2.1.1 Previous analyses on the derivation of restitutive ‘again’

Restitutive ‘again’ is regarded as a secondary interpretation, separate from the repetitive reading, that is found (primarily) with accomplishment and achievement predicates denoting a change of state. In the literature there are two major approaches to deriving it: structural and lexical. We begin with the structural approach, the dominant view in the literature.² The basic idea is that in languages like English and German, a single ‘again’ adjoins to different structural positions, leading to distinct readings (von Stechow 1995; 1996; Beck & Johnson 2004, among others). Specifically, ‘again’ denotes repetition, and has (roughly) the semantics in (5): it takes a predicate of events and an event, and asserts that the predicate is true of the event. Crucially, it triggers a presupposition that there was a preceding event for which the same predicate is also true.³

The repetitive/restitutive readings arise from the different scopes of ‘again’ in syntax. Consider the English goal-PP in (6). Following Beck & Snyder (2001); Beck (2005), we treat the PP as a small clause with a PRO subject. If again scopes over the entire proposition, representing the whole change-of-state event (both the process and the result state), a repetitive interpretation is obtained (see (6b)). If again scopes over the result state alone (e.g., by attaching to the small clause representing the result state), a restitutive reading is obtained (see (6c)).⁴

This analysis is supported by evidence from word order: when English again is preverbal, there is only a repetitive reading (7). This is easily captured under a structural analysis, because again cannot scope over the result state alone if it is preverbal. We will revisit the effect of word order, however, when we discuss Mandarin you.

2.1.2 Restitutive ‘again’ across languages

While ‘again’ modifying a change-of-state predicate sometimes exhibits a repetitive/restitutive ambiguity, availability of the restitutive reading varies both cross-linguistically and language internally. Beck (2005) investigated its availability with goal-PP constructions (e.g., ‘walk to the village’) and with lexical accomplishments (e.g., ‘open’) in 18 languages. She found that availability of a restitutive reading in one construction does not entail its availability in the other (see Table 1).

Moreover, the study unveiled systematic cross-linguistic variation with goal-PPs: a language allows a restitutive reading of ‘again’ with goal-PPs only if the language has (productive) adjectival resultative constructions, such as ‘hammer the metal flat’. Conversely, restitutive ‘again’ with lexical accomplishments is unrelated to availability of resultatives. In some languages there is also variability in judgments for restitutive ‘again’ across different speakers and different lexical-accomplishments verbs: Not only can there be substantial differences in judgment between speakers, but a single speaker may accept a restitutive reading with one verb and reject it with another.

Below we summarize Beck’s account of these patterns, which is couched in a structural analysis.⁵

For the correlation between restititutive ‘again’ with goal-PPs and resultative constructions, she suggested, with Beck & Snyder (2001), that the formation of both resultative and goal-PP constructions requires a special semantic composition rule, termed Principle (R) by von Stechow (1995) and reformulated as Generalized Modification by Snyder (2012). Setting aside many details, this semantic composition rule involves combining a verb with a result phrase, and obtaining an accomplishment event. To illustrate, consider the resultative wipe the table clean. The rule allows the combination of clean as a secondary predicate, transforming an activity into an accomplishment event with “wiping” as the development and “clean” as the culmination. Similarly, the rule permits a manner-of-motion verb (e.g., walk) to combine with a locative PP (e.g., to the village) and form a goal-PP, whose interpretation unfolds in a manner akin to a resultative: walk to the village denotes an accomplishment event with “walking” as its development and “arriving at the village” as its culmination. Consequently, when modified by again, the PP (with a PRO subject), functioning as a result phrase, allows attachment of again, yielding a restitutive reading as in (6c).

Crucially, availability of this semantic composition rule varies across languages. This is called the (R) parameter in Beck (2005) and the Compounding Parameter (TCP) in Snyder (2012). In languages like English, where it is available, a manner-of-motion verb denoting an activity can combine with a PP to form a complex predicate denoting an accomplishment; the PP, serving as a result phrase, can be modified by ‘again’ to yield a restitutive reading. In languages like Spanish and French, however, where the rule is unavailable, goal-PPs are restricted. As shown in (8), a pure manner-of-motion verb (such as ‘float’), denoting an activity with no particular path, cannot combine with a spatial PP to yield a directed-motion event. Spanish (9) and French (10), where a manner-of-motion verb does combine with a directional PP, are said to be structurally different from their English counterparts. Thus Beck (2005) proposes that the PP in (9) is simply an event modifier (i.e., an adjunct without a PRO). Xu & Snyder (2017) tentatively suggest that the French manner-of-motion verb marché in (10) has become semantically “bleached”, allowing it to select a goal as one of its arguments (similar to English go to the village). Importantly, because the PPs are non-propositional and hence unsuitable as attachment sites for ‘again’, there is no restitutive reading.

Unlike goal-PPs, lexical accomplishments do not depend on the special composition rule for restitutive ‘again’. Hence there is no correlation with resultatives. Instead, the restitutive reading is tied to the decomposition property of the verb itself. For example, the transitive verb open in English can be decomposed into the adjective open and a phonologically empty verbal element denoting cause become, as in (11c). The small clause in (11c) represents the result state of Sally opening the door, namely the state of the door being open. Adjoining again to this constituent yields a restitutive reading. Verbs that cannot be decomposed in syntax disallow the restitutive reading. Additionally, Beck (2005) proposes that the decomposition property may vary across speakers and across verbs, yielding inconsistent judgments for lexical-accomplishment verbs.

2.2.1 Various uses of Mandarin you

As shown in Section 1, Mandarin you is polysemous. According to Lü (1999), it has three primary uses: (i) expressing successive actions, which includes its repetitive use (e.g., ta you lai-le ‘he came again’, with you connecting two identical events) and temporal-continuation use (e.g., (4a), with you connecting two different events); (ii) indicating the addition/accumulation of actions, states, or situations (e.g., (4b)), and (iii) conveying certain speaker attitudes (e.g., (4c)).⁶

Due to similarities between some of the uses, scholars have attempted to simplify them. For instance, Lü (1999) combined the meanings of repetition and temporal continuation; Shao & Rao (1985); Biq (1988); Shi (1990) suggested that these uses can be reduced to a core additive/accumulative meaning. To our knowledge, it remains unclear how many distinct yous exist in Mandarin, and we will not try to answer the question here. Instead, we focus on the restitutive reading, which is less often discussed.

According to the cross-linguistic survey in Beck (2005), Mandarin goal-PP constructions modified by you allow the restitutive interpretation, as in (3). However, judgments regarding lexical-accomplishment verbs are somewhat mixed: while several speakers accepted the restitutive reading with hui ‘return’, they rejected it with kai ‘open’ (see Beck 2005: p.30 and p.48, ex(38)). However, this pattern is based on data from three speakers. Other literature, such as Xu (2012) and Liu (to appear), used the disyllabic resultative verb compound da-kai ‘hit-open’ to illustrate the availability of restitutive readings in Mandarin. To further investigate, we consulted with 17 native speakers to see if the patterns reported above hold for a larger sample size. All 17 speakers accepted the restitutive reading with hui ‘return’, while 12 (70.59%) accepted it with kai ‘open’. Fourteen speakers (82.35%) accepted it with da-kai ‘open’, and nine (52.94%) found the restitutive reading more acceptable with da-kai than kai in the same context.⁷ These results, consistent with Beck’s, suggest the restitutive reading is widely available in Mandarin, albeit with some degree of variation across speakers and lexical items.

2.2.2 A previous analysis of restitutive you

As noted, structural accounts of English and German ‘again’ (e.g., von Stechow 1996; Beck & Johnson 2004) attribute different readings to the different attachment sites available to ‘again’ in predicates that can be syntactically decomposed into a higher causing subevent and a lower result state. The restitutive reading is derived when repetition-denoting ‘again’ scopes over the lower result-state constituent, but not the higher causing event. In Mandarin, since you always precedes the predicate, this analysis predicts it should only have a repetitive reading, but the prediction is not borne out (see (3), repeated as (12a)). Yet, some researchers propose that a structural analysis can be maintained (Xu 2012; 2016; Liu 2021; to appear): adopting the inverted Y model of grammar from Chomsky & Lasnik (1977), they propose that repetition-denoting you, having the semantics in (5), can be generated low, move to a pre-verbal surface position, and later reconstruct.

Consider (12a). Following the view of Beck (2005) and Snyder (2012) that Mandarin, like English, provides the special semantic composition rule discussed in Section 2.1.2, we assume the manner verb ‘walk’ combines with a small-clause PP.⁸ This means the PP is a possible adjunction site for ‘again’. Thus (12a) allows both repetitive and restitutive readings (12b)–(12c).

Unlike English again, you moves before the verb and later reconstructs. What motivates this movement? According to Liu (2021), you has an unvalued aspect feature that needs to be valued by the closest Asp probe through specifier-head agreement. To fulfill this requirement, it moves to the specifier position of the closest AspP (which is between vP and TP).

The movement-plus-reconstruction operation allows you to be interpreted as modifying a sub-constituent of the predicate. To our knowledge, this is the only proposal in the literature for the derivation of restitutive you. For illustrative purposes, we adopt this structural analysis. However, one should note that our proposal regarding how Mandarin-learning children acquire the restitutive reading with goal-PPs does not hinge on specific operations such as movement and reconstruction. Other ways of allowing you to semantically modify a sub-constituent of VP might include treating you as a focus-sensitive operator and deriving its restitutive reading through focus association.⁹ (While this strikes us as an interesting possibility, we will not pursue it further here.)

2.3.1 Prior research: Acquisition of restitutive ‘again’ across languages

Prior research is limited and focuses on English or German. Studies using story-telling or elicited-production tasks have shown that English- and German-learning preschoolers correctly produce ‘again’ with change-of-state predicates to express either the restitution of a state or the reversal of an action (Bamberg 1994; Clark et al. 1995). Xu & Snyder’s (2017) study used a Truth-Value Judgment task (TVJT) to show that English-learning preschoolers correctly allow a restitutive interpretation of again with goal-PPs. Using corpus analyses, they also showed that parental uses are infrequent and almost always ambiguous. To explain children’s success they adopt a structural approach, and propose that once children grasp both the repetitive meaning of again and the syntactic structure of English goal-PPs, the availability of restitutive again follows deductively. Moreover, the syntactic structure of English goal-PPs, they suggest, is predictable from the occurrence in English of resultatives and related constructions.

This proposal extends readily to other languages, if it is combined with a subset strategy. For example, children acquiring French will initially assume (correctly) that there is no restitutive ‘again’ with goal-PPs, and they will persist in this belief because they will never receive input (e.g., a resultative construction) that would contradict it.

2.3.2 Open questions for restitutive you

Liu (2009; 2015) and Liu et al. (2011) have investigated children’s knowledge of repetition and temporal-continuation you.¹⁰ Yet, we are unaware of any research on restitutive you. Can young children discern that you, despite its preverbal position, allows a restitutive reading with change-of-state predicates like goal-PPs? The next section addresses this question experimentally. To facilitate comparison with Xu & Snyder’s (2017) findings for English, testing of Mandarin preschoolers will involve children in roughly the same age range, and will use very similar methods and materials.

3.1.1 Participants

Participants included 65 Mandarin-learning children from age 3;05 to 5;11 (12 3-year-olds, 38 4-year-olds and 15 5-year-olds, mean age: 4;07, SD = 0.65 years) in Beijing, China, who were brought to the lab by their parents. In addition, 32 native-speaker adults (mean age: 26;09, range: 19;0–45;11, SD = 8.19 years) participated as controls; they were tested online (via Tencent Meeting) due to COVID19.

3.1.2 Methodology

Our methodology was based on the TVJT (see Crain & Thornton 1998): Participants watched a series of stories alongside a puppet who sometimes did not pay attention. An experimenter narrated the stories using cartoon pictures presented in PowerPoint on a laptop. At the end of each story, a video of a puppet named Parrot appeared on the screen, and Parrot uttered a sentence describing the story. The participant was asked whether Parrot ‘got it right’. If so, the child rewarded him with a smiley stamp. If Parrot got it wrong, the child gave him a banana stamp (since banana is Parrot’s least favorite food). If a child participant rejected the test sentence, he/she was asked to explain why. While child participants were tested individually, adults were tested in groups and were simply asked to mark whether they accepted or rejected Parrot’s utterance. To avoid overanalysis of the test sentences, we did not ask them to explain why Parrot “got it wrong”.

English translations of sample repetitive and restitutive items are provided in (13) and (14), respectively.

Note that in each story there were two characters. Both satisfied the assertion, but only one satisfied you’s presupposition. In (13), the lizard, born under the rock, satisfied the presupposition of restitutive you (i.e., the lizard had been under the rock before). The snail, born near the river, did not satisfy this presupposition. In (14), the dinosaur satisfied the presupposition of repetitive you by having crawled under the tree before. The crocodile did not, as it had not crawled under the tree previously. Each story had two possible test sentences: one match (see (13a) and (14a)) and one mismatch (see (13b) and (14b)). Each participant heard only one sentence per story.

As will be discussed in Section 4.4, prosody influences the interpretation of ‘again’. Stressing you tends to block the restitutive reading, yielding only the repetitive reading, while stressing the predicate favors the restitutive interpretation in an out-of-the-blue context. In our experiment, stress was placed on you in the repetitive ‘again’-sentences (e.g., (14a) and (14b)), and on the verb in the restitutive ‘again’-sentences (e.g., (13a) and (13b)). This prosodic manipulation was implemented to make the test sentences sound natural under the intended readings, allowing us to assess children’s understanding to the fullest extent possible.

3.1.3 Design

To investigate children’s comprehension of repetitive and restitutive you, we manipulated the story context (repetitive versus restitutive) and the target response for the puppet’s utterance (match versus mismatch), creating four trial types: repetitive-match, restitutive-match, ­repetitive-mismatch, and restitutive-mismatch. Participants completed 4 trials of each type, plus 2 training items, 8 plain goal-PP items (without you), and 8 filler items, totaling 34 items.

Because the repetitive reading asymmetrically entails the restitutive reading, the mismatch items for restitutive stories can be rejected under either reading. Therefore, for data analysis, repetitive- and restitutive-mismatch items were grouped into a single condition. As summarized in Table 2, this yielded three conditions: repetitive-match (e.g., (14a)), restitutive-match (e.g., (13a)), and mismatch (e.g., (14b) and (13b)).

Both the test items (with you) and the plain goal-PP items (without you) involved a combination of a manner-of-motion verb and a directional item. The two directional items we used were jin ‘enter’ and dao ‘reach’, which roughly correspond to English in and to. Materials contained the following 8 combinations of manner-of-motion verb and jin/dao: zou-jin ‘walk into’, fei-jin ‘fly into’, tiao-jin ‘jump into’, pao-jin ‘run into’, you-dao ‘swim to’, hua-dao ‘slide to’, piao-dao ‘float to’, pa-dao ‘crawl under’.

Similar to the test items and the plain goal-PP items, stories for the fillers involved two characters: one making the puppet’s utterance true and the other false. Each story had two possible filler sentences, both of which were simple declarative sentences with transitive verbs (e.g., Xiaoyang mai-le yi-jia gangqin ‘Sheep bought a piano’). Participants heard one test sentence per filler story. Filler items served to filter out participants who were not complying with the task and balance match and mismatch items. In Xu & Snyder (2017), about 1/3 of the participants consistently accepted the ‘again’-sentences, as if ignoring again. Some Mandarin-acquiring children might do the same with you. Filler items allowed opportunities to reject the puppet’s utterances. We will elaborate on how filler items were interspersed among the ‘again’-items in Section 3.1.4.

3.1.4 Procedure

Participants first received 2 training items irrelevant to goal-PPs and you (e.g., ‘Smurf didn’t move his bed.’) to get familiarized with the task. Feedback was provided if they did not perform correctly. They then received two blocks of 16 trials each. Test sentences with you and plain goal-PP items without you in the same block involved the same combinations of manner-of-motion verb and jin/dao-NP. (The two directional items jin and dao, translated as ‘enter’ and ‘reach’, roughly correspond to English in and to).

Each block started with 4 plain goal-PP trials, followed by 12 other trials: 4 repetitive trials (e.g., (14)), 4 restitutive trials (e.g., (13)), and 4 filler trials. Each type included an equal number of match and mismatch trials. These 12 trials always began with a repetitive one, with you stressed in the puppet’s utterance. This arrangement was designed to draw participants’ attention to you as they transitioned from judging the assertion of a plain goal-PP to judging the presupposition of you. In the subsequent trials, no more than two trials of the same category or of the same target response were presented consecutively.

As mentioned earlier, participants might ignore you and accept all you-items. To address this, we adjusted the target response of filler items accordingly: if a participant gave the same type of response for two consecutive trials, the next filler item would have the opposite target response.

We created four different versions to control for the order of presentation: Two versions were identical except for the puppet’s utterance. For instance, in (13), one version used (13a) as the test sentence, and the other used (13b). To cancel out item-specific effects due to fatigue or practice, we counterbalanced the two test blocks, resulting in two additional versions. An approximately equal number of participants, both adults and children, received each of these four versions.

The experiment took about 30 minutes for adults and 45 minutes for children. To keep the child participants motivated, we designed the experiment as a game of four levels, each consisting of 8 or 9 items. As children advanced through each level, they were rewarded with an increasing number of stickers (1 for Level 1, 2 for Level 2, 3 for Level 3, and 6 for Level 4). Additionally, they were given breaks between levels to ensure their comfort.

3.2.1 Data coding

Responses from the child and adult participants were recorded offline on an answer sheet and double-checked against a video recording for accuracy. Experimental data and analysis scripts can be accessed via https://osf.io/m6epk/. Three children gave unexpected answers: They neither accepted nor rejected the puppet’s utterance in some trials. These unexpected answers included “the puppet was half right half wrong” (child #07 for one trial), and “I don’t know” (child #37 for 5 trials, child #47 for 3 trials). These were coded as wrong answers.

3.2.2 Data exclusion

Of the 65 child participants, 7 children were first excluded from data analysis for low performance (<75% accuracy) on goal-PP items (n=1) or filler items (n=6). We then excluded data from 23 children who constantly accepted all the you-sentences (acceptance rate ≥ 14/16), as if they were ignoring you. Finally, we excluded data from one child who consistently rejected test sentences (rejection rate ≥ 14/16) and gave anomalous explanations (e.g., ‘because the lizard wasn’t the only one who crawled under the rock’). The explanations suggested the child was both ignoring you and calculating an ad-hoc implicature of uniqueness. We will discuss possible reasons why some children ignored you in Section 5.2. Our current analysis focused on the remaining 34 children (5 3-year-olds, 22 4-year-olds, 7 5-year-olds, age range: 3;08–5;08; mean: 4;07). Our main objective is to address: Among the children who demonstrated sensitivity to you, how well did they comprehend restitutive you in comparison to repetitive you?

3.2.3 Group results

Adults’ and children’s acceptance rates are shown in Figure 1. As expected, adults tended to accept both repetitive- and restitutive-match items, while rejecting mismatch items. Children mirrored the adults, indicating that they understood both the repetitive and restitutive readings of you.

Figure 1

Acceptance rates of adult (N=32) and child (N=34) participants. (Error bars indicate standard error. Dots represent individual participants’ mean acceptance rates.)

Children’s justifications were as expected, although not all children were willing to provide justifications, and those who did were not always consistent across trials. These inconsistencies made it difficult to conduct quantitative analysis. As anticipated, a child could reject a mismatch item for a restitutive story based on either a repetitive interpretation (i.e., which character had performed the action before), as in (15) and (16), or a restitutive interpretation (i.e., which character had been in the location before), as in (17) and (18).

We fitted Generalized Linear Mixed Models (GLMMs) to the adult data, the child data, and the combined data using the lme4 package (Bates et al. 2015b) in R version 4.2.1 (R Core Team 2021). In all models, a participant’s response (1=accept, 0=reject) was the dependent variable. Following Barr et al. (2013), we started with maximal models including all possible random-effect components – random slopes and intercepts by Subject and Item. We then reduced the model’s complexity stepwise until it converged to a non-singular fit. We double checked the simplification of random effects using the buildmer package (Voeten 2020), which automates the process, and obtained consistent results. Following Bates et al. (2015a), we also checked the convergent models for overparameterization by comparing the goodness-of-fit of nested models with likelihood-ratio tests.

Here we focus on models based on the child and combined data.¹¹ For the children, we compared models with and without the fixed factors of (i) Age (in years as a continuous variable) and (ii) the interactions of Age with Condition. Model comparison revealed no significant improvement in fit when we included Age (likelihood-ratio test: χ²(1) = 2.238, p = .135) or the interactions of Age with Condition (likelihood-ratio test: χ²(2) = 1.904, p = .386); therefore, we report here the model with Age excluded.¹² Setting the reference-level to mismatch (Table 3), children accepted both repetitive- and restitutive-match items significantly more often than mismatch items. Furthermore, setting the reference-level to repetitive-match (Table 4), there was no significant difference between restitutive-match and repetitive-match items. These results indicate that children distinguished match from mismatch, and accepted restitutive-match items at approximately the same rate as repetitive-match.

To examine potential differences in behavior between children and adults, we analyzed the combined data. Predictors were Condition (repetitive-match, restitutive-match, mismatch), ParticipantGroup (adult, child), and their interactions. We first set the reference-level to mismatch (Table 5). Participants accepted both repetitive- and restitutive-match items significantly more often than mismatch. There was a significant effect of ParticipantGroup, and there were two significant interactions: ParticipantGroup interacted with both (i) the contrast between mismatch and repetitive-match items, and (ii) the contrast between mismatch and restitutive-match items. This suggests that both groups made a distinction between match and mismatch items, but adults distinguished them to a greater extent. Finally, we set the reference-level to repetitive-match (Table 6). There was no significant difference between participants’ acceptance of restitutive-match versus repetitive-match items. Furthermore, there were no significant interactions with ParticipantGroup. This suggests that neither group performed differently on repetitive-match versus restitutive-match items.¹³

4.1.1 Method

Samples of child-directed speech came from the two longitudinal corpora for Mandarin in Table 7 (Deng & Yip 2018; Zhang & Zhou 2009).

We first located all adult utterances containing both you and a directional item (shang ‘up’, xia ‘down’, jin ‘in’, chu ‘out’, guo ‘across’, lai ‘come’, qu ‘go’, cong ‘from’, dao ‘to’, wang ‘toward’, hui ‘return’, or qi ‘rise’). We then extracted sentences in which you modified a goal-PP, and annotated them as ‘repetitive’, ‘restitutive’, or ‘other’. Two annotators independently coded all relevant utterances, considering the preceding text and up to 50 lines of subsequent text, plus linked audio/video files if available. Disagreements were discussed by the two coders and two additional research assistants until consensus was reached. Utterances for which consensus could not be reached were coded as ambiguous. Uses that were ungrammatical, weird, fragmentary, or incomplete were excluded.

4.1.2 Results

As summarized in Table 8, there were only two parental utterances where you modified a goal-PP (details in Appendix C (§3.1)).¹⁴ One had a repetitive reading, while the other was ambiguous.

4.1.3 Summary

Out of 37,334 utterances across our samples, there were no occurrences of you modifying a goal-PP where the restitutive reading was unambiguously intended. This suggests that direct evidence is extremely rare (if available at all). Consequently, it seems doubtful that children could rely on direct evidence alone to decide whether their target language allows restitutive ‘again’ with goal-PPs.

4.3.1 Prerequisite A: repetitive you

Previous experiments (Liu 2009; 2015; Liu et al. 2011) and our own suggest that preschoolers already know repetitive you. However, the prior studies had small samples, and the high exclusion rate of our study, combined with the entailment relation between repetitive and restitutive readings, might conceivably raise doubts.¹⁵ Therefore, we first re-examine this claim using spontaneous-speech corpora. Second, we propose that children acquire the repetitive meaning of you from parental uses (regardless of predicate type),¹⁶ and we assess this proposal by examining the frequency of repetitive you in child-directed speech.

5.3.1 A Fabricius-Hansen-style lexical analysis

Contrary to the structural analysis, a lexical analysis attributes restitutive ‘again’ to a distinct denotation independent from repetitive ‘again’ (e.g., Jäger & Blutner 2003; Fabricius-Hansen 2001; Pedersen 2015; see Yu 2020: §3.4 and §3.6 for a more in-depth discussion of various lexical analyses).¹⁹ Here, we use the proposal of Fabricius-Hansen (2001) as a representative to illustrate analyses in this spirit.

Fabricius-Hansen proposes that, aside from its repetitive meaning, ‘again’ can have a “counterdirectional” meaning as shown in (26).

P_c in (26) represents a counterdirectional predicate, which characterizes the reverse of P. In plain English, restitutive ‘again’ denotes a relationship between a predicate of events and an event, asserting that the predicate is true of the event. Additionally, it presupposes the existence of a preceding counterdirectional version of the event, e′. The result state of this counterdirectional event, res_Pc(e′), is identical to the prestate of e, pre_P(e).

To see how (26) captures the restitutive interpretation, consider the English example John walked to the village again. The goal-PP predicate represents a walking event by John from an (unspecified) source to a goal (the village). Its counterdirectional predicate can be created by reversing the direction, leading to a motion event by John from the village to the source (see Patel-Grosz & Beck 2019; Iyer 2022; 2023 for more on conceptualizing a counterdirectional predicate). Thus, the sentence presupposes a preceding motion event of John from the village to the source, implying that John must have been at the village before, capturing the restitutive reading.

Given that the restitutive interpretation of ‘again’ is attested in a number of languages, we can hypothesize that a lexical analysis of this kind applies to Mandarin you. This would mean that you has a distinct counterdirectional denotation, as described in (26).

5.3.2 Accounting for the skipping phenomenon

Which analysis, structural or lexical, better explains the skipping phenomena discussed in Section 4.3.2? Consider examples like (22) and contrast them with examples like (27), noted by Liu (2021; to appear). In (22), you can be interpreted as skipping the restructuring verb, whereas in (27), it precedes a non-restructuring verb and loses its skipping ability, allowing only the matrix repetitive reading.

Adopting a structural analysis, Liu (2021; to appear) explains the contrast between (22) and (27) as follows: He proposes that you moves to the specifier position of the closest AspP to check its unvalued aspect feature (cf. Section 2.2.2). In (22), the lower-generated you must move to the AspP in the matrix clause because the restructuring verb xiang ‘want’ does not embed an AspP. In contrast, the clausal complement of the non-restructuring verb shuo ‘say’ contains an AspP that can value you’s unvalued feature, so the lower-generated you does not need to move to the matrix AspP. This means you in (27) was not base-generated inside the embedded clause, which explains the absence of embedded readings.

Under a Fabricius-Hansen-style lexical analysis, why can you be interpreted as counterdirectional in (22), as shown in (22c), but not in (27)? A reviewer suggests this contrast can be explained if we assume that counterdirectional you can reconstruct (under restructuring verbs) in the same way as repetitive you. To elaborate, (22a) is generated by repetitive you taking matrix scope, (22b) by repetitive you taking scope in the embedded clause, and (22c) by counterdirectional you taking scope in the embedded clause. This narrow scope is forced for counterdirectional you, as there is no plausible counter-directional version of the predicate ‘want to close that door’, rendering the matrix scope uninterpretable. Conversely, in (27), all narrow scope readings (for both repetitive you and counterdirectional you) are blocked by the non-restructuring predicate.

Meanwhile, another reviewer suggests that although there is no direct counterargument against a lexical analysis, from an economic perspective, if both the lexical analysis and the structural analysis require a movement and reconstruction approach to cover the entire empirical ground, particularly the skipping effects, the structural account may be argued to be more economical as it requires only one lexical entry of ‘again’.

5.3.3 Accounting for cross-linguistic variation

Beck (2005) argues that Fabricius-Hansen’s lexical analysis fails to account for the cross-linguistic variation in the availability of restitutive ‘again’ with goal-PPs, because goal-PPs typically denote change-of-state events and should be reversible across languages. However, Gehrke (2008) questions the assumption of semantic equivalence of goal-PPs across languages. Building on her argument and a refined analysis of counterdirectional ‘again’ proposed by Iyer (2022), we reconsider its potential in explaining the cross-linguistic data.

To account for the patterns of cross-linguistic and language-internal variation across different types of change-of-state predicates, a lexical analysis will need to posit that the lexical entry for restitutive ‘again’ contains selectional restrictions of some kind. Moreover, these restrictions will need to be specific enough to distinguish between different types of change-of-state predicates, such as English vs. French/Spanish goal-PPs, and French/Spanish goal-PPs vs. lexical-accomplishment verbs. We consider Iyer (2022)’s refined formulation of counterdirectional ‘again’ as a viable candidate for specifying these selectional restrictions. Iyer proposes that counterdirectional ‘again’ requires events involving scalar changes, whether spatial (as in the case of English goal-PPs, where counterdirectional ‘again’ denotes a reversed path reading) or non-spatial (as in the case of a lexical-accomplishment verb, where counterdirectional ‘again’ indicates the reversal of a change).

As discussed in Section 2.1.2, English-type goal-PPs represent accomplishment events, with the manner-of-motion verb specifying the development and the PP specifying the culmination point. These goal-PPs satisfy the selectional restrictions imposed by counterdirectional again as they denote change along a path. Conversely, Spanish/French-type goal-PPs, as argued by Beck & Snyder (2001) and Beck (2005), do not denote accomplishment events, evidenced by their inability to be modified by in-adverbials such as ‘in an hour’. This suggests that they may have a different scale structure from their English counterparts, failing to fulfill the presupposition of counterdirectional ‘again’. This aligns with arguments regarding the Spanish preposition hasta ‘until’ in goal-PPs, which imposes a temporal boundary external to the event, leading to truth conditions similar to those of a spatial goal-PP (see Aske 1989; Beck 2005; Gehrke 2008).

To further examine this hypothesis, we need to delve deeper into the semantics of goal-PPs in individual languages. Additionally, it is necessary to compare the scale structures of goal-PPs with those of other change-of-state predicates (such as lexical-accomplishment verbs) in languages with internal variation. We leave these as directions for future research.

5.3.4 Accounting for the acquisition data

From an acquisition perspective, the lexical analysis by Fabricius-Hansen suggests that children must know the following to determine the availability of counterdirectional you with goal-PPs: (A) you can have a counterdirectional interpretation; and (B) the scale structure of goal-PPs satisfies the selectional requirement of counterdirectional you.

To acquire prerequisite (A), children need to encounter instances of counterdirectional you in contexts where there exists a prior event denoting the reverse of the relevant scalar change associated with the modified predicate. An example is given in (28). Note that this constitutes only a subset of the evidence available to children for acquiring you’s ability to modify a sub-constituent. This is because cases that do not satisfy the counterdirectional presupposition, such as the skipping and high-restitutive examples, would not be included in this subset.

This leaves us with 9 instances of low restitutive among 166 you-utterances (5.4%) in Tong’s child-directed speech and 4 instances of low restitutive among 126 you-utterances (3.2%) in Xuexue’s child-directed speech.

Regarding prerequisite (B), our experiment indicates that preschoolers have already grasped the semantics of goal-PPs, suggesting they know the associated scale structure. Regarding how children acquire this prerequisite, we can consider the tentative proposal on how they acquire the syntax of goal-PPs (cf. Section 4.3.3). Specifically, knowing that Mandarin allows the combination of PPs as secondary predication enables children to infer that Mandarin goal-PPs represent accomplishment events involving scalar changes along a path, which satisfies the selectional requirement of counterdirectional you.

The discussion indicates that a lexical analysis can also explain how Mandarin-speaking children discern the availability of counterdirectional you with goal-PPs. However, the structural approach allows for more general evidence and potential sources for children to rely on, giving it an advantage, especially in situations where the relevant input is of low frequency. Further empirical findings regarding children’s knowledge of other types of change-of-state predicates (e.g., lexical-accomplishment verbs) and their comprehension of restitutive you with these predicates would help to assess which approach offers a better explanation.