to the focus of the sentence (e.g., {Most/None/All/…} of my friends liked it… in (9)) but, more broadly, to what else could have been said. This adjustment is meant to capture the RFR’s ability to be embedded as its own speech act that is separate from the rest of the sentence, rather than having to take scope over the whole utterance, as shown with the appositive relative clause in (10).

Wagner and colleagues focus on the incompleteness component of the RFR, stated in (11), and present experimental evidence from contexts like (12) that the RFR is produced more frequently and perceived as more acceptable in partial answers, compared to complete answers.

Although the previous three accounts seem closely related, they differ in a small but important detail. While all three accounts are compatible with the RFR providing an incomplete answer when the truth of other alternatives is unknown, Constant additionally allows alternatives to be unclaimable, because they are known to be false. This feature captures the fact that the RFR can be followed up with an answer that fully resolves the relevant question, as in (13), which is incompatible with Wagner’s and Wagner et al.’s accounts.

A different account comes from Westera (2019), which can be viewed as elaborating on the relevance of the QUD, highlighted by Wagner et al. (2013). Embedded in a Gricean theory of pragmatics (for more details on the framework, see Westera, 2017), Westera proposes that the RFR – assumed to also cover cases of Contrastive Topic (Büring, 2003) – conveys information about whether a conversational maxim is being violated or adhered to, and what a speaker takes the available QUDs to be. More specifically, by using an RFR, the speaker is taken to indicate that there are at least two QUDs that are being addressed, and that with respect to one QUD, a maxim is being violated (or suspended), while for another QUD, a maxim is complied with. To illustrate this account with the case in (9), we can assume that the main QUD is the explicitly provided question (Did your friends like the movie?), and using the RFR conveys that the answer given does not fully resolve the question, thereby suspending the Maxim of Quantity. As a result, both no one and all are infelicitous, because they fully resolve the question, and consequently, no maxim is violated, contrary to what the RFR is assumed to convey. A possible secondary QUD for this case could be something along the lines of Do you think I should go see the movie? – this is ultimately left to pragmatic reasoning.

Lastly, Göbel (2019) and Göbel and Wagner (2023) shift their attention to the function of the RFR in argumentative dialogues. The observation they make is that the RFR exhibits an asymmetry in replies to statements, depending on the polarity of the initial statement, which they dub valence asymmetry. While the RFR is felicitous when providing a positive counterpoint to a negative statement (14a), it is degraded when the order is reversed and its carrier utterance provides a negative counterpoint to a positive statement (14b).

Notably, this pattern is unexplained by previous accounts, since B’s replies in (14a) and (14b) do not differ in whether alternatives are left open or not. The authors, hence, propose that the RFR conveys the presence of a stronger alternative on a pragmatically inferred scale. For cases like (14), this scale concerns an evaluation, here, of the quality of the bike ride, where the positive reply implies a stronger – or better – alternative to A’s statement, whereas the negative reply implies a weaker – or worse – one. For cases like (9), on the other hand, the scale is one of logical entailment, such that a stronger alternative to most would be all, capturing the pattern in a similar way as previous accounts.

This account of the RFR and the case of the valence asymmetry directly connect to the notion of adjective polarity in the scalar diversity literature, as mentioned earlier. As an illustration, consider the case of the scale <ugly, hideous>, categorized as a pair with negative polarity by Gotzner et al. (2018). On the assumption that ugly and hideous are on a measurement scale regarding beauty with other adjectives like pretty and beautiful, the stronger predicate hideous would actually be lower than ugly on the scale (see Solt, 2015). As a result, the RFR would be predicted to be unacceptable by Göbel and Wagner (2023). This prediction is borne out intuitively for the item in (15).⁴ We would, therefore, expect the RFR to occur less frequently with negative scales than positive scales, and to contribute to the appearance of a polarity effect in scalar diversity, assuming the RFR has its own independent effect on SI rates.

Regarding SI rates, the accounts of the RFR differ in their predictions about its effect on the likelihood of drawing an SI. Ward and Hirschberg (1985), Wagner (2012) and Wagner et al. (2013) can all be argued to predict a decrease in SI rate for the RFR, relative to a Fall: drawing an SI relies on negating a stronger alternative, which is incompatible with having to leave the truth of said alternative open, as required by these accounts.⁵ In contrast, Göbel (2019) and Göbel and Wagner (2023) simply treat the RFR as implying the existence of a stronger alternative, while remaining agnostic regarding its truth value. A possible effect of the RFR could, then, be that highlighting the salience of the relevant alternative leads to an increase in SI rate. The idea that the salience of alternatives can affect SI rate in this way is supported by findings from the written domain from Ronai and Xiang (2024; see also Ronai & Xiang, 2021b; Yang et al., 2018; Zondervan et al., 2008), who found that a prior question that mentions the stronger alternative leads to an increase in SI rate, relative to when the SI-triggering sentence occurs without a question context, or following a question that mentions the weaker scalar term itself. An intermediate position is taken by Constant (2012), whose account is compatible with either an increase or a decrease, given that alternatives can be unclaimable either because they are considered false (SI increase) or because they are not known (SI decrease). Similarly, Westera’s (2019) account allows some flexibility, such that the exact predictions with respect to SI rate are less definitive. On the one hand, the account includes a prediction that the RFR may not exhaustively resolve the main QUD, which would result in a decrease in SI rate. On the other hand, in the cases we are concerned with, the RFR may also pick up on a secondary QUD – so the explicitly mentioned question may no longer be the main QUD, and the RFR may be compatible with an increase in SI rate.

2.4 Previous work on the effect of RFR on SI calculation

While the relation between the RFR and SIs has not been the main concern of the accounts discussed above, there exist two notable studies that have looked at this relation. The first is de Marneffe and Tonhauser (2019), mentioned above, who tested dialogues such as (16), where the reply contains a weaker scalar term, and the question, a stronger alternative.

The authors manipulated whether Julie’s answer was pronounced with a neutral fall (H* L-L%) or an RFR (L*+H L-H%), and asked participants to indicate whether Julie “mean[s] that her hike was exhausting” on a 7-point scale (from definitely no to definitely yes). The results showed that the RFR led to fewer positive responses than a neutral fall, suggesting that it increased the likelihood of drawing a SI. However, while the experiment tested 16 different adjectival scales, the authors’ main focus was not on by-scale variation, leaving open the question of how (or whether) the intonation manipulation interacted with scalar diversity.

Moreover, the conclusion drawn by de Marneffe and Tonhauser (2019) has been questioned by Buccola and Goodhue (to appear), the second study on the RFR and SIs to be discussed here. Crucial to their criticism is the distinction between SIs and ignorance inferences: rather than taking the assertion of a weaker alternative as evidence that the speaker believes the stronger alternative to be false, it can also be understood as indicating that the speaker is simply ignorant regarding its truth value. Crucially, replying no to the questions posed by de Marneffe and Tonhauser is compatible with either type of inference. Thus, the results can be given an interpretation other than the RFR increasing the likelihood of SI calculation.

To address the mapping of intonation onto pragmatic inferences directly, Buccola and Goodhue (to appear) tested which type of inference – ignorance inference or SI – participants would be more likely to draw after hearing a target sentence either with Fall or RFR, as illustrated in (17).

In their first experiment, participants were given one contour and had to choose one of the inference options. Both contours led to SI choices overwhelmingly, without a significant difference between them (although the preference was numerically larger for Fall). The second experiment then gave participants both intonation versions at once and asked them to choose between mapping Fall to SI and RFR to ignorance inference, or Fall to ignorance inference and RFR to SI. Under those conditions, participants showed a preference for the former option, which the authors took as evidence that the RFR conveys uncertainty. While this study did not test the effect of the RFR on the likelihood of SI calculation directly (only via comparison to ignorance inferences) and was restricted to the <some, all> scale, it does add to the body of evidence demonstrating that SI-related interpretations are sensitive to intonational cues.

With this background, we now turn to our own experimental investigation of the role of intonation for scalar diversity.

3.1 Method, materials & design

The stimuli in Experiment 1 consisted of question-answer dialogues containing scalar terms, as in (18). The dialogues featured the following experimental manipulation: the question prompt (Emma’s question) and the target sentence (the participant’s reply) either contained the same weaker scalar term (18a), or the question contained the chosen stronger alternative (18b). There were 60 lexical scales taken from Ronai and Xiang (2024), in addition to 20 fillers. The same vs. strong manipulation was administered within-participants, i.e., each participant saw each item only in one condition in a Latin Square design.

Participants first saw the full dialogue on the screen. After pressing a button, they heard an audio recording of the question (Was the winner happy? or Was the winner ecstatic?) and had to record themselves saying the reply (She was happy.). Emma’s questions were presented auditorily, in addition to in written form, in order to make the task more natural. Afterwards, they were given the task question Given your response, do you think…? (italicized in (18)) and chose between “Yes” and “No” as their answer. In this adapted version of the inference task from van Tiel et al. (2016) (see also, i.a., Pankratz & van Tiel, 2021), if a participant responds with “Yes”, that can be taken to indicate SI calculation: that the participant has enriched happy to not ecstatic. Responding with “No”, on the other hand, suggests that the participant has not calculated the SI and takes happy to be compatible with ecstatic.⁶ Altogether, this method allowed us to gather data on the production rates of relevant contours on the target sentence across conditions and items, as well as examine SI rates in light of a given contour being produced.

Recordings were manually annotated by the second author in terms of the overall contour used by the participant on a given item. The annotator listened to target sentences in Praat. Sentences were presented without the context sentence or knowledge of condition in order to avoid bias. Contours were categorized according to a combination of the visual pitch information available and the auditory impression, given that audio quality was not always sufficient to guarantee accurate pitch tracking. The “a priori” categories originally included five contours:

1. a pitch accent on the scalar item, e.g., happy in (18), and a monotonous final fall – (L+)H* L-L% in ToBI labels (=Fall),

2. a rising pitch accent on the scalar item, followed by a low phrasal accent and a rising final boundary tone – {L*+H/L+H*} L-H% (= RFR),

3. a pitch accent on the auxiliary (if present), which we take to indicate Verum Focus (see Höhle, 1992; Lohnstein, 2015; as well as 3.5 below), followed by a monotonous final fall (= Verum Focus Fall, following Goodhue et al., 2016),

4. a monotonous final rise without a preceding rising accent – L* H-H% (= Rising Declarative, see, e.g., Gunlogson, 2001),

5. Other/Unclear.

However, after initial inspection, two changes were made. First, Rising Declaratives were taken out, due to the contour not occurring sufficiently frequently. Second, as mentioned in Section 1, there was a notably frequent use of a contour with an initial and a final high tone that we labeled “Concession Contour”, illustrated in (19), so it was added as one of the categories.

3.2 Procedure

The experiment was implemented through prosodyExperimenter (https://github.com/prosodylab/prosodylabExperimenter). Participants first saw a welcome screen, followed by a chance to adjust their volume and test their microphone, an online consent form, and a language background questionnaire. Afterwards, there was a test in which participants were played three sounds and had to choose which one was the quietest, which required the use of headphones. For the main part of the experiment, participants provided their production of the target sentence and then answered the question for the inference task, as described above. There were three practice trials after the instructions were received, followed by a total of 80 stimuli. The experiment concluded with a chance to provide feedback. A test version of the experiment can be accessed at https://prosodylab.org/~agobel/conepi/30-scaRFR_Pro2AFC/?SESSION_ID=Glossa&mode=experiment.

3.3 Participants

64 monolingual native speakers of American English were recruited on Prolific and compensated $4 or $5 (depending on time). One participant’s response file was not properly saved and, hence, not annotated. During annotation, participants were excluded if their responses were unnatural (N = 5), or if they were monotonous across items, in that they almost exclusively chose either Fall or Verum Focus Fall (N = 21).⁷ We were, thus, left with 37 participants for the data analysis reported below.

3.4 Results

3.4.1 Production rates

The counts by condition for each category are shown in Figure 1. The first thing to note is that Fall is by far most frequent contour used, comprising about 56% of the total recordings, even after excluding monotonous participants. Next, we can see that the RFR was used almost exclusively in the strong condition. The Concession Contour, on the other hand, trended toward occurring more frequently in the same condition, but was more evenly distributed. Finally, Verum Focus Fall occurred almost exclusively in the same condition. We discuss the implications of these findings below in 3.5.

Figure 1: Production rates by contour and condition in Experiment 1. Lighter colors (left) correspond to the same condition, and darker colors (right), to the strong condition.

3.4.2 SI rates

We next looked at the rate of SI calculation, as measured by the inference task, depending on the contour produced by the participant. We restricted this analysis to Fall as a baseline, RFR as the intended contour of interest, and the Concession Contour for exploratory purposes. SI rates, i.e., the proportion of “Yes” responses, for those three contours by condition are shown in Figure 2.⁸ For the statistical analysis, we fit a logistic mixed effects regression model using the lme4 package in R (Bates et al., 2015). The model predicted Response in the inference task (“Yes” vs. “No”) as a function of Contour (RFR vs. Fall vs. Concession Contour), Condition (same vs. strong) and their interaction. It included the maximal random effects structure supported by the data (Barr et al., 2013): random by-participant and by-item intercepts and slopes for the Condition predictor. Both fixed effects predictors were treatment-coded: in Contour, the Fall level served as baseline, while in Condition, the strong level served as baseline.

Figure 2: Mean SI rates (and SE) by contour and condition in Experiment 1. Lighter colors (left) correspond to the same condition, and darker colors (right), to the strong condition. Circles denote individual participants.

The analysis revealed the following results. First, the same condition produced lower SI rates than the strong condition (Estimate = –1.13, SE = 0.27, z = –4.14, p < 0.001). There was no evidence that this effect differed across contours, i.e., there were no significant interactions (Estimate = –0.58, SE = 0.59, z = –0.98, p = 0.33; Estimate = 0.04, SE = 0.4, z = 0.11, p = 0.92). Second, Fall showed the lowest SI rate (33.5% in the same condition and 45.3% in the strong condition), followed by the Concession Contour (48.3% in the same condition and 61.6% in the strong condition), which produced a significantly higher rate (Estimate = 0.7, SE = 0.31, z = 2.25, p < 0.05). Lastly, the RFR produced the highest SI rate (55.2% in the same condition and 70% in the strong condition), also significantly higher than the baseline Fall (Estimate = 0.89, SE = 0.23, z = 3.81, p < 0.001).

3.5 Discussion

3.5.3 Relation to scalar diversity

While the effect of the RFR on SI rates constitutes an interesting finding for theoretical accounts of the contour, further analyses are needed to more precisely determine how intonation interacts with the phenomenon of scalar diversity. For instance, one important possibility is that those lexical scales that show a high SI rate in written studies might also happen to be the ones produced more often with an RFR in our study, such that RFR rate is a direct correlate of SI rate. If this is the case, then the RFR does not actually encourage SI calculation, and its effect of leading to increased SI rates in Experiment 1 arises, instead, as an epiphenomenon. This hypothetical, whereby the RFR co-occurs with scales that robustly lead to SI, could also receive a different interpretation. Namely, since previous studies of scalar diversity relied on written stimuli, it is conceivable that certain scales were found to lead to higher SI rates than others due to their propensity to be silently read with an RFR intonation. On this view, finding that RFR rates and SI rates are linked would suggest that written studies of scalar diversity suffered from a confound. To investigate these possibilities, we conducted an additional correlational analysis. Figure 3 shows the by-item (that is, by-scale) correlation between RFR productions in the strong condition of Experiment 1 and SI rates from Ronai and Xiang’s (2024) written study, which conducted the same dialogue manipulation on the same stimuli as we did.

Figure 3: By-item correlation between RFR productions in Experiment 1 and SI rates from Ronai and Xiang’s (2024) written study (strong condition).

We find a moderate positive correlation (Pearson’s correlation test: r = 0.45), indicating that the RFR was indeed produced more frequently with scales that are more likely to lead to SI.⁹ This can be interpreted as suggestive evidence that the RFR’s effect on SI rates is indeed related to its co-occurrence with lexical scales that are more likely to lead to SI. Or, alternatively, that a scale’s likelihood of triggering SI calculation is linked (in part) to its propensity to be silently read with RFR. Before drawing any firmer conclusions, however, we will further investigate these possibilities in Experiment 2, which uses a perception task that allows us to assess the contribution of intonation independently of lexical factors.

In 2.1, we raised the possibility that the RFR may interact with predictors of scalar diversity in ways that constitute possible confounds, unless properly controlled for. One such factor is polarity. Göbel (2019) and Göbel and Wagner (2023) suggest that the RFR is only felicitous with positive statements, while Gotzner et al. (2018) have found higher SI rates with negative adjectival scales than with positive ones. On theories of the RFR that predict it to lower SI rates, e.g., because it indexes uncertainty, this would open up the possibility that what results in the polarity effect in scalar diversity is that positive scales are more likely to be silently read with the RFR. In Experiment 1, we found the RFR to increase SI rates, not decrease them, which suggests that the above confound is not at play. Nonetheless, it is worth briefly looking at the effect of polarity on both RFR productions and SI rates. To do this, we analyzed the subset of our lexical scales that had been annotated for polarity by Gotzner et al. (2018) (see their 2.1.2.4. for details). This included 21 adjectival scales that are fully identical across the two studies, as well as <pretty, beautiful>, where we adopted Gotzner et al.’s annotation for <pretty, gorgeous>. Of these 22 scales, the RFR was produced 52 times with positive scales (4.33 average) and 19 times with negative scales (1.9 average). That is, the RFR occurred more than twice as frequently with positive scales, in line with the predictions of Göbel (2019) and Göbel and Wagner (2023). To check the effect of polarity on SI rates, a logistic mixed effects model was fit, predicting Response (“Yes” vs. “No”) by Polarity (treatment-coded, with negative serving as baseline). The model included random intercepts for participants and items. This analysis revealed that positive and negative scales did not differ significantly from each other in their likelihood of leading to SI (Estimate = 0.12, SE = 0.86, z = 0.14, p = 0.89).¹⁰ This means that Experiment 1 ultimately did not reveal evidence supporting the hypothetical conspiracy of the RFR’s polarity asymmetry and effect on SI rates: we actually found that the RFR increases SI rates, and our set of items happened to include adjectival scales that do not show a polarity effect. But it remains the case that factors governing intonational contours overlap with those predicting SI rates, and future work should, therefore, still keep this potential interaction in mind.

4.1 Method, materials & design

We used the same materials as in Experiment 1 (60 experimental stimuli + 20 fillers), but restricted to the strong condition, since the RFR was rarely produced in the same condition. Additionally, both the question prompt (Emma’s question) and the target sentence (now Luke’s reply) were presented auditorily, without the text being visible on the screen. The target sentence occurred with one of three contours: a Fall, the RFR, or the Concession Contour, in a Latin Square design. After listening to one version of the dialogue, participants were asked the same task question (italicized in (22)) as in Experiment 1 – with the only modification being that the target speaker was no longer referred to as you but as Luke, i.e., the task question included Given Luke’s response…. As before, we take a “Yes” response to index SI calculation, and a “No” response to index that the participant has not calculated the SI. A sample item with recordings is shown in (22), and pitch tracks for the three contours are shown in Figure 4.

Figure 4: Pitch tracks for the target sentence It was serious, from the <serious, life-threatening> scale, with Fall in black (audio), RFR in orange (audio) and Concession Contour in purple (audio).

4.2 Procedure

The general procedure was largely the same as for Experiment 1, except there was no mic check. A test version can be accessed at https://prosodylab.org/~agobel/conepi/31-scaRFR_Aud2AFC/?SESSION_ID=Glossa&mode=experiment.

4.3 Participants

90 monolingual native speakers of American English were recruited on Prolific and compensated $2.50. 17 participants were excluded for failing the headphone test. Data from the remaining 73 participants is reported below.

4.4 Results

SI rates – that is, the proportion of “Yes” responses – by contour are shown in Figure 5. To analyze the results, we fit a logistic mixed effects regression model predicting Response (“Yes” vs. “No”) as a function of Contour (Fall vs. RFR vs. Concession Contour). The fixed effects predictor was treatment-coded, with Fall as the reference level. The maximal converging random effects structure included by-participant intercepts and by-item intercepts and slopes. We found significantly higher rates of SI calculation with the RFR than with the Fall (Estimate = 0.4, SE = 0.12, z = 3.25, p < 0.01). The difference between Fall and Concession Contour, on the other hand, was not significant (Estimate = 0.04, SE = 0.12, z = 0.39, p = 0.70).

Figure 5: SI rates (and SE) by contour in Experiment 2. Circles correspond to individual participants.

4.5 Discussion

The results largely replicated the findings from Experiment 1. Fall received the lowest SI rate (54.5%), RFR the highest (62.5%), and the Concession Contour was numerically in between the two (57.4%). However, the differences were much smaller than in Experiment 1, such that only the comparison between Fall and RFR reached statistical significance. This compression may be due to the more mediated nature of the task: rather than judging one’s own production – and by virtue of that, most likely intention – the perception experiment required not only reasoning about the intention of someone else’s choice of intonation, but also how that might affect the hearer. The fact that the experiment was able to replicate the previous data is thus even more notable. As before, the RFR leading to an increase in SI rates supports theoretical accounts where it is analyzed as indicating the presence of a stronger alternative (Göbel, 2019; Göbel & Wagner, 2023), while it is less compatible with those that take the contour to correspond to uncertainty or the alternative being left open (Wagner, 2012; Wagner et al., 2013; Ward & Hirschberg, 1985).

In our discussion of Experiment 1, we raised the possibility that the RFR increasing SI rates is epiphenomenal, i.e., arising as a consequence of it occurring more frequently with items that are more likely to lead to SI to begin with. Experiment 2 was specifically conducted to further probe this possibility by directly manipulating the intonational contour of all items. Since Experiment 2 found the same effect of the RFR as Experiment 1, but this effect now cannot be reduced to by-scale variation in SI rates, as the RFR vs. Fall contrast occurred with all items, we can conclude that the RFR indeed encourages SI calculation.

As mentioned, a different interpretation of the (moderate) by-scale correlation between RFR productions and SI rates is also available. Namely, it could be the case that the reason why certain scales were found to produce higher rates of SI than others in written studies of scalar diversity is that such scales are the ones more likely to be silently read with the RFR. The current Experiment 2 data is also informative with respect to this possibility, as we can check whether the different lexical scales’ relative likelihood of leading to SI remained consistent across different intonational contours. To do this, we calculated rank-order correlations using Kendall’s τ_B.¹¹ This analysis finds that SI rates with the RFR are correlated with both the Fall (τ_B = 0.63) and the Concession Contour (τ_B = 0.67), showing that the relative order of different lexical scales remains largely (though not entirely) the same. This, in turn, suggests that what makes a lexical scale a “high SI rate” scale is not simply its propensity to be silently read with RFR in a written study.

The next section turns to further discussion of what the results of Experiments 1 and 2 tell us about SIs and scalar diversity, as well as intonational contours.