As in (1) and (2), English and Mandarin both allow surface scope readings, i.e., the existential quantifier scopes over the universal quantifier, just as the linear order shows.¹ What distinguishes English from Mandarin is the availability of the inverse scope reading in a simple transitive sentence. In English, the universal quantifier every can scope over the existential quantifier a when every is linearly preceded by a. However, such inverse-scope reading is generally argued to be unavailable in Mandarin.

As a canonical construction in a language, the scope behavior of simple transitives is naturally considered to represent quantifier scope. Thus, English is argued to be a scope-fluid language that allows both surface scope reading and inverse scope reading, while Mandarin is claimed to be a scope-rigid language that only allows surface scope (Huang, 1981, 1982; Lee, 1986; Aoun and Li, 1989, 1993, among others). Scope rigidity as a feature of Mandarin has gradually become well-known. Mandarin and languages with Mandarin-like scope behaviors (such as Japanese, see Hoji, 1985), are often referred to as languages lacking scope ambiguity or obeying scope isomorphism in the linguistic field since the 1980s.

However, as noticed over the years, scope ambiguity cases in Mandarin are not unusual and have been observed in PP datives, PP locative, non-finite clauses, relative clauses, and thetic sentences, resembling their English counterparts concerning scope interpretation, although many of the observed scope ambiguity is not experimentally confirmed yet (Chien and Wexler, 1989; Lee, 1989, 1991, 2002; Chien, 1994; Lee et al., 1999; Lin, 2013, 2015; Liu and Wu, 2016; Wu et al., 2018; Chen, 2020; Gan, 2021, among others). For example, (3).

But the literature debates over whether simple transitives under a non-matrix clause environment show scope ambiguity in Mandarin. For instance, (4).

Aoun and Li (1989) argue that (4) is not ambiguous, like the matrix simple transitives in (2) Mandarin. However, more recent studies (Scontras et al., 2016; Grano, 2017) have suggested that conditional clauses may allow scope ambiguity for doubly quantified transitives as conditional clauses are truncated clauses, different from matrix clauses (Haegeman, 2006, 2012).

In the present study, we conducted an untimed, offline experiment using the Truth-Value Judgment task to test if sentences like (4) allow inverse scope reading and investigate how scope interpretations are affected by other factors. We will report findings from the experiment and provide discussions on the scope-rigidity tag on Mandarin and the rigidity-fluidity dichotomy for quantifier scope interpretations.

Data were processed in the R software environment (version: 3.5.3, R Development Core Team, 2019). To check the statistical significance, the lme4 package (version 1.1-21, developed by Bates et al., 2015a) was used to perform a linear mixed-effects model.⁶

In the literature that used a linear mixed-effects model to analyze acceptability rating, studies differed in their choices of random-effects structures: some studies used a random intercept model and take by-subject variation into consideration (Brendel, 2019), while other studies used a more complex random-effect structure – a random slope model and modeled by-subject and by-item variability in how conditions affect acceptability ratings Harris et al. (2013). In the present study, we used a linear mixed-effects model with two fixed factors “Type of adverbial clauses” and “The presence of le inside adverbial clauses” (as indicated in the experiment design table, i.e., Table 1), and two random intercept effects “participant” and “set” for different participants and a different set of stimuli.

The random intercept model was chosen instead of a random slope model for two reasons. First, although we expect general baseline by-subject and by-item variability in the acceptability ratings, we do not have clear empirical reasons to assume that the effect of fixed factors, such as the presence of le, might be different for different subjects. The two fixed factors we controlled here are presence of le, and adverbial type. They are different from fixed factors like politeness. For politeness, we would use a random slope model and assume the effect of politeness can be different for different subjects, since some subjects may have higher standards for politeness than others. Second, our data do not support a complex random effect structure with random slopes. When fitting a random slope model, a warning massage from R is returned suggesting that this model has a singular fit. After checking singularity for this model using isSignular() function, we used rePCA() to perform a Principal Components Analysis (PCA) for this random slope model and the PCA result shows that such a random slope model can be overparameterized (Bates et al., 2015b; Bross, 2019). In contrast, the random intercept model used in the present study passed both the singularity check and PCA check. ⁷

Before presenting the results of the target sentences in 6 conditions, we will present results from the fillers as the baseline. Among the fillers included in this experiment, there are simple actives like (7) and the given context for these sentences leads to an inverse scope reading as well.⁸ The mean acceptance rate of such context-sentence pairs is 1.27 and the corresponding distribution of the acceptance rates is shown in Figure 2.

Figure 2 shows that the matching between an inverse scope context and a simple active sentence like (7) was rated with a very low score. More than 75% of the participants (77 out of 98 participants) rated below 3, which indicates that most of the participants did not consider the simple actives able to be used to describe an inverse scope context. This result echoes previous studies and claims on the scope rigidity of doubly-quantified simple actives in Mandarin (Su, 2001; Scontras et al., 2016; Gan, 2021).

PP datives like (8) and its minimal pairs Double-Object Constructions (DOCs) like (9) were included as fillers as well.⁹ The mean acceptance rate of context-sentence pairs like (8) is 3.33 while the mean acceptance rate of context-sentence pairs like (9) is 1.59.

Figure 3 shows the distribution of the acceptance rates of PP datives and DOCs: the former was rated with a score greater than or equal to 3 by 63.27% of participants (62 out of 98 participants) but the latter was rated with a score below 3 by 72.44% of the participants (71 out of 98 participants). This suggests that most participants think that PP datives can be used to describe an inverse scope context much more freely than DOCs. This result is in line with findings from studies like Su (2001:53), Gan (2021) and theoretical claims made in studies like Huang (1982), and Aoun and Li (1989: 167).

One may wonder why the mean rating of the context-sentence compatibility on PP datives (a claimed-to-be ambiguous case) is only 3.33, not very close to the possibly highest score 6. As noticed in previous studies, inverse interpretations come at a cost (Anderson, 2004, chapter 2, among others). For example, Scontras et al. (2017) report that the mean ratings for inverse scope reading for English doubly quantified transitives (similar to the (1)) were 4.46 (out of 7), a similar result as the mean ratings for the inverse scope in Mandarin PP datives (3.33 out of 6 in the present study). One may also wonder why the mean rating of context-sentence compatibility on DOCs (a claimed-to-be unambiguous case) is not at or near the floor. As a matter of fact, similar ratings were reported in previous studies, like Gan (2021): the acceptance rate for the picture representing inverse scope reading of sentence like (9) is 16.67%, not that close to 0% either. Meanwhile, experimental studies on English DOCs (also a claimed-to-be unambiguous case) have shown that inverse scope reading although not preferred but available for speakers. For example, Heizmann (2007) reports that inverse scope is accessible for participants 40% of the time for the double object constructions like “Christine showed a visitor every picture by Picasso..” These experimental results suggest that double object constructions in both Mandarin and English may allow some availability of inverse scope reading for some speakers. The speaker variations found in these studies lead us to rethink the dichotomy of scope interpretations, which we will discuss in detail in Section 4.

The mean acceptance rates of the 6 target conditions are shown in Figure 4. The mean ratings of context-sentence matching pairs in each condition were generally around 2.5, significantly higher than the mean ratings for the claimed-to-be unambiguous DOCs and simple actives, but lower than the mean ratings for the ambiguous PP datives.

Before running the comparison between any two conditions using the formula provided earlier¹⁰, we used anova() function to compare an inter-dependent model (response ~ adverbial_type * presence_le) and a non- inter-dependent model (response ~ adverbial_type + presence_le) to check whether these two factors are inter-dependent on each other. The results returned by the anova() show that no significant interaction effect was found between adverbial types and presence of le [β_{yàoshì:presence_le} = −0.61671, SE = 0.37963, β _{yīnwèi:presence_le}  − 0.69506, SE = 0.37960, χ²(2) = 4.0064, p = 0.1349].

Now let us look at the statistical results from the comparison of every two conditions. The formula for the full model is either fm.full1 < − lmer(response ~ adverbial_type + (1|participant) + (1|set), data = data, REML = FALSE), or fm.full2 < − lmer(response ~ presence_le + (1|participant) + (1|set), data = data, REML = FALSE), depending on which two conditions were compared. The reduced model is fm.reduced < − lmer(response ~ (1|participant) + (1|set), data = data, REML = FALSE). For example, the fm.full2 model was compared with the fm.reduced model when performing statistical comparisons between the suīrán_le condition and the suīrán_no le condition, since the two conditions only differ in the presence of le. In contrast, when comparing two conditions which only differ in the adverbial clause type, such as the suīrán_le condition and yàoshì_le condition, the fm.full1 model was compared with the fm.reduced2 model. The test for checking statistical significance among conditions was performed though the likelihood ratio test using the anova() function (Winter, 2013). The value of p returned by anova (fm.full, fm.reduced) represents the effect of the factor “Type of adverbial clauses” or “The presence of le inside adverbial clauses” on the difference between the acceptability rates (i.e., “Response”) of two conditions.

To check the effect of adverbial types, we used anova (fm.full1, fm.reduced). When le is not present, no significant differences in the ratings were found among the three conditions: suīrán_no le condition (mean = 2.49, 95% confidence intervals of the mean = 2.05–2.93, standard error = 0.22), the yàoshì_no le condition (mean = 2.49, 95% confidence intervals of the mean = 2.05–2.93, standard error = 0.22), and yīnwèi_no le condition (mean = 2.65, 95% confidence intervals of the mean = 2.18–3.13, standard error = 0.24). Suīrán_no_le condition was not rated significantly higher than yīnwèi_no_le condition [β = 0.1944, SE = 0.2597, χ²(1) = 0.5529, p = 0.4571], and yàoshì_no_le condition [β = 0.05527, SE = 0.27479, χ²(1) = 0.0401, p = 0.8413]. The ratings for yīnwèi_no_le condition were not significantly different from the ratings for yàoshì_no_le either [β = 0.05527, SE = 0.27479, χ²(1) = 0.0401, p = 0.8413].

Among the three conditions where le is present, adverbial type significantly affected ratings: context-sentence ratings on suīrán_le condition (mean = 3.07, 95% confidence intervals of the mean = 2.56–3.58, standard error = 0.25) were significantly higher than ratings on yīnwèi_le target sentences [mean = 2.53, 95% confidence intervals of the mean = 2.05–3.01, standard error = 0.24, β = −0.5373, SE = 0.2682, χ²(1) = 3.9649, p = 0.04646], and on yàoshì_le target sentences (mean = 2.53, 95% confidence intervals of the mean = 2.05–3.01, standard error = 0.24, β = −0.5708, SE = 0.2745, χ²(1) = 4.2607, p = 0.039). However, no significant difference in the ratings was found between the yīnwèi_le condition and the yàoshì_le condition [β = 0.008792, SE = 0.276280, χ²(1) = 0.0018, p = 0.966].

The comparison formula for checking the effect of presence of le is: anova (fm.full2, fm.reduced), where the two models differ only in whether presence_le is included as a fixed factor. There was no significant difference between the yàoshì_le condition and the yàoshì_no le condition [β=0.04082, SE = 0.29403, χ²(1) = 0.0195, p = 0.889], nor between the yīnwèi_le condition and the yīnwèi_no le condition [β = −0.1107, SE = 0.2666, χ²(1) = 0.1764, p = 0.6745]. However, suīrán_le was rated significantly higher than its minimal pair condition suīrán_no le [β = 0.5913, SE = 0.2484, χ²(1) = 5.526, p = 0.01874]. In a word, the suīrán_le condition is the only condition among the six conditions that show a significant difference from its minimal pair conditions.

The results also show that for the conditions with the presence of le, the mean ratings on context-sentence compatibility of target adverbial clauses with resultative verbs are higher than the target adverbial clauses with durative verbs, while the pattern is reversed for conditions without the presence of le (Table 2). To check if the inter-dependence exists between verb types and presence of le, we used anova(fm.verb1, fm.verb2) where fm.verb1 < − lmer(response ~ adverbial_type + presence_le * VerbType + (1|participant) + (1|set), data = data, REML = FALSE) and fm.verb2 < − lmer(response ~ adverbial_type + presence_le + VerbType +  (1| participant) + (1 | set), data = data,REML = FALSE). The interaction between the presence of le and the verb type was found to be significant: context-sentence ratings on target sentences with durative verbs and le were significantly different from the ratings on other target sentences [β = −1.0629, SE = 0.3613, χ²(1) = 8.5726, p = 0.003413].

In the experiment design, three different existential quantificational phrases (in the form of number + classifier + noun and positioned in the subject of an adverbial clause) were used across the 6 sets in the stimuli to balance out the potential effect of different numerals on scope interpretation. Table 3 presents the differences in mean ratings caused by differences in existential quantificational phrases: for each target condition, the mean rating is generally higher when the existential quantificational phrases are in the form of liǎng (‘two’)/sān (‘three’) + classifier + noun than when they are in the form of yī (‘a/one’) + classifier + noun.

In addition, we investigated both intra-participant and by-participant distribution of the ratings to see if and how participants respond differently. Interestingly, the histogram plot in Figure 5 and the density plot in Figure 6 both show a bimodal distribution of the ratings on target context-sentence pairs for each target condition. In other words, about half of the participants think that the target adverbial clauses with the linear order of ∃ over ∀ match a ∀ over ∃ scenario, while the other half of the participants do not think so. Among 98 participants, the number of participants who rated the context-sentence pairs in each condition with a score greater than 2 is as follows:

The bimodal distribution of the ratings on target context-sentence pairs is also found after data normalization. We normalized the responses with a z-score and the distribution of normalized ratings is in Figure 7, wherein we can see similar bimodal distribution patterns as we have seen in Figures 5, 6. ¹¹

Overall, the results reveal interesting results about the behaviors of quantifier scope in Mandarin adverbial clauses: (a) inverse scope is allowed for Mandarin adverbial clauses although there is variation among participants; (b) the type of adverbial clauses only affects the context-sentence compatibility when le is present (the mean ratings of suīrán_le is much higher than yàoshì_le and yīnwèi_le); (c) different verb types are inter-dependent with the presence of le factor and together affect context-sentence compatibility; (d) participants tend to give a higher rating on the context-sentence compatibility when the existential quantificational phrases are in the form of liǎng (‘two’)/sān (‘three’) + classifier + noun compared to yi (‘a’/‘one’) + classifier + noun.

Although the mean rating of context-sentence matching pairs in each target condition (Figure 4) is just in the range of 2.5–3.0, the results still confirm that it is possible to have inverse scope reading of doubly-quantified adverbial clauses. Scontras et al. (2017) reported an average rating of 4.46 on a 1 to 7 scale for inverse scope reading and claimed the availability of inverse scope reading in English simple transitives based on this rating. Our results are based on a 0 to 6 scale, and the structures examined in the present paper are simple transitives under adverbial clauses, a much more complex structure than the ones examined in Scontras et al. (2017). Complex structures generally are associated with lower ratings (Gibson and Thomas, 1999), so it is expected to see relatively lower mean ratings in this study. Moreover, the mean rating of context-sentence matching pairs in each condition is much higher than the mean rating of doubly-quantified simple actives (which are included as fillers, mean = 1.27), suggesting that inverse scope reading is more available under the environment of adverbial clauses. Putting aside the factors we controlled in the stimuli and just focusing on the target sentences and contexts which favor inverse scope (see the numbers that are shaded with gray in Tables 2, 3), we can see that the mean ratings of the sentence-context matching pairs would be higher—close to or over 3, very similar to the mean rating of doubly-quantified PP datives, which is just 3.33. Additionally, about one-fifth of the participants (18 out of 98) consistently gave a rating higher than 2 on sentence-context matching pairs for all target sentences they were asked; it means that the inverse scope reading is fully available for these participants regardless of adverbial clause type, presence of aspect marker or embedded verb type. Therefore, this average range of 2.5 to 3.0 acceptability ratings in this study, we claim, characterizes that inverse scope reading is available for the doubly-quantified simple transitives under adverbial clauses.

The mean ratings on context-sentence pairs for doubly-quantified transivites under adverbial clauses are much higher than on context-sentence pairs for matrix simple transivites. The results support Scontras et al. (2016) and Grano (2017)’s conjecture that conditional clause environment contributes to scope ambiguity, and provide evidence against Aoun and Li (1989)’s claim that (4) is purely scope-rigid, just as the matrix simple transitives.

The fact that simple actives could have inverse scope readings under an adverbial clause environment but not under a matrix clause environment, then suggests that clause environment matters here. The results regarding quantifier scope in adverbial clauses provide an empirical challenge to the long-standing scope-rigidity view of Mandarin, which argues for a one-to-one mapping between the linear order of quantificational phrases and scope interpretation. Previous approaches which inherit the idea of isomorphism, such as the Isomorphism Principle (10) by Huang (1982),¹² and the Linearity Principle (11) by Lee (1986, 1991), cannot account for the availability of inverse scope in Mandarin adverbial clauses.

(A commands B iff neither dominates the other and the first minimal clause dominating A also dominates B.)

Since the existential quantificational phrase inside the adverbial clauses does not have a mutual c-commanding relation with the universal quantificational phrase inside the adverbial clause, these approaches would all wrongly predict that the target sentences are purely scope-rigid with surface scope only.

Similarly, the doubly-quantified transitives under adverbial clauses are wrongly predicted to show surface scope only under the Scope Principle (12) and Minimal Binding Requirement (13) proposed by Aoun and Li (1989, 1993).

The scopal contrast between unambiguous case (14a) and unambiguous case (14b) can be represented as in the following example wherein x1 and x2 are the variables of quantificational phrase 1 (QP1) and quantificational phrase 2 (QP2) after quantifier raising. According to Aoun and Li (1989), the availability of inverse scope is related to the existence of a trace, more precisely, whether there is a trace of the higher QP over which the lower QP can have a wide scope.

There is no overt movement involved in the simple actives under doubly-quantified adverbial clauses unless we assume that the doubly-quantified simple actives under adverbial clauses have subject raising process like English matrix actives do (15) to give universal quantificational phrase the pathway to scope over the trace t_i after quantifier raising to the edge of VP. However, the assumption would require us to come up with some magical ad hoc techniques to assure that the subject-raising process is only applicable for simple transitives under an adverbial clause in Mandarin, but not applicable for matrix simple transitives in Mandarin.

The results also propose challenges to previous approaches on quantifier scope that consider thematic hierarchy as a factor in the scope interpretation. Lee (1991: 204) proposes to have (16) in addition to the Linearity Principle (11). He attributes the scope ambiguity to “joint effects of the linearity principle and a thematic hierarchy” following the proposal made by Xu and Lee (1989).

According to Xu and Lee (1989), a quantificational phrase carrying the thematic role in Group A is more likely to take wide scope over a quantificational phrase carrying the thematic role in Group B. When the scope predicted by the thematic hierarchy in (16) conflicts with the scope predicted by the linear order, scope ambiguity arises.

For example, in a PP dative construction: verb – direct object- gei- indirect object, thematic hierarchy in (16) predicts that the indirect object (the goal) to take wide scope over the direct object (theme), but the linear order predicts direct object scoping over the indirect object. Therefore, the quantifier scope ambiguity of doubly quantified PP dative constructions (9) is expected under this account.

However, Xu and Lee (1989) and Lee (1991)‘s account fails to take the argument structures into consideration. The thematic hierarchy assumed in (1) is dubious under the widely held hierarchy of thematic roles in the literature: Agent > Theme > Goal > Location > Source (see discussions about thematic structures at Carrier-Duncan, 1985; Baker, 1988; Belletti and Rizzi, 1988; Larson, 1988, 1990, 2014; Jackendoff, 1990). This account also assumes scope ambiguity comes from the joint influence of word order and thematic hierarchy assumed in (16), but not from quantifier raising. It conflicts with the argument that quantifier raising exists in Mandarin and contributes to scope interactions in Mandarin, just as what quantifier raising would do in other languages (Lin, 2003b, 2013, 2015; Grano, 2017 among others). For example, in (17) where the universal quantifier embedded in the PP scopes over the existential quantifier, similar to the inverse linking cases studied in the literature (see more discussion on inverse linking and quantifier raising in Bobaljik and Wurmbrand, 2012; Antonyuk, 2019).

Moreover, the joint account of the thematic hierarchy in (16) and the linear word order for scope interpretations, would wrongly predict (18) being scope frozen, as both the thematic hierarchy in (16) and the linear word order predict two students (agent) scope over every problem set (theme). But, our results suggest that the inverse scope reading of sentences like (18) is available to a large portion of participants. 71% of participants (70 out of 98 participants) gave a rating higher than 3 at least once for such sentences.”

‘Although two students answer(ed) every problem set correctly, Haidian team still did not get selected to join the Math Olympiad training program.’

(Context given along with this sentence: The rules of the qualification exam for the Math Olympiad training team are: each team consists of three members and there are three problem sets in total; for a team, each of the three problem set needs to be answered by two members of that team and a team is possible to join the Math Olympic training program when that team gives correct answers for all three problem sets. Three members of the Haidian team are Xiao Wang, Xiao Jiang and Xiao Zheng. Xiao Wang and Xiao Jiang answered the first two problem sets correctly. Xiao Jiang and Xiao Zheng answered the last problem set correctly. The Haidian team met the selection criteria, but they were not selected to join the training program. Xiao Wang, Xiao Jiang, and Xiao Zheng were very sad.)

As shown above, the results suggest that we need more refined accounts beyond the existing syntactic accounts (Huang, 1982; Aoun and Li, 1989) or semantic accounts (Xu and Lee, 1989 and Lee, 1991). The results call for rethinking the long-standing dichotomy view of quantifier scope in Mandarin Chinese and call for rethinking the existing approaches to scope interpretations. Our results demonstrate that inverse scope of simple transitives under adverbial clauses is available in Mandarin Chinese, although Mandarin simple transitives are claimed to be scope rigid. Our conjecture for the different scope behaviors between simple matrix transitives and simple transitve under adverbial clauses is that clause size matters for scope permutation, an idea that has been noted in Lin (2013), Grano (2017), and Wu et al. (2018) and is worthy of further study.

The availability of the inverse scope reading of doubly-quantified simple transitives under adverbial clauses calls for a modification of the theoretical claim that scope rigidity is a property of Mandarin Chinese. Figures 5, 6 show that a large number of participants gave very high ratings for the context-sentence matching pairs in the stimuli, which would be unexpected if scope-rigidity/fluidity were a language property and Mandarin was a scope-rigid language. Furthermore, the results presented in Figures 5, 6 also provide evidence against the dichotomy of scope interpretations at a specific syntactic construction level. If scope-rigidity were the property of a specific syntactic construction and adverbial clause environment were considered as a pure scope-rigid or scope-fluid environment, we would not expect a bimodal distribution of the data at all. In fact, we found that about half of the 98 participants think that the target adverbial clauses with the linear order of ∃ over ∀ match an ∀ over ∃ scenario, while the other half of the participants disagree with it. The bi-modal distribution of the data suggests that it is more than the dichotomy of scope interpretations that affects the scope interpretations.

Bimodal distribution of scope interpretations has been observed in previous experimental scope studies. Scontras et al. (2016) report that half of the 30 surveyed English speakers find sentences like (19) ambiguous while the other half do not.

According to Scontras et al. (2016), two different grammars of relativization in English is a potential explanation for the observed bi-modal distribution of scope interpretations. Scontras et al. (2016) argue that, if English restrictive relative clauses, like what Hulsey and Sauerland (2006) suggested, are structurally ambiguous between the head-internal, raising structure and the matching structure then it is likely that some speakers apply one structure whereas other speakers apply another.¹³

Experimental studies on scope interpretations of other languages also observed bimodal distribution on acceptance of inverse scope interpretations. Han et al. (2007) found that only about half of the 160 surveyed Korean speakers allow negation to take scope over a quantificational phrase in the object position for Korean sentences like (20). Based on the finding, Han et al. (2007) argued that there might be two populations of native speakers that have two different grammars: one with a verb-raising mechanism and one without.

Both Han et al. (2007) and Scontras et al. (2016) suggest the bimodal distribution of the acceptance of inverse scope readings may come from structural ambiguity in speakers’ grammar. Following this suggestion, the bimodal distribution we observed in the present study could potentially come from the structural ambiguity of adverbial clauses. Adverbial clauses have been argued to have dual status: central adverbial clauses vs. peripheral adverbial clauses, where the former has less root functional projections available, but the latter has more root functional projections available (See Haegeman, 2002 and subsequent works for the dual status discussions on English and German adverbial clauses, and Lu 2003, 2008; Pan and Paul, 2018, Wei, 2018, Wei and Li, 2018 for the related discussions on Mandarin). It is then possible that some speakers apply the peripherical structure while others apply the central structure of an adverbial clause and correspondingly give divergent ratings on the availability of inverse scope reading. If it were the case, we would predict that doubly-quantified transitives under the peripheral adverbial clause status have more comparable to the matrix doubly-quantified transitives with respect to scope interpretations. But to testify to such prediction, we need further study to give clear and unified criteria on the categorization of peripheral versus central adverbial clauses, which we do not have at this moment due to conflicting claims in the literature.

Additionally, the results echo Zhou and Gao (2009)’s generalization that the lexical information of verbs may have effects on scope judgments. Zhou and Gao (2009) found that, in an offline judgment task, surface scope reading is more readily accessible than the inverse scope reading for the action verbs, and the locative verbs, while for the psych verbs, the surface scope reading and the inverse scope reading are equally accessible. With respect to thematic relations between subjects and objects, the durative verbs and resultative verbs used in the present study are comparable to the locative verbs and action verbs used by Zhou and Gao (2009) respectively. In the present study, when the verb is a durative verb, the quantified subject expresses a theme and the quantified object expresses a location; when the verb is a resultative verb, the quantified subject expresses an agent and the quantified object expresses a theme. Although the present study does not directly compare the influence of verb types on which scope reading is more accessible, we observed a similar pattern as Zhou and Gao (2009) mentioned in their paper: when the verbs are locative verbs, the inverse scope reading was judged with a bit higher average rating for locative verbs than for action verbs. Participants in the present study gave an average rating of 2.82 on the context-sentence pair for the target sentences with durative verbs (xiézhù ‘assist’, bùzhì ‘decorate (a room)’, kānshǒu ‘guard’) and an average rating of 2.43 on the context-sentence pair for the target sentences with resultative verbs (chīdiào ‘eat up’, dáduì ‘answer (questions) correctly’, dāchū ‘build up’). It suggests that participants in the present study judged inverse scope readings are more accessible for the target sentences with durative verbs than for the target sentences with resultative verbs. In other words, the thematic information of the verbs does affect the scope interpretations.

We also observed that the combination of verbs and aspect marker le could have a significant effect on the context-sentence ratings. Our results show that when the verbs are resultative verbs, higher average ratings on context-sentence compatibility were found for the sentences with aspect marker le than without le. The pattern is reversed when the verbs are durative verbs. At this moment, the inter-dependence between verb type and the presence of le remains to be accounted for, although we may attribute the observed inter-dependence pattern to the sentence naturalness and frequency of the combination of verbs and aspect markers. As mentioned in the experiment design, when the embedded verbs are resultative verbs (chīdiào ‘eat up’, dáduì ‘answer (questions) correctly’, dāchū ‘build up’), they are more naturally compatible and more frequently used with the aspect marker le, and no other temporal adverb or temporal phrase is necessarily required. Durative verbs, like xiézhù ‘assist’ or kānshǒu ‘guard’, tend to take temporal phrases/ adverbs when combined with le. For instance, ta yijing kānshǒu-le san-tian de damen ‘he has already guarded the front door for 3 days’, in which yijing ‘already’ and san-tian ‘3 days’ indicate how long the state of guarding door has been.

The effect of the internal structure of quantificational phrases is also shown in the results. When the existential quantificational phrase is in the form of yi ‘a/one’ + classifier + noun, the context-sentence rating is generally lower, suggesting that yi ‘a/one’ is more unfavorable for existential quantificational phrases taking narrow scope. This finding echoes the observations in the literature that existential quantifier yi tends to be interpreted as referential/ specific by both children and adults and then be assigned with a wide scope reading (Lee, 1986; Chien, 1994; Liu, 1997; Scontras et al., 2017; Yang and Wu, 2020). On the other hand, it is noticeable that yi ‘a/one’ does not correspond to a lower context-sentence rating in the yàoshì conditional clause. It could be the case that the hypothetical environment of conditional clauses overriding the preferred referential interpretation of yi; as a result, the quantified subject in the form of yi + classifier+noun gets more availability to have scope permutation with the universal quantificational phrase in the embedded object position. This interaction between the internal structure of quantificational phrases and adverbial clause type again suggests that scope interpretations may be constrained by factors including semantics, pragmatics, and processing strategy.

In this section, we discussed the implications of the results. We showed that the previous proposals to Mandarin quantifier scope interpretation have difficulty in accounting for the availability of inverse scope readings in doubly-quantified simple transitives under Mandarin adverbial clauses. The results call for a refined scope account that dispenses with the isomorphic view of Mandarin quantifier. Bimodal distribution on the on the acceptance of inverse scope readings draw our attention to the intra-participant variance, which again calls for rethinking the dichotomy view of quantifier scope in languages. In the end, the observed other factors that may affect scope behaviors, including verb type, and numbers, draw our attention on the influence of lexical information on quantifier scope interpretations.

In this paper, we have examined the scope behaviors in Mandarin doubly-quantified transitives under adverbial clauses (suīrán ‘although’, yàoshì ‘if’ and yīnwèi ‘because’) through an untimed, offline experiment using Truth-Value Judgment Task. The results of this experiment demonstrate that i) inverse scope readings are judged to be available in Mandarin doubly-quantified transitives under adverbial clauses but a bimodal data distribution is observed; ii) the ratings on the compatibility of inverse-scope context and target sentences do not vary significantly based on the type of adverbial clauses; iii) verb types and the presence of aspect maker le are inter-dependent and together have a significant effect on scope interpretations; (iv) participants tend to give a lower rating on the context-sentence compatibility when the existential quantificational phrases are yi (‘a’/‘one’) + classifier + noun compared to liǎng (‘two’)/sān (‘three’) + classifier + noun.

These experimental results suggest the following theoretical implications. First, scope rigidity as a language parameter of Mandarin is not a sufficient account for the results observed in the present study. Second, the dichotomy of scope interpretations at a syntactic construction level is not adequate to explain scope behaviors either, as bimodal data distribution was found within the same syntactic environment, which is little surveyed in the literature. Third, the speaker variations, especially the bimodal distribution of scope interpretations, may come from the complexity of the examined syntactic structures (e.g., central versus the peripherical status of adverbial clauses), which calls for more research on how structural ambiguity affects scope interpretations. Fourth, lexical information of verbs and numbers should also be taken into consideration in the future for discussions on scope interpretations.

Given that the reported findings are collected from 98 native speakers, a decent number of samples, and participants were given different target sentences randomly, we can reasonably assume that the differences in ratings on the context-sentence pairs result from the different factors that were manipulated in the study. Meanwhile, we admit there are some limitations of the present study. One limitation is the present design did not include a controlled group, which may degrade the validity of the findings. Another limitation is that the present study used written narratives to present an inverse-scope reading scenario and asked participants to judge if the written target sentences match the scenario. The findings of the present study are then limited to the scope interpretations of written Mandarin, with factors like prosody uninvestigated. We also admit that the written narratives used in the present study to represent the contexts were comparably lengthier than the ones used by Zhou and Gao (2009), which may cause extra reading time and processing costs for participants. It is possible that participants in this study found the narrative interesting to read but got distracted by trivial information and then missed the most significant information to make the most faithful scope judgments. At this moment, we have no direct comparisons among different ways of presenting contexts: detailed written narrative, condensed written narratives, oral or audio narratives, act-out storytelling, or pictures, and yet no clear answers about which way is the best way to present a context for a Truth-Value Judgment Task. We will leave the evaluation of methodologies to future work.

With these limitations noted, a number of directions for future study can be pursued. One direction is to add a controlled group to the experiment design, take further measures to exclude the potential confounding factors in the acceptability experiment, and then experimentally test the scope interpretations using oral materials (Ionin and Luchkina, 2018; Kırcalı et al., 2021) or pictures (Scontras et al., 2017) or condensed written narratives (Zhou and Gao, 2009) as materials. Another direction is to change the offline judgment task into an online judgment task (Anderson, 2004) to investigate the online processing of scope interpretations by setting a limited time duration for the experiment and recording participants’ response times across conditions. The present study investigates the scope of interactions between bare-numeral quantificational phrases and strong distributive-universal quantificational phrases, but not all quantifiers behave with the same properties (Beghelli and Stowell, 1997). Therefore, another direction to pursue is to manipulate the types of quantifiers and experimentally investigate if scope interactions are different from the results we observed in the present study.

As the present study argues against the scope rigidity tag on Mandarin, it would be also interesting to extend the present study to other non-matrix syntactic environments in Mandarin, for example, testing the scope interpretations in Mandarin embedded nonfinite clauses, where, the inverse scope reading is available according to Lin (2013), but Gan (2021) disagrees. From a crosslinguistic perspective, it would be fruitful to extend the study to experimentally test the doubly quantified transitives under adverbial clauses in some other claimed-to-be “scope-rigid” languages.

The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.

The studies involving human participants were reviewed and approved by Stony Brook University, the Office of Research Compliance, IRB2019-00115. Written informed consent for participation was not required for this study in accordance with the national legislation and the institutional requirements.

HW contributed to the conception and design of the study, organized the database, performed the statistical analysis, wrote the first draft of the manuscript, and worked on the manuscript revision, read, and approved the submitted version.

This study is supported by the Faculty Development Fund awarded to the author by the School of Modern Languages at Georgia Institute of Technology.

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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