1 INTRODUCTION

Plural expressions pose a challenge to communication. Consider, for instance, a plural noun phrase like my classmates and its role in the following two sentences:

At first glance, it might seem that the interpretation of the noun phrase and the interpretation of the sentences in which the noun phrase appears are straightforward. The plural expression my classmates simply refers to those individuals that are my classmates, and the sentences are statements about those individuals. However, on closer inspection, (1a) and (1b) turn out to communicate very different statements. The predicate had a coffee in (1a) assigns a property to individual classmates: the sentence states that each of them had one coffee. In contrast to (1a), the predicate surrounded the podium does not assign a property to individual classmates, but to the whole group: (1b) makes a statement about my classmates as a group to the effect that together, they surrounded the podium.

Examples (1a) and (1b) include predicates that clearly distinguish between the two roles that the plurality my classmates plays in interpretation, but this is often not the case in regular conversation. For example, the sentence in (2) below makes two mutually exclusive statements. It might express that individual items cost $50, in which case all the items as a group cost more than $50, or it might express that all the items as a group cost $50, in which case the individual items cost less than that. Following the formal semantics literature, we will henceforth refer to the first interpretation as distributive and the second interpretation as collective (see Landman 1995; Nouwen 2012; Dotlačil to appear; Champollion to appear and references therein for more details on the two interpretations).

The fact that sentences with plural noun phrases can be understood in two very different ways raises a non-trivial issue about alignment between production and comprehension. How do speakers and hearers converge on one interpretation when talking about multiple entities? And how are the two interpretations represented in grammar?

In semantic research, the dominant account of the distributive/collective ambiguity assumes that the two interpretations are structurally different. It is assumed that language has a silent operator, D, which in most instances can be paraphrased as ‘each’. When the operator is present, the resulting sentence receives the distributive reading, and when it is not, the sentence receives the collective reading (Roberts 1990, Lasersohn 1995; see Schwarzschild 1996 and Landman 2000 for a more nuanced picture). This position has been supported in psycholinguistic research, in particular, by findings in the processing of distributive and collective interpretations presented in Frazier et al. (1999).¹

In the study of Frazier et al. (1999), participants read sentences with a conjoined noun phrase subject and whose verb+object predicates were compatible with collective and distributive interpretations. The predicates were disambiguated towards their collective interpretation (by the adverb together) or their distributive interpretation (by the quantifier each). When the disambiguator followed the predicate, as in (3), encountering the distributive disambiguator (each) yielded more processing difficulties than encountering the collective disambiguator (together). Participants read the underlined region more slowly in (3a) than in (3b), and they regressed more often in (3a) than in (3b) from the same region.

Importantly, when the disambiguators preceded the predicate, (4), no contrast between each and together was observed. That is, (4a) did not show processing difficulties compared to (4b). This excluded the possibility that processing difficulties observed in (3) could simply be due to the fact that distributive readings are more complex in their interpretation.

To explain the data, Frazier et al. (1999) propose that distributive/collective readings are a case of ambiguity, similar to the kind of lexical ambiguity exemplified by homonyms. Assuming that the processor has to commit to one interpretation when it encounters an ambiguity, and that the processor prefers collective readings of ambiguous predicates, readers will run into problems in the post-predicate disambiguation towards distributivity, (3a). No such problems are expected for (3b). Furthermore, since the sentences in (4) are disambiguated before the predicate is read and the processor has to commit to a reading, (4) should not cause difficulties either. This explanation treats the contrasts in (3) and (4) as a kind of semantic garden-path effect, and fits well with the dominant position in semantic research: the effect arises because readers by default assume the absence of the D operator when reading (3), which is incompatible with the later disambiguation towards the distributive reading in (3a).

One issue that remains open and that we address in this paper is why readers prefer the collective reading of predicates like carried one suitcase (see also Boylan et al. 2011 for additional support that this preference exists). Frazier et al. (1999) mention two possible explanations, but note that their experiment cannot decide between them. On one hand, it is possible that the processor selects the structure/representation that is the simplest, while still compatible with the processed words.² Since the distributive reading requires the presence of an extra silent operator D, the processor picks the collective reading if possible. Under this view, the preference for collective readings is driven by structural considerations. Alternatively, it is possible that readers select the reading that is simpler in the sense of introducing fewer events and entities.³ Consider the sentence Sam and Martha carried one suitcase. The distributive reading requires the existence of two events of carrying one suitcase, and it is compatible with there being two suitcases in total. In contrast, only one suitcase and one event of carrying one suitcase is assumed in the collective reading. Under this view, the preference for collective readings is driven by interpretational complexity considerations.

We add a third possible explanation for the pattern in (3) and (4). Frazier et al. (1999) treat the two instances of together in (3b) and (4b) as identical lexical items that are syntactically integrated in more or less the same way, and this also holds for the two instances of each in (3a) and (4a). The adverb together is, indeed, commonly treated as a manner adverb irrespective of whether it appears in a pre-VP or a post-VP position.⁴ The situation for each is less straightforward. The linguistic literature takes the postverbal each in (3a) and the preverbal each in (4a) to be related but nonetheless distinct items, each associated with a specific syntax and semantics. Preverbal each is usually taken to be a VP modifier (much like together), but postverbal each, a.k.a. binominal each, is syntactically part of the NP it modifies (Burzio 1986, Safir and Stowell 1988). The two quantifiers also differ in their semantics. Postverbal, but not preverbal, each places a restriction on the meaning of the direct object, requiring it to express cardinality. This restriction is the reason for the unacceptability of (5a) below: the direct object NP every movie is a universal quantifier and does not express cardinality, unlike one movie in (5b) (Szabolcsi 2011, a.o.). The sentence in (5c) shows that preverbal each places no such restrictions on the object. Differences like the one shown in (5) led semanticists to analyze postverbal each differently from preverbal each (see Zimmermann 2002; Blaheta 2003; Dotlačil 2012; Champollion 2016b).

With this in mind, let us again consider the argument in Frazier et al. (1999). The observed slowdown for postverbal each compared to together, as opposed to no difference between preverbal each and together, was taken to reveal the preference of the parser for the collective interpretation of the ambiguous predicate, followed by reinterpretation in (3a). However, since the two types of each have different syntactic and semantic characteristics, the slowdown observed in (3a) could be attributed to the syntactic and semantic differences between preverbal and postverbal each. For example, it could be attributed to the fact that readers have to consider the extra semantic requirements that postverbal each places on the object. That is, the observed slowdown could be due to the complexity of postverbal each.

We present two novel self-paced reading experiments whose goal is to replicate the findings of Frazier et al. (1999) with distributive disambiguators other than each, and to explain why readers exhibit a preference for collective readings.

In the first experiment, we follow the design of Frazier et al. (1999), but instead of using each as the disambiguator of distributive readings, we employ individually, which is a manner adverb and should not show a distinct behavior in its preverbal and postverbal positions compared to other manner adverbs like together. This is supported by (6), which shows that, in contrast to each, the position of individually is not sensitive to the type of object. Furthermore, (7) shows that individually, unlike each, can be conjoined with together, corroborating the claim that individually and together are both manner adverbs.

Given the close affinity of individually to together, the effect of individually in the two positions can be directly compared to the effect of together. In other words, using only adverbs as disambiguators minimizes the risk of confounds in the current study, and should eliminate the possibility that the findings of Frazier et al. (1999) are due to a greater complexity of postverbal each compared to preverbal each.

In the second experiment, we leverage the observation made in the semantic literature (Link 1987; Roberts 1990; Lasersohn 1989; 1995; Moltmann 1997; Winter 2000; 2001; Kratzer 2008; Dotlačil 2010; Champollion 2010; 2016a; 2017; de Vries 2017, among others) that the D operator is only needed for non-lexical (syntactic) predicates. As an example, take (8) below. The predicate smile expresses a property that holds of single individuals, that is, (8) states that every boy smiled. However, there is no reason to assume that this reading is generated by means of a D operator. It is simply part of our lexical knowledge that smiling is a property that holds of single individuals. When we hear (8), we learn that a group of boys has the property of smiling, but because of this inherent meaning of smile, which is roughly ‘the individual’s lips move upwards’, it follows that whenever smiling is truthfully predicated of a group, it must be truthfully predicated of all (or at least a majority of) the individuals in that group (see also Krifka 1989; Yoon 1996; Landman 2000; Kratzer 2008, a.o., for more details).

The situation is different for syntactically complex predicates like carried one suitcase in (9) below. Even if we assume that carrying is a property of atomic individuals, we would only arrive at the meaning that each boy did the carrying action, and the boys all carried one (and the same) suitcase. The issue is the quantifier one suitcase: unless we assume the presence of a D operator, we do not have a way to derive that there were multiple suitcases, one per boy. That is, without a D operator, (9) relates a group of boys and one suitcase by means of the predicate carry. The carry relation might distribute down to individual boys in the group, but it still relates each of them to the one suitcase under discussion.

However, we can get a distributive reading for (9) if we postulate the presence of a covert D operator. Recall that D can be roughly interpreted as each, and note that the paraphrase the boys each carried one suitcase does express that multiple suitcases were carried, one per boy.⁵

The second experiment will study whether distributive/collective reinterpretation is processed differently when the predicate is lexical, as in (8), and when it is constructed in syntax, as in (9), whose distributive reading requires a quantificational element, the D-operator. As we will see, there is indeed a contrast between cases in which distributivity can be purely lexical and cases in which distributivity has to be phrasal and triggered by a quantificational element. We take that as evidence that the preference for collective readings is not due to the interpretational simplicity of collective readings, and argue that our findings are compatible with the position that the processor chooses simpler structures, i.e., structures without the D operator.

2 EXPERIMENT 1

The design of this experiment followed Frazier et al. (1999). We investigated the processing of sentences that had a plural entity in subject position, using plural definites, e.g., the students. Each sentence included either the adverb individually, which forces a distributive interpretation,⁶ as in (10a) and (10c) below, or the adverb together, which forces a collective reading,⁷ as in (10b) and (10d). The second manipulation was the position of these adverbs: they appeared either preverbally/early, as in (10a) and (10b), or postverbally/late, as in (10c) and (10d).

The logic behind this experiment was identical to that of Frazier et al. (1999). If readers non-randomly select one reading when encountering a plural NP + predication, and if a subsequent reinterpretation is costly, we expect to observe processing difficulties either in (10c) or (10d), once the disambiguating adverb following the predicate is read and integrated.

Frazier et al. (1999) observed that distributive reinterpretation was costly, and accounted for this processing difficulty by assuming that the processor initially selected the collective reading. By the same reasoning, we would expect to see processing difficulties in (10c) as compared to (10d). If, however, (10d) turns out to be more difficult than (10c), we can conclude that the processor selects the distributive interpretation by default, and the reinterpretation towards a collective reading is what incurs an additional processing cost.

The early cases, (10a) and (10b), control that the processing cost is due to reinterpretation, and it is not caused by the inherent costs associated with distributive or collective readings simpliciter.

2.2 RESULTS AND DISCUSSION

As expected, responses to questions did not pose significant problems to participants. The median correct response to fillers and target items was 95% correct, with 85 participants having at least 88% of responses correct. Two participants, however, were clear outliers, answering only 79% and 82% of the questions correctly. These participants were removed from all subsequent analyses. The final number of participants whose data we analyzed: 85.

Prior to the analysis of reading times (RTs), we removed extremely fast (<50 ms) and slow (>3000 ms) responses, as is common in analyses of self-paced reading studies (see, for example, Futrell et al. 2018). Less than 1 percent of all the data was eliminated in this way. Secondly, we log-transformed RTs to mitigate their characteristic right-skewness. We probed for (very fast or very slow) outliers among readers by checking mean logRTs per participant. No participant’s mean logRT was more than 2.5 standard deviations away from the grand mean, so we retained the RT data from all 85 participants.

Following Trueswell et al. (1994), among others, we factored out the influence of word length and word position by running a linear mixed-effects regression that had intercept-only random effects for subjects and two fixed effects – word length in characters and word position in the sentence. The resulting residualized log reading times were used for all subsequent analyses.

The main regions of interest (ROIs) were the adverb, the predicate and the three words following the disambiguated predicate (the spillover region). The ROIs are underlined in (12).

(12)	a.	The girls individually wrote a sonnet after they had read Shakespeare.
	b.	The girls together wrote a sonnet after they had read Shakespeare.
	c.	The girls wrote a sonnet individually after they had read Shakespeare.
	d.	The girls wrote a sonnet together after they had read Shakespeare.

The graphical summary of logRTs starting with adverbs in the early position is presented in Figure 1. LogRTs are also summarized in a table in Appendix.

Figure 1

Exp. 1, LogRTs per word in the predicate, adverb and spillover regions. The position AdverbEarly shows LogRTs for adverbs individually and together in the early position. The position AdverbLate shows LogRTs for adverbs individually and together in the late position.

For each region, we constructed a mixed-effects model with three treatment-coded fixed effects: ADVERB (TOGETHER or INDIVIDUALLY; the former was the reference level), POSITION (EARLY or LATE, the former was the reference level); the interaction of ADVERB and POSITION. Following one of the recommendations in Barr et al. 2013, all our models included the maximal random-effect structure for subject and items. Since the lme4 R package, which is commonly used for estimating mixed-effects models, did not converge with the maximal random-effect structure, we used Bayesian models estimated with Stan (Carpenter et al. 2017) and brms (Bürkner 2017). The structure of prior distributions and the sampling details of the models are provided in the Appendix.

In Figure 2, we show the posterior distributions of the fixed effects on two words, the adverb and the first word in the spillover region. We focus on these two words because these were the only cases in which the 89% credible intervals of at least one parameter exclude 0. On the adverb, we see that in the early position individually decreases residualized logRTs (posterior distribution of INDIVIDUALLY: 89% credible interval: ⟨–0.08, –0.014⟩, median = –0.05, p(β < 0) = 0.98).⁹¹⁰ We also observe an interaction of LATE POSITION:INDIVIDUALLY, which almost fully removes the speedup due to individually (posterior distribution of INDIVIDUALLY:LATE POSITION: 89% credible interval: ⟨0.005, 0.12⟩, median = 0.05, p(β > 0) = 0.96). On the first spillover word, the word after, we see that LATE POSITION leads to a slowdown in reading (posterior distribution of LATE POSITION: 89% credible interval: ⟨0.01, 0.08⟩, median = 0.04, p(β > 0) = 0.98). Second, there is a positive interaction of LATE POSITION and INDIVIDUALLY (posterior distribution of LATE POSITION:INDIVIDUALLY: 89% credible interval: ⟨0.02, 0.11⟩, median = 0.063, p(β > 0) = 0.99). No other region of interest shows a posterior distribution of a parameter that is overwhelmingly (p(β) > 0.95) positive or negative.

Figure 2

Posterior distributions of parameters of interest on Adverb and the first word in the spillover (the word after in (12)). A thick horizontal line represents 80% highest posterior density interval (HDPI) of a parameter, a thin horizontal line represents 89% HDPI of a parameter. The dashed vertical line is at the position of o. Filled circles represent median values.

Focusing on the effect observed on the spillover, we see that postverbal adverbs lead to a slowdown in reading, and the slowdown is even more pronounced when the postverbal adverb is the distributive disambiguator individually. The latter effect can also be observed on the adverb, even though the interaction INDIVIDUALLY:LATE POSITION is less dominantly positive on that word. Both effects are replications of Frazier et al. (1999).

The slowdown caused by postverbal adverbs on the first spillover word is orthogonal to our main research question. It possibly reflects the cost associated with adverb-predicate integration. No such cost would be observable for preverbal adverbs, since these were read before the predicate and could have already been integrated while reading the predicate itself. The effect might alternatively be due to the fact that adverbs are usually preferred and more frequent in preverbal than postverbal positions (see the frequency data in Ko 2016). While the preference is well-known for subject-oriented and speaker-oriented adverbs (e.g., Haider 2004), the results of the present experiment suggest that the preference might also hold for manner adverbs such as together and individually.

More importantly for us, the postverbal-position slowdown is further modulated by the positive interaction LATE:INDIVIDUALLY. This shows that the postverbal adverb disambiguating towards the distributive reading incurs a processing cost above and beyond any processing cost caused by postverbal adverbs in general. The observed interaction is compatible with the position that readers select the collective interpretation of ambiguous predicates, and that the distributive reinterpretation is costly. The findings generalize the results of Frazier et al. (1999) beyond the disambiguator each, and are incompatible with the hypothesis that the processing difficulty associated with postverbal each can be fully explained by the semantic complexity of binominal each.

There are two alternative explanations that we can discard. First, one could think that the observed slowdown caused by the postverbal adverb individually is just due to some general cost associated with this adverb (e.g., because the adverb individually is less frequent and morphologically more complex than together). If this was so, however, we would also expect individually to be read more slowly than together in preverbal position, which does not actually happen. In fact, we observed the exact opposite: individually is read faster than together preverbally when we control for word length. Furthermore, the effect of preverbal adverb type does not spill over to any of the words on the predicate wrote a sonnet, showing again that individually is not intrinsically harder to process than together.

The second alternative explanation we can discard is that distributive readings themselves cause processing difficulties, rather than the reanalysis towards distributivity. It would follow from this second alternative explanation that the early disambiguator towards distributivity should also be a cause of processing difficulties, again contrary to the experimental results.

We thus conclude that the cost of reinterpretation from collectivity to distributivity is genuine. What remains unclear is why the processor should prefer collective readings. The second experiment addresses this question.

3 EXPERIMENT 2

After excluding the option that the results of Frazier et al. (1999) are simply due to the complexity of postverbal each, we are left with two possible explanations for why the processor should prefer collective over distributive interpretations. One explanation is that the processor is sensitive to structural economy considerations and prefers structures without the D operator. Alternatively, the processor is sensitive to interpretational economy/complexity considerations, and prefers collective readings because they are simpler in the sense that they introduce fewer entities, or other simpler interpretational objects compared to distributive readings. For example, in the sentence Two boys carried one suitcase, the collective reading postulates just one event and one suitcase, whilst the distributive reading postulates two events and is compatible with there being two suitcases, such that each event+suitcase is associated with one of the two boys. Since the collective reading postulates fewer events, and possibly also fewer objects, than the distributive reading, the preference for interpretational economy selects the collective reading.

In semantic research, it has been argued at least since Scha (1981) that the D operator is not needed across the board to obtain distributive readings for any predicate. Consider (13).

The predicate meet does not express a property of single individuals but a property of groups. Under most semantic theories, it is assumed that the predicate applies to some kind of plurality – a plurality of girls in (13a). The lexical meaning of the predicate will ensure that even though the predicate applies to the group, we learn something about individual girls when hearing (13a) – for example, that every girl, or at least a majority of the girls, was at the same location.

A similar analysis can be given to (13b). Even though we deal with a predicate that expresses a property of individuals (sleep), it is possible to assume that the predicate sleep applies to the plurality of girls. Due to the lexical meaning of the predicate, we learn something about individual girls from (13b) – that is, that all (or at least most of) the girls are asleep. This is sometimes dubbed a vagueness account of distributivity (cf. Winter 2000), or an underspecification account (cf. Champollion to appear). We will use the latter label.

It is hard to see how the underspecification account could generalize to examples like (14).

Even if we assume that sleep can apply to a group and express that every individual, or most individuals, sleep, as we did above, we would only derive the meaning that there was one narrow bed and every girl slept on it. However, the distributive reading of (14) is more appropriately paraphrased as ‘the girls each slept on a narrow bed’ and requires, in the pragmatically most plausible interpretation, that there were as many beds as there were girls.

More generally, the underspecification account derives distributivity as a by-product of the lexical meaning in (13b). The same strategy, however, would only work for (14) if we assume that the whole predicate slept on a narrow bed is stored in the lexicon. If it is not, something else has to be responsible for deriving the distributive reading of (14).

That something else, so the semantic literature argues, is phrasal distributivity, triggered by the distributivity operator, or the D operator for short. In most accounts (see Champollion to appear for a recent summary), the D operator appears at the VP level and modifies the whole predicate. In (14), this would be the predicate slept on a narrow bed. For our purposes, it suffices to say that the operator is interpreted in the same way as each (Heim et al. 1991; see Schwarzschild 1996 for a more nuanced view), i.e., the D-enriched sentence (14) can be paraphrased as ‘the girls each slept on a narrow bed’. This paraphrase correctly highlights that the distributive reading expresses that each girl slept on a different narrow bed, and there were as many beds as girls.

Before proceeding, let us reiterate one crucial issue about D operators in relation to (14). We need the D operator not because the verb sleep is understood distributively, but because the whole predicate sleep on a narrow bed is so interpreted – in particular, narrow beds have to covary with the girls. The distributive interpretation of this whole complex VP poses a challenge to the underspecification account, since the underspecification account should operate only on lexical units. In contrast to that, other VPs that are complex, but that receive a distributive interpretation exclusively driven by their verbs, would not be problematic for the underspecification account. Consider the following example:

The most likely interpretation is that there was one particular noise, but each boy heard the noise individually, on his own. The paraphrase signals that hearing is distributive. Yet, since the noise does not covary with the boys, this paraphrase can be captured by assuming that hear is specified as signaling the relation between individuals (each individual who hears) and some object (what is heard), and the distributive reading arises through the lexical means. That is, since the distributivity is fully located on the verb only, no D operator is needed. See Champollion (2019) and references therein for a more detailed discussion of lexical and phrasal distributivity.

Let us now see how the phrasal and lexical distributivity might help us explain why we observe the preference for collective readings in processing. If the parser preferred simpler structures, i.e., structures lacking a null operator such as the D operator, we should see processing preferences for collective readings of syntactically-built predicates as in (14), but we should not see such preferences for one-word predicates, (13). On the other hand, if the parser generally preferred collective readings, we should see across-the-board processing preferences for collectivity, whether the predicates are syntactically-assembled (14) or not (13b). For example, if the parser preferred interpretations with fewer semantic objects, then the parser should preferentially select the collective reading of both (14) and (13b), since in both cases the collective interpretation postulates only one collective event, unlike the distributive reading.

To test these two hypotheses, we designed a self-paced reading experiment with 8 conditions, exemplified in (16). The predicate could be one word only and the reading could be established based on the lexical knowledge, or the predicate consisted of several (3 or 4) words. In the first case, the predicate was a verb, e.g., won. In the second case, the predicate was the same verb followed by an object, e.g., won an award. For all the items, the verb was chosen in such a way that it could be followed by a direct object, but an intransitive version in which the object is absent would also be grammatical.

Both collective and distributive readings were possible with the chosen predicates, in both the transitive and the intransitive version. As in Experiment 1, the predicate was disambiguated as collective or distributive by two adverbs, namely collectively and individually. We use collectively instead of together since collectively matches the other disambiguation adverb, individually, more closely in length and morphological structure, while still forcing the non-distributive reading. The disambiguation could happen either before or after the predicate. All conditions are presented in (16).

As the items were relatively complex, we also included an acceptability subtask into the experiment. This was used to check that predicates with and without objects were equally acceptable in the distributive and the collective disambiguation, i.e., both interpretations were equally possible with either predicate.

Let us summarize our predictions for the self-paced reading part of the experiment. If the preference for collectivity is driven by structural considerations, we expect the processor to choose collective readings only for syntactically complex predicates, i.e., when the direct object is present. Consequently, the reinterpretation towards distributivity should incur processing costs only for object-present cases. When the object is absent, the processor has no reason to prefer collective readings over distributive ones. That is, we expect a three-way interaction between adverb position, adverb type and the presence of a direct object. However, if the preference for collective readings is driven only by considerations of interpretational complexity measured in terms of the number of entities postulated in the semantic model, we expect late distributive disambiguation to cause processing difficulties regardless of the presence of the object. This is because the collective reading of any predicate postulates fewer entities, i.e., fewer events, than the distributive reading of the same predicate. Thus, a two-way interaction between the position of the adverb and the type of adverb is predicted in this case.

3.2 RESULTS AND DISCUSSION

The comprehension questions were not difficult for participants: the average accuracy was 90% of answers correct. However, two outlier participants answered only 73% and 66% of questions correctly, so they were excluded from subsequent analyses. All the other participants answered at least 79% of the questions correctly.

The descriptive summary of the acceptability data is provided in Table 1. The acceptability data was analyzed using mixed-effects ordinal probit models, with the following treatment-coded fixed effects: OBJECT (ABSENT or PRESENT, the former was the reference level), ADVERB (COLLECTIVELY or INDIVIDUALLY, the former was the reference level), POSITION (EARLY or LATE, the former was the reference level); the interaction of ADVERB and POSITION; the interaction of OBJECT and POSITION; the interaction of ADVERB and OBJECT; and the three-way interaction ADVERB, POSITION, OBJECT. The model included the full random-effect structure for subjects and items. The Bayesian model was estimated using Stan and brms (cf. Bürkner and Vuorre 2019). The structure of prior distributions and the sampling details of the model are provided in the Appendix.

Table 1

Descriptive summary of the acceptability subtask. Participants responded by selecting a value on the five-point Likert scale ⟨–2, –1, 0, 1, 2⟩.

ADVERB	DISAMBIGUATION	OBJECT	RESPONSE (MEDIAN)	RESPONSE (MEAN)	RESPONSE (SD)
collectively	early	null	1	1.036	0.950
collectively	early	object	1	1.104	0.886
collectively	late	null	1	1.096	0.967
collectively	late	object	1	0.915	0.953
individually	early	null	1	0.967	0.973
individually	early	object	1	1.029	0.972
individually	late	null	1	1.175	0.921
individually	late	object	1	0.802	1.066

Posterior distributions are graphically summarized in Figure 3. Negative values indicate decreased acceptability, while positive values indicate increased acceptability. Only one parameter has a posterior distribution with a 89% credible interval that excludes 0: the negative interaction of LATE POSITION:OBJECT (89% credible interval: ⟨–0.69, –0.15⟩, median = –0.41, p(β > 0) = 0.992). That is, sentences with adverbs following multi-word predicates were judged as worse, irrespective of adverb type. We take this to once again indicate that English speakers disprefer adverbs in postverbal position. This finding from the acceptability subtask matches one of the findings in Experiment 1, where increased RTs were observed for postverbal adverbs (recall that in Experiment 1, all predicates consisted of a verb + an object). 89% credible intervals of all the other parameters include zero. In particular, no factor with INDIVIDUALLY shows a fully negative or a fully positive credible interval, suggesting that readers did not find distributive readings of the predicates in the experiment as less or more acceptable than collective readings. This suggests, in turn, that items in this experiment were just as compatible with distributive construals as they were with collective construals. Thus, if we are to observe any difficulties with distributive readings when we turn to incremental processing in the self-paced reading part of the study, we can be reasonably confident that these are not due to the decreased acceptability of the distributive or collective interpretation of the predicates.¹¹

Figure 3

Posterior distributions of parameters of interest in the acceptability study. A thick horizontal line represents the 80% highest posterior density interval (HDPI) of a parameter, a thin horizontal line represents the 89% HDPI of a parameter. The dashed vertical line marks the position of 0. Filled circles represent median values. Negative values indicate that the parameter decreases acceptability, while positive values indicate that the parameter increases acceptability.

For the analysis of RTs, we proceeded in the same way as in Experiment 1. We removed RTs that were faster than 50 ms and slower than 3000 ms, and we log-transformed RTs. As in Experiment 1, we probed for (very fast or very slow) outliers among readers by checking mean logRTs per subject. Two subjects had a mean logRT more than 2.5 standard deviations away from the grand mean and were removed from the final analysis of RTs. The final number of participants whose data we analyzed: 51. The influence of word length and word position was also factored out in the same way as in Experiment 1.

The main regions of interest (ROIs) were the adverb, the predicate and the three words following the disambiguated predicate, the spillover region. The ROIs are underlined in (18).

(18)	a.	The girls individually won an award during the science fair.
	b.	The girls collectively won an award during the science fair.
	c.	The girls won an award individually during the science fair.
	d.	The girls won an award collectively during the science fair.
	e.	The girls individually won during the science fair.
	f.	The girls collectively won during the science fair.
	g.	The girls won individually during the science fair.
	h.	The girls won collectively during the science fair.

The graphical summary of logRTs is presented in Figure 4. LogRTs are also summarized in a table in the Appendix.

Figure 4

Exp. 2, logRTs per word in the predicate, adverb and spillover regions. The position AdverbEarly shows logRTs for the adverbs individually and collectively in the early position. The position AdverbLate shows logRTs for the adverbs individually and collectively in the late position. The top graph shows RTs for conditions without the object, the bottom graph shows RTs for conditions in which the object was present.

For each region, we estimated a Bayesian mixed-effects model with the same fixed effects as in the acceptability study (ADVERB, POSITION, OBJECT and their interactions). The models had a maximal random-effect structure and were estimated using Stan and brms. The structure of prior distributions and the sampling details of the models are provided in the Appendix.

Posterior distributions of the parameters on the adverb and spillover regions are summarized graphically in Figure 5, Figure 6, Figure 7, and Figure 8.

Figure 5

Posterior distributions of parameters of interest on the adverb individually/collectively. A thick horizontal line represents the 80% highest posterior density interval (HDPI) of a parameter, a thin horizontal line represents the 89% HDPI of a parameter. The dashed vertical line marks the position of 0. Filled circles represent median values.

Figure 6

Posterior distributions of parameters of interest on the 1st word in the spillover. A thick horizontal line represents the 80% highest posterior density interval (HDPI) of a parameter, a thin horizontal line represents the 89% HDPI of a parameter. The dashed vertical line marks the position of 0. Filled circles represent median values.

Figure 7

Posterior distributions of parameters of interest on the 2nd word in the spillover. A thick horizontal line represents the 80% highest posterior density interval (HDPI) of a parameter, a thin horizontal line represents the 89% HDPI of a parameter. The dashed vertical line marks the position of 0. Filled circles represent median values.

Figure 8

Posterior distributions of parameters of interest on the 3rd word in the spillover. A thick horizontal line represents the 80% highest posterior density interval (HDPI) of a parameter, a thin horizontal line represents the 89% HDPI of a parameter. The dashed vertical line marks the position of 0. Filled circles represent median values.

Figure 5, corresponding to the adverbs individually/collectively, shows that the LATE POSITION stands out as a positive effect (89% credible interval: ⟨0.02, 0.14⟩, median = 0.08, p(β > 0) = 0.987). The slowdown due to LATE POSITION is most likely related to the slowdown caused by late adverbs in Experiment 1 and, possibly, to the interaction of LATE ADVERB:OBJECT in the acceptability study. These results repeatedly show that readers incur a processing cost when integrating adverbs that appear in a post-predicate position. The effect, while interesting on its own, is not of primary concern to us. Another effect stands out in the same region: the interaction LATE POSITION:INDIVIDUALLY (89% credible interval: ⟨–0.21, –0.04⟩, median = –0.13, p(β < 0) = 0.991). This signals that late disambiguation towards distributivity with lexical predicates (i.e., predicates that consist just of one word, the intransitive verb) speeds up reading. The speed-up is diminished in the case of phrasal predicates, since most of the posterior probability mass of the three-way interaction OBJECT PRESENT:LATE POSITION:INDIVIDUALLY is positive (median = 0.067, p(β > 0) = 0.82).

Figure 6, corresponding to the first word in the spillover (the word during in (18)), shows that the posterior distribution of LATE POSITION is once again positive (89% credible interval: ⟨0.028, 0.144⟩, median = 0.09, p(β > 0) = 0.991). This slowdown has likely the same explanation as the same slowdown observed on the adverb.

Figure 7, corresponding to the second word of the spillover (the word the in (18)), shows that OBJECT PRESENT clearly affects reading times by causing a speed-up (89% credible interval: ⟨–0.12, –0.03⟩, median = –0.075, p(β < 0) = 0.995). This effect is probably caused by the fact that objects add extra information and increase the predictability of the follow-up regions. This facilitating role of direct object is orthogonal to our main investigation. We also see that OBJECT PRESENT:LATE POSITION is associated with a slowdown (89% credible interval: ⟨0.004, 0.14⟩, median = 0.074, p(β < 0) = 0.961), which matches the decreased acceptability of the same condition.

Finally, Figure 8, corresponding to the third word of the spillover (the word science in (18)), shows two conditions that clearly stand out. First, there is a negative interaction of LATE POSITION and ADVERB INDIVIDUALLY (89% credible interval: ⟨–0.18, –0.05⟩, median = –0.114, p(β < 0) = 0.997). Second, there is a dominant positive effect associated with the three-way interaction OBJECT PRESENT, LATE POSITION and ADVERB INDIVIDUALLY (89% credible interval: ⟨0.07, 0.28⟩, median = 0.19, p(β > 0) = 0.998). Thus, while the late disambiguation towards distributivity with lexical predicates (i.e., predicates that consist just of one word, the intransitive verb) speeds up reading, the effect is clearly reversed when the predicate consists of the verb + an object. In that case, disambiguation towards distributivity slows down reading. The effect can also be clearly observed in Figure 9 on the word science (the last word in the figure).

Figure 9

Exp. 2, LogRTs on the third word of the spillover, i.e., the third word after the predicate + the adverb (the word science in (18)). The graph shows a three-way positive interaction between ADVERB, POSITION and OBJECT: late distributive disambiguation speeds up reading when the object is null (left panel), but slows down reading when the object is present (right panel).

4 GENERAL DISCUSSION

Based on the two experiments, we can conclude that readers have processing difficulties when they read a predicate that is in principle compatible with both collective and distributive interpretations, and they learn afterwards that the predicate should be interpreted distributively.

The findings extend the results of Frazier et al. (1999) in two significant ways. First, we found that the slowdown is not caused just by the postverbal disambiguator each, but appears with another distributive disambiguator, the adverb individually. This is important to establish since each in postverbal position affects interpretations in other ways than just enforcing distributivity. Observing the effect with the disambiguator individually gives us stronger evidence that it is really the reinterpretation towards distributivity that incurs processing cost.

Second, we saw that the distributive reinterpretation of predicates consisting of a verb + an object is costly. But the distributive reinterpretation of one-word predicates (intransitive verbs) is not harder than the collective reinterpretation. This second finding fits well with formal semantics research arguing that, in the case of one-word predicates, the distributive/collective reading can just follow from our lexical knowledge, but in the case of complex predicates, that is, multi-word expressions whose interpretation is syntactically mediated, something more has to be said – specifically, the presence of a D-operator is needed.¹² Thus, the distributive reinterpretation is costly only when distributive interpretations are triggered by a covert quantificational element that can take scope, the D-operator. Our findings match well with research on structural priming of distributive and non-distributive readings of pluralities, which provides evidence that the two readings involve different mental and structural representations (Maldonado et al. 2017). We will now discuss in detail what our results mean for the theory of distributivity and collectivity, and the processing of these readings.

5 CONCLUSION

We studied the interpretation of plural expressions like the students, focusing on the question of how the processor establishes the distributive/collective interpretation of predicates accompanying such plural expressions.

We reported the results of two self-paced reading experiments. In the first experiment, we built on Frazier et al. (1999) and replicated their finding that the human processor favors collective readings over distributive ones. Based on the results of the second experiment, we argued that the preference for collective readings is only observed when the distributive reading arises via phrasal distributivity, and the preference disappears in the case of lexical distributivity.

The findings provide evidence that the distinction between collective and distributive readings is a case of ambiguity, at least for phrasal predicates. They also indicate that the processor might give more weight to some sources of evidence during incremental interpretation. Specifically, syntactic information and structural simplicity might contribute stronger processing constraints than mental model simplicity, at least when this simplicity/complexity is measured in terms of the number of events or entities that the processor needs to postulate during incremental interpretation.

FUNDING INFORMATION

Jakub Dotlačil was supported by a Rubicon grant and VENI grant from the Netherlands Organization for Scientific Research. Adrian Brasoveanu was supported by an SRG grant from the UC Santa Cruz Committee on Research.

COMPETING INTERESTS

The authors have no competing interests to declare.