Syntactic and Discourse Features in Chinese Heritage Grammars: A Case of Acquiring Features in the Chinese Sentence-Final Particle ba

: This study investigates how syntactic and discourse features of Chinese sentence-ﬁnal particles (the question particle ba and the suggestion particle ba ) are reconﬁgured in Chinese heritage grammars. It has been argued that features of the Chinese particles ba are present in English but are conﬁgured di ﬀ erently. An acceptability judgment task, a discourse completion task, and a translation task were adopted in this study. In total, 35 Chinese heritage speakers and 18 Chinese native speakers took part in this study. The results show that none of the heritage speaker groups had any problem in conﬁguring the discourse feature of the suggestion particle ba and the syntactic features of the question particle ba . However, none of them could successfully reconﬁgure the discourse feature of the question particle ba . It seems that the e ﬀ ects of dominant language transfer, reduced Chinese input, and limited processing resources play roles in the reconﬁguration of discourse features in heritage grammars. As compared to previous L2 studies regarding the same phenomenon, heritage speakers with more and early Chinese input seem to have advantages over L2 learners in terms of syntactic features. L2 learners are found to be slightly better than heritage speakers in terms of reconﬁguring some discourse properties.


Introduction
Heritage speakers are those simultaneous or sequential bilinguals whose weaker language corresponds to the minority language of their society and whose stronger language is the dominant language of that society (Polinsky 2018b) 1 . These speakers' acquisition of their heritage language is considered an important issue in the field of language acquisition, as it bridges L1 and L2 acquisition. Many studies involving heritage speakers concern their ultimate achievements in their heritage language (Montrul 2009), the effects of language transfer from the dominant language (Montrul 2010;Montrul and Ionin 2012), and heritage language attrition (Montrul 2002(Montrul , 2008(Montrul , 2011aPallier 2007;Polinsky 2011), as well as their differences from L1 learners and L2 learners (Montrul 2010;Montrul and Foote 2014;Polinsky and Kagan 2007;Rothman 2007). Recently, a significant body of research has explored the underlying characteristics of Spanish heritage speakers (Cuza 2012(Cuza , 2016Valenzuela 1

Features of SFPs ba
Features, as the undividable ultimate building blocks of language (Chomsky 2005;Jackendoff 2002) have long been the focus of much linguistic research in both the theoretical and applied linguistic fields. For Jackendoff (2002), words in the lexicon are fully specified with lexical, syntactic, and even discourse pragmatic features already, and no syntactic procedures are needed to enable the specification of features. It is these features that explain linguistic variations. The analysis of the linguistic phenomena in question (i.e., the SFPs ba) will be based on this feature perspective.

Discourse Features of the Suggestion SFP ba
The suggestion SFP ba in Chinese mainly types a suggestion sentence, as shown in (1). In (1b), with the assistance of the suggestion SFP ba, it sounds soft to signify a suggestion. In contrast, in (1a) without the particle, the tone of the sentence is very harsh, as in giving an order. Therefore, we propose  (Chao 1968, p. 807) However, there is no suggestive SFP in English. The [suggestion] feature is realized by several suggestive structures-for example, 'Let's (Let us) . . . ', 'We/You/They/He'd (We/You/They/He had) better . . . '. Sentences without such structural elements are merely general statements; compare (2a-c) and (3a-c).
(2) a. We are going to the park this afternoon.
b. We are going inside as it is going to rain outside. c. We will finish this work before starting something new.
(3) a. Let's go to the park this afternoon.
b. We'd better go inside as it is going to rain outside. c. Shall we finish this work before starting something new?

Syntactic and Discourse Features of the Question SFP ba
The question SFP ba in Chinese has both syntactic ([Q] and [-wh]) and discourse ([confirmation seeking]) features. In syntax, the addition of the question SFP ba to a declarative sentence converts the sentence into a question, as shown in (4). It is merely a declarative sentence in (4a), but in (4b) the addition of the particle at the end of the sentence means that it becomes a question. Thus, there is a syntactic [Q] feature attached to this particle. Furthermore, interrogative wh-phrases are not allowed to be present in an SFP ba question, i.e., a syntactic [-wh] feature is attached to this particle; see (5) for an example.
In discourse, the use of the question SFP ba in a sentence presents the speaker's attitude of certainty in the conversation (Hu 1987;Lu 1985;Qu 2006). In other words, the use of the question SFP ba provides an assumption and asks for a confirmation (Xu 2003). In (4b), the speaker asks the SFP ba question with some certainty and expects an answer to confirm his/her assumptions. Therefore, a discourse [confirmation seeking] feature is attached to this particle.
(4) a. In English, tag questions "express a need for confirmation of the statement expressed in the declarative" (Huddleston and Pullum 2005, p. 164). We propose that the functions (typing a question, asking for confirmation) and restrictions (disallowing interrogative wh-phrases) of the question SFP ba are manifested by the tag questions in English, which is in accordance with Tang (2015aTang ( , 2015bTang ( , 2016aTang ( , 2016b. The tag question in English (e.g., The dog is yours, is it/isn't it/right?) mainly consists of a declarative clause (i.e., The dog is yours), which expresses the view of the speaker, and a tag clause (i.e., is it/isn't it/right?), which indicates that the speaker wishes his/her view to be confirmed. The tag part of the question can be viewed as a reduced form of the yes-no question, whose content can be recovered from the preceding declarative clause (Huddleston and Pullum 2005). There are two categories of tag questions in English: the canonical tag question, and the invariant tag question. The former can be further divided into the non-disjunctive question (e.g., The dog is yours, is it?) and the disjunctive question (e.g., The dog is yours, isn't it?); the latter uses right, yeah and is very colloquial (e.g., The dog is yours, right?). In syntax, both types of tag question in English are conjunction structures (Kayne 2016;Sailor 2009), which have two individual CPs. Kayne (2016) argues that the declarative clause in the English tag question is labeled as the external conjunct, i.e., John is a student, and the yes-no tag as the internal conjunct, i.e., isn't he a student, as in (6b). He also proposes that these two conjuncts are connected by a disjunctive conjunction F. Sailor (2009) suggests that the surface derivation of the tag question is due to ellipsis of the repeated NP or VP, as in (6), where the tag question in (6a) is a result of the deletion of the NP a student in (6b). As for the derivation of invariant tag questions, i.e., those with 'right', 'yeah', etc., Kayne (2016) points out that there is a silent element, ISN'T THAT, as in (7b) in the internal conjunct. In this sense, the internal conjunct of the invariant tag questions is also a fully-fledged CP. Therefore, we propose that the [Q], [-wh] and [confirmation seeking] features, as with the Chinese question SFP ba, are attached to the internal conjunct of the tag question in English, which is a fully-fledged CP (the tag part), specifically the C of the CP.  categories of tag questions in English: the canonical tag question, and the invariant tag question. The former can be further divided into the non-disjunctive question (e.g., The dog is yours, is it?) and the disjunctive question (e.g., The dog is yours, isn't it?); the latter uses right, yeah and is very colloquial (e.g., The dog is yours, right?). In syntax, both types of tag question in English are conjunction structures (Kayne 2016;Sailor 2009), which have two individual CPs. Kayne (2016) argues that the declarative clause in the English tag question is labeled as the external conjunct, i.e., John is a student, and the yes-no tag as the internal conjunct, i.e., isn't he a student, as in (6b). He also proposes that these two conjuncts are connected by a disjunctive conjunction F. Sailor (2009) suggests that the surface derivation of the tag question is due to ellipsis of the repeated NP or VP, as in (6), where the tag question in (6a) is a result of the deletion of the NP a student in (6b). As for the derivation of invariant tag questions, i.e., those with 'right', 'yeah', etc., Kayne (2016) points out that there is a silent element, ISN'T THAT, as in (7b) in the internal conjunct. In this sense, the internal conjunct of the invariant tag questions is also a fully-fledged CP. Therefore, we propose that the In fact, as pointed out by Tang (2016b), Chinese does have tag questions that have a parallel underlying syntactic structure as tag questions in English. There are also canonical and invariant forms of tag questions in Chinese (Li and Thompson 1981;Tang 1988Tang , 2015aTang , 2015bTang , 2016aTang , 2016bsee examples 8, 9). The surface derivation of both forms of Chinese tag questions is also due to ellipsis of the repeated element (which is a CP in Chinese, as in 8, but an NP or VP in English, as in 6), as well as the existence of a silent null element (which is an empty category e in Chinese, as in 9, but a silent element ISN'T THAT in English, as in 7).
(8) a. Nǐ yào táotàidiào zhè pǐ m ǎ, shì ma? 2SG will eliminate this CL horse COP MA 'You will eliminate this horse, will you?' (Tang 1988, p (Tang 2016b, p. 31) What, then, is the role of the question SFP ba? In line with Yan and Yuan (2020), we agree that it is an 'additional' means to realize the function of English tag questions in Chinese.
Furthermore, there is an additional fact that we cannot ignore, which is that Chinese has an SFP ma that has same syntactic features (both [Q] and [-wh]; see examples 10, 11) as the question SFP ba. Unlike the question SFP ba, there is an [information seeking] discourse feature in the SFP ma. That is, in an SFP ma yes-no question (e.g., 10b), genuine information is being sought from the listener; thus Languages 2020, 5, x FOR PEER REVIEW categories of tag questions in English: the canonical tag question, and the invariant tag question former can be further divided into the non-disjunctive question (e.g., The dog is yours, is it?) an disjunctive question (e.g., The dog is yours, isn't it?); the latter uses right, yeah and is very collo (e.g., The dog is yours, right?). In syntax, both types of tag question in English are conjun structures (Kayne 2016;Sailor 2009), which have two individual CPs. Kayne (2016) argues th declarative clause in the English tag question is labeled as the external conjunct, i.e., John is a st and the yes-no tag as the internal conjunct, i.e., isn't he a student, as in (6b). He also proposes that two conjuncts are connected by a disjunctive conjunction F. Sailor (2009) suggests that the su derivation of the tag question is due to ellipsis of the repeated NP or VP, as in (6), where th question in (6a) is a result of the deletion of the NP a student in (6b). As for the derivation of inv tag questions, i.e., those with 'right', 'yeah', etc., Kayne (2016) points out that there is a silent ele ISN'T THAT, as in (7b) in the internal conjunct. In this sense, the internal conjunct of the invaria questions is also a fully-fledged CP. Therefore, we propose that the [Q], [-wh] and [confirm seeking] features, as with the Chinese question SFP ba, are attached to the internal conjunct of th question in English, which is a fully-fledged CP (the tag part), specifically the C of the CP.
(6) a. John is a student, isn't he? In fact, as pointed out by Tang (2016b), Chinese does have tag questions that have a pa underlying syntactic structure as tag questions in English. There are also canonical and inv forms of tag questions in Chinese (Li and Thompson 1981;Tang 1988Tang , 2015aTang , 2015bTang , 2016aTang , 2016. The surface derivation of both forms of Chinese tag questions is also due to ellip the repeated element (which is a CP in Chinese, as in 8, but an NP or VP in English, as in 6), a as the existence of a silent null element (which is an empty category e in Chinese, as in 9, but a element ISN'T THAT in English, as in 7).
(8) a. Nǐ yào táotàidiào zhè pǐ m ǎ, shì ma? 2SG will eliminate this CL horse COP MA 'You will eliminate this horse, will you?' (Tang 1988, p (Tang 2016b, p What, then, is the role of the question SFP ba? In line with Yan and Yuan (2020), we agree is an 'additional' means to realize the function of English tag questions in Chinese.
Furthermore, there is an additional fact that we cannot ignore, which is that Chinese has a ma that has same syntactic features (both [Q] and [-wh]; see examples 10, 11) as the question S Unlike the question SFP ba, there is an [information seeking] discourse feature in the SFP ma. T in an SFP ma yes-no question (e.g., 10b), genuine information is being sought from the listener In fact, as pointed out by Tang (2016b), Chinese does have tag questions that have a parallel underlying syntactic structure as tag questions in English. There are also canonical and invariant forms of tag questions in Chinese (Li and Thompson 1981;Tang 1988Tang , 2015aTang , 2015bTang , 2016aTang , 2016bsee examples 8, 9). The surface derivation of both forms of Chinese tag questions is also due to ellipsis of the repeated element (which is a CP in Chinese, as in 8, but an NP or VP in English, as in 6), as well as the existence of a silent null element (which is an empty category e in Chinese, as in 9, but a silent element ISN'T THAT in English, as in 7).  (Tang 2016b, p. 31) What, then, is the role of the question SFP ba? In line with Yan and Yuan (2020), we agree that it is an 'additional' means to realize the function of English tag questions in Chinese.
Furthermore, there is an additional fact that we cannot ignore, which is that Chinese has an SFP ma that has same syntactic features (both [Q] and [-wh]; see examples 10, 11) as the question SFP ba. Unlike the question SFP ba, there is an [information seeking] discourse feature in the SFP ma. That is, in an SFP ma yes-no question (e.g., 10b), genuine information is being sought from the listener; thus either a positive answer (like 'Yes, he can') or a negative one ('No, he can't') would be suitable, but no particular answer is necessarily expected. This is in contrast to the question SFP ba question, as in (4b).

Previous Research
On the basis of the linguistic comparison between Chinese and English in terms of the features of the SFPs ba in the above section, it seems that the realization of relevant features is asymmetric across the two languages. In other words, there is structural ambiguity between Chinese and English. For the suggestion SFP ba, there seems to exist a one-to-many mapping between Chinese and English, whereas for the question SFP ba there is a many-to-one mapping (also see Yan and Yuan 2020). The structural ambiguity, which has been summarized by Müller (1998), states that in language acquisition, if a phenomenon has two possible structures in one language but only one in another language, only the similar structure shared by the two languages will be kept. That is, the structure that is not shared will be abandoned in learners' grammars. Scontras et al. (2017) showed that in a situation where English allows both surface and inverse interpretations of doubly quantified sentences (e.g., A shark attacked every pirate, which can be interpreted in two different ways: a. There was a single shark that attacked multiple pirates, or b. For each pirate, there was a (different) shark that attacked him.), English-dominant heritage speakers of Mandarin lack scope ambiguities in their Mandarin heritage grammar, which allows only interpretation (a) for the above English sentence. This demonstrates that heritage speakers prefer a one-to-one surface mapping from structure to interpretation. Ronai (2018) followed up on Scontras et al.'s work and found that both Hungarian-dominant heritage speakers of English and English-dominant heritage speakers of Hungarian disallow inverse interpretations of doubly quantified sentences (Hungarian is like Mandarin, disallowing inverse interpretation of scope ambiguity). This further demonstrates that heritage speakers tend to prefer a simplified structure, and they struggle with one-to-many mappings between form and meaning in their heritage grammars. Polinsky (2018b) also concluded that heritage speakers may have morphology problems, as they overextend regular tense morphology and they prefer to reduce multiple allomorphs into one. However, Anderssen et al. (2018) found a different result; in their study, the acquisition of possessive DPs by English-dominant heritage speakers of Norwegian was investigated. In Norwegian, both Possessive-N and N-Possessive are allowed; however, only Possessive-N is allowed in English. Their results show that Norwegian heritage speakers overuse N-Possessive structures and this effect is proficiency related; it seems that learners "inhibit" similar structures between the two languages, thus contradicting to structural ambiguity arguments (i.e., Müller 1998; among others).
In terms of the Chinese SFPs, Wen (2014) studied the pragmatic development of 48 learners of Chinese in producing requests through a discourse completion task. One of her research findings showed that Chinese learners behaved differently from Chinese native speakers, particularly in the use of pragmatically functional particles and phrases such as the suggestion SFP ba and the tag-question appealer xíngma ('OK') for permission. Wen also found that learners have problems with opaque and similar non-literal expressions such as xíngma ('OK') and hăobùhăo ('OK'). By comparing the performance of requests in the grammars of Chinese heritage learners and L2 learners, Wen (2019) found that the SFP ba was rarely produced by heritage and L2 learners, although it was frequently used by Chinese native speakers. Furthermore, she also found that the heritage speakers slightly under-produced tag-questions in comparison with L2 learners, and therefore she argued that the heritage speakers adopted a more conservative strategy. This is in line with Dekeyser (2005), in that the optionality of a form and meaning connection leads to a lack of transparency, which increases the acquisition difficulties.
Using a similar experimental design (see Section 4 for details) but a different learner group, Yan and Yuan (2020) investigated features of the question and suggestion SFPs ba and their behaviors in the grammars of English-speaking L2 learners of Chinese. This study concluded that L2 learners have no problem with the features of the suggestion SFP ba, but have substantive problems with both the syntactic [Q] and the discourse [confirmation seeking] features of the question particle ba, and only at advanced levels could L2 learners successfully reconfigure the discourse [confirmation seeking] feature. These results suggest that the input and the L1-L2 (i.e., English-Chinese) structural difference in realizing the features of the particles significantly affected the successful acquisition of the features. In particular, the 'one-to-many' form-meaning mapping imposes great difficulties for L2 learners.
In this study, we look further at the re-configuration of the features of the SFPs ba in heritage grammars. With relatively more and earlier input than L2 speakers of Chinese, but also with influence from the dominant language (English), we expect to discover whether the syntactic and discourse feature properties carried by the Chinese SFPs ba will exhibit any differences for heritage speakers.

This Study
In particular, we are interested in the following questions: (1) How are the syntactic and discourse features represented in Chinese heritage speakers' grammars?
(2) What are the possible hidden mechanisms that influence their successful acquisition?

Participants
In total, 35 Chinese heritage speakers and 18 Chinese native speakers participated in this study. Table 1 gives detailed information about the participants. All the heritage speakers were born and raised in an English-speaking country, except for six who reported immigrant status (before the age of 5). They all reported English as their dominant (native) language. Almost all the heritage speakers had frequent exposure to Chinese, including both Mandarin and dialects, since they were young (32 reported 'always', 3 'seldom')-i.e., in their family there was at least one parent frequently speaking Chinese to them. Among these heritage speakers, 71.4% (25 out of 35) had exposure to Mandarin. The remaining 28.6% had exposure to Chinese dialects, which were mainly the Cantonese and Fujian dialects 2 . In this study, the amount of naturalistic exposure and formal learning of Chinese by heritage speakers were combined and seen as early input for these speakers 3 . Data collection took place in four universities in Beijing and Shanghai in China while the heritage speakers were taking a Chinese language course. All the Chinese native speakers were born and raised in northern China, and none of them had ever been to an English-speaking country. They were mainly post-graduate students majoring in Arts and Humanities at a university in Beijing. The heritage speakers were divided into two proficiency groups according to their performance in an established cloze test, which consisted of two short passages with 40 blanks (cf. Yuan 2014Yuan , 2015Yuan and Dugarova 2012). The Chinese native speakers also participated in the cloze test, and they were treated as the baseline group. Results of a one-way ANOVA and post hoc Tukey tests indicate that all the groups were significantly different from each other (F (2, 50) = 123.537, p < 0.001).

Acceptability Judgment Task (AJT)
The Acceptability Judgment Task explicitly asks participants to judge sentences as acceptable or not. In particular, this task is used to test whether participants have acquired the syntactic [Q] and [-wh] features of the question SFP ba. Examples are shown in (12) and (13). Participants who accepted the sentence in (12a), and at the same time rejected that in (12b), counted as evidence that [Q] and [-wh] features were attached to the question ba in their Chinese grammars. Meanwhile, control sentences, as shown in (13), were also included to ensure that the acceptance or rejection of the experimental sentences was not for any lexical or structural reasons.
The major consideration in adopting the AJT in this study is because of its advantages in providing acceptance and especially rejections of the structures. Mackey and Gass (2005) have pointed out that the AJT explicitly provides evidence of what participants include and particularly exclude in their grammars. In this study, we are interested in syntactic features (i.e., [Q] and [-wh] features), which were tested by asking participants to judge grammatical and ungrammatical sentences. However, ungrammatical sentences never (or at least rarely) occur in real linguistic environments. AJT can thus provide us with at least some evidence of the learners' rejection of ungrammatical sentences.
There were four tokens for each of the four types. In total there were 16 test items, and they were randomized with 128 other sentences that were used either to test other aspects of L2 Chinese grammars or to serve as distractors. In the AJT, as well as in the tasks in the following sections, only basic everyday words were included in the tasks. Words that might be new or difficult for the participants were provided with their English translations. The instructions were given to the HSs in English and to the Chinese native speakers in Chinese. This task was designed with the E-Prime 2.0 software, and sentences were presented on a computer monitor one by one. Participants were tested individually. They were required to press a key to indicate their judgment of the degree of the acceptability of each sentences: key 'A' represented 'completely unacceptable', key 'D' 'probably unacceptable', key 'J' 'probably acceptable', and key 'L' 'completely acceptable'. A separate key 'T' was used to represent the option 'I don't know'. To make these keys and their representations clearer, small word tags were stuck on the relevant keys. Participants were also given six practice examples before they begin the main test.

Dialogue Completion Task (DCT)
The acquisition of the [confirmation seeking] feature of the question ba and the [suggestion] feature of the suggestion ba were tested in this task. The DCT allows us to see whether participants can distinguish different particles in a specific context which particularly favors only one particle. Many prior studies have provided evidence that the DCT is a valid instrument to investigate discourse or pragmatic features (Mackey and Gass 2005;Pinto and Raschio 2007;Rose 2009;Wen 2014Wen , 2019. In terms of practical issues (i.e., space and time limitations on the tasks in the project), the dialogues in this task were designed to be miniature and as self-evident as possible. However, the data elicited from this task can still provide us with information about specific and authentic situations for social communication and pragmatic purposes.
Participants were presented with short dialogues which had a part missing. Their task was to choose the most appropriate item to complete the dialogue. In the instructions the participants were particularly asked to read the whole conversation and told that only the single most appropriate answer should be chosen. This was to exclude cases where participants may have found more than one item that was suitable to complete the conversation, thus ensuring that only the most appropriate item was selected. The list of items provided was de (an auxiliary word), yòu ('again'), SFP ma, SFP ba, SFP ne, SFP le, and SFP a. Examples are shown in (14) and (15). In (14), the question SFP ba was expected mainly due to the answer from Speaker B, which implies that Speaker A already knows that Speaker B can speak Chinese (as suggested by Speaker B's utterance 'nǐ zěnme zhīdào?'). There were four tokens for each SFP, randomized with 30 other sentences, which either tested other aspects of Chinese grammars or served as distractors and fillers. This task was administered before the other two tasks to avoid any priming effects.

Translation Task (TT)
The translation task asks participants to translate Chinese sentences into English ones. It was used to supplement the results of the other tasks; specifically, it allows us to see what potential English counterparts exist for the Chinese question SFP ba and suggestion SFP ba in heritage speakers' grammars, and further to see whether there is any effect from the dominant language. Since there are no SFPs in English, it is important to see how the features of the Chinese SFPs ba are manifested in English, which was the dominant language of the Chinese heritage speakers studied in this research. There was only one token for each SFP in this task. In addition, there were also 9 other sentence types, which tested other aspects of Chinese grammars 6 . This task was administered after the two tasks described above in order to avoid any priming effects. Examples are shown in (16) and (17) The translation task asks participants to translate Chinese sentences into English ones. It was used to supplement the results of the other tasks; specifically, it allows us to see what potential English counterparts exist for the Chinese question SFP ba and suggestion SFP ba in heritage speakers' grammars, and further to see whether there is any effect from the dominant language. Since there are no SFPs in English, it is important to see how the features of the Chinese SFPs ba are manifested in English, which was the dominant language of the Chinese heritage speakers studied in this research. There was only one token for each SFP in this task. In addition, there were also 9 other sentence types, which tested other aspects of Chinese grammarsP 5 F 6 P . This task was administered after the two tasks described above in order to avoid any priming effects. Examples are shown in (16) and (17)

AJT: Syntactic Features of the Question SFP ba
Participants were first screened by their acceptance of control sentences (i.e., those in 13). Those who failed to accept at least three out of the four tokens in each control sentence type were excluded 5 It may be argued that at a first glance at Speaker A's utterance in (14), the SFP ma may be a possible candidate. However, in the instruction for the task, participants were explicitly told that to complete the task they should read the whole conversation including the response from Speaker B and should only choose the single most appropriate answer. The utterance by Speaker B in (14) indicates that the question SFP ba, not the SFP ma, is required in Speaker A's utterance. However, as a reviewer has pointed out, we cannot totally exclude the possibility that participants' errors were from their sloppy reading, such as neglecting the second sentence. Future research adopting other tasks may reveal more evidence on this. 6 The Chinese native speakers did not participate in this task as it was designed to see how learners of Chinese treat the SFPs in their native English.

AJT: Syntactic Features of the Question SFP ba
Participants were first screened by their acceptance of control sentences (i.e., those in 13). Those who failed to accept at least three out of the four tokens in each control sentence type were excluded from further analysis in this task. The results showed that all participants successfully accepted those sentences. Table 2 shows the descriptive results for all groups. 5 It may be argued that at a first glance at Speaker A's utterance in (14), the SFP ma may be a possible candidate. However, in the instruction for the task, participants were explicitly told that to complete the task they should read the whole conversation including the response from Speaker B and should only choose the single most appropriate answer. The utterance by Speaker B in (14) indicates that the question SFP ba, not the SFP ma, is required in Speaker A's utterance. However, as a reviewer has pointed out, we cannot totally exclude the possibility that participants' errors were from their sloppy reading, such as neglecting the second sentence. Future research adopting other tasks may reveal more evidence on this. 6 The Chinese native speakers did not participate in this task as it was designed to see how learners of Chinese treat the SFPs in their native English. Recall that participants were making judgments on an acceptability scale. In the data analysis, participants' judgments were transformed into numerical values, where 1 stands for 'completely unacceptable', 2 for 'probably unacceptable', 3 for 'probably acceptable', and 4 for 'completely acceptable'. Therefore, participants' judgments ranged from 1 to 4. For the [Q] feature (i.e., experimental A sentences) of the question SFP ba, both the HS advanced group and the Chinese native group were able to accept these sentences (mean scores > 3), but the HS high-intermediate group showed indeterminacy in accepting them. However, all groups rejected the ungrammatical sentences (i.e., those where a wh-phrase occurs in a question SFP ba sentence; mean scores approaching 1).
Linear mixed-effects models were performed to find whether there was any statistical difference among the variables (fixed factors and random factors). In this study, R (R Core Team 2014) and lme4 (Bates et al. 2013) were applied to perform a linear mixed-effects analysis of the relationships between different fixed factors. The fixed factors included Condition (i.e., grammatical (G) vs. ungrammatical (UG) sentences), Group (Chinese native, HS advanced, HS high-int), Age, and Length (i.e., number of words included in each sentence). As random effects, we have intercepts for subjects and items, as well as by-subject and by-item random slopes included.
The results from the mixed-effects models show that both the HS advanced group and the HS high-intermediate group (all t < |2|, p > 0.05) were found not to be significantly different from the Chinese native group in accepting the grammatical experimental A sentences (i.e., testing the [Q] feature). However, the high-intermediate group was found to be significantly different from the Chinese native group in rejecting the ungrammatical experimental B sentences (t > |2|, p < 0.05; see Table 3). Therefore, these results suggest that all HS groups are able to reconfigure the [Q] feature of the question SFP ba, as well as the [-wh] feature, except the high-intermediate group. Notes: reference level for condition=UG (ungrammatical), for group=Chinese native; Model formula: ratingsc ondition * cage * clength 7 + factor (group) + condition: factor (group) + (1 + condition|subject) + (1|item); here values of t > |2| can be informally considered significant (Gelman and Hill 2007); *** p < 0.001.

DCT: Discourse Features of Suggestion SFP ba and Question SFP ba
In the analysis of data in this task, all participants' selections of items were converted into numerical values. Specifically, if they selected the expected SFP ba in relevant dialogues, their selections received a score of 1; otherwise, they received a score of 0. The 'I don't' know' option was treated as a missing value.

[Suggestion] Feature of Suggestion SFP ba
As shown in Table 4, the mean scores of the participants in all groups were close to the ceiling score of 4. Generalized linear mixed-effects models were conducted to see whether there was any statistical difference between groups. In the models, the fixed factors included Group (Chinese native, HS advanced, HS high-int), Age, and Length (i.e., the number of words included in sentences). As random effects, we included intercepts for subjects and items, as well as by-subject and by-item random slopes. The results show that there were no statistically significant differences between any pairs of groups (z < |2|, p > 0.05). This indicates that all the heritage groups were able to select the expected suggestion SFP ba in required dialogues, and they had no problem with the [suggestion] feature of the suggestion SFP ba.

[Confirmation Seeking] Feature of Question SFP ba
The participants were first screened by their acceptance (3 out of 4 tokens) of the experimental A sentences in (12a), which indicates their knowledge of the question SFP ba as used in questions (i.e., a [Q] feature of this SFP). The rationale for this is that being a question (having a [Q] feature) for a question SFP ba is the prerequisite for investigation of the [confirmation seeking] feature of the SFP. None of the participants had a problem with the experimental A sentences in (12a), and no one was excluded. Table 5 shows the results. These results clearly show that Chinese native speakers selected the expected question SFP ba in required dialogues, as their mean scores were at 3.78 (close to the ceiling 4). However, heritage speakers at advanced levels were indeterminate (mean score at 1.95) in selecting the expected SFP ba in required dialogues, and those at high-intermediate levels tended not to select the question SFP ba (mean score was only 0.94). 7 Here 'cage' stands for age (centered), 'c' is abbreviated for centered, 'clength' for length (centered), 'ratings' for the acceptability scores. In the models, we included the length (centered) as a factor. However, due to the collinearity issue, its effect is converged with condition and thus cannot be obtained in the models; it is not reported here.
Languages 2020, 5, 26 13 of 21 A generalized linear mixed-effects analysis was applied to examine the statistical relationships between different fixed factors. The results are summarized in Table 6 and show that both the Chinese heritage high-intermediate and advanced speakers were significantly different from the Chinese native group (both z > |2|, p < 0.001). Therefore, it seems that all heritage speaker groups have difficulty in reconfiguring the [confirmation seeking] feature of the question SFP ba. Since heritage speakers in two proficiency groups did not select the expected question SFP ba in the required dialogues, we were curious to see what items that they preferred rather than the expected question SFP ba. An error analysis was conducted, to give us more information about the behavior and nature of the question SFP ba in the heritage speakers' Chinese grammars. Specifically, we analyzed the cases where the participants consistently (3 out of 4 tokens) selected items other than the expected question SFP ba. The results are presented in Figure 1. As shown in Figure 1, more than 90% of the heritage speakers at both high-intermediate and advanced levels selected the SFP ma in contexts favoring the question SFP ba. This suggests that all heritage speakers have difficulty making a clear distinction between the [confirmation seeking] feature attached to the question SFP ba and the [information seeking] feature of the SFP ma.

TT: Feature Mapping between Chinese SFP ba and English Structures
Participants' translations were counted and converted into percentages, except for the Chinese native speakers as they did not take part in this task. The results are presented in Figures 2 and 3.
For the suggestion SFP ba, as shown in Figure 2, more than 87% of the heritage speakers translated the sentences containing the suggestion SFP ba into suggestion sentences in English (e.g., Let's go and study Chinese together), which indicates that in the heritage speakers' Chinese grammars, suggestion SFP ba sentences are treated as suggestions in their dominant language, i.e., English. This further suggests that the heritage speakers have established the mapping between Chinese suggestion SFP ba sentences and English suggestion sentences. As shown in Figure 1, more than 90% of the heritage speakers at both high-intermediate and advanced levels selected the SFP ma in contexts favoring the question SFP ba. This suggests that all heritage speakers have difficulty making a clear distinction between the [confirmation seeking] feature attached to the question SFP ba and the [information seeking] feature of the SFP ma.

TT: Feature Mapping between Chinese SFP ba and English Structures
Participants' translations were counted and converted into percentages, except for the Chinese native speakers as they did not take part in this task. The results are presented in Figures 2 and 3.

TT: Feature Mapping between Chinese SFP ba and English Structures
Participants' translations were counted and converted into percentages, except for the Chinese native speakers as they did not take part in this task. The results are presented in Figures 2 and 3.
For the suggestion SFP ba, as shown in Figure 2, more than 87% of the heritage speakers translated the sentences containing the suggestion SFP ba into suggestion sentences in English (e.g., Let's go and study Chinese together), which indicates that in the heritage speakers' Chinese grammars, suggestion SFP ba sentences are treated as suggestions in their dominant language, i.e., English. This further suggests that the heritage speakers have established the mapping between Chinese suggestion SFP ba sentences and English suggestion sentences. In terms of the question SFP ba, before analysis of the data, participants were first screened by their acceptance of experimental sentence A in (12a), similar to the rationale in the DCT (see Section 5.2.2). Since all participants met the screening criterion, no participant was excluded. Figure 3 presents the percentages of the heritage speakers' translation of the question SFP ba sentences into English structures. It shows that only 25% of the high-intermediate heritage speakers translated the question SFP ba sentences into tag questions in English (e.g., Xiǎohóng likes travelling, doesn't she/right/yeah?). There was an increase at advanced levels (58%). However, more than 41% of the heritage speakers at both high-intermediate and advanced proficiency levels translated the question SFP ba sentences into other structures in English. A closer examination shows that all these translations were general yes-no questions in English (i.e., Does Xiǎohóng like travelling?). This indicates that heritage speakers have problems with interpreting Chinese question SFP ba sentences as tag questions in English (instead, they interpret them as yes-no questions, similar to the English equivalent of the SFP ma), even at advanced levels. This converges with the findings in DCT.

Comparing Heritage Speakers and L2 Learners in the Acquisition of the Same Features: Addressing Question (1)
Representations of the features of the SFPs ba in Chinese heritage speakers' grammars are different from those in English-speaking L2 learners' Chinese grammars. Recall that Yan and Yuan (2020)   For the suggestion SFP ba, as shown in Figure 2, more than 87% of the heritage speakers translated the sentences containing the suggestion SFP ba into suggestion sentences in English (e.g., Let's go and study Chinese together), which indicates that in the heritage speakers' Chinese grammars, suggestion SFP ba sentences are treated as suggestions in their dominant language, i.e., English. This further suggests that the heritage speakers have established the mapping between Chinese suggestion SFP ba sentences and English suggestion sentences.
In terms of the question SFP ba, before analysis of the data, participants were first screened by their acceptance of experimental sentence A in (12a), similar to the rationale in the DCT (see Section 5.2.2). Since all participants met the screening criterion, no participant was excluded. Figure 3 presents the percentages of the heritage speakers' translation of the question SFP ba sentences into English structures. It shows that only 25% of the high-intermediate heritage speakers translated the question SFP ba sentences into tag questions in English (e.g., Xiǎohóng likes travelling, doesn't she/right/yeah?). There was an increase at advanced levels (58%). However, more than 41% of the heritage speakers at both high-intermediate and advanced proficiency levels translated the question SFP ba sentences into other structures in English. A closer examination shows that all these translations were general yes-no questions in English (i.e., Does Xiǎohóng like travelling?). This indicates that heritage speakers have problems with interpreting Chinese question SFP ba sentences as tag questions in English (instead, they interpret them as yes-no questions, similar to the English equivalent of the SFP ma), even at advanced levels. This converges with the findings in DCT.

Comparing Heritage Speakers and L2 Learners in the Acquisition of the Same Features: Addressing
Question (1) Representations of the features of the SFPs ba in Chinese heritage speakers' grammars are different from those in English-speaking L2 learners' Chinese grammars. Recall that Yan and Yuan (2020) investigated the same features of the SFPs ba in L2 grammars using a similar research design, finding that L2 learners have no problem with the discourse [suggestion] feature of the suggestion SFP ba and the syntactic [-wh] feature of the question SFP ba, but they do have difficulties with the syntactic [Q] feature and the discourse [confirmation seeking] feature of the question SFP ba. However, the findings in this study show that in the heritage speakers' Chinese grammars, the [Q] feature of the question SFP ba was successfully reconfigured, which suggests an advantage of heritage speakers over L2 learners in terms of acquiring this syntactic feature. Heritage speakers at high-intermediate levels are indeterminate in reconfiguring the [-wh] feature of the question SFP ba, which seems like a lower level of competence in comparison with L2 learners in terms of acquiring this syntactic feature. However, at advanced levels both heritage and L2 learners have no problem with this feature. We argue that this optionality in acquiring the [-wh] feature is probably a temporary confusion with wh-phrases in Chinese 9 , which does not lead to permanent representational problems in heritage grammars. This confirms the argument of Montrul (2012) that heritage speakers have a better mastery of the syntactic features in comparison with L2 learners.
With respect to the [confirmation seeking] feature, though both heritage speakers and L2 learners have substantial problems in successfully reconfiguring it (as shown in the DCT and the TT), which is in line with Keating et al. (2011) and Montrul (2012), the English-speaking L2 learners outperformed the heritage speakers, since L2 advanced learners were found to be able to reconfigure this discourse feature successfully by Yan and Yuan (2020). As for the discourse [suggestion] feature of the suggestion SFP ba, similar to its behavior in the grammars of L2 learners, it is also successfully represented in the grammars of Chinese heritage speakers. Therefore, it seems that not all discourse features pose difficulties to heritage speakers and L2 learners.
Furthermore, the heritage speakers do not always have advantages over L2 learners regarding the acquisition of properties at the (syntax-)discourse level, i.e., in terms of the [confirmation seeking] discourse feature (Wen (2019) reports a similar finding). Montrul (2012) has summarized that there is a vulnerability in the syntax-discourse domain for heritage language grammars, but the findings of this study show that this may not be across the board as the heritage speakers seem to have no problem at all with the [suggestion] discourse feature. In terms of the Vulnerability Hypothesis (de Prada Pérez 2019), it seems that the discourse [confirmation seeking] feature, which may have a more variable 9 In Chinese, some non-interrogative wh-phrases are able to appear in SFP ba questions, for example, Tā zài chī shenme ba? 3SG PROG eat something BA 'He(She) is eating something, isn't /is he(she)?/right?' distribution, i.e., more than one form can be used in the target Chinese, causes the most mapping and reconfiguration difficulties for heritage speakers. However, the discourse [suggestion] feature and the syntactic [Q] and [-wh] features, which may be categorical, seem to impose little difficulty for heritage speakers. Nevertheless, since this study did not intentionally test the Vulnerability Hypothesis since the frequency/distribution of the features of the SFPs ba are not calculated, more research is called for to further test this speculation. If this is on the right track, however, it seems that the Vulnerability Hypothesis may have more explanatory power than the Interface Hypothesis in heritage and bilingual acquisition.
6.2. Possible Factors Affecting the Acquisition of Features of the Question SFP ba: Addressing Question (2) The role of dominant language transfer: as shown by Lee (2016), Montrul (2010), and Montrul and Ionin (2012), dominant language transfer has been found at both semantic and syntax-semantic/pragmatic interfaces, affecting the restructuring of heritage grammars. Difficulties in reconfiguring the [confirmation seeking] feature of the question SFP ba in Chinese heritage grammars may be also due to the same reason. Recall that this feature has different realizations in Chinese and English (see Section 2.2 for details), whereby it is attached to the question SFP ba in one single CP, but it is on the C of the internal CP in the English tag questions. Therefore, it is probable that this different syntactic structural realization prevents a smooth and successful reconfiguration of the [confirmation seeking] feature of the question SFP ba in heritage grammars. In other words, the dominant language, English, which has a different realization of the [confirmation seeking] feature, has led to difficulty in acquiring this feature among Chinese heritage speakers.
Even worse, as demonstrated in Section 2.2, there are canonical tag questions in Chinese (i.e., using shì ma, 'will you'; duìbuduì, 'right' as tags), which are syntactically the same as those used in English, and these might further 'enhance' heritage speakers' confidence that the question SFP ba sentences are different from the tag questions in English. This is in line with the findings of Yan and Yuan (2020), who have also found that English-speaking L2 learners of Chinese have substantive difficulties in acquiring the [confirmation seeking] feature of the question SFP ba. However, Yan and Yuan (2020) further shows that even though it is difficult, advanced English-speaking L2 learners do finally reconfigure this feature of the question SFP ba. Why, then, do heritage speakers, especially those with more and earlier Chinese input, have problems even at advanced levels? This may be explained as follows.
Input as a possible factor: Polinsky and Scontras (2020) have concluded that the unique representations of heritage speakers (i.e., their deviations from either/both heritage baseline and dominant language baseline) are probably due to the input that they have gained. In particular, the quantity (i.e., their exposure to and recency of the heritage language) and the quality (the community size) of their input all contributes to their final achievements in heritage language acquisition. In this study, though the majority of heritage speakers have early and frequent exposure to Chinese, this was up to the age of 7 (we only obtained information about participants' language backgrounds until that age in this research). That is, in the absence of evidence about their Chinese exposure after this age, we cannot exclude the possibility that it might be the lower exposure and lack of recency of Chinese (in contrast with their dominant language English) that has resulted in their problems with reconfiguring the [confirmation seeking] feature of the question SFP ba.
Effects of limited processing resources: it has been argued that limitations in processing resources, as well as the additional cost of handling a less proficient language, may be factors affecting the acquisition of heritage languages (Polinsky and Scontras 2020;Ronai 2018;Scontras et al. 2017;among others). Under such processing pressures, heritage speakers tend to adopt a simplified structure and a one-to-one surface mapping from structure to interpretation. Dekeyser (2005), Wen (2014), Wen (2019) and Yan and Yuan (2020) all show that the optionality of a form and meaning connection leads to a lack of transparency, and thus increases acquisition difficulties. Therefore, as demonstrated in this study, because of the similarity in structure, Chinese heritage speakers prefer the mapping of Chinese SFP ba questions onto English yes-no questions (i.e., similar to the SFP ma question being the equivalent of the English yes-no question). They adopt this preference instead of treating them as tag questions in English, which requires the recognition of an additional mapping besides the canonical ones.
However, this study to some extent contradicts the findings of Anderssen et al. (2018), who found that heritage speakers inhibited similar structures between the target and their dominant languages. We propose that this may due to the fact that the form-meaning mappings in this study are more complex as compared to Anderssen et al. (2018), requiring recognition of the sequential order of N and possessives. In addition, heritage speakers' preferences for one-to-one form and meaning mappings may also explain the effects of successful reconfiguration in terms of different discourse features of the question SFP ba and the suggestion SFP ba in heritage grammars. Recall that the [suggestion] discourse feature of the suggestion SFP ba, which requires a one-to-many mapping between Chinese and English, was readily acquired by heritage speakers in this study, but the [confirmation seeking] feature of the question SFP ba, which requires a many-to-one mapping between Chinese and English, imposes substantive difficulties. We propose that this is probably a manifestation of the fact that the one-to-many form and meaning connection between the target heritage language (i.e., Chinese) and the dominant language (i.e., English) is easier than many-to-one form and meaning connections in heritage language acquisition. This lends further support to the findings in Yan and Yuan (2020) in terms of the form-meaning mappings in L2 Chinese.

Pedagogical Implications
The findings of this study suggest that the successful acquisition of features of the SFPs ba (especially discourse features of the question SFP ba) by heritage speakers requires disentangling similar particles and structures, distinguishing different feature realizations, and obtaining enough input. Kupisch and Rothman (2018) have argued that formal training between later childhood and early adulthood can facilitate the acquisition of heritage languages. Therefore, pedagogical measures may have influential effects on the successful acquisition of the features of the SFPs ba. However, current textbooks and formal teaching do not explicitly highlight the relationship between question SFP ba sentences and English tag questions. Awareness of the differences between the question SFP ba and its English counterparts, as well as its relationship with Chinese canonical tag questions, will enhance heritage speakers' ability to notice relevant evidence from the target input. Furthermore, differences between similar features of similar particles, i.e., the yes-no question particle ma and the question SFP ba, should also be highlighted and explicitly compared in formal teaching. In addition, since both suggestion and question SFPs ba are discourse particles, robust input, especially from spoken Chinese and from a variety of native speakers, should also be incorporated in formal teaching.

Limitations and Future Directions
Although this study has provided insightful findings concerning the acquisition of syntactic and discourse features by Chinese heritage speakers, there are a number of limitations. First, several methods have been adopted to investigate the relevant features attached to the suggestion and question SFPs ba, but it is necessary to add more methods from different dimensions to gain more evidence and further triangulate the data. Though AJT in this study provided us with understanding of relevant syntactic features, data from online processing tasks (such as reaction time studies or eye-tracking studies) would provide us with more knowledge about the implicit representations of syntactic features. Moreover, though the DCT is a valid method to obtain insights about the nature of discourse features, production tasks involving natural contexts and discourses could provide more in-depth data. Furthermore, besides the TT task, qualitative methods such as interviews should be incorporated in future studies to better explore the underlying mechanisms behind the performance of heritage speakers.
Second, although we tried to control for the language backgrounds of the heritage speakers in this research, it would be better to collect data from one unified Chinese language group (either Mandarin or a single dialect). This would give more confidence to conclude that the findings are influenced by the factors under investigation, rather than being artifacts of different Chinese dialects. Third, as Kupisch and Rothman (2018) have highlighted, knowledge of heritage speakers in terms of their heritage language should be considered native, and thus future investigation of heritage speakers could compare their grammars with matched bilingual native groups to provide more insights.

Conclusions
This study investigated the representations of features of suggestion and question SFPs ba in the grammars of English-dominant Chinese heritage speakers. The results show that the features of the suggestion SFP ba and the syntactic features of the question SFP ba are properly represented, but the discourse feature of the question SFP ba poses a difficulty for Chinese heritage speakers. We argue that not all syntactic and discourse features are problematic in heritage language acquisition, and a transfer effect from the dominant language, the effect of input, as well as limitations in processing resources may all have contributed to the deviation in the heritage speakers' performance. Future studies are invited to particularly examine the quantity and quality of input that heritage speakers obtain in acquiring a heritage language, as well as their online instant processing of relevant feature properties.
Funding: This research received no external funding.