Glossa Psycholinguistics

1.1 Interpreting maximum standard absolute adjectives

In the semantics and pragmatics literature, many have claimed that deriving imprecise interpretations of MSAAs involves a pragmatic adjustment (Burnett, 2014; Carston, 2010; Lasersohn, 1999; Leffel et al., 2016; Lewis, 1979; Recanati, 2010; Wilson & Sperber, 2012, i.a.; but see Lassiter & Goodman, 2013, for a different view). One popular theory, for example, describes MSAAs as being associated with closed scales (i.e., with a clear beginning and an end) and as being end-point oriented (Kennedy, 2007; Kennedy & McNally, 2005). MSAAs require that their arguments have the maximal degree of the appropriate property (Syrett et al., 2010): When a line is described as straight, it means that it has the maximal degree of straightness, i.e., it is at the endpoint of the straightness scale. In this approach, a literally false description is tolerated as being “close enough” if a high degree of precision is not pragmatically relevant (see Lasersohn, 1999). From a psychological perspective, it could be said that this view would consider precision (i.e., the requirement that the argument possesses the maximal degree of the appropriate property) to be part of the encoded meaning of MSAAs. The meaning can be modified contextually, but this is a potentially costly pragmatic adjustment.

Another view that considers imprecision to involve a pragmatic adjustment is that of Relevance Theory (RT; Sperber & Wilson, 1986/1995). In RT, imprecision is seen as a variety of lexical broadening, the outcome of a mechanism of ad hoc concept construction. Through this mechanism, the encoded meaning of words is contextually loosened in accordance with context-specific expectations to include a larger set of possible referents (Carston, 2002, 2010). Following this view, there is a continuum of pragmatic instances of broadening, ranging from approximation (i.e., imprecision) all the way to cases typically described as figurative language, such as metaphor (Sperber & Wilson, 2008; Wilson & Carston, 2006, 2007). This view, which treats imprecise uses as a variety of ad hoc construction, presupposes a precise semantics of MSAAs which is subject to pragmatic broadening in context. However, the broader relevance-theoretic account of the contextualized interpretation of substantive words (nouns, verbs, adjectives) is also compatible with a view in which these adjectives are semantically underspecified regarding their precision (Carston, 2002, 2013, 2016). In fact, this is the position taken in much of the recent literature on the representation of word meanings: because most substantive (open-class) words are associated with several related senses (i.e., they are polysemous), it is assumed that the different senses are pragmatically derived from a single underspecified representation which encompasses all the semantically related senses of the word that are known to the language user (e.g., Carston, 2013, 2016; Frisson, 2009; Pietroski, 2005; Ruhl, 1989). While there is some experimental evidence to support this claim (Beretta et al., 2005; Frisson & Pickering, 2001; Pickering & Frisson, 2001; Pylkkänen et al., 2006; Rabagliati & Snedeker, 2013), what exactly this underspecified representation amounts to remains a matter of contention (Falkum & Vicente, 2015; Vicente, 2018). In the case of MSAAs, such an underspecified representation would have to exclude the requirement that an argument possess the maximal degree of the property (i.e., the requirement to be precise), considering that it would have to allow both precise and imprecise interpretations.

To sum up, while the semantic literature on MSAAs broadly posits that precision is part of the meaning of these adjectives, work on the mental representation of word meanings suggests that MSAAs could be underspecified regarding their degree of precision, with this information being filled in by the relevant context. One way of testing these hypotheses is to examine the relative comprehension cost of interpreting MSAAs.

1.2 The cost of deriving precise and imprecise interpretations

From the views described above, it is possible to derive a processing account that sees precision as part of the encoded literal meaning of MSAAs. According to this semantic view, understanding MSAAs imprecisely should generally bring about a comprehension cost relative to understanding them precisely. A plausible alternative to this view can be derived from the literature on underspecified lexical entries. According to such an underspecification view, precision is not part of the lexical meaning of MSAAs and should instead be contextually derived. Comprehension costs associated with precise and imprecise readings will depend on their contextual availability.

Two studies investigating the comprehension of precise and imprecise interpretations of MSAAs lend credence to the semantic view. Consider first the landmark study of Syrett et al. (2010), who introduced a presupposition assessment task to directly investigate how both children (ages 3–5) and adults interpret sentences containing MSAAs. In the first of their three experiments, participants heard a request that presupposed the existence or the uniqueness of a referent (e.g., Show me the full one, when said of a jar). This put the participants in a position to choose one of three options – to choose between one of two jars, which varied with respect to their fullness, or else a third option, indicating neither. In one felicitous use condition, there was a referent that cohered with a precise reading (a full jar). In another infelicitous use condition, there were instead two unsatisfactory referents (two half-empty jars, one fuller than the other). The results showed that both children and adults correctly picked the right referent in the felicitous condition, thus displaying an ability to derive precise interpretations. In the infelicitous condition, adults tended to reject both referents (88% rejection rate in Experiments 1 and 3), while the children did so only 40% of the time. The children were more likely to select the referent closest to the precise standard, e.g., they chose the jar with the most liquid at least 60% of the time in all three experiments. Upon closer inspection, the authors noted that children took significantly longer to select a referent in the infelicitous condition, relative to the felicitous condition. This led the authors to formulate an explicit linking hypothesis regarding the relationship between the derivation of an imprecise interpretation of an MSAA and picture selection time. They argued that understanding imprecision requires a contextually-motivated assessment of how much deviation from the maximal standard will be tolerated. This assessment involves reasoning that goes past the computation of semantic content, and as such, the authors argue, it should come with an added cost relative to deriving a precise interpretation.

The second relevant paper, from Bambini et al. (2013), compared the processing profile of three different types of pragmatic enrichment (metaphor, metonymy and approximation) to their respective literal counterparts via timed sensicality judgements. They found that participants took longer to react to sentences with an approximative interpretation of an adjective (That land is flat), relative to sentences with a more precise, literal interpretation (That spatula is flat). Participants also displayed lower accuracy in their sensicality judgements in the approximative condition, relative to the literal condition. Within the approximative group, the study included imprecise usages of MSAAs, such as straight and full. Their study also included approximative usages of color adjectives (black, red, pink, yellow, etc.) as well as of several other adjective types (silent, blinding, long, unchanged, boiling, etc.).

Given the findings of Bambini et al. (2013) and Syrett et al. (2010), one might argue that precision is part of the lexical meaning of MSAAs, with imprecision requiring a pragmatic adjustment that requires additional effort. However, we see it as premature to jump to that conclusion. Here we make five observations, four with respect to Syrett et al. (2010) and one more with respect to Bambini et al. (2013), that give us pause. First, Syrett et al. (2010) investigated only two MSAAs across their experiments: full (Experiments 1 and 2) and straight (Experiment 3). Second, in each of their experiments, their participants only saw a single trial facilitating an imprecise interpretation. Third, given that a majority of adults in the study were quite intolerant of imprecision, it could not be determined – for lack of sufficient data – whether the reaction time delays for imprecision found for children would also hold for adults. It is an open question whether this pattern would persist if adults saw a visual referent described imprecisely that was closer to the precise maximal standard. Fourth, and as far as Bambini et al. (2013) is concerned, it is difficult to make strong claims based on this study, since MSAAs made up only a small part of their item set, and MSAAs are different in their semantics from the other adjectives that they tested (see, e.g., Kennedy, 2007). A fifth comment on previous studies pertains to the marked differences in interpretation. While Syrett et al. (2010) found that adults were rather intolerant of imprecision (rejecting imprecise interpretations 80% of the time), Bambini et al. (2013) found that their participants accepted approximative interpretations at a rate of 87%. In addition, a study of how imprecise adjectives generate contrastive reference effects suggests that imprecise interpretations are readily available (Leffel et al., 2016).

How can these incompatible findings be accounted for? One possibility is that they arise because of differences in the degree of pragmatic slack (Lasersohn, 1999) that participants were asked to tolerate (e.g., interpreting a half-empty jar as full vs. an only slightly bent line as straight). This makes it critical to consider the effect of a referent’s conceptual distance from the precise standard on both comprehension rate (i.e., tolerance of imprecision) and comprehension effort.

A second critical factor to consider is the role of context when it elicits different expectations regarding the level of precision. Previous research has shown that reasoning about a speaker’s intended level of precision affects how people answer questions (Potts, 2012), and how they acquire the precise meanings of MSAAs from imprecise input (Lee & Kurumada, 2021). Additionally, speaker-specific contextual information can be used as a cue to decide whether to accept or reject an imprecise interpretation of a numeral expression (Beltrama & Schwarz, 2022). Information stemming from the visual context also constrains comprehension. Leffel et al. (2017) found that the degree to which an image matched the precise standard of an expression involving an MSAA (e.g., the number of stripes on a shirt described as a plain t-shirt) determined the acceptance of the picture as an accurate referent of the expression, with participants only tolerating a minimal amount of imprecision. Aparicio et al. (2016) argued that the context-sensitivity of MSAAs is due to pragmatic reasoning about the threshold for imprecision. In an eye-tracking Visual World study, they found that (precisely used) MSAAs generate contrastive reference effects, but do so later than relative adjectives (such as tall or big). They conclude that MSAAs carry an additional processing cost (compared to relative adjectives) because of the need to contextually set the precision threshold.

These results point to the specific context-sensitivity of MSAAs, but, critically, do not speak to the potential differences in how contextual expectations help comprehenders reach precise and imprecise interpretations of MSAAs. This needs to be elucidated, considering some of the claims made in the literature on semantic underspecification. There, it has been reported that when specific contextual expectations are raised, the processing effort of polysemous words is reduced, so that no single sense of a word can be said to be more salient than another. Frisson and Pickering (2007) make this claim for the case of metonymy. They report that while unfamiliar metonymies (She often read Needham) are read more slowly than literal counterparts (She often met Needham), this effect disappears when sentences are embedded in an appropriate context. Frisson (2009) sees this as evidence for an underspecified lexical representation: Even when a name has never been heard before and a metonymic interpretation should, prima facie, require additional effort, this effort disappears when contextual expectations are met.

An underspecification view of MSAA comprehension would, therefore, posit that when contextual expectations are given, precise and imprecise readings of MSAAs should not differ in their comprehension effort. This is because precise and imprecise senses of an MSAA should be derived from a single lexical meaning that is underspecified regarding precision (and, contrary to the semantic view, there is no requirement that the argument possess the maximal degree of a relevant property).

1.3 The present work

Our study has two overarching goals. First, we aim to build on previous empirical studies on imprecise MSAAs (e.g., Bambini et al., 2013; Syrett et al., 2010) to understand whether discrepancies regarding participants’ tolerance for imprecision can be explained by the varying effect of a referent’s conceptual distance from a precise standard. This will additionally help us understand how different degrees of precision are comprehended and how this influences comprehension effort. This issue is addressed in Experiment 1. Second, we aim to better understand the processing cost associated with deriving contextually-licensed precise and imprecise interpretations of MSAAs. To do this, we tested how expectations of precision and a referent’s conceptual distance from a precise maximal standard interact to mediate the comprehension rate and effort of precise and imprecise MSAAs. In turn, this should help us better understand the encoded lexical meaning of MSAAs, by testing the semantic and underspecified views of MSAAs. This is the focus of Experiment 2. In Experiment 3, we present a more direct test of the two hypotheses, by investigating the processing cost of precise and imprecise interpretations during self-paced reading.

2.1 Norming study 1

The first step was to create visual depictions of objects that would be perceived as systematically varying in distance from the precise maximal standard of the described property (e.g., a line with different degrees of straightness). For this purpose, we made one precise and one imprecise picture for each of our critical items. We then asked a group of 30 participants to state whether each of the images depicted the intended adjective. For example, participants read the sentence Show me the straight line, and were asked to select the target picture, a distractor picture, or to state that neither of the pictures showed a straight line. We then examined the results, averaged by each critical item. Depending on how often each imprecise image was accepted as the target to the sentence, we created 2 additional versions of each image, so that each item would have 3 different degrees of imprecision. In other words, if one of the target pictures in Figure 1 had an average rating of ~50%, we created one image with a higher level of imprecision and one with a lower level of imprecision, in order to have three degrees of imprecision per item, in addition to a precise condition, and one unrelated control condition (depicting the correct property, but applied to an incorrect referent), creating all of the images shown in Figure 1. If an image had an average rating of ~80%, we created two images that were incrementally more imprecise, and if an image had an average rating of ~30%, we created two incrementally more precise images. After creating two new pictures per item, we conducted a pilot study with 90 participants, in order to examine whether the average ratings in each one of the three categories (Imprecise 1, Imprecise 2, and Imprecise 3) would match our expectations. (We also collected reaction times for this pilot study, in order to calculate the required number of participants for Experiment 1, as we explain below in 2.4.) The pilot study confirmed that, on average, our images captured the intended degrees of imprecision. Pictures in the control condition were accepted as correct in 4% of all trials. Pictures in the Imprecise 3 condition were accepted 27% of the time, pictures in the Imprecise 2 condition, 57% of the time, and pictures in the Imprecise 1 condition, 78% of the time. Finally, pictures in the Precise condition were accepted 100% of the time. We take this as confirmation that the images were perceived as displaying distinct levels of imprecision.

Figure 1: Example of a target trial in Experiment 1 in the five conditions.

2.2 Materials and design

Experiment 1 was programmed using PCIbex software (Zehr & Schwarz, 2018) and was run via the internet. It was based on the seminal task developed by Syrett et al. (2010), but we introduced various changes to adapt the task to a web-based paradigm and to best allow for the use of multiple MSAAs. In each trial, participants saw three images. One image was always a red X. The other two were the Target and Distractor images. Participants could only select the images using the J, K, and L keys of their keyboard, representing the picture in the left side, middle, and right side of their screens, respectively. The Distractor picture displayed an object with a mismatched property (e.g., a completely curved line). The Target picture changed according to the experimental condition. It was either a perfectly straight line (Precise condition), a slightly squiggly line (Imprecise 1 condition), an even squigglier line (Imprecise 2 condition), a very squiggly line (Imprecise 3 condition) or a picture depicting an unrelated object that could also be felicitously described as straight (e.g., a road). We introduced this final control condition so that there would be cases in which participants should unequivocally select the red X, i.e., reject both Target and Distractor images. This means that Experiment 1 had one factor with five levels. Participants read a sentence in each trial instructing them to select one of the pictures (Show me the straight line). The sentence was always shown above the three images. The position of the images was pseudo-randomized: The red X always appeared in the middle, and the positions of the target and distractor images were randomized between left and right. This way, participants knew that the potential referent could only appear in one of two locations, and that if neither of them was appropriate, they had to always press the K key. An example of the visual display and corresponding sentence in each of the five conditions is shown in Figure 1.

We created a total of 12 critical items. Each item consisted of a combination of a sentence (e.g., Show me the straight line, in Figure 1) and the possible pictures in each condition. The sentence was identical across conditions. The 12 critical items used 6 different MSAAs (straight, round, clean, empty, full, and closed), meaning that there were two items per MSAA (e.g., straight line as well as straight arrow, round cookie and round sun). The 5 versions of each critical item were distributed across five lists in a Latin Square fashion, so that each participant would only see a single version of each item (the lists of each experiment are available on the OSF repository). Additionally, we created 16 filler trials. The filler trials had the same structure as the critical trials, but used different types of adjectives, such as gradable adjectives (e.g., Show me the long snake; the adjectives were big, tall, long, old, fat, skinny), color adjectives (e.g., Show me the pink pants; the adjectives were green, pink, blue, yellow, purple) and emotional adjectives (Show me the happy friends; the adjectives were angry, happy, surprised, disgusted). Half of the fillers required selecting the red X as the correct response (e.g., the sentence was Show me the skinny dog, but the two pictures showed cats and not dogs), while the other half had a unique correct target image.

2.3 Procedure

Participants were told that they would read a sentence asking them to select an image. They were told that if it was not possible to select an image based on that instruction, they should select the red X instead. Prior to the experiment, they were shown an image depicting how their right hand should remain poised above the response keys (J, K, and L) and how they should only use their right index finger to press the J key, their middle finger to press the K key and their ring finger to press the L key. They were further told that it was paramount to use this response method only, and to select an image as quickly as possible. They saw 4 practice trials (involving color and relative adjectives only) before beginning the experiment, two of which required selecting the red X as the correct response. After the practice trials, instructions were repeated, emphasizing the importance of response speed and of the required position of the hand. All critical and filler items were then presented in a pseudo-randomized order, making sure that there was at least one filler item in between critical trials. Participants took 8 minutes on average to complete the study.

2.4 Participants

For Experiment 1, we recruited 200 right-handed monolingual speakers of American English between the ages of 18 and 35. They were recruited using the Prolific recruitment portal and were given the equivalent of 0.7 dollars as compensation. This number was determined after conducting an a priori power analysis via simulations using the R package SIMR (Green & MacLeod, 2016), based on the results of the pilot study. To start, we used the parameters of the linear model fitted to the reaction times of the pilot data to simulate 1000 new data sets. The only parameter we changed was the effect size found in the pilot for the difference in picture selection time between Precise and Imprecise 1 conditions (Cohen’s D = 0.38). We replaced it with a more conservative estimate (Cohen’s D = 0.2), given how small-scale experiments tend to exaggerate the estimate of the magnitude of an effect (Button et al., 2013; Ioannidis, 2008). The results showed that with 200 participants, we would expect to have 80% power to detect a true effect that is at least as big as the assumed estimate of Cohen’s D = 0.2.

2.5 Predictions

In Experiment 1, we examined both the picture selection rate (i.e., did participants choose the target image, or the red X?) and the picture selection time (i.e., how long did it take participants to accept the target picture as the referent?). First, in terms of picture selection rate, we hypothesized that acceptance of a target picture as the intended referent would gradually decrease as the depicted property moves away from the standard. However, in contrast to the findings of Syrett et al. (2010) for adults, we predicted that participants would accept imprecise pictures in the Imprecise 1 condition as adequate referents for the adjective, at a level greater than chance. This prediction is based on the observation that people routinely use and understand adjectives imprecisely.

In terms of picture selection time, we predicted that – in the absence of a discourse context allowing participants to adjust their expectations – participants would be significantly faster to select the target picture as the referent in the Precise condition compared to all other conditions, in line with the findings of Syrett et al. (2010). This would suggest that imprecise interpretations of MSAAs are derived at a cost, relative to precise ones, when participants do not have enough prior information to adjust their expectations. This prediction is in line with what a semantic view of the encoded meaning of MSAAs would predict. Further, we predicted that there would also be a gradient effect of condition on picture selection time, with reaction times in the Imprecise 1 condition being shorter than in the Imprecise 2 and Imprecise 3 conditions. The Imprecise 3 condition should show the overall longest reaction times. These findings would suggest that distance from a precise maximal standard is a determining factor in the comprehension of MSAAs. More specifically, these findings would suggest that the precise maximal standard is the one that most closely aligns with the semantics of the MSAAs, with the retrieval of a stored sense from the lexicon being less costly than adjusting the sense of the adjective to fit the depicted degree of imprecision.

2.6 Analysis and results

Prior to analysis, we removed participants who scored lower than 75% accuracy on the filler trials, as per our pre-registration. This reduced the total number of participants to 198. We then chose to deviate from our pre-registration (where we stated that RTs shorter than 200 ms and longer than 10000 ms would be removed) by not removing any outliers based on picture selection time. We decided on this given the evidence that outlier-removal strategies based on RTs can bias the means across conditions, a bias which increases with larger sample sizes (Miller, 1991). We maintained this deviation from the pre-registration for Experiment 2. Further, we deviated from our pre-registration (in this and in the subsequent experiments) by analyzing the picture selection rate using a treatment-contrast coding scheme. This was done to match the contrast coding scheme used to model reaction times, and to better examine the pattern of interactions in Experiments 2 and 3. All analyses for Experiments 1, 2 and 3 were conducted using R (R Core Team, 2020) and R-Studio (RStudio Team, 2020). For data processing, visualization and analysis, we used the following packages: ggplot2 (Wickham, 2016), lme4 (Bates et al., 2007), Rmisc (Hope, 2013), MASS (Ripley et al., 2013), dplyr (Wickham et al., 2020), DoBy (Højsgaard, 2012), papaja (Aust & Barth, 2017), here (Müller, 2017), and afex (Singmann et al., 2015).

2.6.1 Picture selection rate

To examine the picture selection rate, we fitted a mixed-effects logistic regression model. Responses were coded as 1 if they selected the target, and 0 if they selected the red X. Trials in which participants selected the distractor image were removed prior to analysis, resulting in the exclusion of 25 trials, or around 1% of the data. The model had a treatment-contrast coding scheme, with the Precise condition coded as the intercept. This coding scheme allows us to evaluate tolerance for imprecision relative to a precise interpretation. The random effects structure of the model included random intercepts by items and by participants and a random slope by items, excluding random correlations between intercepts and slopes (in R syntax: selected ~ condition + (1|participant) + (1+ condition||Item)). This was the maximal converging model, following Barr et al. (2013). The model shows that all imprecise conditions were accepted at a significantly lower rate relative to the Precise condition (all p-values < 0.001). The Precise condition showed an acceptance rate of 99.6%, followed by the Imprecise 1 (89%), the Imprecise 2 (50%), and the Imprecise 3 (18%) conditions. The Control condition was rejected 97.3% of the time. The results can be visualized in Panel A of Figure 2, and the output of the model is summarized in Table 1.

Figure 2: Target picture selection (Panel A) and raw reaction times (Panel B) for Experiment 1. Error bars show confidence intervals.

Table 1: Logistic regression model of picture selection in Experiment 1.

term	$\widehat{\mathit{\beta }}$	95% CI	z	p
Precise vs. Imprecise 1	–2.96	[–4.71, –1.20]	–3.30	.001
Precise vs. Imprecise 2	–6.14	[–7.62, –4.66]	–8.13	<.001
Precise vs. Imprecise 3	–8.21	[–9.75, –6.67]	–10.46	<.001
Precise vs. Control	–10.69	[–12.56, –8.82]	–11.22	<.001

• Note. Model used a treatment-contrast coding scheme.

2.7 Discussion

Experiment 1 resulted in two main findings. First, we found that participants were overall very tolerant of imprecision: Pictures in the Imprecise 1 condition were accepted as correct referents around 90% of the time. However, as seen in Figure 1A, there was a steep decline in acceptance for the remaining imprecise conditions: Pictures in the Imprecise 2 condition were accepted in only 50% of all trials, and pictures in the Imprecise 3 condition were accepted in approximately 17% of trials. These differences in acceptance rate relative to Syrett et al. (2010) could be explained by the type of materials used: The degree of imprecision displayed by the target referent in the infelicitous condition of Syrett et al. (2010) was arguably most similar to the referent in the present study’s Imprecise 3 condition. Second, we found a delay in reaction times for deriving imprecise – relative to precise – interpretations. This confirms the findings of Syrett et al. (2010) – who found that children took longer to accept imprecise, relative to precise, interpretations in the absence of context – and extends it to an adult population and to 6 different MSAAs.

These findings suggest that in the absence of any prior contextual expectations, participants readily tolerate a slight degree of imprecision (pictures in the Imprecise 1 condition) but nevertheless show a processing cost relative to a precise interpretation. This is in line with the findings and conclusions of Syrett et al. (2010), according to which MSAAs require their argument to possess a maximal degree of the relevant property (i.e., to be precise). Deviations from this standard require contextually adjusting the interpretation, resulting in additional processing cost. This speaks in favor of the semantic view of the meaning of MSAAs. That said, note that Experiment 1 took place in the absence of a supporting discourse context: Though there was a visual and sentential context for interpreting the MSAA, expectations of precision were not specified. It could be that if specific expectations for precision are set, the processing cost will vary accordingly, similarly to the findings of Frisson and Pickering (2007) for metonymy. In Experiment 2, we investigate this by examining how an explicit discourse context influences the interpretation of the target sentences containing MSAAs.

3.1 Norming study 2

We created contexts that could generate opposing expectations regarding the relevance of precision for the interpretation of the critical items used in Experiment 1. For each of our critical items, we came up with single-sentence discourse contexts that would either make precision highly relevant for the interpretation (strict context) or not relevant at all (loose context). Figure 3 shows an example of each of the contexts for one critical item (all contexts can be found in the supplementary materials on the project’s OSF page). After this, we set out to confirm our intuitions by having a group of participants rate the expectation of precision raised by each context.

Figure 3: Example of two context sentences for a critical item in Experiment 2.

We conducted a rating study on PCIbex in which each participant read a sentence and rated it on a continuous slider scale ranging from 0–100. We recruited 50 participants on Prolific (who did not take part in any of the other studies) and assigned them to one of two experimental lists with an equal distribution of strict and loose contexts for each of our items. Their task was to rate the likelihood of the target referent having a high degree of precision of the intended property. For example, for the critical item in Figure 1, we asked participants how straight they thought the line drawn by Jasmine was going to be. We additionally added 5 filler contexts that should unequivocally generate strong negative expectations, e.g., the context described a boy with a blue crayon, and the question asked, How red do you think the crayon is going to be?. Overall, participants confirmed our intuitions and rated items in the strict context as generating expectations of precision (each strict context rated 70 or higher, on average). All but 2 of the items in the loose context were rated as not generating expectations of precision (i.e., ratings of around 50 or lower). The contexts of these two items were changed to further reduce the relevance of precision. We then incorporated all contexts into the paradigm used in Experiment 1, to create Experiment 2.

3.2 Materials and design

Experiment 2 was similar to Experiment 1, with one addition: a discourse context was introduced for each item. This resulted in a 2 × 5 design, with the factors PICTURE TYPE (levels: Precise, Imprecise 1, Imprecise 2, Imprecise 3 and Control) and CONTEXT (levels: loose and strict). Since each item had 10 versions, they were distributed across 10 lists, so that one participant would see only one version of each item.

The context sentences for critical items generated expectations regarding whether a precise amount of the relevant property (which the adjective in the target sentence refers to) would be relevant (or not) for the interpretation of the target sentence. For example, in Figure 3, the strict context leads the reader to expect a perfectly straight line, while the loose context does not. The context sentences in the filler items did not highlight precision, but instead provided information that was critical for selecting the correct picture. This was done to make sure that participants paid attention to the context sentence as well as to the pictures. As a result, we changed half of the filler items of Experiment 1, so that the target sentence would refer back to the context sentence in these cases, i.e., selecting the correct picture required remembering the context (e.g., the context says that Luca’s friends are happy, and the target sentence says, Show me Luca’s friends; see the OSF repository for a full list of critical and filler items).

3.3 Procedure

In each trial, participants first read the one-sentence context, and were instructed to press the spacebar after reading it. The context sentence was displayed for a mandatory minimum of 2 seconds. Immediately after pressing the spacebar, the target sentence appeared, together with the three pictures (Target, Distractor and a red X), analogously to Experiment 1. Participants took 12 minutes, on average, to complete the task.

3.4 Participants

As with Experiment 1, we conducted a power analysis via simulations based on pilot data (N = 200), to determine the number of participants needed for Experiment 2. The goal was to determine the number of participants needed to find an interaction effect between the levels Precise and Imprecise 1 of the factor PICTURE TYPE and the two levels of the factor CONTEXT (i.e., loose and strict). Crucially, we assumed a more conservative effect size (Cohen’s D = 0.2) for this interaction than the one found in the pilot study (Cohen’s D = 0.32). The power analysis showed that with 360 participants, we should have over 80% power to find a more conservative effect size than the one found in the pilot for said interaction. We therefore recruited 360 right-handed monolingual speakers of American English between the ages of 18 and 35 on the Prolific recruitment platform. Participants received the equivalent of 1 dollar as compensation for their participation in the study.

3.5 Predictions

Regarding picture selection, we had two main predictions. First, as in Experiment 1, we hypothesized that acceptance of the target picture as a referent for the MSAA would decrease as the depicted property moved further away from the precise standard. Second, we expected this to be mediated by the type of context that participants read prior to the target picture. When the context elicits a loose expectation, we expected that pictures in the Imprecise 1 condition (i.e., only slightly imprecise referents) would be accepted at rates comparable to pictures in the Precise condition. We expected the remaining two imprecise conditions (Imprecise 2 and Imprecise 3) to be accepted at lower rates, reflecting the effect of conceptual distance from the threshold found in Experiment 1. Conversely, we expected there to be very little tolerance for imprecision in the strict context conditions, given that only the Precise condition is compatible with the contextual expectations. We, therefore, expected all imprecise conditions to be at chance (around 50% acceptance) or below.

The response times are of importance to the question of the encoded meaning of MSAAs. If precision is part of the encoded meaning of MSAAs and imprecise interpretations are necessarily reached only with added effort (even when contextual expectations of precision are low, as they are in the loose contexts), acceptance times in the Precise condition should be faster than in the Imprecise 1 condition, regardless of context. This would be in line with a semantic view. Alternatively, if the lexical representation of MSAAs is underspecified for precision (with no advantage for precise interpretations), response times should be wholly dependent on context, with the Precise condition being faster than the Imprecise 1 condition following strict contexts, and the Imprecise 1 condition delivering shorter response times than the Precise condition following loose contexts. This would be in line with an underspecification view.

3.6 Analysis and results

3.6.1 Picture selection rate

Picture selection rates were analyzed similarly to Experiment 1. First, participants with an accuracy lower than 75% on the filler items were removed from further analysis. We also removed the data from 3 participants who completed the experiment despite not meeting the recruitment criteria. This reduced the total number of participants to 351. We then excluded all trials in which participants selected the Distractor image as the referent, which amounted to removing 125 trials (3% of the data). We fitted a logistic regression model to the remaining data. The model had two predictors: PICTURE TYPE, and CONTEXT, both coded using treatment-contrast coding, with the Loose context – Precise condition as the baseline. The dependent variable was the type of picture selected, with 0 signifying the red X, and 1 signifying the Target picture.

The model included random intercepts by items and by participants as well as random slopes for both factors and their interaction by items, a random slope term for CONTEXT by participants, and no random correlations between intercepts and slopes (R syntax: selected ~ PICTURE TYPE * CONTEXT+ (1 + CONTEXT ||participant) + (1 + PICTURE TYPE * CONTEXT ||Item).

The results can be visualized in Panel A of Figure 4, and Table 3 shows the output of the model. Figure 4A shows that there was a stepwise decrease in acceptance rate of imprecise referents in the loose contexts. However, as seen in Table 3, acceptance in the Loose – Imprecise 1 condition was significantly higher than in the Loose – Precise condition (z-value = 2.23, p < 0.05). This suggests that the contextual manipulation led participants to accept a slightly imprecise interpretation of the MSAAs at a higher rate than a precise interpretation when contextual expectations of precision were low. There was also an interaction between the “top” two PICTURE TYPE conditions (Precise and Imprecise 1) and CONTEXT (z-value = 5.37, p < 0.001): the preference for imprecise interpretations in the loose context was reversed in the strict context. Further, differences in expectations for precision had an impact on all imprecise conditions: There were interactions between all levels of imprecision (relative to the precise condition) and CONTEXT.

Figure 4: Target picture selection (Panel A) and raw reaction times (Panel B) for Experiment 2. Error bars show confidence intervals.

Table 3: Logistic regression model of picture selection in Experiment 2, loose conditions.

term	$\widehat{\mathit{\beta }}$	95% CI	z	p
Loose – Precise vs. Loose – Imprecise 1	0.69	[0.08, 1.30]	2.23	.026
Loose – Precise vs. Loose – Imprecise 2	–1.25	[–1.71, –0.80]	–5.37	<.001
Loose – Precise vs. Loose – Imprecise 3	–2.68	[–3.22, –2.14]	–9.74	<.001
Loose – Precise vs. Loose – Control	–7.56	[–8.89, –6.23]	–11.15	<.001
Loose – Precise vs. Strict – Precise	3.51	[1.95, 5.06]	4.42	<.001
(Precise vs. Imprecise 1)*CONTEXT Interaction	–5.90	[–7.52, –4.29]	–7.17	<.001
(Precise vs. Imprecise 2)*CONTEXT Interaction	–5.98	[–7.55, –4.40]	–7.44	<.001
(Precise vs. Imprecise 3)*CONTEXT Interaction	–6.09	[–7.76, –4.42]	–7.15	<.001

• Note. Both factors used a treatment-contrast coding scheme.

3.7 Discussion

Experiment 2 examined the comprehension of sentences containing precise and imprecise usages of MSAAs when these are embedded in simple discourse contexts that differ in the type of elicited expectations of precision. The contextual manipulation had a global effect on both the acceptance rate and measures of comprehension effort, which led to a series of important findings. First, in terms of picture selection rate, contextual expectations clearly mediated the interpretation of the adjectives: Pictures in the Imprecise 1 condition were accepted significantly more often than pictures in the Precise condition when an imprecise interpretation was compatible with the discourse context (loose context). Further, context improved the likelihood of acceptance of the visual referent for all degrees of imprecision, as evidenced by the interactions between all PICTURE TYPE conditions and CONTEXT reported in Table 3. Changes in the absolute percentages of tolerated imprecision are also noteworthy: Following the strict context, the Imprecise 2 and Imprecise 3 pictures were accepted as referents 35% and 13.8% of the time, respectively. Following the loose contexts, these rates went up to 78% and 49.8%. This surge in acceptance illustrates the extent to which comprehenders are flexible during the interpretation of sentences containing MSAAs. There are, however, limits to this flexibility: Pictures in the Imprecise 1 condition were accepted at a fairly high rate in the strict contexts (~68%), suggesting that small degrees of imprecision might be highly conventionalized and can hardly be eliminated by a biasing discourse context.

Central to our investigation are the results regarding picture selection time. Here, we found an interaction in picture selection time between the top levels of PICTURE TYPE (Imprecise 1 and Precise) and CONTEXT. This finding is, in principle, compatible with the underspecification view: Comprehension effort is mediated by contextual expectations, suggesting that both precise and imprecise interpretations of MSAAs require a similar contextual adjustment that results in added cost. However, there was also a main effect of PICTURE TYPE: The precise condition was overall faster than the Imprecise 1 condition, regardless of context. This result is in line with the semantic view: Despite contextual expectations, precise interpretations were generally derived at a lower cost, relative to imprecise interpretations. This raises the question of the source of the interaction between both factors. A visual inspection of Panel B of Figure 4 suggests that the difference is not driven by changes in the acceptance time of imprecise interpretations in the loose contexts, but by speedier acceptance times of precise readings in the strict contexts. This is supported by the pairwise comparisons: There was no significant difference between Loose context – Imprecise 1 and Strict context – Imprecise 1 (t = 0.4, p = .9) or between Strict context – Imprecise 1 and Loose context – Precise (t = 1.78, p = .33), while Strict context – Precise was faster than all other conditions.

The pattern is, overall, more compatible with a semantic view of the lexical representation of MSAAs: Raising the contextual expectations of precision facilitated the comprehension of the critical sentences when these aligned with the semantics of the MSAAs, while lowering the expectations resulted in additional pragmatic work to derive an imprecise interpretation, even when such an interpretation was highly supported by the context. This accounts for both the main effect of PICTURE TYPE, and the interaction between both factors. The results would be harder to explain from an underspecification perspective, which would posit that the source of the interaction should be a contextual facilitation when expectations align with the visual referent.

4.1 Materials, design, procedure and predictions

Experiment 3 was similar to Experiment 2, but had a different sequence of events in each trial, and the structure of the target sentence was modified. Participants first read the discourse context (loose or strict; the contexts were identical to those used in Experiment 2) and simultaneously saw a single image (the Target image in the conditions Precise, Imprecise 1, Imprecise 2, Imprecise 3 or Control of Experiments 1 and 2; see Figure 1). This “context slide” was displayed for a mandatory minimum of 2 seconds, and participants had to press the spacebar to continue. Then, participants read a critical sentence (containing an MSAA) in a self-paced, moving-window manner. After this, participants had to indicate whether the picture seen at the beginning matched the story as a whole (i.e., the context and the target sentence) by using the F key (did not match) or the J key (matched). An example of a target sentence is shown in (1) below, and the procedure is illustrated in Figure 5. Slashes indicate the boundaries of the sentence regions shown to participants at one time.

Figure 5: Example of the sequence of events in a single trial of Experiment 3.

Participants pressed the spacebar for the next region to appear on their screen. Sentences in critical items had five sentence regions, with the relevant MSAA always in the second region. We measured reading times of regions 2–5, i.e., from the point at which the adjective appears until the end of the sentence. We also adapted the 16 filler items of Experiment 2 in a similar way. Filler target sentences had between 4 and 6 sentence regions. In half of them (8 trials), the picture matched the story, while in the other half, it did not. As in the previous experiments, participants had to score at least 75% accuracy in the filler trials (i.e., 12 trials) in order to be included in the analysis.

Our predictions relate to both the reading times and the story-picture verification task. Regarding reading times, if it is the case that precision is part of the encoded meaning of MSAAs, sentences in the Strict context – Precise condition should be read significantly faster, overall, than sentences in the Loose context – Imprecise 1 condition. Further, there should either be no difference between the Loose context – Imprecise 1 and Loose context – Precise conditions (as was the case in Experiment 2), or the Loose context – Precise condition should be faster than the Loose context – Imprecise 1 condition. This pattern of results would confirm the findings of Experiment 2 and suggest that, despite contextual expectations, a precise interpretation of an MSAA is easier to derive than an imprecise interpretation. Alternatively, if it is the case that the encoded meaning of MSAAs is not precise, there should be a “full” interaction between context and picture type: The Loose context – Imprecise 1 condition should be faster than the Loose context – Precise condition, and there should be no difference between the Loose context – Imprecise 1 and Strict context – Precise conditions, i.e., between the two felicitous cases. Our predictions refer to the collapsed reading times of regions 2–5, to account for the possibility that effects might only become visible in one of the spill-over regions after processing the adjective, as is commonly the case in self-paced reading paradigms. As a post-hoc measure, we also examined the reading times of individual regions to determine the earliest moment at which effects (if any) become visible.

Regarding the post-trial picture-story verification, we anticipated findings similar to those of Experiment 2. There, we found that picture selection of the target was mediated by contextual expectations: Acceptance of all imprecise conditions (Imprecise 1, 2, and 3) increased in the presence of loose contexts, relative to when they followed strict contexts. In Experiment 3, we can examine whether this pattern holds when participants are merely asked to state whether the picture matched the story, instead of comparing the picture to the distractor. In sum, Experiment 3 presents a more stringent test of how contextual expectations mediate tolerance for imprecision, by allowing us to examine how the sentences are processed independently of the potential effort attributed to selecting a matching visual referent. If the findings of Experiment 2 represent how participants pragmatically adjust the meaning of MSAAs to tolerate different degrees of imprecision, we should find a similar pattern of results in Experiment 3. Alternatively, if the results of Experiment 2 are influenced by the comparison process of the task, we might find a different pattern in Experiment 3.

4.2 Participants

Our goal was to match the number of participants in Experiment 2, which was 360. For this, we recruited 390 right-handed monolingual speakers of American English between the ages of 18 and 35 on the Prolific recruitment platform, assuming that some might not meet our inclusion criteria (i.e., achieve at least 75% accuracy on the post-trial story-picture verification task). The final number of participants was 371. Participants received 1 dollar as compensation for their participation in the study.

4.3 Analysis and results

4.3.1 Picture-story verification

We fitted a logistic regression model to analyze the picture-story verification data. For this, we used the full 5 × 2 design, as was done in Experiment 2 for the picture selection data. The dependent variable was the key pressed, with J coded as 1 and F coded as 0. The factors PICTURE TYPE and CONTEXT were coded with a treatment-contrast coding scheme (as was done in Experiment 2). The model had the Loose – Precise condition as the baseline. The random effects structure included random intercepts and slopes for both factors and their interaction by items and by participants, suppressing the random correlations between intercepts and slopes (R syntax: selected ~ PICTURE TYPE * CONTEXT + (1 + PICTURE TYPE * CONTEXT ||participant) + (1 + PICTURE TYPE * CONTEXT ||Item).

As seen in Panel A of Figure 6, the results were similar to those of Experiment 2: there was a step-wise decrease in the acceptance rate of imprecise referents in the loose contexts. Further, as Table 6 shows, there was an interaction between the top two PICTURE TYPE conditions (Precise and Imprecise 1) and CONTEXT (though, in contrast to Experiment 2, this interaction did not result in the Imprecise 1 condition having a higher acceptance rate than the Precise condition in loose contexts). In fact, there were interactions between all levels of imprecision relative to the Precise condition and CONTEXT, as was the case in Experiment 2.

Figure 6: Picture-story verification accuracy (Panel A), sentence raw reading times (Panel B) and raw reading times by individual region (Panel C) for Experiment 3. Error bars show confidence intervals.

Table 6: Logistic regression model of picture-story verification in Experiment 3, loose conditions.

term	$\widehat{\mathit{\beta }}$	95% CI	z	p
Loose – Precise vs. Loose – Imprecise 1	–1.36	[–1.91, –0.80]	–4.79	<.001
Loose – Precise vs. Loose – Imprecise 2	–2.78	[–3.19, –2.38]	–13.33	<.001
Loose – Precise vs. Loose – Imprecise 3	–3.65	[–4.09, –3.21]	–16.09	<.001
Loose – Precise vs. Loose – Control	–5.58	[–6.54, –4.62]	–11.45	<.001
Loose – Precise vs. Strict – Control	1.05	[0.43, 1.68]	3.31	.001
(Precise vs. Imprecise 1)*CONTEXT Interaction	–1.59	[–2.42, –0.77]	–3.78	<.001
(Precise vs. Imprecise 2)*CONTEXT Interaction	–1.76	[–2.43, –1.09]	–5.14	<.001
(Precise vs. Imprecise 3)*CONTEXT Interaction	–2.06	[–2.87, –1.25]	–5.00	<.001

• Note. Both factors used a treatment-contrast coding scheme.

4.4 Discussion

The results of Experiment 3 broadly confirm the findings of Experiment 2: In terms of picture-story verification, participants tolerated more imprecise interpretations when precision was not relevant for the interpretation (loose contexts) than when it was (strict contexts). The interaction between the top levels of the factor PICTURE TYPE and CONTEXT further suggests that participants manage to adjust their precise and imprecise interpretations accordingly. However, the picture-story verification results must be interpreted carefully, seeing as the task itself was rather vague: We asked participants whether a picture “matched” a story, instead of directly asking them to select the intended referent (as in Experiments 1 and 2).

Experiment 3 does allow for a better interpretation of the processing data relative to Experiments 1 and 2. Here, the reading times suggest that imprecise interpretations come at a cost across the board: It takes participants less time to read sentences eliciting precise readings than those eliciting imprecise ones. This effect is visible in the first spill-over region, i.e., the sentence region immediately after the MSAA was read. Together, the results from the picture-story verification task and the self-paced reading task support our interpretation of the findings of Experiment 2, by suggesting that the advantage for precision is not exclusively related to the decision-making process of selecting a visual referent.

5.1 Limitations and future directions

A limitation of the current study is the relatively ambiguous measure of picture selection time used in Experiments 1 and 2, given how it conflates processing the adjective and deciding between possible visual referents. This was overcome in Experiment 3, where we find a pattern of results similar to Experiment 2, using only self-paced reading. However, self-paced reading brings with it other limitations. While Experiment 3 shows a processing advantage for precision across all sentence regions, the first region to show an effect on its own is the one after the MSAA (the so-called spill-over region). This leaves the question open as to whether this effect reflects later stages in processing (because it does not appear immediately upon encountering the adjective), or whether it reflects a lag in the signal (because self-paced reading is a coarse measure of processing). It is, therefore, possible that using more time-sensitive measures (such as eye-tracking or EEG, for example) that tap into the earliest comprehension stages (i.e., as soon as the MSAA is integrated with the utterance), one would find no differences between precise and imprecise readings, in line with the underspecification view, as stated by Frisson (2009).

While we agree that a stronger test of the underspecification view requires a more fine-grained measure, the current results are still relevant to this debate. First, we adopted the design of the seminal study by Syrett et al. (2010), which allows us to more readily compare our results to theirs (Experiments 1 and 2). Second (and though we remain agnostic regarding the precise locus of the effect), it is still the case that throughout the entire comprehension process, precise interpretations were less effortful than imprecise ones, even when processing was measured without an explicit decision-making task (Experiment 3). This seems largely incompatible with underspecification views, which posit that speakers zero in on the contextually appropriate sense after first activating the underspecified meaning. One possible objection is that our loose contexts were not sufficiently biased towards the imprecise interpretations, and that more naturalistic and/or elaborate contexts raising low expectations of precision might have reduced or even eliminated the additional processing effort found for imprecise interpretations, compared to precise interpretations, in our study. While we cannot completely rule out this possibility, all our loose contexts were considered not to generate expectations of precision in our norming study, although the ratings were not as unequivocal as for the strict contexts.

Further, it is important to note that it is outside of the scope of the current investigation to spell out exactly what the lexical entries of MSAA would look like, according to an underspecification account. It is possible that such an account would have the lexical representation of absolute adjectives be like that of relative adjectives, as posited by Lassiter and Goodman (2013). In that account, the difference in interpretation between the two adjective types is not given by the semantics of the adjectives, but by the prior expectations that interpreters have regarding the statistical properties of the relevant comparison class. If prior expectations are contextually shifted, imprecise interpretations could be preferred to precise interpretations. This is not entirely distinct from what we observe in our data, where we find that shifting the prior expectations of precision results in changes in the interpretation of the MSAAs. However, from a psycholinguistic perspective, it would be ideal for such an underspecification account to make predictions regarding how the processing cost of imprecision is mediated by context, which Lassiter and Goodman (2013) do not make. In the current article, we are concerned with formulating what such an account would predict in terms of processing, and not with the explication of the account per se.

A loose thread presents itself from a developmental perspective. In the study by Syrett et al. (2010), it was consistently found that children were more tolerant of imprecision, compared to adults. Syrett et al. (2010) speculate that adults might have been more tolerant of imprecision had the materials been closer to the precise standard. This intuition finds some support in the present experiments, where even in the absence of context, our adult participants accepted imprecise interpretations quite frequently. But how would children perform in our task? We could assume that they would likely show remarkable tolerance for imprecision in Experiment 1. But would they be able to modulate this according to contextually-raised expectations of precision? We leave this question open for future studies.