2.1. A threshold for generalization

Learning a language requires discovering rules that correctly generalize beyond a finite sample of data. The Tolerance Principle (TP) is a theory of how such generalizations are formed (Yang Reference Yang2005, Reference Yang2016). Specifically,

1. (6) Let a rule R be defined over a set of N items (e.g. words). R is productive (i.e. can generalize to novel instances) if and only if e, the number of items among N that do not support R, does not exceed θ_N:

   $e\le {\theta }_N=\frac{N}{\ln N}$

If e exceeds θ_N, the learner can only memorize the attested items as following R but will not generalize beyond.

The TP is a parameter-free learning model. Productivity is determined by two input values (i.e. N and e), which are cardinality values in an individual learner’s experience: a categorical prediction is then made without additional degrees of freedom. By its very nature, the TP is only concerned with the provisional coverage of a hypothesis with respect to the learner’s experience such as vocabulary. This proves especially important for the language acquisition process. It is now well established that the core properties of the grammar must be learned on a very modest vocabulary. Research has shown that across languages, the vocabulary size for two-year-olds is only in the range of 200–300 words, and the most advanced three-year-olds may have up to 1,000 words (Fenson et al. Reference Fenson, Dale, Reznick, Bates, Thal, Pethick, Tomasello, Mervis and Stiles1994; Bornstein et al. Reference Bornstein, Cote, Maital, Painter, Park, Pascual, Pêcheux, Ruel, Venuti and Vyt2004); the categories (e.g. verbs, prepositions) over which syntactic operations are defined are even smaller. The TP has the mathematical property that a smaller value of N, the set of lexical items over which a rule is defined, requires a proportionally smaller amount of positive evidence to warrant productivity. It is therefore easier for learners to learn rules when their vocabulary size is small, as is the case for young children. Furthermore, the early vocabulary is strongly correlated with frequencies of usage (Goodman et al. Reference Goodman, Dale and Li2008): high-frequency words are, of course, more likely to be attested in the syntactic processes they support, thereby effectively enhancing the evidence available to the child learner to form generalizations.

Because of its simplicity, the TP has been widely applied to learning problems in phonology, morphology, and syntax, and has been shown to have implications for language change (e.g. Björnsdóttir Reference Björnsdóttir2021; Hsieh Reference Hsieh2021; van Tuijl & Coopmans Reference van Tuijl and Coopmans2021; Pearl & Sprouse Reference Pearl and Sprouse2021; Trips & Rainsford Reference Trips and Rainsford2022; Dresher & Lahiri Reference Dresher, Lahiri, Los, Cowie, Honeybone and Trousdale2022; Henke Reference Henke2022; Kodner Reference Kodner2023; Belth Reference Belth2023, Reference Belth2025; Thoms et al. Reference Thoms, Adger, Caroline Heycock and Smith2025; Kanampiu et al. Reference Kanampiu, Martin and Culbertson2025; Nowenstein Reference Nowenstein2026). All these studies use corpus data to approximate the vocabulary of learners/speakers and to calculate productivity predictions, and they are supported with converging evidence from experiments, naturalistic production, dialectal surveys, historical sources, etc. Additional evidence for the TP comes from artificial language and pattern learning studies: the experimental stimuli and their frequencies are under strict control and the outcome of learning (i.e. the status of rules) can be assessed and tested precisely. For example, Schuler et al. (Reference Schuler, Yang and Newport2016) show that the TP correctly predicts generalization when a rule covers 5 out of 9 items in the training data (θ ₉ = 4) and no generalization when a rule covers only 3 out of 9. Shi & Emond (Reference Shi and Emond2023) provide an even more stringent test. Fourteen-month-old infants with no experience with the Russian language heard 16 three-word Russian sentences (denoted as ABC) playing in the background while playing in the lab. Some of the sentences were followed by a word order alternation that switched the order of two words (e.g. ABC → BAC). For one group of infants, 11 of the 16 sentences were attested with the alternation; for the other group, only 10 were. When tested on novel ABC sentences, only the former but not the latter group recognized the alternation in the training data. The results were predicted by the TP: θ ₁₆ = 5,Footnote ⁸ thus only 11/16 constitutes sufficient evidence for generalization but not 10/16, despite being the clear majority. Recall that the infants had no knowledge of Russian and were otherwise engaged with other activities: the TP must be a general learning principle independent of its domain of operation (see Guilbeault et al. Reference Guilbeault, Caplan and Yang2026 for an application to decision-making under uncertainty).

At the moment it is not clear why the TP should work as well as it does. Nor is it clear how the brain actually implements something like the TP. Quite importantly, the experimental results show that unlike the dominant approach to learning (e.g., Russell & Norvig Reference Russell and Norvig2004), generalization is not probabilistic. For example, a rule that applies with a probability 0.56 (5/9; Schuler et al. Reference Schuler, Yang and Newport2016) generalizes, but one that applies with a probability 0.63 (10/16; Shi & Emond Reference Shi and Emond2023) does not.Footnote ⁹ It is critical that the learner tracks both the numerator and denominator values. It is unclear how ratio tracking is implemented in the neurological system although behavioral evidence for such quantitative processing is ubiquitous across tasks and species (e.g. Aslin & Newport Reference Aslin and Newport2012) as is the evidence for threshold-like principles of learning and decision-making (e.g. Gold & Shadlen Reference Gold and Shadlen2007).

2.2. Generalizing movement

Our approach to bridge verbs can be viewed as a case study in an alternative approach to movement phenomena in language (Legate & Yang Reference Legate and Yang2025). The traditional view, as indicated by terms such as “islands,” seeks to identify both universal principles and language-particular choices (e.g. Chomsky Reference Chomsky1981; Rizzi Reference Rizzi1982; Chomsky Reference Chomsky1986) that restrict movement, which is by itself free and unlimited (“Move alpha”). Language acquisition is about learning what is impossible.

Our alternative view, as developed in Legate & Yang (Reference Legate and Yang2025), is that language acquisition is about learning what is possible. Instead of identifying conditions that prohibit movement, this theory aims to characterize the conditions that allow movement, and more precisely, how children discover them. The underlying intuition is that children must receive positive input to determine what is possible in their language. From this perspective, that clause-embedding verbs are by default non-bridge does not need to be stated as an independent property of the grammar. By default, nothing is possible, until the child encounters positive evidence that it is possible; hence, long-distance wh-movement (for a wh-movement language) or construal (for a wh-in situ language) is impossible until the child encounters evidence that it is.

For languages that lack bridge verbs altogether (e.g. certain varieties of German and Russian), the learner presumably will never encounter wh-questions across a clause-embedding verb, and so will never consider the possibility for their language. For a language that does exhibit long-distance questions, like English or Mandarin, the child presumably will encounter such questions in the input. Our proposal assumes only that a key component of the child’s acquisition of such questions is centered around the identity of the matrix verb; this much seems inescapable. The theoretical explanation of this is immaterial – it could be due to the selectional properties of the matrix verb (selecting a CP complement versus adjunct, selecting a DP versus CP, etc.), or the need to learn a movement/construal step from the embedded CP to the matrix VP (adopting the long-standing insight that non-local dependencies are composed of local steps), or something else. Regardless, the task of the child is to determine which verbs allow for long-distance wh-questions across them. Initially, the child will hear some clause-embedding verbs attested as bridge verbs, supporting lexically specific categorizations, for example, Vthink allows bridging.Footnote ¹⁰ As the child encounters more long-distance questions, the task becomes to determine whether a sufficient number of clause-embedding verbs are attested as bridges, calculated according to the Tolerance Principle, to justify generalizing the bridging property, either to an easily identifiable natural class of clause-embedding verbs, or to the category of clause-embedding verbs as a whole. In the coming section, we present two corpus analyses examining the use of clause-embedding verbs in English and in Mandarin child-directed speech. We shall see that the input available to children justifies generalizing the bridge property to the class of clause-embedding verbs as a whole in Mandarin, but not in English, where the bridge property remains lexically specific.

3.1. English CHILDES

We conducted a principled examination of the use of clause-embedding verbs in child-directed English from the CHILDES corpus (MacWhinney Reference MacWhinney2000). Our study makes use of a 13-million-word (2.7-million-utterance) corpus of child-directed speech, which corresponds to about two to three years of linguistic input for typical child learners. The corpus has been lemmatized and part-of-speech tagged (MacWhinney Reference MacWhinney2000). While the annotation is not perfect, it does facilitate effective extraction of sentential patterns, aided by the fact that child-directed sentences are very simple – the average sentence length is about 5 words – so that even hierarchically organized structures can be approximated by linear string-based searches. The automatic search results were submitted for manual inspection and correction when necessary. The corpus contains approximately 188,000 wh-questions. Of these, just over 500 are long-distance questions, where extraction originates from an embedded CP, corresponding to a frequency of roughly one every other day. English-learning children start to produce long-distance wh-questions relatively early, at a mean age of 2;10, albeit still about six months after the emergence of matrix questions. As in adult speech, long-distance questions are also relatively rare in children’s speech: only 200 out of a total of 12,000 wh-questions (Stromswold Reference Stromswold1995).

Approximately 80 of the clause-embedding verbs from Richter & Chaves (Reference Richter and Chaves2020) appeared at least once in declarative sentences in the child-directed corpus, including 10 out of the 15 bridge verbs in the above list. Even if all ten were attested in long-distance extraction, this would be nowhere near the threshold for generalization (which is 62 out of 80), predicting that the attested bridge verbs are simply lexically memorized. The actual data is even sparser: only five bridge verbs are attested with long-distance extraction in the child-directed input corpus at all. Recall that there are only just 500 long-distance questions to begin with. Given the statistical sparsity of linguistic structures (e.g. Yang Reference Yang2013), it is not surprising to find that think, followed by say, constitute the majority of the sample. The other three bridge verbs were, in fact, used exactly once each, reproduced below:

1. (7) What do you suppose tigers eat then?

   What are we going to decide they are?

   What would you recommend that I take?

There is no chance for bridgeability to ever emerge as a productive process. Nor do the attested bridge verbs seem to form any coherent lexical class: factivity, for example, is clearly inadequate as discussed earlier. Limiting the verbs to children’s vocabulary yields similar results, while providing a more developmentally appropriate illustration of the learning process: after all, not all clause-embedding verbs, some of which are fairly low in frequency, will be learned as such by children. By the age of acquiring long-distance wh-questions, children should have approximately 20 clause-embedding verbs in their vocabulary (Li Reference Li2023; Diessel & Tomasello Reference Diessel and Tomasello2001). For there to be a productive rule that all clause-embedding verbs are bridge verbs, one needs at least 14 out of the 20 clause-embedding verbs to be explicitly used as bridge verbs in the input. The mere 5 bridge verbs that appear in the English CHILDES corpus do not suffice. Therefore, the learner lexicalizes the attested bridge verbs but does not generalize beyond – the state of the grammar as originally described by Chomsky (Reference Chomsky, Culicover, Wasow and Akmajian1977).

3.2. Mandarin CHILDES

A search for Mandarin clause-embedding verbs in the Mandarin section of the Chinese CHILDES corpus (henceforth the Mandarin CHILDES) yields drastically different results from English. We took all adult utterances from the corpus (approximately 3.6 million words), all of which are dependency parsed. We identified verbs that take embedded CP complements based on the dependency parsing, and then manually verified that they were genuinely used as CP-embedding verbs in the corpus. There are a total of 48 CP-embedding verbs in the corpus. Select examples of CP-embedding verbs in the Mandarin CHILDES corpus are shown in (8). We then collected the most frequent 20 CP-embedding verbs: we are not aware of any study that specifically targets Mandarin-learning children’s vocabulary of CP-embedding verbs, so we used the estimates from English-learning children’s vocabulary discussed earlier (Diessel & Tomasello Reference Diessel and Tomasello2001; Li Reference Li2023) in light of the robust findings that children’s vocabulary size and composition develop at comparable rates across languages including Mandarin (Hao et al. Reference Hao, Shu, Xing and Li2008; Bornstein et al. Reference Bornstein, Cote, Maital, Painter, Park, Pascual, Pêcheux, Ruel, Venuti and Vyt2004). The list of verbs is shown in Table 1.

Table 1.

The top 20 most frequent clause-embedding verbs in the Mandarin CHILDES corpus

Table 1. Long description

The table is organized into two columns and three rows.

Row 1. The left column is labeled Attested with both w h-argument and w h-adjunct questions. The right column lists the following verbs with English translations: kan see, shuo say, zhidao know, juede feel or think, gaosu tell, jiang speak, xiwang hope, tingshuo hear, xiang think, pa worry, jide remember, jiandao see, cai guess, and ganjue feel.

Row 2. The left column is labeled Attested only with w h-argument questions. The right column lists: shuoming explain, faxian discover, xihuan like, haipa fear, and xie write.

Row 3. The left column is labeled Not attested with w h-questions. The right column lists: jiazhuang pretend.

We then searched for long-distance wh-questions among the sentences with the verbs in Table 1 taking finite complement clauses, where the wh-elements originate inside the complements of these verbs. Select examples from the corpus of CP-embedding verbs used as bridge verbs are shown in (9). Since the previous literature on bridge effects in Mandarin makes a distinction between argument and adjunct wh-questions, we conducted the search for the two wh-types separately. Among the 20 verbs, 19 are attested with wh-argument questions, 14 are attested with wh-adjunct questions, and there is only one ( jiazhuang , “pretend”) that does not appear in long-distance wh-questions of either type.

Assuming the Tolerance Principle, a rule that applies to 20 items is productive if it holds for at least 14 items (following the equation in (6), the generalization threshold for 20 items is 20 – θ ₂₀ or 14). Our counts for both wh-argument and wh-adjunct clear the threshold of productive generalization. Mandarin-speaking children should thus posit a productive rule that all clause-embedding verbs are bridge verbs.

In the following sections, we put this prediction to the test in a series of acceptability judgment experiments with Mandarin speakers.

4.1. Methods

4.1.3. Procedures

The stimuli sentences were presented to the participants one at a time, and the participants were asked to rate how acceptable the sentences sound to them using a continuous sliding scale. The left end of the scale was labeled completely unacceptable, and the right end was labeled completely acceptable in Mandarin. An example trial is shown in Figure 1.

Figure 1.

Example experimental interface.

Each participant was tested on 8 verbs: 2 bridge verbs and 6 unclassified verbs, randomly sampled from the pool of 3 bridge verbs and 11 unclassified verbs.

4.2. Results

All ratings on the sliding scale were transformed to a numeric value between 0 and 1, with 0 representing the completely unacceptable end of the scale, and 1 representing the completely acceptable end. Figure 2 shows the average acceptability ratings for sentences containing the three canonical bridge verbs. Figure 3 shows the average acceptability ratings for sentences with each unclassified verb, compared to the average ratings for the bridge verb sentences.

Figure 2.

Acceptability ratings for the bridge verb sentences in Experiment 1.

Figure 2. Long description

A multi-panel figure containing three line graphs. All graphs share a common Y axis labeled Mean acceptability rating ranging from 0.00 to 1.00 and an X axis labeled Condition with two points: short and long. A legend at the bottom indicates that solid lines represent argument w h-type and dashed lines represent adjunct w h-type.

* The first panel on the left is titled shuo say. The argument line shows a slight decrease from approximately 0.70 at short to 0.65 at long. The adjunct line shows a sharper decrease from approximately 0.75 at short to 0.48 at long.

* The middle panel is titled cai guess. The argument line remains nearly flat at approximately 0.50 for both short and long conditions. The adjunct line shows a decrease from approximately 0.60 at short to 0.42 at long.

* The third panel on the right is titled renwei think. The argument line shows a very slight decrease from approximately 0.70 at short to 0.68 at long. The adjunct line shows a significant decrease from approximately 0.70 at short to 0.50 at long.

All data points include vertical error bars with horizontal caps indicating confidence intervals.

Figure 3.

Acceptability ratings for the unclassified verb sentences compared against the bridge verb sentences in Experiment 1.

Figure 3. Long description

A grid of 11 line graph panels, each representing a specific verb: juede, xiwang, shuoming, xiang, pa, xihuan, jide, jiazhuang, haipa, ganjue, and xie.

Each panel shares a common layout:

- The Y-axis represents Mean acceptability rating from 0.00 to 1.00.

- The X-axis represents Condition with two points: short and long.

- Each panel is split into two sub-charts: argument on the left and adjunct on the right.

- Two data series are plotted: bridge verbs in orange and unknown verbs in teal, both with error bars.

General Trends:

- In the argument sub-charts, ratings for both bridge and unknown verbs remain relatively stable or show a slight decline from short to long conditions. Bridge verbs consistently score higher than unknown verbs, except in juede and jiazhuang where they overlap.

- In the adjunct sub-charts, there is a sharp downward trend for both verb types from the short to the long condition. The bridge verbs typically start at a higher rating around 0.75 and drop to approximately 0.50, while unknown verbs start lower around 0.50 and drop to approximately 0.35.

- The gap between bridge and unknown verbs is most pronounced in verbs like xihuan, xiang, and xie, where the teal line for unknown verbs is significantly lower than the orange line for bridge verbs across all conditions.

First, we fitted a linear mixed effect regression model predicting the acceptability ratings of the bridge verb sentences with the sum-coded fixed effects of dependency length (short vs. long), wh-type (argument vs. adjunct), and their interaction. The model also includes the maximal by-participant and by-item random effect structure. There is a significant main effect of dependency length (β = 0.063, SE = 0.0093, t = 6.77, p < 0.001) where the long dependency sentences were rated lower than the short dependency ones. There is also a significant main effect of wh-type (β = -0.021, SE = 0.0073, t = -2.88, p < 0.01) where the wh-adjunct sentences were rated lower than the wh-argument ones. Crucially, there is also a significant interaction of dependency length and wh-type (β = 0.050, SE = 0.0075, t = 6.60, p < 0.001), where the length penalty is larger for the wh-adjunct sentences than for the wh-argument sentences. This suggests that there is an “argument-adjunct asymmetry” in extraction penalty even for the three canonical bridge verbs.

Then, for each of the unclassified verbs we tested, we fitted a linear mixed effect regression model predicting the acceptability ratings with the sum-coded fixed effects of dependency length (short vs. long), wh-type (argument vs. adjunct), and their interaction, as well as the maximal by-participant and by-item random effect structure allowing convergence. The model estimates are shown in Table 2. The dependency length main effect is significant for all unclassified verbs except for haipa “fear” (for which the effect is marginally significant), where the long dependency conditions are rated lower than the short dependency conditions. The wh-type main effect is significant for only one unclassified verb: jiazhuang “pretend,” where sentences with wh-adjuncts are rated lower than those with wh-arguments. The interaction effect is significant for six of the unclassified verbs: juede “feel/think,” xiwang “hope,” pa “worry,” jiazhuang “pretend,” haipa “fear,” and ganjue “feel,” where the extraction length penalty is greater for the wh-adjunct sentences than for the wh-argument sentences.

Table 2.

Estimates for LMER models predicting the acceptability of Exp.1 sentences containing each unclassified verb with sum-coded fixed effects of dependency length (short vs. long), wh-type (argument vs. adjunct), and their interaction, as well as the maximal by-participant and by-item random effect structures allowing convergence. Shaded boxes represent statistically significant effects

Table 2. Long description

The table consists of 13 columns. The first column lists the verbs: juede, xiwang, shuoming, xiang, pa, xihuan, jide, jiazhuang, haipa, ganjue, and xie. The remaining columns are grouped into three main categories: Dependency Length, Wh-type, and Interaction. Each category contains four sub-columns: beta, S E, t, and p.

Key statistical findings include:

* Dependency Length: Significant positive effects (p < 0.05) for all verbs except haipa (p = 0.076). The highest t-value is for jide (t = 6.42, p < 0.001).

* Wh-type: Only jiazhuang shows a significant effect (beta = -0.066, t = -4.44, p < 0.001). All other verbs are non-significant (p > 0.15).

* Interaction: Significant interactions (p < 0.05) are observed for juede, xiwang, pa, jiazhuang, haipa, and ganjue. The strongest interaction effect is for xiwang (t = 4.72, p < 0.001).

Next, we move on to examine whether the unclassified verbs behave like bridge verbs or not. Since there is a possibility that the bridge status of verbs may be specific to a particular type of wh-element, the following analysis was done for the wh-argument conditions and the wh-adjunct conditions separately. For each of the unclassified verbs tested, we pooled all the sentence ratings for that verb together with the ratings for the bridge verb sentences, and fitted a linear mixed-effects regression model predicting acceptability with the fixed effects of verb type (bridge vs. unclassified), dependency length (short vs. long), and their interaction. Also included were the maximal by-participant and by-item random effect structures allowing convergence. The regression model estimates are shown in Table 3, with significant effects shaded gray.

Table 3.

Estimates for LMER models predicting the acceptability of Exp.1 sentences containing the bridge verbs and each unclassified verb with sum-coded fixed effects of dependency length (short vs. long), verb type (bridge vs. unclassified), and their interaction, as well as the maximal by-participant and by-item random effect structures allowing convergence. Shaded boxes represent statistically significant effects

Table 3. Long description

The table is organized with columns for beta, S E, t, and p values grouped under three main headers: Dependency Length, Verb Type, and Interaction. Each row represents a specific verb with sub-rows for Argument and Adjunct structures.

* juede (feel/think): Argument shows no significant effects. Adjunct shows significant Dependency Length (beta 0.12, p < 0.001) and Verb Type (beta -0.033, p < 0.05).

* xiwang (hope): Argument shows significant Verb Type (beta 0.064, p < 0.001). Adjunct shows significant Dependency Length (beta 0.11, p < 0.001) and Verb Type (beta 0.051, p < 0.001).

* shuoming (explain): Argument shows significant Dependency Length (beta 0.023, p < 0.05) and Verb Type (beta 0.079, p < 0.001). Adjunct shows significant effects across all three categories, including Interaction (beta 0.040, p < 0.001).

* xiang (think/presume): Adjunct shows significant Interaction (beta 0.036, p < 0.01).

* pa (worry): Argument shows significant Dependency Length (beta 0.068, p < 0.001) and Interaction (beta 0.051, p < 0.001).

* xihuan (like): Adjunct shows significant Interaction (beta 0.037, p < 0.001).

* jide (remember): Argument shows significant Interaction (beta -0.039, p < 0.01).

* haipa (fear), ganjue (feel), and xie (write) primarily show significant main effects for Dependency Length and Verb Type in Adjunct positions but no significant interactions.

For a variety of verb/wh-type combinations, there are significant main effects of dependency length and/or verb type, where the long dependency sentences are rated as less acceptable than the short dependency sentences, and the sentences with unclassified verbs are rated lower than those with the three canonical bridge verbs. There are also significant interaction effects of dependency length and verb type for the following four verb/wh-type combinations: shuoming “explain” with wh-adjunct, xiang “think/presume” with wh-adjunct, pa “worry” with wh-argument, and jide “remember” with wh-argument. For the first three verb/wh-type combinations, the interaction effect is in the direction where the length penalty is greater for the canonical bridge verbs than for the unclassified verbs. For jide “remember” with wh-argument, the length penalty is greater for jide than for the canonical bridge verbs. There is no significant interaction between dependency length and verb type for any of the other verb/wh-type combinations.

To further confirm that the unclassified verbs are indeed bridge verbs, we verified the null interaction between dependency length and verb type with a Bayes factor analysis. Using the R package BayesFactor (Morey et al. Reference Morey, Rouder, Jamil and Morey2015), we estimated the Bayes factors comparing the regression models reported in Table 3 with ones that are otherwise identical but lack the interaction term, using three different prior width settings (medium, wide, and ultra-wide). The Bayes factor estimates are shown in Table 4.

Table 4.

Bayes factors for the Dependency Length * Verb Type interaction terms of the models reported in Table 3, estimated using the BayesFactor package in R (Morey et al. Reference Morey, Rouder, Jamil and Morey2015)

Table 4. Long description

The table is organized into five columns: Verb, Wh-type, and three Prior width categories: Medium, Wide, and Ultra-wide.

* juede (feel/think): Argument type has values of 0.12, 0.096, and 0.066. Adjunct type has values of 0.11, 0.082, and 0.068.

* xiwang (hope): Argument type has values of 0.35, 0.22, and 0.17. Adjunct type has values of 0.12, 0.087, and 0.057.

* shuoming (explain): Argument type has values of 0.15, 0.11, and 0.076.

* xiang (think/presume): Argument type has values of 0.12, 0.10, and 0.059.

* pa (worry): Argument type has values of 0.11, 0.076, and 0.056. Adjunct type has values of 0.12, 0.090, and 0.061.

* xihuan (like): Argument type has values of 0.13, 0.11, and 0.062.

* jide (remember): Adjunct type has values of 0.12, 0.057, and 0.057.

* jiazhuang (pretend): Argument type has values of 0.14, 0.10, and 0.066. Adjunct type has values of 0.13, 0.088, and 0.057.

* haipa (fear): Argument type has values of 0.16, 0.10, and 0.071.

* ganjue (feel): Argument type has values of 0.15, 0.099, and 0.070. Adjunct type has values of 0.18, 0.11, and 0.075.

* xie (write): Argument type has values of 0.15, 0.095, and 0.067.

Following previous conventions, we take BF < 0.3 as evidence for the null hypothesis (Rouder et al. Reference Rouder, Speckman, Sun, Morey and Iverson2009). All Bayes factors calculated are below 0.3, except for one: the verb xiwang “hope” with wh-argument under a medium prior width setting, where BF = 0.35, suggesting an inconclusive result. But we should note that the interaction effect for xiwang with wh-argument is numerically in the direction where the length penalty for xiwang is smaller than the length penalty for the canonical bridge verbs. Even if the experiment is underpowered and we failed to detect a significant effect for xiwang, the verb xiwang should still be classified as a bridge verb since it induces a significantly smaller penalty than the canonical bridge verbs.

4.3. Discussion

There are two main takeaways from Experiment 1.

First, there is no clear bridge/non-bridge distinction among the verbs tested in Experiment 1. If an unclassified verb behaves like a non-bridge verb, the length penalty (i.e. the acceptability degradation of having a wh-dependency crossing the verb) should be greater for the unclassified verb than for the canonical bridge verbs. Among all twenty-two combinations of unclassified verbs and wh-types tested in Experiment 1, we only found jide “remember” to behave like a non-bridge verb when the wh-element moving across it is a wh-argument. Three combinations ( shuoming “explain” with wh-adjunct, xiang “think/presume” with wh-adjunct, pa “worry” with wh-argument) showed smaller length penalty than the canonical bridge verbs, and all other combinations showed no significant difference in length penalty compared to the bridge verbs. The null effects are further confirmed by a Bayes Factor analysis. These results suggest that with the sole exception of jide “remember,” all the unclassified verbs tested should be classified as bridge verbs.

As for jide , it also does not display the properties one would expect for a non-bridge verb in Mandarin. Note that jide only behaves like a non-bridge verb with respect to wh-arguments. When the wh-element moving across it is a wh-adjunct, jide behaves bridge-like. This pattern is in fact the opposite of the previous generalization by Tsai (Reference Tsai1994): non-bridge verbs in Mandarin are claimed to restrict wh-adjuncts but not wh-arguments. Although our account cannot explain why jide restricts wh-arguments but not wh-adjuncts, this puzzling observation poses a challenge for alternative accounts of the bridge effects alike. Furthermore, jide is in fact attested as a bridge verb with wh-arguments in CHILDES despite the bridge-like effect observed in the experiment. One naturally occurring example in CHILDES was shown earlier as (9a). The existence of such examples suggests that the bridge-like effect with jide should be considered a subliminal island effect: an effect where the movement penalty is statistically detectable, but sentences affected are still naturally produced and perceived as marginally or even fully acceptable by speakers (Keshev & Meltzer-Asscher Reference Keshev and Meltzer-Asscher2019; Almeida Reference Almeida2014; Tanaka Reference Tanaka2025). Subliminal island effects arguably reflect processing-level penalties, as opposed to true grammatical constraints (Keshev & Meltzer-Asscher Reference Keshev and Meltzer-Asscher2019). If so, jide should still be considered a bridge verb.Footnote ¹¹

The second key takeaway from Experiment 1 concerns the argument-adjunct asymmetry of the bridge effect. Our findings reject the existence of such an asymmetry: among the verbs we tested, there is simply no bridge effect for all but one verb; the only verb that induces a potential bridge effect is jide “remember,” and it restricts wh-arguments as opposed to wh-adjuncts, the opposite of the claimed asymmetry. But this does not mean that the previous generalizations were entirely spurious: we did find significant interaction effects between dependency length and wh-type for a majority of the verbs we tested, suggesting that wh-adjunct induces a greater extraction penalty than wh-argument. However, this effect also applies to the three canonical bridge verbs, and thus simply reflects a general penalty on long-distance wh-adjunct dependencies and is orthogonal to the bridge effect. This general penalty on long-distance wh-adjunct dependencies in Chinese has been attested in previous experimental studies (Lu et al. Reference Lu, Thompson and Yoshida2020; Kim et al. Reference Kim, Li and Lu2023). The exact source of this penalty is unclear. Here we offer two speculations: first, this asymmetry possibly arises due to the lower frequency of embedded clausal questions with wh-adjuncts like why, versus wh-arguments like who. Alternatively, there could be a higher processing cost associated with long-distance wh-adjunct questions than wh-argument questions, since a wh-adjunct question shares the same argument structure as its wh-argument counterpart but contains one extra adjunct, which may add to complexity and processing cost. Further psycholinguistic work is needed to pinpoint the source of this penalty on long-distance wh-adjunct dependencies.

In sum, Experiment 1 shows no evidence for a clear bridge/non-bridge division among the verbs tested, and challenges the argument-adjunct asymmetry of the bridge effect claimed in the previous literature. These results provide support for our account of the bridge effect: based on the corpus analysis, we found that a vast majority of clause-embedding verbs are used as bridge verbs in Mandarin child-directed speech for both wh-argument dependencies and wh-adjunct dependencies, clearing the threshold for children to acquire a productive rule that all clause-embedding verbs in Mandarin are also bridge verbs for both types of wh-elements. This prediction is verified by the findings of Experiment 1.

One caveat of Experiment 1 is that the verbs we tested are relatively high in frequency and are likely acquired early by children, since they all appear at least once in the Mandarin CHILDES corpus. It is possible that Mandarin-speaking children have direct exposure to these verbs being used as bridge verbs in their input, and thus have acquired their bridge status directly through lexical learning, as opposed to through a productive rule as we hypothesized. To tease apart this alternative possibility from our account, we need to examine verbs that are highly infrequent: ones that are unlikely to be present in children’s input even in declarative sentences, let alone in sentences with long-distance wh-dependencies. If the findings in Experiment 1 are solely the result of lexical learning, we would expect at least some of the infrequent verbs to remain non-bridge verbs; if Mandarin speakers acquire a productive rule that all clause-embedding verbs are bridge verbs, infrequent verbs that are acquired late in the acquisition process should also gain bridge status. We test these predictions in Experiment 2.

5.1. Methods

5.1.2. Materials

A total of 14 clause-embedding verbs were tested: the three canonical bridge verbs ( shuo “say,” cai “guess,” renwei “think”), and 11 unclassified verbs: huaiyi “doubt,” jiancheng “maintain,” fouren “deny,” baoyuan “complain,” chengren “concede,” jieshou “accept,” baozheng “assure,” toulu “disclose,” zhengshi “verify,” chongshen “reiterate,” and rentong “agree.” The 11 unclassified verbs satisfy all of the following criteria: first, each of them appears at least once taking a finite complement clause in Penn Chinese Treebank 9.0 (Xue et al. Reference Xue, Zhang, Jiang, Palmer, Xia, Chiou and Chang2016), a corpus of approximately 2 million words of parsed written text such as news articles, government documents, and magazine articles. Although we are not aware of studies on adult Mandarin speakers’ vocabulary, we draw support from the well-established practice in the study of English that words appearing at least once per million can be regarded as familiar to typical speakers (Nagy & Anderson Reference Nagy and Anderson1984). This establishes that the verbs tested in Experiment 2 are clause-embedding verbs in adult grammar. Second, the unclassified verbs do not appear in the Mandarin CHILDES corpus as clause-embedding verbs. This suggests that they are relatively infrequent in child-directed speech compared to the verbs tested in Experiment 1, and thus are likely acquired later by children. Third, their English counterparts are non-bridge verbs based on the classification by Richter & Chaves (Reference Richter and Chaves2020). We further confirmed the non-bridge status of their English counterparts through a post hoc analysis of Huang et al. (Reference Huang, Almeida and Sprouse2025). In a large-scale acceptability rating experiment, Huang et al. (Reference Huang, Almeida and Sprouse2025) tested sentences such as (12a, b).

1. (12) Example stimuli from Huang et al. (Reference Huang, Almeida and Sprouse2025), for the verb think.

   1. a. short: Who thought that the duchess would invite the arrogant knight?

   2. b. long: Who did the princess think that the duchess would invite?

The contrast between the long and short conditions in Huang et al. (Reference Huang, Almeida and Sprouse2025) represents the penalty of extracting a wh-element across the clause-embedding verb. We compared the extraction penalties of the English counterparts of each of the unclassified verbs tested in Experiment 2 against two uncontroversial bridge verbs in English, say and think. For each unclassified verb, we fitted a linear mixed-effect regression model predicting sentence acceptability z-score with the sum-coded fixed effects of dependency length (long vs. short), verb type (unclassified vs. bridge), and their interaction, as well as a random by-participant intercept. The model outputs are shown in Table 5. For every unclassified verb, there is a significant interaction between dependency length and verb type, suggesting that the length penalty is significantly larger for the unclassified verb than for the canonical bridge verbs say and think. This further verifies that the English counterparts of the unclassified verbs tested in Experiment 2 are indeed non-bridge verbs.

Table 5.

Post hoc analysis results of Huang et al. (Reference Huang, Almeida and Sprouse2025). The table shows the estimates for LMER models predicting the acceptability of the test sentences containing the two canonical bridge verbs in English (say, think), and each unclassified verb with sum-coded fixed effects of dependency length (short vs. long), verb type (bridge vs. unclassified), and their interaction, as well as a random by-participant intercept

Table 5. Long description

A table with 13 columns and 12 rows including headers. The columns are grouped into three main categories: Dependency length, Verb type, and Interaction. Each category contains four sub-columns: beta, S E, t, and p.

* doubt: Dependency length (beta 0.67, t 7.54, p less than 0.001); Verb type (beta 0.59, t 7.41, p less than 0.001); Interaction (beta minus 0.48, t minus 4.25, p less than 0.001).

* maintain: Dependency length (beta 0.42, t 5.25, p less than 0.001); Verb type (beta 0.55, t 7.07, p less than 0.001); Interaction (beta minus 0.23, t minus 2.29, p less than 0.05).

* deny: Dependency length (beta 0.57, t 5.92, p less than 0.001); Verb type (beta 0.72, t 8.21, p less than 0.001); Interaction (beta minus 0.38, t minus 3.15, p less than 0.01).

* complain: Dependency length (beta 0.80, t 8.76, p less than 0.001); Verb type (beta 0.87, t 10.35, p less than 0.001); Interaction (beta minus 0.61, t minus 5.21, p less than 0.001).

* concede: Dependency length (beta 0.54, t 6.46, p less than 0.001); Verb type (beta 0.55, t 7.21, p less than 0.001); Interaction (beta minus 0.35, t minus 3.27, p less than 0.01).

* accept: Dependency length (beta 0.73, t 7.60, p less than 0.001); Verb type (beta 0.82, t 9.37, p less than 0.001); Interaction (beta minus 0.54, t minus 4.45, p less than 0.001).

* assure: Dependency length (beta 0.85, t 9.24, p less than 0.001); Verb type (beta 0.82, t 9.52, p less than 0.001); Interaction (beta minus 0.66, t minus 5.43, p less than 0.001).

* disclose: Dependency length (beta 0.75, t 8.32, p less than 0.001); Verb type (beta 0.57, t 7.05, p less than 0.001); Interaction (beta minus 0.56, t minus 4.89, p less than 0.001).

* verify: Dependency length (beta 0.52, t 6.96, p less than 0.001); Verb type (beta 0.37, t 5.17, p less than 0.001); Interaction (beta minus 0.33, t minus 3.39, p less than 0.001).

* reiterate: Dependency length (beta 0.41, t 4.79, p less than 0.001); Verb type (beta 0.47, t 5.94, p less than 0.001); Interaction (beta minus 0.22, t minus 2.04, p less than 0.05).

* agree: Dependency length (beta 0.43, t 5.53, p less than 0.001); Verb type (beta 0.29, t 3.97, p less than 0.001); Interaction (beta minus 0.24, t minus 2.47, p less than 0.05).

5.2. Results

Like in Experiment 1, all ratings on the sliding scale were transformed to a numeric value between 0 and 1, with 0 representing the completely unacceptable end of the scale, and 1 representing the completely acceptable end. Figure 4 shows the average acceptability ratings for sentences containing the three canonical bridge verbs. Figure 5 shows the average acceptability ratings for sentences with each unclassified verb, compared to the average ratings for the bridge verb sentences.

Figure 4.

Acceptability ratings for the bridge verb sentences in Experiment 2.

Figure 4. Long description

A multi-panel figure with three line graphs arranged horizontally. Each graph shares a Y-axis labeled Mean acceptability rating from 0.00 to 1.00 and an X-axis labeled Condition with two points: short and long. A legend at the bottom indicates that a solid line represents argument W H type and a dashed line represents adjunct W H type.

* The first graph, titled shuo say, shows the argument rating starting at approximately 0.75 for short and slightly decreasing to 0.68 for long. The adjunct rating starts at 0.78 for short and drops sharply to 0.45 for long.

* The second graph, titled cai guess, shows the argument rating starting at 0.50 for short and remaining nearly flat at 0.52 for long. The adjunct rating starts higher at 0.62 for short and drops to 0.35 for long.

* The third graph, titled renwei think, shows the argument rating starting at 0.70 for short and decreasing slightly to 0.65 for long. The adjunct rating starts at 0.72 for short and drops sharply to 0.38 for long.

All data points include vertical error bars and horizontal confidence interval markers.

Figure 5.

Acceptability ratings for the unclassified verb sentences compared against the bridge verb sentences in Experiment 2.

Figure 5. Long description

The grid contains 11 panels, each representing a specific verb. Each panel has a Y-axis for Mean acceptability rating from 0.00 to 1.00 and an X-axis for Condition with short and long categories. Each panel is split into two sub-plots: argument on the left and adjunct on the right. Data is plotted for bridge verbs in orange and unknown verbs in teal.

* Row 1: huaiyi (doubt), jiancheng (maintain), fouren (deny), baoyuan (complain).

* Row 2: chengren (concede), jieshou (accept), baozheng (assure), toulu (disclose).

* Row 3: zhengshi (verify), chongshen (reiterate), rentong (agree).

In all panels, the argument sub-plots show relatively stable ratings between short and long conditions, with bridge and unknown lines often overlapping or remaining parallel near the 0.50 to 0.75 range. In contrast, the adjunct sub-plots show a sharp linear decrease in acceptability from the short to the long condition for both verb types. In most cases, the orange bridge verb line remains higher than the teal unknown verb line, particularly in the adjunct condition for verbs like fouren, chengren, jieshou, and baozheng.

First, we fitted a linear mixed effect regression model predicting the acceptability ratings of the bridge verb sentences with the sum-coded fixed effects of dependency length (short vs. long), wh-type (argument vs. adjunct), and their interaction. The model also includes the maximal by-participant and by-item random effect structure. There is a significant main effect of dependency length (β = 0.090, SE = 0.0080, t = 11.20, p < 0.001) where the long dependency sentences were rated lower than the short dependency ones. There is also a significant main effect of wh-type (β = –0.039, SE = 0.0064, t = –6.09, p < 0.001) where the wh-adjunct sentences were rated lower than the wh-argument ones. Crucially, there is also a significant interaction of dependency length and wh-type (β = 0.070, SE = 0.0061, t = 11.44, p < 0.001), where the length penalty is larger for the wh-adjunct sentences than for the wh-argument sentences. This suggests that there is an argument-adjunct asymmetry in extraction penalty for the three canonical bridge verbs. These results are qualitatively the same as in Experiment 1.

Then, for each of the unclassified verbs we tested, we fitted a linear mixed effect regression model predicting the acceptability ratings with the sum-coded fixed effects of dependency length (short vs. long), wh-type (argument vs. adjunct), and their interaction, as well as the maximal by-participant and by-item random effect structure allowing convergence. The model estimates are shown in Table 6. All unclassified verbs tested showed significant main effects of dependency length, where long dependency sentences were rated lower than short dependency sentences. Four of the unclassified verbs also showed significant main effects of wh-type, where wh-adjunct sentences were rated lower than wh-argument sentences. Crucially, all unclassified verbs showed significant interaction effects between dependency length and wh-type: the dependency length effect is greater when the wh-element is a wh-adjunct than a wh-argument. Just like the three canonical bridge verbs, the unclassified verbs in Experiment 2 also demonstrate an argument-adjunct asymmetry in extraction penalty.

Table 6.

Estimates for LMER models predicting the acceptability of Exp.2 sentences containing each unclassified verb with sum-coded fixed effects of dependency length (short vs. long), wh-type (argument vs. adjunct), and their interaction, as well as the maximal by-participant and by-item random effect structures allowing convergence. Shaded boxes represent statistically significant effects

Table 6. Long description

The table contains 11 rows of verbs with their corresponding statistical values for beta, S E, t, and p across three main categories.

1. huaiyi (doubt): Dependency Length beta 0.070, p less than 0.001; Wh-type beta -0.017, p 0.21; Interaction beta 0.081, p less than 0.001.

2. jiancheng (maintain): Dependency Length beta 0.089, p less than 0.001; Wh-type beta -0.020, p 0.12; Interaction beta 0.081, p less than 0.001.

3. fouren (deny): Dependency Length beta 0.069, p less than 0.001; Wh-type beta -0.022, p 0.13; Interaction beta 0.072, p less than 0.001.

4. baoyuan (complain): Dependency Length beta 0.090, p less than 0.001; Wh-type beta -0.057, p less than 0.001; Interaction beta 0.060, p less than 0.001.

5. chengren (concede): Dependency Length beta 0.094, p less than 0.001; Wh-type beta -0.012, p 0.11; Interaction beta 0.088, p less than 0.001.

6. jieshou (accept): Dependency Length beta 0.10, p less than 0.001; Wh-type beta -0.014, p 0.33; Interaction beta 0.043, p less than 0.01.

7. baozheng (assure): Dependency Length beta 0.048, p less than 0.01; Wh-type beta -0.038, p less than 0.01; Interaction beta 0.038, p less than 0.01.

8. toulu (disclose): Dependency Length beta 0.087, p less than 0.001; Wh-type beta -0.11, p less than 0.001; Interaction beta 0.073, p less than 0.001.

9. zhengshi (verify): Dependency Length beta 0.069, p less than 0.001; Wh-type beta -0.087, p less than 0.001; Interaction beta 0.049, p less than 0.001.

10. chongshen (reiterate): Dependency Length beta 0.050, p less than 0.001; Wh-type beta -0.0063, p 0.63; Interaction beta 0.039, p less than 0.05.

11. rentong (agree): Dependency Length beta 0.11, p less than 0.001; Wh-type beta -0.021, p 0.098; Interaction beta 0.077, p less than 0.001.

We then examine whether the unclassified verbs behave like bridge verbs or not. Just like in Experiment 1, the following analysis was done for the wh-argument conditions and the wh-adjunct conditions separately. For each unclassified verb/wh-type combination, we pooled all the sentence ratings for that verb together with the ratings for the bridge verb sentences, and fitted a linear mixed-effect regression model predicting acceptability with the fixed effects of verb type (bridge vs. unclassified), dependency length (short vs. long), and their interaction. Also included were the maximal by-participant and by-item random effect structures allowing convergence. The regression model estimates are shown in Table 7, with significant effects shaded gray.

Table 7.

Estimates for LMER models predicting the acceptability of Exp.2 sentences containing the bridge verbs and each unclassified verb with sum-coded fixed effects of dependency length (short vs. long), verb type (bridge vs. unclassified), and their interaction, as well as the maximal by-participant and by-item random effect structures allowing convergence. Shaded boxes represent statistically significant effects

Table 7. Long description

The table presents statistical data for several verbs, each divided into Argument and Adjunct rows. The columns are grouped into three main categories: Dependency Length, Verb Type, and Interaction, each containing sub-columns for beta, S E, t, and p values.

* huaiyi (doubt): For Adjunct, Dependency Length beta is 0.15, p is less than 0.001.

* jiancheng (maintain): For Adjunct, Dependency Length beta is 0.17, p is less than 0.001.

* fouren (deny): For Adjunct, Dependency Length beta is 0.15, p is less than 0.001; Verb Type beta is 0.059, p is less than 0.001.

* baoyuan (complain): For Argument, Dependency Length beta is 0.025, p is less than 0.05. For Adjunct, Dependency Length beta is 0.16, p is less than 0.001; Verb Type beta is 0.023, p is less than 0.05.

* chengren (concede): For Adjunct, Dependency Length beta is 0.17, p is less than 0.001; Verb Type beta is 0.043, p is less than 0.001.

* jieshou (accept): For Argument, Dependency Length beta is 0.035, p is less than 0.001; Verb Type beta is 0.11, p is less than 0.001. For Adjunct, Dependency Length beta is 0.15, p is less than 0.001; Verb Type beta is 0.076, p is less than 0.001.

* baozheng (assure): For Adjunct, Dependency Length beta is 0.12, p is less than 0.001; Verb Type beta is 0.11, p is less than 0.001; Interaction beta is 0.037, p is less than 0.001.

* toulu (disclose): For Argument, Verb Type beta is negative 0.027, p is less than 0.01. For Adjunct, Dependency Length beta is 0.16, p is less than 0.001; Verb Type beta is 0.044, p is less than 0.001.

* zhengshi (verify): For Argument, Dependency Length beta is 0.020, p is less than 0.05. For Adjunct, Dependency Length beta is 0.14, p is less than 0.001; Verb Type beta is 0.043, p is less than 0.001; Interaction beta is 0.021, p is less than 0.05.

* chongshen (reiterate): For Argument, Dependency Length beta is 0.020, p is less than 0.05; Verb Type beta is 0.10, p is less than 0.001. For Adjunct, Dependency Length beta is 0.12, p is less than 0.001; Verb Type beta is 0.071, p is less than 0.001; Interaction beta is 0.039, p is less than 0.001.

* rentong (agree): For Adjunct, Dependency Length beta is 0.17, p is less than 0.001; Verb Type beta is 0.047, p is less than 0.001.

There are three verb/wh-type combinations that showed significant interaction effects between dependency length and verb type: baozheng “assure” with wh-adjunct, zhengshi “verify” with wh-adjunct, and chongshen “reiterate” with wh-adjunct. The significant interaction effects were all in the direction such that the unclassified verbs induced a smaller length penalty than the canonical bridge verbs, suggesting that the unclassified verbs are also bridge verbs. For all other verb/wh-type combinations tested, there is no significant interaction between dependency length and verb type. This suggests that there is no evidence for any of the tested verbs being non-bridge verbs.

Since our argument for bridge status of the tested verbs depends on null effects, we further verified the null interaction effects reported in Table 7 with a Bayes factor analysis. Using the R package BayesFactor (Morey et al. Reference Morey, Rouder, Jamil and Morey2015), we estimated the Bayes factors comparing the regression models reported in Table 7 with ones that are otherwise identical but lack the interaction term, using three different prior width settings (medium, wide, and ultra-wide). The Bayes factor estimates are shown in Table 8.

Table 8.

Bayes factors for the Dependency Length * Verb Type interaction terms of the models reported in Table 7, estimated using the BayesFactor package in R (Morey et al. Reference Morey, Rouder, Jamil and Morey2015)

Table 8. Long description

The table consists of five columns: Verb, Wh-type, and three columns under the heading Prior width (Medium, Wide, and Ultra-wide).

* huaiyi (doubt): Argument (0.31, 0.20, 0.15); Adjunct (0.12, 0.078, 0.061).

* jiancheng (maintain): Argument (0.16, 0.087, 0.065); Adjunct (0.13, 0.092, 0.066).

* fouren (deny): Argument (0.18, 0.14, 0.095); Adjunct (0.18, 0.12, 0.080).

* baoyuan (complain): Argument (0.10, 0.098, 0.065); Adjunct (0.13, 0.087, 0.059).

* chengren (concede): Argument (0.13, 0.090, 0.061); Adjunct (0.17, 0.22, 0.093).

* jieshou (accept): Argument (0.29, 0.25, 0.18); Adjunct (0.18, 0.11, 0.083).

* baozheng (assure): Argument (0.12, 0.090, 0.057).

* toulu (disclose): Argument (0.11, 0.079, 0.055); Adjunct (0.11, 0.077, 0.059).

* zhengshi (verify): Argument (0.12, 0.077, 0.054).

* chongshen (reiterate): Argument (0.11, 0.076, 0.051).

* rentong (agree): Argument (0.12, 0.077, 0.061); Adjunct (0.18, 0.12, 0.099).

Following previous conventions, we take BF < 0.3 as evidence for the null hypothesis (Rouder et al. Reference Rouder, Speckman, Sun, Morey and Iverson2009). All Bayes factors calculated are below 0.3, except for one: the verb huaiyi “doubt” with wh-argument under a medium prior width setting, where BF = 0.31, suggesting an inconclusive result. But the interaction effect under question is in fact numerically in the opposite direction of a bridge effect: the length penalty for huaiyi is smaller than the length penalty for the three canonical bridge verbs. Therefore, the Bayes factor analysis provides further support for the lack of a bridge/non-bridge distinction among the verbs tested in Experiment 2.

5.3. Discussion

Experiment 2 replicates the results of Experiment 1. The two main conclusions of Experiment 1 are further confirmed with Experiment 2: first, there is no clear bridge/non-bridge verb distinction among the clause-embedding verbs in Mandarin; second, the so-called argument-adjunct asymmetry of the bridge effect in Mandarin simply reflects a general penalty on long-distance wh-adjunct dependencies, which is orthogonal to the bridge effect.

Experiment 2 also goes one step beyond Experiment 1 by testing clause-embedding verbs that are low in frequency. These verbs are most likely acquired much later than the verbs tested in Experiment 1, since none of the unclassified verbs in Experiment 2 appear in the Mandarin CHILDES corpus. These verbs are used in adult speech as clause-embedding verbs, but rarely in sentences with wh-dependencies. We checked the distribution of these verbs in two corpora of written text and adult speech: the Penn Chinese Treebank 9.0 (approximately 2 million words), and the BLCU Chinese Corpus (15 billion characters, approximately 8 billion words). In these two corpora, none of the unclassified verbs tested appear along with long-distance wh-dependencies. It is highly unlikely that children would ever encounter these verbs directly used as bridge verbs in the input during acquisition. Therefore, their bridge status strongly supports our hypothesis that during acquisition Mandarin speakers acquire a productive rule that all clause-embedding verbs are bridge verbs, and this rule applies to every clause-embedding verb acquired thereafter, including ones without direct evidence for their bridge status in the input.

Alternative accounts that attribute the bridge status of verbs to their lexical meaning cannot capture the results of Experiment 2. Recall that the English counterparts of the verbs tested in Experiment 2 are non-bridge verbs based on the classification by Richter & Chaves (Reference Richter and Chaves2020) and a post hoc analysis of Huang et al. (Reference Huang, Almeida and Sprouse2025). If the bridge status of a verb is determined solely by its lexical meaning (e.g. factors such as factivity), we would expect the Mandarin counterparts of non-bridge verbs in English to also be non-bridge verbs in Mandarin. Experiment 2 shows that the opposite is true.

6.1. Methods

6.2. Results

Like in Experiments 1 and 2, all ratings on the sliding scale were transformed to a numeric value between 0 and 1, with 0 representing the completely unacceptable end of the scale, and 1 representing the completely acceptable end. Figure 6 shows the average acceptability ratings for sentences containing the three canonical bridge verbs. Figure 7 shows the average acceptability ratings for sentences with each unclassified verb, compared to the average ratings for the bridge verb sentences.

Figure 6.

Acceptability ratings for the bridge verb sentences in Experiment 3.

Figure 6. Long description

A multi-panel figure with three line graphs arranged horizontally. Each graph shares a common Y-axis labeled Mean acceptability rating ranging from 0.00 to 1.00 and an X-axis labeled Condition with two categories: declarative and long.

* The first panel on the left is titled shuo say. The declarative condition has a mean rating of approximately 0.75 with error bars extending from 0.70 to 0.80. The long condition shows a decrease to a mean of approximately 0.42 with error bars from 0.38 to 0.48.

* The middle panel is titled cai guess. The declarative condition has a mean rating of approximately 0.55 with error bars from 0.50 to 0.60. The long condition shows a decrease to a mean of approximately 0.35 with error bars from 0.32 to 0.40.

* The third panel on the right is titled renwei think. The declarative condition has a mean rating of approximately 0.68 with error bars from 0.62 to 0.72. The long condition shows a decrease to a mean of approximately 0.35 with error bars from 0.30 to 0.40.

In all three panels, a solid black line connects the two data points, showing a consistent downward trend from the declarative condition to the long condition.

Figure 7.

Acceptability ratings for the unclassified verb sentences compared against the bridge verb sentences in Experiment 3.

Figure 7. Long description

A multi-panel figure containing 11 line graphs arranged in a 3 by 4 grid with the final slot empty. Each graph has a Y axis labeled Mean acceptability rating from 0.00 to 1.00 and an X axis labeled Condition with two points: declarative and long. Two lines are plotted in each graph: an orange line for bridge and a teal line for unknown.

Row 1 from left to right:

* huaiyi doubt: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.55 and drops to 0.35.

* jiancheng maintain: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.60 and drops to 0.30.

* fouren deny: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.58 and drops to 0.28.

* baoyuan complain: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.62 and drops to 0.40.

Row 2 from left to right:

* chengren concede: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.58 and drops to 0.32.

* jieshou accept: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.45 and drops to 0.30.

* baozheng assure: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.35 and drops to 0.22.

* toulu disclose: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.55 and drops to 0.40.

Row 3 from left to right:

* zhengshi verify: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.52 and drops to 0.30.

* chongshen reiterate: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.38 and drops to 0.32.

* rentong agree: Bridge starts at 0.65 and drops to 0.38. Unknown starts at 0.52 and drops to 0.32.

In all graphs, the orange bridge line remains higher than the teal unknown line, and both show a downward trend from the declarative condition to the long condition.

First, we fitted a linear mixed effect regression model predicting the acceptability ratings of the bridge verb sentences with the sum-coded fixed effect of dependency type (declarative vs. long), and the by-participant and by-item random intercepts and slopes for the fixed effect. There is a significant main effect of dependency type (β = 0.28, SE = 0.020, t = 14.12, p < 0.001) where the long dependency condition was rated lower than the declarative condition. This suggests that even for the canonical bridge verbs, extracting wh-adjuncts from their complements leads to acceptability degradations.

Then, we move on to examine whether the unclassified verbs behave like bridge verbs or not. For each unclassified verb, we pooled all the sentence ratings for that verb together with the ratings for the bridge verb sentences, and fitted a linear mixed-effects regression model predicting acceptability ratings with the fixed effects of verb type (bridge vs. unclassified), dependency type (declarative vs. long), and their interaction. Also included were the maximal by-participant and by-item random-effect structures allowing convergence. The regression model estimates are shown in Table 9, with significant effects shaded gray.

Table 9.

Estimates for LMER models predicting the acceptability of Exp.3 sentences containing the bridge verbs and each unclassified verb with sum-coded fixed effects of dependency type (declarative vs. long), verb type (bridge vs. unclassified), and their interaction, as well as the maximal by-participant and by-item random effect structures allowing convergence. Shaded boxes represent statistically significant effects

Table 9. Long description

The table presents estimates for L M E R models predicting acceptability across three main categories, each with sub-columns for beta, S E, t, and p values.

* huaiyi (doubt): Dependency type beta 0.12, p less than 0.001; Verb type beta 0.039, p less than 0.001; Interaction beta 0.017, p 0.13.

* jiancheng (maintain): Dependency type beta 0.14, p less than 0.001; Verb type beta 0.031, p less than 0.01; Interaction beta negative 0.00043, p 0.96.

* fouren (deny): Dependency type beta 0.15, p less than 0.001; Verb type beta 0.039, p less than 0.001; Interaction beta negative 0.0090, p 0.33.

* baoyuan (complain): Dependency type beta 0.12, p less than 0.001; Verb type beta 0.015, p 0.20; Interaction beta 0.014, p 0.16.

* chengren (concede): Dependency type beta 0.13, p less than 0.001; Verb type beta 0.029, p less than 0.01; Interaction beta 0.0061, p 0.55.

* jieshou (accept): Dependency type beta 0.11, p less than 0.001; Verb type beta 0.081, p less than 0.001; Interaction beta 0.033, p less than 0.001.

* baozheng (assure): Dependency type beta 0.097, p less than 0.001; Verb type beta 0.012, p less than 0.001; Interaction beta 0.042, p less than 0.001.

* toulu (disclose): Dependency type beta 0.11, p less than 0.001; Verb type beta 0.025, p less than 0.05; Interaction beta 0.030, p less than 0.001.

* zhengshi (verify): Dependency type beta 0.13, p less than 0.001; Verb type beta 0.052, p less than 0.001; Interaction beta 0.012, p 0.21.

* chongshen (reiterate): Dependency type beta 0.081, p less than 0.001; Verb type beta 0.078, p less than 0.001; Interaction beta 0.058, p less than 0.001.

* rentong (agree): Dependency type beta 0.12, p less than 0.001; Verb type beta 0.042, p less than 0.001; Interaction beta 0.023, p less than 0.05.

There are five verbs that showed significant interaction effects between dependency length and verb type: jieshou “accept,” baozheng “assure,” toulu “disclose,” chongshen “reiterate,” and rentong “agree.” The significant interaction effects were all in the direction such that the unclassified verbs induced a smaller extraction penalty than the canonical bridge verbs, suggesting that the unclassified verbs are also bridge verbs. For all other verbs tested, there is no significant interaction between dependency length and verb type. This suggests that there is no evidence for any of the tested verbs being non-bridge verbs.

To further confirm the null interaction effects reported in Table 9, we conducted a Bayes factor analysis using the BayesFactor package in R (Morey et al. Reference Morey, Rouder, Jamil and Morey2015). We estimated the Bayes factors comparing the regression models reported in Table 9 with ones that are otherwise identical but lack the interaction term, using three different prior width settings (medium, wide, and ultra-wide). The Bayes factor estimates are shown in Table 10.

Table 10.

Bayes factors for the Dependency Length * Verb Type interaction terms of the models reported in Table 9, estimated using the BayesFactor package in R (Morey et al. Reference Morey, Rouder, Jamil and Morey2015)

Table 10. Long description

The table consists of four columns and seven rows. The first column lists the Verb Type, while the remaining three columns are grouped under the heading Prior width, categorized as Medium, Wide, and Ultra-wide.

* Row 1: huaiyi (doubt) has values of 0.43 for Medium, 0.31 for Wide, and 0.23 for Ultra-wide.

* Row 2: jiancheng (maintain) has values of 0.096 for Medium, 0.074 for Wide, and 0.054 for Ultra-wide.

* Row 3: fouren (deny) has values of 0.13 for Medium, 0.095 for Wide, and 0.070 for Ultra-wide.

* Row 4: baoyuan (complain) has values of 0.18 for Medium, 0.12 for Wide, and 0.088 for Ultra-wide.

* Row 5: chengren (concede) has values of 0.13 for Medium, 0.083 for Wide, and 0.061 for Ultra-wide.

* Row 6: zhengshi (verify) has values of 0.23 for Medium, 0.16 for Wide, and 0.11 for Ultra-wide.

Following previous conventions, we take BF < 0.3 as evidence for the null hypothesis (Rouder et al. Reference Rouder, Speckman, Sun, Morey and Iverson2009). All Bayes factors calculated are below 0.3, except for one: the verb huaiyi “doubt” under medium and wide prior width settings. But the interaction effect under question is in fact numerically in the opposite direction of a bridge effect: the length penalty for huaiyi is smaller than the length penalty for the three canonical bridge verbs. Therefore, the Bayes factor analysis provides further support for the lack of a bridge/non-bridge distinction among the verbs tested in Experiment 3.

6.3. Discussion

Experiment 3 replicates the findings of Experiment 2 while controlling for the confound resulting from the variable attachment compatibility between the clause-embedding verbs and the wh-adjunct weishenme . The unclassified verbs tested all induced extraction penalties similar to or smaller than those induced by the canonical bridge verbs, and thus should also be categorized as bridge verbs. This finding supports our hypothesis that there is no bridge/non-bridge distinction in Mandarin.

7.1. Implications for theories of bridge effect

Our findings have important implications for the theory of bridge effects. Recall our earlier discussion of the various accounts of the bridge effect. Pragmatic accounts attribute the bridge/non-bridge distinction to the lexical meaning and the discourse functions of the clause-embedding verbs (Erteschik-Shir Reference Erteschik-Shir1973, Reference Erteschik-Shir2007; Ambridge & Goldberg Reference Ambridge and Goldberg2008; Lu et al. Reference Lu, Pan and Degen2025). For example, factive verbs (e.g. regret, discover) encode the speakers’ commitment to the truth of their complement clauses (i.e. their complements are presupposed) as part of their lexical entries (Kiparsky & Kiparsky Reference Kiparsky, Kiparsky, Bierwisch and Heidolph1970). As a result, it is pragmatically odd and hence unacceptable to form a wh-question seeking information about something embedded inside the complement of factive verbs. Our findings challenge these pragmatic accounts: if lexical properties such as factivity determined the bridge status of clause-embedding verbs, we would expect a very limited degree of crosslinguistic variation in the bridge/non-bridge distinction. Factive verbs like regret and discover, regardless of which language they are in, should encode factivity. However, we observed that in Mandarin, all clause-embedding verbs (including ones whose English counterparts are non-bridge verbs) are in fact bridge verbs, contrary to the prediction of the pragmatic accounts. Notably, among the verbs tested in the current study, jide “remember,” xihuan “like,” toulu “disclose” behave like factive verbs: when they are used in sentences to take CP complements, the embedded content in the complements would be interpreted as presupposed.Footnote ¹² This is shown in examples (15)–(17): native speakers interpret the embedded proposition “Wangwu hit Lisi” as presupposed in all six sentences. Importantly, the meaning projects over sentential negation in (15b), (16b), and (17b), a signature of presupposition. Despite the fact that their complements are interpreted as presupposed, jide , xihuan and toulu behaved as bridge verbs in our experiments,Footnote ¹³ and were attested as bridges in our corpus study.

Our findings also show that the ECP-based accounts of bridge effects (Tsai Reference Tsai1994; Kayne Reference Kayne1981; Cinque Reference Cinque1990; Kiparsky & Kiparsky Reference Kiparsky, Kiparsky, Bierwisch and Heidolph1970; Rooryck Reference Rooryck1992; Adams Reference Adams1985; Rizzi Reference Rizzi1990) do not apply to Mandarin. These accounts analyze the embedded CPs introduced by non-bridge verbs as syntactically distinct from the complement CPs of bridge verbs, by virtue of being adjuncts or adnominals, or bearing nominal features that regular CP complements to V lack. Despite their differences, these accounts all attribute the islandhood of non-bridge verb complements to the ECP: any wh-adjunct traces at the edge of these special CPs would not be properly governed. As a result, they all make the same prediction that the bridge/non-bridge distinction should only hold for wh-adjuncts but not wh-arguments. Whether or not this argument-adjunct asymmetry holds true in other languages aside, we did not find such an asymmetry in Mandarin. In Experiments 1 and 2, we showed that wh-adjunct extractions from clausal complements are rated lower than wh-argument extractions, but the contrast is driven by a general penalty on long-distance wh-adjunct dependencies which applies even to the canonical bridge verbs and is thus orthogonal to the bridge effect.

Notably, our results do not constitute a direct challenge to the ECP itself. The ECP could still apply in general, but the bridge status of verbs is not derived from the adjunct/complement status of the embedded clauses they introduce, and therefore the ECP does not apply to restrict extractions from embedded CPs.

Furthermore, although there is no argument-adjunct asymmetry of the bridge effect in Mandarin, there could still be such an asymmetry in other languages. Therefore, it is possible that the ECP-based accounts of bridge effects still apply to such languages where there is an argument-adjunct asymmetry. Note, however, that our learning-based account of the bridge effect can capture any asymmetries between types of wh-elements, based on their distributions in the input data. See Legate & Yang Reference Legate and Yang2025 for related discussion compatible with the current approach.

7.2. Implications for theories of language acquisition

The study supports a learning-theoretical treatment of bridge effects, which is empirical and language specific. The bridge/non-bridge status of clause-embedding verbs in a speaker’s grammar is determined by the type of input the speaker is exposed to and the generalizations, if any, they draw from the input. The input forms a relatively small vocabulary during the period of child language acquisition; the resulting knowledge is likely stable. For example, the CP-embedding verbs in Experiment 2 are quite rare and are only found in printed materials. Even though they are unattested as bridge verbs, subjects treat them as bridge verbs, just like the high-frequency bridge verbs attested in a modest child-directed corpus – exemplifying the productive extension of knowledge (Section 3.2). By contrast, their counterparts in English are judged as non-bridge verbs (Huang et al. Reference Huang, Almeida and Sprouse2025), since the set of bridge verbs is lexicalized and does not generalize, which is also learned during the period of language acquisition (Section 3.1).

It is important to stress that the learning-theoretic account requires positive evidence in the input data. As such, an argument-adjunct asymmetry in the bridge effect is not inherent: any wh-element, including wh-adjuncts, could be immune to the bridge effect as long as the learner witnesses enough positive evidence for a wh-element crossing (overtly or covertly) clause-embedding verbs to posit a productive rule that all clause-embedding verbs are transparent to that particular wh-element. In principle there could be a language without a bridge/non-bridge distinction among the clause-embedding verbs, or an argument-adjunct asymmetry in extraction penalty from clausal complements, a possibility not predicted by any other accounts discussed above. In this study, we show that Mandarin is such a language.

The contrast between Mandarin and English also highlights the importance of type frequency in the acquisition of the bridge effect. The current account assumes that the learners track the proportion of clause-embedding verbs (i.e. types) that are explicitly used as bridge verbs in the input as opposed to the token frequency. This contrasts with probabilistic approaches to movement that learn by calibration of token frequencies (Reali & Christiansen Reference Reali and Christiansen2005; Perfors et al. Reference Perfors, Tenenbaum and Regier2011; Pearl & Sprouse Reference Pearl and Sprouse2013). For example, Pearl & Sprouse (Reference Pearl and Sprouse2013) suggests that the ungrammaticality of syntactic island violations results from the low probabilities of local dependencies defined over trigrams of successive projections. Because language acquisition consumes a finite amount of data, it is essential for the Pearl & Sprouse (Reference Pearl and Sprouse2013) model to implement smoothing: a small amount of probability mass must be reserved for all trigrams, which will increase for the attested and decrease for unattested. In effect, the absence of evidence constitutes evidence of absence, and it becomes stronger when the sample size gets larger. The original study did not deal with lexical effects such as bridge phenomena, but a subsequent study on bridge verbs (Dickson et al. Reference Dickson, Pearl, Futrell, Ettinger, Hunter and Prickett2022) follows the same strategy: all CP-embedding verbs are asserted as bridge verbs with a baseline frequency of 0.5 in the corpus, which are then adjusted according to their empirical frequencies in the input data.Footnote ¹⁴ This approach may yield appropriate results for a language such as English: Only those attested as bridge verbs will steadily increase their probabilities. But baking in the assumption of lexical learning is effectively telling the child that they are acquiring a language like English, and runs into difficulties with a language like Mandarin, where even low-frequency verbs never attested in long-distance dependencies are treated as bridge verbs (Experiments 2 and 3). Lexical learning and generalization need to be a conclusion that the child learner discovers about their input language.

7.3. The origins of bridge verbs

Our distributional learning treatment of bridge verbs is inherently empirical. It detects their distributional regularity, or the lack thereof, in the input data but has nothing direct to say on the origin of their drastically different profiles between English and Mandarin, and indeed, across languages more generally. Here we enter some speculative grounds but our reasoning is still rooted in learnability considerations advocated throughout.

As discussed in Section 1 in the context of English, and then amplified across the three experiments in Mandarin, it is clear that the semantic properties of CP-embedding matrix verbs cannot provide a causal explanation for bridge effects. Nevertheless, semantic factors may still be reflected as tendencies across languages, at least for those that show the bridge vs. non-bridge distinction. We suggest that the crosslinguistic tendencies arise through the factors affecting language use, which will in turn have consequences on the grammar acquired and then transmitted to later generations in an iterative process. In the case of bridge verbs, such factors notably include the discourse functions of clause-embedding verbs, verb frequencies, and their interactions that were pointed out in previous studies.

If the complement of a verb is likely to be presupposed, the embedded contents are naturally less likely to be questioned since they are already in the common ground (Kroch Reference Kroch1989; Goldberg Reference Goldberg, Sprouse and Hornstein2013; Oshima Reference Oshima2006). Therefore, clause-embedding verbs that allow for presupposition projection (i.e. the “presupposition holes”: Karttunen Reference Karttunen1973) have the tendency to be non-bridge verbs crosslinguistically. On our approach, however, these pragmatic properties are not grammatically determinative, but simply affect the likelihood of such a verb being used with a long-distance dependency. Such discourse-pragmatic tendencies are not absolute: given the right circumstances and context, some adult speaker may well use a presupposition-projecting verb in a long-distance wh-question, which has the potential of being internalized as positive evidence by the child language learner.

Verb frequency, a property of language use, is also likely to play a major role in shaping the bridge verbs within and across languages. High verb frequency provides more opportunities for the verb to occur with a long-distance dependency in the learner’s input. Their high frequencies will also make them more likely to be acquired by children and stably transmitted across generations. By contrast, verbs that are much lower in frequency rarely appear in young children’s input at all, let alone appear with long-distance dependencies spanning them. As a result, they are more likely to be non-bridge verbs crosslinguistically. It is thus not surprising that for languages like English, the bridge verbs tend to be high in frequency (Liu et al. Reference Liu, Ryskin, Futrell and Gibson2022) even though the frequency effects are by definition stochastic and there are plenty of high-frequency CP-embedding verbs that are not bridge verbs (e.g. know, see, remember, forget) as discussed in Section 1.

Tendencies are, of course, just tendencies. The item-by-item process by which a verb becomes a bridge or falls into disuse cannot account for the wholesale differences between Mandarin and English. In particular, recall that the ratio of bridge verbs in a language such as English is very low, even among the most frequent CP-embedding verbs that form the basis of language acquisition (Section 3.1): the profile of language use would have to change radically to turn English into a Mandarin-like language. An excavation into the history of these languages offers an interesting clue as to the source of the difference between them, although a full investigation must be left for future research.

So far as we know, the history of embedded clauses in English has been a matter of continuity. There have been occasional claims in prominent reference works (e.g. Mitchell Reference Mitchell1985) that clausal embedding in English evolved over time, “(a)s the loose association of clauses (parataxis) gives way to more precise indications of logical relationship and subordination (hypotaxis)” (Baugh & Cable Reference Baugh and Cable2013, 238). However, the quantitative analysis of historical corpora finds no evidence to support such a claim as the ratio of clause embedding has remained largely stable from the earliest attested period of Old English onward (Walkden Reference Walkden, Porck and Luisella2024).Footnote ¹⁵ Indeed, long-distance wh-movement can be found in Old English (Allen Reference Allen1980). It is likely that English has always maintained a lexicalized bridge vs. non-bridge distinction, which is also implicated in various other syntactic processes across the Germanic family (e.g., Vikner Reference Vikner1995; Broekhuis & Corver Reference Broekhuis and Corver2016).

The diachrony of clausal embedding in Chinese is, by contrast, very different, which we believe may hold the key to the uniform availability of bridge verbs. Classical Chinese can be divided into the Archaic period and the Middle period demarcated by the Han Dynasty (second century BCE). It is well documented (e.g. Pulleyblank Reference Pulleyblank1995) that CP-embedding was essentially absent in Archaic Chinese: the language employed multiple clauses (parataxis) or nominalized clauses with clause-internal markers such as zhi (18a) and qi (18b):

These markers began to disappear in Middle Chinese. The contrast can be seen in (19), which presents two very similar sentences in Archaic Chinese (19a) and Early Middle Chinese (19b).

In the absence of the nominalizer, structures that were previously analyzed as nominalized would instead be analyzed as CP-embedding. If CP-embedding indeed emerged in Middle Chinese, it must have, as an incipient change, appeared with relatively few matrix verbs. Generalization is very easy for small N’s under the Tolerance Principle. Plausibly, a productive generalization that all CP-embedding verbs are bridge verbs was formed immediately and has been stably transmitted since: a novel CP-embedding verb, once incorporated into the language, was immediately treated as a bridge verb very much as we have demonstrated in Experiments 2 and 3.