2.1 The incompleteness effect

As mentioned above, VDCs in Mandarin are themselves incomplete unless supplemented by a continuing proposition, regardless of whether or not the copula shi is present. For example, in (6a) the ‘but’-continuation presents a contrast between the initial verb copy (‘eat’) and a negative VP ‘not eating until full’; in (6b), the contrast is a more indirect one between ‘eat’ and a complex proposition ‘he thought (it) wasn’t tasty’; finally, (6c) shows that the continuation need not involve negation.

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(6) (Did Yijun eat?) a. CHI, Yijun (shi) chi le, keshi mei chi-bao. eat Yijun COP eat ASP but NEG eat-full ‘As for eating, Yijun (did) eat, but didn’t eat until full.’ b. CHI, Yijun (shi) chi le, keshi ta juede bu hao-chi. eat Yijun COP eat ASP but 3SG think NEG good-eat ‘As for eating, Yijun (did) eat, but she thought (it) wasn’t tasty.’ c. CHI, Yijun (shi) chi le, keshi ta hai neng zai chi. eat Yijun COP eat ASP but 3SG still can again eat ‘As for eating, Yijun (did) eat, but she could still eat more.’.

The incompleteness effect and the requirement of a contrastive continuation of Mandarin shi-VDCs has been well documented (Chao Reference Chao1968, Lee Reference Lee and Anne-Marie Di Sciullo2003, Shyu Reference Shyu and Ching-Hsiun Lin2007, Cheng and Vicente Reference Cheng and Vicente2013, Zhong Reference Zhong2016) but has not been systematically and formally analyzed. Vicente (Reference Vicente2007) and Cheng and Vicente (Reference Cheng and Vicente2013) dub the contrastive continuation as an adversative implicature of VDCs in Spanish and Mandarin, respectively (see also Bastos Reference Bastos2001 on similar “but-effects” in Brazilian Portuguese). With respect to the status of the contrastive continuation as an implicature, Vicente (Reference Vicente2007) observes that predicate doubling in Spanish, which normally gives rise to an adversative implicature as shown in (7a), may have the implicature cancelled under certain conditions, for example, when something other than the verb is focused, as in (7b). This suggests the inference that follows from (7a) is indeed an implicature, in particular a conversational implicature due to the Maxim of Manner.

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(7) a. Leer, Juan ha leído un libro (pero...) read.INF J has read a book but ‘As for reading, Juan has read a book (but still...).’ b. Leer, Juan ha leído AKIRA read.INF J has read A ‘As for reading, Juan has read AKIRA.’.

(Vicente Reference Vicente2007: 66)

At first glance, the incompleteness inference of a Mandarin VDC without shi also seems cancellable. For instance, (8) alone can be a felicitous response to the question ‘Did Yijun eat noodles?’, where focal stress falls on the object fan ‘rice’.

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(8) (Did Yijun eat noodles?) Chicomma ta chi-le FAN. eat 3SG eat-ASP rice ‘As for eatingcomma she ate RICE.’.

Another example is (9b), provided by a reviewer who once again observes that (9b) is complete as a response to (9a), thus raising the question of whether the incompleteness effect is obligatory for VDCs without shi or merely a cancellable implicature.

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(9) a. Huanggua ni dou mei qiecomma xi le ma? cucumber you even NEG cut wash ASP PRT ‘You didn’t even cut the cucumber. Did you wash it?’ b. Xicomma wo xi le. wash 1SG wash ASP ‘As for washingcomma I washed it.’.

Notice, however, that the initial verbs in these VDCs are necessarily unstressed, and the focal stress falls on something in the main clause (e.g., the object in (8), and second verb copy in (9b)). Such an intonation pattern results in a different interpretation of these doubling constructions, according to which the initial verb is a topic in Li and Thompson’s (Reference Li and Thompson1981) sense, in other words, what the main clause is about. This topical interpretation requires the initial verb to be anaphoric to a previously mentioned expression – which is satisfied in both (8) and (9b) – but does not require the initial verb to contrast with an alternative. If the initial verbs in these examples are stressed, the incompleteness effect becomes mandatory and not cancellable, just like the data in (1)–(6). The VDCs in Mandarin with which we will be concerned only include those with a stressed initial verb.

On the other hand, a potential counterexample to the generalization that a VDC with the first verb stressed is incomplete is (10), a felicitous response in the same context containing two conjoined VDCs with both initial verbs stressed and without shi. But like (9b), the second VDC in (10) is “complete” in appearing without continuation.

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(10) (Same context as in (9a)) QIEcomma wo mei qiecomma dan XIcomma wo xi le. cut 1SG NEG cut but wash 1SG wash ASP ‘As for cutting (it)comma I didn’t; as for washing (it)comma I did.’.

I will return to (10) as well as (9b) in section 2.3, where it will be argued that the incompleteness effect of a VDC correlates with a licensing condition: Incompleteness would not be mandatory if all subquestions can be answered within the same discourse strategy, as is the case in (10).

2.2 Büring’s (Reference Büring2003) theory of contrastive topics

Contrastive topic (CT) constructions in English are encoded with a fall-rise contour (Jackendoff Reference Jackendoff1972, Büring Reference Büring2003, among many others). In (11a) below, the subject Fred is a CT (indicated by the subscript ‘CT’) that is accompanied by a focus (‘F’), beans. In (11b), the pattern is reversed. The different CT+F markings have semantic consequences: While (11a) can answer the question What did Fred eat? in a context where the topic of different individuals eating different things is under discussion, (11b) cannot. The latter is only felicitous as a response to the question Who ate the beans? in the same context.

Büring (Reference Büring2003) develops a non-compositional pragmatic theory in which English CTs have a CT-value (in parallel to F-marked expressions having a focus semantic value; Rooth Reference Rooth1992) that is generated based on the following CT-value formation rule:

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(12) CT-value formation (Büring 2003: 519) a. Step 1: Replace the focus with a wh-word and front the latter; if focus marks the finite verb or negation, front the finite verb instead. b. Step 2: Form a set of questions from the result of step 1 by replacing the contrastive topic with some alternative to it.

Taking (11a) as example, step 1 turns it into the question ‘What did Fred eat?’, and step 2 forms the set of questions in (13) out of step 1, which is the CT-value evoked in (11a).

Long description

Left parenthesis 13 right parenthesis double left square bracket left parenthesis 11a right parenthesis double right square bracket superscript c t equals left curly bracket 'What did Fred eat?' comma 'What did Mary eat?' comma ellipsis right curly bracket equals left curly bracket left curly bracket x ate y vertical bar y element of D subscript e right curly bracket vertical bar x element of D subscript e right curly bracket.

The (sub)questions in (13) are all connected to the more general, overarching question Who ate what? in a hierarchical discourse structure, and the relation between a (sub)question and the overarching question is understood as a strategy of inquiry (Roberts Reference Roberts2012). Since the CT-value formation rule generates a different CT-value when CT-marking falls on a different phrase, it follows that (11a) and (11b) have distinct meanings.

From here, Büring (Reference Büring2003) addresses another semantic property of CT-marking, namely that it conveys additional discourse-related meaning. For instance, (11a) infers that other people ate other things (than beans). Büring suggests that such inferences arise as a conversational implicature: Given that the CT-marking on Fred indicates the existence of a complex discourse structure containing questions of the form What did x eat?, and that the speaker of (11a) only mentions Fred rather than providing a more informative answer, we can conclude that while she is aware of other people having eaten, she is not aware whether they ate beans or not.Footnote ³

In addition, Büring (Reference Büring2003: 533) uses the following dialogue to illustrate cases where step 1 in (12) involves focus marking on a finite verb/auxiliary. According to him, both A1 and A2 in (14) have the CT-value in (15), and the focus on did can signal verum focus.

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(14) Q: How many (of the 74) abstracts got accepted? SQ1: Did any abstracts get accepted? A1: (Yescomma) SOME subscript CT abstracts DID subscript F get accepted. SQ2: Did most abstracts get accepted? A2: (Yescomma) MOST subscript CT abstracts DID subscript F get accepted.

Long description

Equation 15 states that double-bracket of left parenthesis 14A1 right parenthesis superscript c t equals double-bracket of left parenthesis 14A2 right parenthesis superscript c t equals the set of Q such that Q abstracts got accepted, where Q is an element of D subscript e t comma t. This is approximately equivalent to the question: Did X abstracts get accepted?.

The derivation of the CT-value (15) utilizes the assumption (Büring Reference Büring2003: 532) that polar questions denote singleton sets of propositions. Thus, when the focus of the sentence S falls on a verb/auxiliary, CT-marking in S yields a set of polar questions, rather than a set of wh-questions.

2.3 Deriving the incompleteness effect

I propose that Mandarin VDCs are essentially a kind of CT construction, where the initial stressed verb is a CT. Concentrating on the VDCs without shi for the moment, the key idea regarding the incompleteness effect of VDCs is the following: They obligatorily trigger a set of implicit subquestions by virtue of CT-marking while only addressing one subquestion, and the fact that there is at least one other subquestion raised but unresolved results in the perceived incompleteness. For instance, the CT-marking in (16), realized through word-level stress on the initial verb, triggers the set of subquestions in (17) but only answers the first (‘Did Yijun eat?’), leading to the perception that (16) itself is not complete.

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Left parenthesis 17 right parenthesis left curly bracket 'Did Yijun eat question mark' comma 'Did Yijun eat until full question mark' comma ellipsis right curly bracket equals 'For every relevant action P comma did Yijun do P question mark' left parenthesis CT hyphen value of left parenthesis 16 right parenthesis right parenthesis.

More concretely, I propose (18) for Mandarin VDCs, following Büring (Reference Büring2003). Here I will only illustrate simple VDCs containing a one-place verb; other types of verbs can be analyzed similarly.

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(18) CT-value formation of Mandarin VDCs a. Step 1: Form a polar question from a VDC excluding the initial stressed verb copy. Formally: {P(a)}, where P is the denotation of V of a VDC and a the subject b. Step 2: Form a set of polar questions from the result of Step 1 by replacing the copied verb with some alternative to it. Formally: {{P'(a) | P' \u0018 Det}}, where P' is a variable ranging over the denotations of alternative verbs.

It is obvious that (18) is parallel to (12) except that the VDC data under discussion do not involve focus (cf. “sole-CT” sentences in Büring Reference Büring2003). We can use (16) to illustrate how (18) works. Step 1 generates the singleton set of propositions in (19a), which amounts to the polar question Did she eat?, following Büring (Reference Büring2003) and also Biezma and Rawlins’s (Reference Biezma and Rawlins2012) proposal that polar questions denote singleton sets of propositions.Footnote ⁴ In step 2, let us first assume for simplicity that there is only one alternative to chi ‘eat’, namely the resultative compound chi-bao ‘eat until full’. Replacing chi in (19a) with this alternative yields the set of polar questions in (19b), which is the CT-value assigned to (16). In other words, step 2 builds a non-singleton set of polar questions out of a singleton set of polar questions.

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(19) Deriving the CT-value of (16) a. {'Yijun ate'} = 'Did Yijun eat?' (step 1) b. {{'Yijun ate'}, {'Yijun ate until full'}} = {'Did Yijun eat?', 'Did Yijun eat until full?'} = 'For every action P in the set {'eat', 'eat until full'}, did Yijun do P?' (step 2).

This, I argue, is the source of the incompleteness of VDCs: By uttering (16), the speaker S indicates she acknowledges the relevance of the complex discourse containing the two polar subquestions in (19b), and yet S only asserts (16) to respond to one of them. This leads to the observed incompleteness: At least one evoked subquestion is not answered by the VDC alone. In the present analysis, the incompleteness of VDCs amounts to the lack of a complete set of answers that can resolve all the subquestions triggered by the initial verb copy (i.e., the CT).

Notice that this account makes no prediction with regard to how a VDC should be made complete; all that is required is that there be at least one implicit subquestion in the CT-value that needs to be addressed. The felicity of the examples in (4), repeated below in (20), is expected because either the continuation in (20a) or that in (20b) can respond to the polar subquestion in the CT-value (‘Did Yijun eat much?’) that is not addressed by the first clause.

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(20) a. CHI, Yijun chi le, keshi mei chi hen-duo. eat Yijun eat ASP but NEG eat very-much ‘As for eating, Yijun ate, but didn’t eat much.’ b. CHI, Yijun chi le, erqie chi-le hen-duo. eat Yijun eat ASP and eat-ASP very-much ‘As for eating, Yijun ate and ate a lot.’.

Following Büring (Reference Büring2003) and Muñoz Pérez and Verdecchia (Reference Pérez, Carlos and Verdecchia2022), I take the activation of the CT-value to be part of the conventional meaning of the CT-marking in a VDC, whereas the content of alternative subquestions is a matter of conversational implicature.

Note furthermore that the CT-value formation rule (18) does not guarantee that there must be a subquestion that is unresolved by the VDC or any previous utterance. While CT-marking generates at least two subquestions, something more needs to be said about the subquestions to ensure at least one of them remains unresolved after the VDC is uttered (hence the incompleteness effect). This is crucial, since otherwise cases like (9b) could be felicitous and complete when the initial verb is stressed, because the evoked subquestions {‘Did you cut the cucumber?’, ‘Did you wash the cucumber?’} can both be resolved by (9b) together with the preceding question (9a). Recall also that (10), reproduced below as (21), is fine. How does adding the first clause (‘as for cutting (it), I didn’t’), which is already given in (9a), “cancel” the incompleteness effect of the second VDC?

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(21) (Same context as in (9a)) QIEcomma wo mei qiecomma dan XIcomma wo xi le. cut 1SG NEG cut but wash 1SG wash ASP ‘As for cutting (it)comma I didn’t; as for washing (it)comma I did.’.

I submit that what governs the infelicity of (9b) and the felicity of (21) is the following condition in (22):

This condition underlies the incompleteness of typical VDCs discussed earlier, including (9b) if the initial verb is stressed: They are incomplete because at least one subquestion has not been answered yet within the same strategy. Crucially, even if the subquestion ‘Did you cut the cucumber?’ is already answered by (9a), the latter is uttered by a different speaker and thus is not within the same discourse strategy as (9b). Thus, (9b) does not satisfy (22). On the other hand, (21) constitutes a “complete” strategy in which the subquestions activated by the two VDCs can all be resolved by the latter within the same strategy. Specifically, the first VDC in (21) activates the subquestions in (23a), and the second VDC those in (23b). These four subquestions are each part of the strategy to resolve a larger QUD (e.g., ‘What did you do?’), and the two VDCs in (21) altogether provide the complete answers to the four subquestions, thereby also resolving the larger QUD.

In short, a VDC can appear without a continuation, or in a strategy-final position, if the condition (22) is satisfied; whenever it is not, incompleteness arises. The incompleteness effect of a VDC therefore is an inference that can be “cancelled” by certain discourse conditions.

2.4 Further arguments for VDCs as CT constructions

The idea that VDCs resemble CT constructions aligns well with the observation by previous studies that VDCs are context-sensitive: The verb copies are contextually anaphoric to a related current question under discussion (QUD; Roberts Reference Roberts2012). Thus, (24) is felicitous but (25) is not under respective QUDs.

(modeled on Zhong Reference Zhong2016: 149–150)

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Numbered linguistics example from a textbook. Example number: (25). English context sentence in parentheses: (I watched a movie yesterday.) Two lines of Chinese and gloss follow, each marked with a hash symbol indicating an acceptability-marked utterance. Chinese line: hash CHI comma Yijun chi le comma buguo ellipsis. Gloss line: eat Yijun eat ASP but. The label ASP appears in small capitals. English translation line, marked with a hash and opening single quote: As for eating comma Yijun ate comma but ellipsis closing single quote. The example is laid out in three aligned lines: the Chinese plus pinyin line, the word-by-word gloss line beneath it and the free English translation on the final line. Hash symbols precede the Chinese and translation lines. Ellipses appear at the end of both the Chinese and translation lines, indicating the utterance is incomplete.

The example (26) shows a wh-question can also serve as a QUD for a VDC:Footnote ⁵

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Example Number: (26) Question: (What did Yijun read?) Mandarin: KAN, ta kan-le zhe-ben shu, buguo... Gloss: read 3SG read-ASP this-CL book but Translation: 'As for reading, she read this book, but…'.

(modeled on Zhong Reference Zhong2016: 150)

On the other hand, while the topic-hood of the initial copy of a VDC is widely acknowledged (Lee Reference Lee, Arika Okrent and Boyle2000, Reference Lee and Anne-Marie Di Sciullo2003; Liu Reference Liu2004; Shyu Reference Shyu and Ching-Hsiun Lin2007; Cheng and Vicente Reference Cheng and Vicente2013; Zhong Reference Zhong2016; Yang and Wu Reference Yang and Yicheng2017), the initial verb does not always (just) mark a topical element in the current discourse, and therefore should not be considered a discourse/aboutness topic. For instance, the QUD in (27) makes the verbal expression ‘drink’ a salient topic, but the VDC can be a felicitous response with ‘eat’ as the initial verb copy. The QUD in (28) does not even explicitly include any topical verbal expression, and yet the responding VDC is also fine.

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(27) (Did Yijun drink?) CHIcomma Yijun chi lecomma buguo mei he. eat Yijun eat ASP but NEG drink ‘As for eatingcomma Yijun atecomma but didn’t drink.’.

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(28) (What did Yijun do at the party?) CHI, Yijun chi-le yidian, buguo mei he dongxi. eat Yijun eat-ASP some but NEG drink thing ‘As for eating, Yijun ate a little, but didn’t drink anything.’.

Importantly, these properties of verb doubling are also characteristic of CTs. The following examples in (29), all from Büring (Reference Büring, Caroline Féry and Ishihara2016), show that a CT can function as a partial topic, a shifting topic, and a purely implicational topic, respectively. One can see that (28) is analogous to (29a) (both introducing a partial answer to a wider QUD) and (27) to (29b) (both introducing a partial answer that does not directly address the QUD). Lastly, (29c) is a complete answer to the indicated QUD but additionally implies a question about other individuals in other places.

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(29) a. (Which guest brought what?) Fred subscript CT brought the beans subscript F. b. (Will Bo come to school today?) Yesterday subscript CT he was sick subscript F. c. (Where was the gardener at the time of the murder?) The gardener subscript CT was in the house subscript F.

(Büring Reference Büring, Caroline Féry and Ishihara2016: 68–70)

The implicational property of (29c) is precisely what we have seen in many VDC examples discussed so far: A VDC implies an implicit, unresolved question inquiring about some verbal alternative (or “does not deliver all the information that is expected” (Krifka Reference Krifka2008: 268)), thus rendering itself an incomplete utterance. For the same reason, even though the initial verb of a VDC evokes alternatives, it should not be treated as a focus because a sentence with focus can completely resolve a wh-question but a VDC cannot do so without a continuing clause.

More generally, VDCs exhibit what Krifka (Reference Krifka2008) calls delimitation in that they do not wholly satisfy the current informational needs of the common ground (CG), which would be satisfied by an additional expression, for example, a continuing clause specifying an alternative of the doubled verb. This is a semantic feature also shared by frame setters such as the adverbial healthwise in (30b).

(Krifka Reference Krifka2008: 269)

In terms of CG management, Krifka (Reference Krifka2008) argues that whereas a CT diverges from the expectation that information about a more comprehensive or distinct entity is given, a frame setter indicates that the information provided is restricted to a particular dimension of what is expected. Discourse/aboutness topics do not structure CG management in such manners.

Finally, recall that Cheng and Vicente (Reference Cheng and Vicente2013) suggest Mandarin VDCs carry an adversative implicature that can be also observed for Spanish predicate doubling, and that Vicente (Reference Vicente2007) further proposes that in Spanish the implicature is conversational due to its cancellability. However, Muñoz Pérez and Verdecchia (Reference Pérez, Carlos and Verdecchia2022) take a different standpoint by arguing that predicate doubling in Spanish represents CT constructions in which the first predicate is a CT exactly in Büring’s (Reference Büring2003) sense. They use the term “continuation effect”, which corresponds to “incompleteness effect” in this article, to refer to the indication by the initial predicate that there is at least one alternative partial question which should be addressed to resolve a bigger question. For Muñoz Pérez and Verdecchia (Reference Pérez, Carlos and Verdecchia2022), evoking alternative questions is a conventional implicature of CTs, and therefore of Spanish predicate doubling, which does not go away even if something other than the verbal predicate is focused, as (31b) shows (cf. (7b)).

Long description

(31) a. ¿Qué leyó Jorge? ¿El libro o el artículo? what read.3SG Jorge the book or the article ‘What did Jorge read? The book or the article?’ b. [Leer]CT, leyó [el artículo]F, (el libro solo lo ojeó). to.read read.3SG the article the book only it had.a.look.at.3SG ‘As for reading, he read the article, (the book, he had a look at it).’.

(Muñoz Pérez and Verdecchia Reference Pérez, Carlos and Verdecchia2022: 1176)

If this characterization and analysis are on the right track, the relation between Mandarin VDCs and Spanish predicate doubling is stronger than what Vicente (Reference Vicente2007) implies. I hold that studies such as Muñoz Pérez and Verdecchia (Reference Pérez, Carlos and Verdecchia2022) support the more general picture in which predicate doubling is associated with CT-based strategies of inquiry (see Jasinskaja Reference Jasinskaja, Caroline Féry and Ishihara2016 and references therein for similar CT-like doubling phenomena in Slavic languages). Mandarin VDCs are yet another manifestation of this crosslinguistic pattern.

Overall, given the above considerations, the proposal that Mandarin VDCs are CT constructions seems plausible. An utterance involving a CT or VDC is embedded under a larger discourse structure in which the utterance represents a partial answer that addresses a subquestion, leaving some other subquestion(s) triggered but unaddressed.

3.1 Cheng and Vicente (Reference Cheng and Vicente2013) on VDCs

On the surface, VDCs resemble cleft constructions in Mandarin as the latter also contain the copula shi (Chao Reference Chao1968, Huang Reference Huang1988), as (32) shows.

Cheng and Vicente (Reference Cheng and Vicente2013) propose a cleft analysis for VDCs, according to which the initial verb is related to the second via overt head movement, as shown in (33) below. This structure follows Cheng’s (Reference Cheng2008) general theory of Mandarin clefts in taking the complement of the copula shi to be a Small Clause (SC); in VDCs, the subject of the SC is a vP, which is followed by a null pro predicate that moves to the left of shi (i.e., predicate inversion). Support for the movement analysis includes locality effects and lexical identity effects.

Long description

(33) [CP V subscript i [XP pro subscript PRED shi [SC [vP ... V subscript i ...] t subscript PRED]]].

(Cheng and Vicente Reference Cheng and Vicente2013: 8)

Moreover, Cheng and Vicente maintain that shi is interpreted as verum focus (Höhle Reference Höhle and Joachim Jacobs1992), which affirms the truth of the proposition in its scope. By focalizing the event argument introduced by the lower verb, a VDC asserts that the event under discussion did take place. According to this view, the VDC in each of (6a)–(6c) would assert that an ‘eating’ event did occur, and contrast such a proposition not with alternatives of the verb (‘drink’, ‘walk’, etc.) but with the polar alternative ‘not eating’ (Cheng and Vicente Reference Cheng and Vicente2013: 6).

Unfortunately, it is unclear how the presence of verum focus and the syntactic structure based on (33) should deliver the incompleteness or contrastive effect: Verum focus per se does not render a proposition incomplete, and V-movement is a purely syntactic operation. In addition, in none of the examples in (6a)–(6c) is the semantic contrast between the first clause and the second one between positive polarity and negative polarity. This seems to cast doubt on Cheng and Vicente’s (Reference Cheng and Vicente2013) characterization of the verum focus function of shi. The full meaning of VDCs therefore has remained unexplained under their syntactic account, and indeed under all other accounts of VDCs I am aware of (e.g., Zhong Reference Zhong2016, Yang and Wu Reference Yang and Yicheng2017). In what follows, I will first discuss and reject the treatment of shi in VDCs as a verum marker, and then suggest a different account.

3.2 Is shi in VDCs a marker of verum focus?

To determine whether shi marks verum focus, we can take a closer look at the contexts, namely QUDs, that license shi-VDCs. If they overlap those licensing verum, there is good chance that shi is a marker of verum. However, this does not seem to be the case.

The literature on verum has shown that it is not licensed under just any polar question. The observations by Gutzmann et al. (Reference Gutzmann, Hartmann and Matthewson2020) illustrated below exemplify this point: (34B), but not (34B’), is a felicitous answer to the neutral polar question (34A). But if the question is biased, as in (35A), using verum is possible. This means that verum does more than address a simple polar QUD.

(Gutzmann et al. Reference Gutzmann, Hartmann and Matthewson2020: 12)

Another way to license verum is to make both alternatives salient in the QUD, as in (36A). The verum sentence (36B) would be infelicitous if (36A) is just Is it raining?.

Along with other observations, Gutzmann et al. (Reference Gutzmann, Hartmann and Matthewson2020) propose the interpretation in (37) for verum, which they regard as a semantic operator, rather than a focus marker. This interpretation is based on the conclusion that a verum is licensed when the context involves either an open conflict between salient alternatives in the QUD or a final settlement of the QUD.Footnote ⁶

Long description

Left parenthesis 37 right parenthesis left bracket verum right bracket superscript u comma c left parenthesis p right parenthesis equals check mark. If the speaker c subscript s wants to prevent qud left parenthesis c right parenthesis from being downdated with negation p.

(Gutzmann et al. Reference Gutzmann, Hartmann and Matthewson2020: 39)

If a QUD downdated with $\neg p$, then it is settled toward $\neg p$. The term downdate is from Engdahl (Reference Engdahl, Olivier Bonami and Cabredo-Hofherr2006); see also Gutzmann and Castroviejo (Reference Gutzmann, Castroviejo, Olivier Bonami and Cabredo-Hofherr2011). The superscript u stands for use-conditional (Gutzmann Reference Gutzmann2015) and c for context.

Crucially, as the first examples of this paper have established, shi-VDCs are perfectly fine as responses to neutral polar questions; their QUDs can, but need not, include both alternatives or be biased. More concretely, (1) can answer (38a) (which is neutral without any speaker bias), (38b) (an alternative question), as well as (38c) (which is biased toward a positive answer).

Long description

(38) a. Yijun chi le ma? Yijun eat ASP PRT 'Did Yijun eat?' (neutral polar question) b. Yijun chi le haishi mei chi? Yijun eat ASP or NEG eat 'Did Yijun eat or did she not eat?' (alternative question) c. Yijun shi-bu-shi chiF le? Yijun COP-NEG-COP eat ASP 'Is it the case that Yijun ateF?' (biased polar question).

If shi marks verum in the Mandarin VDC, it is unclear why the latter isn’t subject to the same licensing conditions as verum in other languages. One might attempt to say that shi is a special marker for the kind of verum which is “relative to” a CT sentence. But since the function of verum when applied to p is to prevent a QUD from being downdated with $\neg p$, one should expect shi to perform the same function in a VDC if it marks verum; in other words, a shi-VDC should be licensed only when the QUD meets the “open conflict” or “final settlement” requirement, a requirement that is independent of whether the shi-VDC additionally evokes another subquestion to be answered. However, this is not the case: a shi-VDC is always possible when it is a direct response to a neutral polar question. Thus, despite the popular view that CT constructions, or the predicate doubling phenomena that are semantically parallel to CT constructions, involve a CT plus verum/polarity focus (Vicente Reference Vicente2007, Gyuris Reference Gyuris2009, Jasinskaja Reference Jasinskaja, Caroline Féry and Ishihara2016, Kamali and Krifka Reference Kamali and Krifka2020, Muñoz Pérez and Verdecchia Reference Pérez, Carlos and Verdecchia2022), I hesitate to extend this view to Mandarin shi-VDCs.

This does not mean the copula shi can never be used to express verum. Ye (Reference Ye, Joseph, Lamp, Dreier and Kwon2020) observes that when shi itself is stressed (indicated by capital letters), its prejacent sentence receives a verum-like reading, as in (39a). Also, when stress falls on the verb xihuan ‘like’ in the absence of shi, as in (39b), the verum interpretation results. By contrast, if only the object phrase is stressed, as in (39c), shi is interpreted as a focus marker conveying the exhaustivity that Lisi likes pragmatics only, thus rendering the second clause ‘He also likes syntax’ infelicitous.

Long description

Typed linguistics example numbered (39), arranged as three subexamples labeled a., b. and c. Each subexample shows a Chinese sentence line, a gloss line with abbreviations and an English translation in single quotation marks. Uppercase emphasis is used on SHI in (a), XIHUAN in (b) and YUYONGXUE in (c). In (c), a parenthesized clause begins with “(#” and ends with “.)” and the English translation also contains “(#He also likes syntax)”. (39) a. Lisi SHI xihuan yuyongxue. Ta ye xihuan jufaxue. Lisi COP like pragmatics 3SG also like syntax ‘Lisi DOES like pragmatics. He also likes syntax.’ b. Lisi XIHUAN yuyongxue. Ta ye xihuan jufaxue. Lisi like pragmatics 3SG also like syntax ‘Lisi LIKES pragmatics. He also likes syntax.’ c. Lisi shi xihuan YUYONGXUE. (# Ta ye xihuan jufaxue.) Lisi COP like pragmatics 3SG also like syntax ‘It is pragmatics that Lisi likes. (#He also likes syntax)’.

(Ye Reference Ye, Joseph, Lamp, Dreier and Kwon2020: 359–361)

In other words, verum in Mandarin is expressed through word-level stress, either on verbs or on a copula. In a shi-VDC, however, it is the initial verb copy that is stressed, rather than ${shi}_{{\scriptsize{\text{VDC}}}}$. Even though this study does not experimentally investigate the prosody of VDCs, it is expected that the initial verb should display higher pitch range and longer duration than a discourse topic, along the lines of Hao et al.’s (Reference Hao, Jeannette, Marijn, Jiayi, Erika, Anissa and Boris2024) findings on nominal CTs in Mandarin.Footnote ⁷ Given the above empirical considerations, we can conclude that ${shi}_{{\scriptsize{\text{VDC}}}}$ does not indicate verum.

Still, one may wonder why ${shi}_{{\scriptsize{\text{VDC}}}}$ is generally taken to correspond to auxiliaries such as do or the adverb indeed in English (e.g., in Cheng and Vicente Reference Cheng and Vicente2013), both contributing emphasis. At the very least, however, the auxiliary do does not always convey verum focus. Wilder (Reference Wilder2013) has observed that while does is the only accented word in (40b), both patients and does are phonologically prominent in (41b) (see also Grimshaw Reference Grimshaw2010). In addition, patients in (41b) has the fall-rise contour that is typical of English CT constructions.

(Wilder Reference Wilder2013: 145)

(Wilder Reference Wilder2013: 146)

The two instances of does are also semantically distinct: Only (40b) expresses focus on the positive polarity of the sentence and contrasts it with the negation of the sentence. In Wilder’s (Reference Wilder2013) terms, only the auxiliary in (40b) instantiates verum focus, whereas that in (41b) does not and is even optional to the CT sentence. Even though Wilder (Reference Wilder2013) does not propose an analysis for the “emphatic do” in cases like (41b), it is clear that English “emphatic do” does not always indicate verum focus. This supports the conclusion that while ${shi}_{{\scriptsize{\text{VDC}}}}$ appears to be translatable to emphatic do/indeed, ${shi}_{{\scriptsize{\text{VDC}}}}$ is not necessarily a marker of verum focus. In the next section, a new approach to ${shi}_{{\scriptsize{\text{VDC}}}}$ will be given, which takes it to be not a focus marker but an element that exhibits association with contrastive topic.

3.3 ${\textit{Shi}}_{{{\scriptsize{\text{VDC}}}}}$ and association with contrastive topic

In section 3.1, it was mentioned that the unstressed copula shi in examples like (39c) is a focus marker that conveys exhaustivity. This naturally raises the possibility that ${shi}_{{\scriptsize{\text{VDC}}}}$ is the same element. This section will briefly present Ye’s (Reference Ye, Joseph, Lamp, Dreier and Kwon2020) account on shi as a focus marker, discuss why it is not suitable for ${shi}_{{\scriptsize{\text{VDC}}}}$, and then argue for an alternative analysis.

Ye (Reference Ye, Joseph, Lamp, Dreier and Kwon2020) argues that the exhaustivity of shi originates from the maximality presupposition that its prejacent is a possible complete answer to a current QUD. Specifically, shi has the semantics in (42a): It simply asserts its prejacent but contributes a maximality component as defined in (41b) (roughly following Velleman et al. Reference Velleman, Beaver, Destruel, Bumford, Onea, Coppock and Anca Chereches2012) in the presupposition. In prose, max$_S(p)$ returns a proposition which is strictly stronger than all alternative propositions in the current QUD of the context S, CQ_S (i.e., CQ_S is the most immediate question under discussion of the “QUD stack” in S in Roberts Reference Roberts2012).

Long description

Left parenthesis 42 right parenthesis. a. Double left parenthesis shi double right parenthesis superscript S equals lambda p dot lambda w colon MAX subscript S left parenthesis p right parenthesis left parenthesis w right parenthesis dot p left parenthesis w right parenthesis. b. MAX subscript S left parenthesis p right parenthesis equals lambda w dot for all q element of CQ subscript S comma left parenthesis q greater than subscript S p right parenthesis right arrow not q left parenthesis w right parenthesis.

(Ye Reference Ye, Joseph, Lamp, Dreier and Kwon2020: 362)

Suppose three branches of linguistics are under discussion in S, syntax, semantics, and pragmatics. The set of propositions in the CQ of (39c) is (43), where alternatives stronger than $\textit{like}(\textit{prag})$ are excluded (indicated by strikethrough) by the maximality presupposition of shi.

Long description

Left parenthesis 43 right parenthesis CQs of left parenthesis 38c right parenthesis equals left brace like left parenthesis prag right parenthesis comma like left parenthesis sem right parenthesis comma like left parenthesis syn right parenthesis comma like left parenthesis prag circled plus syn right parenthesis comma like left parenthesis prag circled plus sem right parenthesis comma like left parenthesis sem circled plus syn right parenthesis comma like left parenthesis prag circled plus sem circled plus syn right parenthesis right brace.

As a result, (39c) is necessarily exhaustive because the assertion and maximality presupposition together exclude all alternatives of $\textit{like}(\textit{prag})$: If $\textit{like}(\textit{prag})$ is true and all stronger alternatives are (presupposed to be) false, then $\textit{like}(\textit{sem})$ and $\textit{like}(\textit{syn})$ must both be false.

Applying (42) to ${shi}_{{\scriptsize{\text{VDC}}}}$ would be problematic, however, as noted by a reviewer: If ${shi}_{{\scriptsize{\text{VDC}}}}$ is such a focus marker, shi-VDCs would have the copied verb associated with a maximality presupposition and CT at the same time. Such a pattern is predicted to be impossible, because a proposition cannot be a complete answer and also a partial answer to the same CQ.Footnote ⁸ This is borne out by (44), where the CT is Lisi and the focus marker shi is associated with the pronoun ta.

Long description

(44) * Lisi ne, shi TA xihuan yuyongxue. Lisi CT COP 3SG like pragmatics Intended: ‘As for LisiCT, it is heF that likes pragmatics.’.

(Ye Reference Ye, Joseph, Lamp, Dreier and Kwon2020: 366)

I now argue that a new account of ${shi}_{{\scriptsize{\text{VDC}}}}$, which is partially modeled on Ye’s (Reference Ye, Joseph, Lamp, Dreier and Kwon2020) maximality-encoding shi but differs from it in a number of important aspects, allows for a straightforward explanation of the obligatory adversative continuation of shi-VDCs. The basic idea is that ${shi}_{{\scriptsize{\text{VDC}}}}$ evokes an alternative question Q to the CQ which could have been asked but was not, and the semantics of ${shi}_{{\scriptsize{\text{VDC}}}}$ requires that Q have a negative answer. The negative answer to Q then leads to the obligatory ‘but’-continuation. Since ${shi}_{{\scriptsize{\text{VDC}}}}$ relates to a competing alternative of the CQ, it can be said to associate with CT in this new analysis.

Before detailing the analysis, let us note that the shi-VDC (1) can be an (incomplete) response to the neutral polar question in (45a) or the A-not-A question formed with the focus marker shi in (45b), which expresses the speaker’s bias toward a positive answer (Ye Reference Ye, Joseph, Lamp, Dreier and Kwon2020). However, the same shi-VDC cannot take the wh-question in (46) as its CQ; compare the VDC without shi in (26).

Long description

(45) Appropriate CQ for (1) (CHI, Yijun shi subscript VDC chi le . . . ): a. Yijun chi le ma? Yijun eat ASP PRT ‘Did Yijun eat?’ b. Yijun shi-bu-shi chi subscript F le? Yijun COP-NEG-COP eat ASP ‘Is it the case that Yijun ate subscript F?’.

Long description

(46) Inappropriate CQ for (1) (CHIcomma Yijun shi subscript VDC chi le . . .): Yijun zuo-le shenme divided by naxie (shi)? Yijun do-ASP what divided by which thing ‘What divided by Which (thing divided by things) did Yijun do?’.

The contrast above indicates that ${shi}_{{\scriptsize{\text{VDC}}}}$, unlike the focus marker shi, is not anaphoric to a current wh-question. Rather, the CQ of a shi-VDC is restricted to a polar question. Put differently, the presence of ${shi}_{{\scriptsize{\text{VDC}}}}$ imposes the constraint on the context that the latter must contain a polar question.

My proposal is as follows. A shi-VDC is a CT construction identical to a VDC without shi, both containing a CT-marked verb copy that triggers a CT-value and providing an answer to one of the subquestions in the CT-value, except that ${shi}_{{\scriptsize{\text{VDC}}}}$ contributes the presupposition that some alternative question to the CQ (the question immediately preceding the shi-VDC), which entails the CQ, has a negative answer. The entailment relation between questions is defined in (47) (following Groenendijk and Stokhof Reference Groenendijk, Stokhof, J. van Benthem and ter Meulen2011, Roberts Reference Roberts2012).

For instance, the question ‘Did Yijun eat and play?’ entails the question ‘Did Yijun eat?’ because every complete answer to the former, as listed in (48), also completely resolves the latter.

The denotation of ${shi}_{{\scriptsize{\text{VDC}}}}$ is given in (49a), where S is the context and qmax_S stands for the question-based maximality operator with the semantics in (49b). In prose, ${shi}_{{\scriptsize{\text{VDC}}}}$ asserts its prejacent p and presupposes that some question in the set of alternative current questions (henceforth AltCQ) which entails (‘$\models$’) the CQ has a negative answer. The last part of (49b) ($\forall q \in Q [\neg q(w)]$) says every proposition inside Q is negated; since Q here is a polar question, formally a singleton set of propositions, the $\forall$-quantification is trivially satisfied. Finally, the denotation of AltCQ in context S is informally characterized as in (49c), where the notion of pertinence is taken from Büring (Reference Büring, Caroline Féry and Ishihara2016): A question is pertinent to S if it is relevant to the current discussion in S and not resolved.

Long description

Equation forty-nine consists of three parts labeled a, b and c. Part a defines shiv sub VDC superscript S as a function of p and w using QMAX. It is expressed as bracket shiv sub VDC bracket superscript S equals lambda p, lambda w, such that QMAX sub S of p applied to w, times p applied to w. Part b defines QMAX sub S of p as lambda w, such that there exists Q subscript left parenthesis st comma t right parenthesis in ALT CQ sub S, where Q entails CQ sub S and for all q in Q, not q applied to w. CQ sub S is the current question under discussion of p in the context S. Part c defines ALT CQ sub S as the set of Q sub S, where Q sub S is an alternative to CQ sub S and pertinent to the current discussion in the context S.

Two remarks are in order. First, I am assuming that an alternative of the CQ is obtained by replacing the verb in the CQ with an alternative verbal expression, similarly to how focus alternatives are obtained from a focused sentence in Rooth’s (Reference Rooth1992) system. Since the members in the AltCQ set must take the form of polar questions, as explained below, the CQ itself must also be a polar question – in other words replacing the verb in a member of AltCQ with a different verb results in another polar question. This explains the observation that a shi-VDC always responds to a polar question.

Here is why the members in the AltCQ set must be polar questions. Suppose, first, that the relevant AltCQ of the shi-VDC Chi, Yijun shi chi le $\dots$ ‘As for eating, Yijun ate$\dots$’ can be the wh-question ‘What did Yijun do?’. Such an AltCQ entails ‘Did Yijun eat?’ per (47), but negating all propositions in its denotation – in other words {‘Yijun ate’, ‘Yijun ate until full’, $\dots$} contradicts the assertion that Yijun ate. Hence, a shi-VDC cannot have a wh-question as a relevant AltCQ. Next, suppose a neutral polar question $?p$ denotes the set of propositions $\{p, \neg p\}$, rather than the singleton $\{p\}$. Negating both p and $\neg p$ clearly also leads to contradiction, because p and $\neg p$ cannot both be true. It follows that the proposed semantics of ${shi}_{{\scriptsize{\text{VDC}}}}$ in (49) guarantees that members of the AltCQ of a shi-VDC must be polar questions. The idea that a neutral polar question denotes a singleton (Büring Reference Büring2003, Biezma and Rawlins Reference Biezma and Rawlins2012) is crucial to the present analysis.

The second remark is that members in AltCQ represent alternative questions that could have been asked in place of the CQ, and are therefore not the subquestions which address the same larger QUD together with the CQ. In terms of Büring’s (Reference Büring2003) model of d(iscourse)-trees, this means AltCQ may consist of SubQ1 in (50a) and SubQ1$'$ in (50b) (as opposed to SubQ1 and SubQ2 in (50a), both dominated by the same node), which are different ways to resolve the same QUD using the same CT-based strategy. The alternatives in AltCQ are not the members in the CT-value triggered by the initial verb copy and therefore may not be logically independent of one another.

Long description

The image contains two diagrams labeled a and b, each illustrating a question tree related to Yijun's actions. Diagram a starts with the question 'QUD: What did Yijun do?' branching into three sub-questions: 'SubQ1: Did Yijun eat?', 'SubQ2: Did Yijun drink?' and 'SubQ3: Did Yijun ...?'. Diagram b also begins with 'QUD: What did Yijun do?' but branches into two sub-questions: 'SubQ1 prime: Did Yijun eat and drink?' and 'SubQ2 prime: Did Yijun ...?'. The diagrams visually represent different ways to inquire about Yijun's activities, with diagram a focusing on separate actions and diagram b combining eating and drinking into one query.

Formulated this way, ${shi}_{{\scriptsize{\text{VDC}}}}$ is similar to Ye’s (Reference Ye, Joseph, Lamp, Dreier and Kwon2020) focus marker shi in that both require something to be false: For the latter, alternative propositions stronger than shi’s prejacent are false, whereas for the former it is the answer to an alternative question entailing the CQ that is false. The two kinds of shi therefore also diverge in two aspects. First, ${shi}_{{\scriptsize{\text{VDC}}}}$ is associated with CT, not focus, in the sense that its domain of quantification consists of alternative questions to the CQ rather than the propositions in the denotation of a wh-QUD. Second, ${shi}_{{\scriptsize{\text{VDC}}}}$ has a weaker maximality presupposition, which involves existential rather than universal quantification. In other words, it merely requires there be one alternative question to be negatively answered.

To illustrate with an example, consider (51) again, where the CQ is ‘Did Yijun eat?’:

Since the qmax operator demands that there be an alternative polar question Q that entails the CQ, let us assume Q is ‘Did Yijun eat and play?’, which differs from the CQ only in the verbal expression and is pertinent to the current discussion about what Yijun did. Moreover, since qmax also demands that every proposition in Q’s denotation be false, (51) implies $\neg[\textit{eat}(\textit{Yijun}) \wedge \textit{play}(\textit{Yijun})]$ as part of the presupposition of ${shi}_{{\scriptsize{\text{VDC}}}}$, which is tantamount to saying that ‘Yijun ate’ is the only true proposition and that ‘Yijun played’ is false. Ye’s (Reference Ye, Joseph, Lamp, Dreier and Kwon2020) semantics of the focus marker shi would derive the same result for this case, but we have done so by analyzing ${shi}_{{\scriptsize{\text{VDC}}}}$ with association with CT, in particular with the alternative questions of the CQ, the latter being a member in the CT-value triggered by a CT.

The proposal that a shi-VDC is a CT construction and that ${shi}_{{\scriptsize{\text{VDC}}}}$ operates on alternative questions has immediate consequences. Since (51) evokes a CT-value, its incompleteness effect is derived in the same way as VDCs without shi, as discussed in section 2. Moreover, it explains why (51) cannot be continued by $\textit{play}(\textit{Yijun})$, because this proposition contradicts ${shi}_{{\scriptsize{\text{VDC}}}}$’s presupposition. On the other hand, the continuation of (51) can be the negation of $\textit{play}(\textit{Yijun})$, because $\textit{eat}(\textit{Yijun})$ $\wedge$ $\neg\textit{play}(\textit{Yijun})$ is consistent with the presupposition of ${shi}_{{\scriptsize{\text{VDC}}}}$. The proposal also accounts for the fact that a shi-VDC is felicitous as a response to a polar question but not a wh-question, because (a) the qmax operator requires that every proposition in the denotation of some question Q (in AltCQ) be false, and this is only possible if Q is a polar question, and (b) Q and the CQ of a shi-VDC are alternatives to each other that differ only in the verbal expression. Relatedly, the proposal that shi-VDCs are anaphoric not to a wh-QUD but to polar questions avoids the theoretical issue surrounding (44) above.

As for the continuing clause of the shi-VDC, note that it does not have to involve negation at the matrix level; recall the two examples (6b) and (6c), repeated below in (52).

Long description

(52) a. CHI, Yijun (shi) chi le, keshi ta juede bu hao-chi. eat Yijun COP eat ASP but 3SG think NEG good-eat ‘As for eating, Yijun (did) eat, but she thought (it) wasn’t tasty.’ b. CHI, Yijun (shi) chi le, keshi ta hai neng zai chi. eat Yijun COP eat ASP but 3SG still can again eat ‘As for eating, Yijun (did) eat, but she could still eat more.’.

Under my analysis, (52a) and (52b) can evoke the alternative current questions in (53a) and (53b), respectively. The negative answer to (53a), together with the assertion of the shi-VDC in (52a), derives the result that Yijun didn’t think it was tasty; similarly, the shi-VDC in (52b) implies that Yijun can eat more by presupposing the negative answer to (53b).

I assume something like the reverse of negative raising might be at work for (52a), allowing the matrix-level negation on ‘Yijun thought it was tasty’ to be realized by the continuation of (52a) instead, with negation occurring in the embedded clause.Footnote ¹⁰

Taking stock, just like the VDC without shi, the CT-value of the shi-VDC is triggered by CT-marking on the initial verb copy and derived through the two-step formation in (18). Crucially, ${shi}_{{\scriptsize{\text{VDC}}}}$ interacts with alternatives of the CQ compositionally, such that some alternative question of the CQ which entails the CQ is answered negatively. In the next section, I address some observations and questions raised by reviewers.Footnote ¹¹

3.4 Further discussion

The following two questions arise thanks to a reviewer. First, a shi-VDC does not always require other alternatives to be false, as evidenced by the example (54) where the con-tinuation is additive.

Long description

(54) CHIcomma shi chi le. Women zai qu he dianr ba. eat COP eat ASP 1PL more go drink a.bit PRT ‘As for eatingcomma I did eat. Let’s go for a drink.’.

Second, ${shi}_{{\scriptsize{\text{VDC}}}}$ could be analyzed as verum focus in cases like (55b) and (56b). In each example, the shi-VDC answers a polar QUD and the adversative continuation cannot be taken as an answer to the same QUD or as an alternative to the shi-VDC.

Long description

(55) a. Ta chi le ma? 3SG eat ASP PRT ‘Did he eat?’ b. CHI, ta kending shi chi le, zhishi ni mei kanjian. eat 3SG definitely COP eat ASP just 2SG NEG see ‘As for eating, he definitely did eat, it’s just that you didn’t see it.’.

Long description

(56) a. Ta mei chi ba? 3SG not eat PRT ‘He didn’t eat?’ b. CHI, ta queshi shi chi le, zhishi ni bu zhidao. eat 3SG indeed COP eat ASP just 2SG NEG know ‘As for eating, he indeed did eat, it’s just that you don’t know.’.

Regarding (54), notice that even though no adversative clause is present, the second clause still implies that ‘drinking’ has not been done. The current analysis that ${shi}_{{\scriptsize{\text{VDC}}}}$ requires an alternative question to be negatively answered is still applicable if we take ‘Did I eat and drink?’ to be the alternative of ‘Did I eat?’. In this case, the negative answer is implicit but can be inferred by the second clause in (54). On the other hand, an utterance such as ‘Let’s go home!’ or ‘See you tomorrow!’, which does not imply anything else to be done, does sound odd as a continuation of the shi-VDC.Footnote ¹²

As for the data in (55) and (56), they actually present two separate issues: (i) whether ${shi}_{{\scriptsize{\text{VDC}}}}$ does express verum focus and (ii) whether the continuing clause in (55b) and (56b) can be considered an alternative of the respective shi-VDC. First, adverbs such as kending ‘definitely’ or queshi ‘indeed’ do intuitively express an emphasis on the truth of a sentence, and I agree that these adverbs may signal verum in a sentence, possibly in a way similar to really (Romero and Han Reference Romero and Han2004). Nonetheless, even if such adverbs introduce verum, it does not follow that ${shi}_{{\scriptsize{\text{VDC}}}}$ in (55b) and (56b) is also verum; it is consistent with my proposal to say that ${shi}_{{\scriptsize{\text{VDC}}}}$ has the semantics in (49) while a shi-VDC can be made a verum sentence by an additional adverb.

Second, notice that (55a) and (56a) may actually not be entirely neutral polar questions, because the continuations ‘you didn’t see’ and ‘you didn’t know’ in the b-sentences signal rejection of the bias expressed by the a-sentences that ‘he ate’ is likely false. As shown in (57), the same continuation would be infelicitous if it is part of the response to someone who simply wonders whether it is raining.

Long description

(57) (Is it raining?) # Xia shi xia lecomma zhishi ni bu zhidao. fall COP fall ASP just 2SG NEG know #‘As for rainingcomma it is rainingcomma it’s just that you don’t know.’.

It seems reasonable, therefore, to interpret (55a) and (56a) not as simple polar questions, but as implicit embedded questions such as (58a) to which the biased question (58b) is an alternative (per pertinence and the form of a polar question), and (55b) and (56b) as a response to (58a).

The rest is computed as before: Since ${shi}_{{\scriptsize{\text{VDC}}}}$ requires (58b) be answered negatively, speaker-b conveys that speaker-a’s suspicion is not confirmed, and the continuation ‘you didn’t see/know (it)’ is just one way to imply this negative answer (i.e., speaker-a’s suspicion was wrong because she didn’t see/know it). On this approach, the CQ and its alternatives are allowed to differ not just in the verbal constituent because the CT-marked verb is interpreted inside an embedding structure. The discussion above is admittedly just a sketch of the path toward a better solution, but I will leave the details for future research.

Next, as observed by a reviewer, (59) shows that a sequence of VDCs is possible in which ${shi}_{{\scriptsize{\text{VDC}}}}$ appears in the first.

Suppose the CQ here is ‘Did Lisi eat?’, and eating, drinking, and playing are the only three things Lisi may have done. According to the current analysis, the presence of ${shi}_{{\scriptsize{\text{VDC}}}}$ indicates at least one alternative that entails the CQ has a negative answer. If we take the polar question ‘Did Lisi eat, drink, and play?’ to be such an alternative, we correctly predict (59) to be felicitous because the negative answer to the alternative, i.e., $\neg[\textit{eat}(\textit{Lisi}) \wedge \textit{drink}(\textit{Lisi}) \wedge \textit{play}(\textit{Lisi})]$, is compatible with $\textit{eat}(\textit{Lisi}) \wedge \textit{drink}(\textit{Lisi})$. Note that this is another argument against applying Ye’s (Reference Ye, Joseph, Lamp, Dreier and Kwon2020) maximality semantics to ${shi}_{{\scriptsize{\text{VDC}}}}$, because it would wrongly rule out the second VDC in (59).

Another of this reviewer’s observations is (60), which indicates that a shi-VDC seems unable to appear in a strategy-final position (marking the answer to the final subquestion within a strategy; Constant Reference Constant2014). This is surprising given my analysis, since the requirement of the second CT (that there be at least one subquestion with the form ‘Did Lisi do x?’ that is not addressed by the second shi-VDC) and the weak maximality presupposition of the second ${shi}_{{\scriptsize{\text{VDC}}}}$ (that some alternative question entailing ‘Did Lisi eat?’, such as ‘Did Lisi eat and drink?’, has a negative answer) seem both satisfied.

Long description

(60) CHIcomma Lisi (shi) chi lecomma HEcomma ta (*shi) mei he. eat Lisi COP eat ASP drink3SG COP NEG drink Intended: ‘As for eatingcomma Lisi did eatcomma but he didn’t drink.’.

A possible explanation is to say that the qmax operator must apply non-vacuously. For (60), the subquestions introduced by the first CT ‘eat’ are {‘Did Lisi eat?’, ‘Did Lisi drink?’}, and those introduced by the second CT ‘drink’ are ‘Did Lisi not eat?’, ‘Did Lisi not drink?’. The first VDC resolves ‘Did Lisi eat?’ and ‘Did Lisi not eat?’, while the second shi-VDC resolves ‘Did Lisi drink?’ and ‘Did Lisi not drink?’. Adding ${shi}_{{\scriptsize{\text{VDC}}}}$ to the first VDC would enforce the presupposition that some question entailing ‘Did Lisi eat?’ (e.g., ‘Did Lisi eat and drink?’) has a negative answer, and this weak maximality effect is not vacuous because the first VDC could be otherwise continued by ‘$\dots$and he also drank’ if ${shi}_{{\scriptsize{\text{VDC}}}}$ is absent. Now, adding ${shi}_{{\scriptsize{\text{VDC}}}}$ to the second VDC in (60) would require either one of (61a) and (61b) to have a negative answer (assuming no other events are relevant). The negative answer to (61a) is (62a), and that to (61b) is (62b). Crucially, (62a) contradicts the assertive content of (60), and therefore cannot be the presupposition of ${shi}_{{\scriptsize{\text{VDC}}}}$, while (61b) is already entailed by the first VDC in (59).

Long description

Left parenthesis 62 right parenthesis. a. Not left parenthesis Lisi ate and Lisi didn't drink right parenthesis equals not left parenthesis Lisi ate right parenthesis or Lisi drank. b. Not left parenthesis Lisi didn't eat and Lisi didn't drink right parenthesis equals Lisi ate or Lisi drank.

Overall, we see that adding ${shi}_{{\scriptsize{\text{VDC}}}}$ to the second VDC in (60) does not produce any effect because the presupposition it contributes is either contradictory or already entailed. Hence, although the weak maximality presupposition of ${shi}_{{\scriptsize{\text{VDC}}}}$ is compatible with both VDCs in (60), it may well be the ban on vacuous application that causes the ungrammaticality.Footnote ¹³ In fact, this view predicts that ${shi}_{{\scriptsize{\text{VDC}}}}$ can never appear in a strategy-final position, because its presupposition would always come out vacuous. This prediction is borne out by (63):

Long description

(63) CHI, Lisi (shi) mei chi, HE, ta (*shi) he le. eat Lisi COP NEG eat drink 3SG COP drink ASP Intended: ‘As for eating, Lisi didn’t eat, but he did drink.’.

3.5 The adversative coordinator ‘but’

One issue that has not been dealt with is the use of keshi ‘but’ or buguo ‘but’ in the continuation clause of a shi-VDC. I submit that the instance of ‘but’ here is a counterexpectational coordinator, which serves to signal certain relations between the propositions it conjoins on the one hand and the propositions in the relevant QUD on the other hand, in the sense of Toosarvandani (Reference Toosarvandani2014).

In his QUD-based treatment across three uses of but (counterexpectational, corrective, and semantic opposition), Toosarvandani (Reference Toosarvandani2014) proposes (64) as the unifying lexical entry, where “ϕ but ψ” entails the conjunction of ϕ and ψ and presupposes that there is one proposition in the relevant QUD set that is implied by ϕ (through a weak implicational relation “$\Rightarrow$”), and that there is also one proposition in the QUD whose negation is implied by ψ.

Long description

Sixty-four. Lexical entry of 'but'. Left square bracket phi but psi right square bracket equals. At-issue colon. Left square bracket phi right square bracket logical and left square bracket psi right square bracket. Presupposition colon. There exists p colon p element of QUD left parenthesis left square bracket phi right square bracket implies p right parenthesis logical and. There exists p colon p element of QUD left parenthesis left square bracket psi right square bracket implies not p right parenthesis.

(Toosarvandani Reference Toosarvandani2014: 25)

Relevant to the present discussion is the counterexpectational use of but, where both conjuncts ϕ and ψ are associated with the same proposition of opposite polarity from the QUD set. Consider the discourse in (65), where (65b) takes (65a) as the relevant QUD, which contains at least the proposition $\textit{clumsy}(\textit{the-player})$. The presupposition of but, according to (64), requires there be a proposition p in the QUD such that $\textit{tall}(\textit{the-player})$ implies p but $\textit{agile}(\textit{the-player})$ implies $\neg p$; see (66). For this use of but, p is $\textit{clumsy}(\textit{the-player})$ in both implicational relations. Under the assumption that a tall player may indeed be expected to be clumsy and an agile player is certainly not clumsy, the required implicational relations are satisfied, hence the counterexpectational meaning of but.

Long description

(66) a. (64A) = {clumsy(the-player)} b. (64B) = At-issue: tall(the-player) ∧ agile(the-player); Presupposition: ∃p : p ∈ QUD(tall(the-player) ⇒ p) ∧ ∃p : p ∈ QUD(agile(the-player) ⇒ ¬p). The text is organized as a numbered item with subparts (a) and (b) and includes a labeled split between 'At-issue' and 'Presupposition' followed by two existential statements. The notation is formal academic and typeset in math/logic format.

(Toosarvandani Reference Toosarvandani2014: 27)

The situation of a shi-VDC conjoined with an adversative clause is similar, except that the VDC is associated with alternative questions to its CQ, instead of alternative propositions in a QUD set. Taking (67) as an example, whose AltCQ is given in (68a), one can see that the conjunctive proposition $\textit{eat}(\textit{Yijun}) \wedge \textit{drink}(\textit{Yijun})$ can be implied by $\textit{eat}(\textit{Yijun})$, and the negation of it can be implied by $\neg\textit{drink}(\textit{Yijun})$. That is, ‘Yijun ate’ (weakly) implies ‘Yijun ate and drank’, and ‘Yijun didn’t drink’ also implies (entails, in fact) ‘Yijun didn’t (both) eat and drink’. This does seem intuitively correct: Upon hearing (67), it is possible for one to infer that (the speaker believes) if Yijun ate, she should have drunk as well, based on whatever considerations are relevant. Since the denotation of AltCQ is a set of polar questions, not a set of propositions, I will borrow the special membership relation ‘$^{\textrm{*}}{\in}$’ in (68c) from Constant (Reference Constant2014) to ensure that the existential quantification in the presupposition of ‘but’ can “access” relevant propositions in AltCQ.

Long description

(67) [CHI] subscript CT, Yijun shi chi le . . . eat Yijun COP eat ASP ‘As for eating, Yijun did eat . . .’.

Long description

Left parenthesis 68 right parenthesis. a. A set containing: eat left parenthesis Yijun right parenthesis; drink left parenthesis Yijun right parenthesis; and eat left parenthesis Yijun right parenthesis logical and drink left parenthesis Yijun right parenthesis. b. Left square bracket Yijun ate comma but did not drink right square bracket equals. At-issue colon eat left parenthesis Yijun right parenthesis logical and not drink left parenthesis Yijun right parenthesis. Presupposition colon. There exists p colon p superscript star element of A L T C Q left parenthesis eat left parenthesis Yijun right parenthesis implies p right parenthesis. Logical and. There exists p colon p superscript star element of A L T C Q left parenthesis not drink left parenthesis Yijun right parenthesis implies not p right parenthesis. c. q superscript star element of C if and only if q occurs somewhere within C.

(Constant Reference Constant2014: 93)

More importantly, ‘but’ is typically (though not universally) used to mark the continuing clause of a shi-VDC because the negative answer to an alternative question that entails the CQ of the shi-VDC is simply the negation of a proposition that entails the shi-VDC. From here, it follows that there is necessarily such a proposition somewhere in AltCQ that is implied by the continuing clause. In another word, for a shi-VDC, an implicational relation from $\neg p_2$ to $\neg[p_1 \wedge p_2]$ is always satisfied, where p ₁ is the assertion of the shi-VDC and p ₂ is the propositional content of the CQ’s alternative that is not addressed by the shi-VDC itself (‘Yijun drank’ in this example). This explains why ‘but’ is a natural marker for the adversative continuing clause.

To summarize, I have shown that the present account can explain the obligatory adversative continuation of shi-VDCs by utilizing the semantics of ${shi}_{{\scriptsize{\text{VDC}}}}$ as a marker presupposing a weak, higher-order maximality on alternatives to a CQ, and that the use of ‘but’ in the continuation can also be captured by adopting Toosarvandani’s (Reference Toosarvandani2014) analysis. The requirement of an adversative continuation is thus accounted for without analyzing ${shi}_{{\scriptsize{\text{VDC}}}}$ as a marker for verum focus.

4.1 VP doubling constructions

Although we have so far only dealt with the (shi-)VDCs in which doubled expressions are bare verbs, more than a V can be copied in this doubling construction. Example (69a) shows a case where a VP constituent including a V and an object can be copied altogether; in (69b) the resultative verbal compound chi-bao ‘eat until full’ is copied; and in (69c) the Neg-V sequence is copied. As with VDCs, the initial predicate copy must be stressed.

Long description

(69) a. MAI HUA, Yijun shi mai hua le ... buy flower Yijun COP buy flower ASP 'As for buying flowerscomma Yijun did buy flowers ...' b. CHI-BAOcomma Yijun shi chi-bao le ... eat-full Yijun COP eat-full ASP 'As for eating to fullcomma Yijun did eat until full ...' c. MEI QUcomma Yijun shi mei qu ... NEG go Yijun COP NEG go 'As for not goingcomma Yijun indeed didn\u0019t go ...'.

Following the qmax-based analysis of ${shi}_{{\scriptsize{\text{VDC}}}}$, we may take (69a) to immediately follow the CQ ‘Did Yijun buy flowers?’ and ${shi}_{{\scriptsize{\text{VDC}}}}$ to activate the alternative to the CQ in (70), a pertinent polar question that contains two different VP expressions. Example (69a) further requires an adversative continuation as usual, as (70) entails the CQ and is presupposed by ${shi}_{{\scriptsize{\text{VDC}}}}$ to be answered negatively.

Long description

(70) ‘Did Yijun buy flowers and go jogging?’ (alt. question of the CQ of (69a)).

Consequently, the continuation must be something like ‘Yijun didn’t go jogging’. VP doubling constructions can therefore be analyzed in a parallel manner to VDCs.

Sometimes the CT-marked phrase is not identical to the main predicate, as in (71).

Given the semantic equivalence between (71) and (69a), I assume (71) is an elliptical form of (72) instead, where the main predicate contains an elided object phrase.

Notice, however, that there are independent rules governing when a subconstituent in a Mandarin VP can be elided and when not. Example (69b), repeated below as (73a), cannot take the form of (73b). That is, the verb-resultative compound disallows the deletion of the resultative morpheme, even though the CT-marked VP chi-bao ‘eat until full’ can in principle provide the antecedent for the anaphoric deletion of bao ‘full’.

Long description

(73) a. CHI-BAO, Yijun shi chi-bao le ... eat-full Yijun COP eat-full ASP 'As for eating until full, Yijun did eat until full...' b. * CHI-BAO, Yijun shi chi-bao le ... eat-full Yijun COP eat-full ASP Intended: Same as (73a).

What governs the deletion as seen above seems to also be what governs ellipsis in topic configurations in Mandarin more generally. For instance, in a ‘speaking-of’ topic construction such as (74a), the object phrase in either the topic or the comment clause can be elided, but the resultative morpheme in the comment cannot, as in (75b). If we take the initial and second VP-copies of (72) to correspond (at least structurally) to the topic and comment in (74a), respectively, then the grammaticality of (72) is no surprise. Similarly, bao ‘full’ in the main predicate of (73b) cannot be dropped just as bao in the comment clause of (75b) cannot.

Long description

(74) a. Shuodao mai hua, Yijun shi mai hua le ... speaking.of buy flower Yijun COP buy flower ASP 'Speaking of buying flowers, Yijun did buy (flowers) ...' b. Shuodao mai hua, Yijun shi mai hua le ... speaking.of buy flower Yijun COP buy flower ASP 'Speaking of buying, Yijun did buy (flowers) ...'.

Long description

(75) a. Shuodao chi-bao, Yijun shi chi-bao le ... Line break speaking.of eat-full Line break Yijun COP eat-full ASP Line break ‘Speaking of eating, Yijun did eat until full ...’ Line break b. * Shuodao chi-bao, Yijun shi chi-bao le ... Line break speaking.of eat-full Line break Yijun COP eat-full ASP Line break Intended: same as (75a).

It should therefore be safe to assume that VP doubling cases like (73b) are ruled out not on semantic grounds, but on the grounds of more general anaphoric deletion rules of topic constructions in Mandarin, which will not be investigated further in this article.

Yet another type of doubling constructions which does not straightforwardly follow from the current proposal is shown in (76), where the main predicate contains more elements than a bare verb but only the verb head is copied.

Long description

(76) a. (Do you want to eat?) CHIcomma wo shi xiang chi ... eat 1SG COP want eat ‘As for eatingcomma I do want to eat.’ b. (Will you certainly eat?) CHIcomma wo shi yiding hui chi ... eat 1SG COP certainly will eat ‘As for eatingcomma I will certainly eat ...’.

(Cheng and Vicente Reference Cheng and Vicente2013: 6)

Once again, we may assume the surface forms of such examples are derived through ellipsis of partial material in the initial VP copy, as in (77):

Long description

(77) a. (Do you want to eat?) XIANG CHI, wo shi xiang chi ... want eat 1SG COP want eat 'As for wanting to eat, I do want to eat...' b. (Will you certainly eat?) HUI CHI, wo shi yiding hui chi ... will eat 1SG COP certainly will eat 'As for going to eat, I am certainly going to eat...'.

Nonetheless, at least in some cases, the initial verb copy is a bare V. Suppose Yijun and I walk past a candy shop and she says (78a) to me. In this scenario, I could felicitously respond with (76a) above, but (78b) would be odd for me to say. The intuition is that (78b) is infelicitous because the question ‘Do you want to eat candies?’ is not available from this context, or, in Büring’s (Reference Büring, Caroline Féry and Ishihara2016) terms, is not identifiable. A felicitous response to (78a) would be the counterpart of (78b) without the initial xiang ‘want’, namely (76a), which does not require the QUD ‘Do you want to eat candies?’.

Long description

(78) a. Ni mai yixie tang lai chi ba! 2SG buy some candy come eat PRT ‘Buy some candies to eat!’ b. # XIANG CHI, wo shi xiang chi, keshi mei qian (mai lai chi). want eat 1SG COP want eat but NEG money (mai lai chi). #'As for wanting to eat, I do want to eat, but I have no money to buy some (to eat).'.

The puzzle, therefore, is how to generate the right CT-value for (76a) in a context in which the copied constituent is just the V head of a larger VP, but not the VP with deletion.

My tentative analysis is the revised CT-value formation rule in (79). In particular, step 2 is relaxed to allow an alternative subquestion to differ from the one formed in step 1 in more material than the copied verb, if the alternative subquestion contains the copied verb.

Long description

(79) Revised CT-value formation of Mandarin VDCs (cf. (18)) a. Step 1: Form a polar question from a VDC excluding the initial verb copy. Formally: {P(a)}, where P is the VP-denotation of a VDC and a the subject b. Step 2: Form a set of polar questions from the result of step 1 by re-placing a subconstituent of the latter with some alternative to it which contains the copied verb. Formally: {{P′(a)} | P′ ∈ D_et}, where P′ is a variable ranging over denotations of alternative VPs which contain the V head.

This revision does not affect anything established so far, but can solve the problem currently under discussion. Given (79), the CT-value {‘Do you want to eat candies?’, ‘Will you eat candies?’, ‘Do you have money to buy candies to eat?’} can be generated for (76a) because all the subquestions contain the copied V ‘eat’.Footnote ¹⁴ This flexibility allows (76a) to be a felicitous (partial) answer to a wide range of QUDs, and can moreover account for the adversative continuation ‘but I have no money’, because the subquestion ‘Do you have money to buy candies to eat?’ can also be derived through (79) (of course, the adversative continuation has to be interpreted as ‘but I have no money to buy candies to eat’). I conclude that (79) is the more inclusive CT-value formation rule that can capture all the VDCs presented up to this point, although (18) suffices to account for the VDCs in which the initial copy is identical to the lower copy (putting aside aspectual marking).

4.2 Object preposing constructions

In Mandarin, the incompleteness effect and adversative inference typical of VDCs are also observed for constructions where an object phrase is preposed, either to a sentence-initial position, as in (80), or to a lower periphery position between the subject and VP, as in (81).

Long description

(80) Zhei-ge xuesheng, wo xihuan, nei-ge, wo bu xihuan. this-CL student 1SG like that-CL 1SG NEG like ‘This student I like, that one I don’t.’.

(Paul Reference Paul2002: 700)

Long description

(81) a. Wo zhe-pian lunwen xihuan, *(na-pian lunwen bu xihuan). 1SG this-CL paper like that-CL paper NEG like ‘This paper, I like, but that paper, I don’t.’ b. Wo cai chi le, fan hai mei chi. 1SG vegetables eat ASP rice yet NEG eat ‘I have already eaten the vegetables, but not the rice.’.

(Tsai Reference Tsai1994: 138)

(Paul Reference Paul2002: 700)

In particular, it is noted by many (Tsai Reference Tsai1994, Ernst and Wang Reference Ernst and Wang1995, Paul Reference Paul2002, Badan Reference Badan2007) that the SOV sentences in (81) require a contrastive or “list” reading of some sort, which can be manifested by a continuing conjunct. This is precisely the signature property of VDCs. In addition, SOV sentences need not be followed by an adversative ‘but’-clause: (81a) can be continued by ‘$\dots$and that paper, I also like’, and (81b) by ‘$\dots$and I also ate rice’. This pattern clearly resembles that of (4b). By contrast, the “list” reading is not obligatory to (80), in which the preposed object can function as a discourse topic; however, if the object is stressed (Pan Reference Pan, M. M. Jocelyne Fernandez-Vest and Valin2015) or pronounced with a higher pitch range and longer duration than a discourse topic (Hao et al. Reference Hao, Jeannette, Marijn, Jiayi, Erika, Anissa and Boris2024), the “list” reading becomes salient.

Based on a series of syntactic tests, Badan (Reference Badan2007) identifies the preposed objects in Mandarin SOV sentences as CTs, which I believe is correct. What remains to be accounted for is the source of the contrastive component. I argue that in an object preposing construction, the preposed object is interpreted as a CT, following Badan (Reference Badan2007), and moreover that the meaning of the construction can be derived through the three-step formation rule in (82), which is modeled on (18).Footnote ¹⁵

Long description

(82) CT-value formation of Mandarin object preposing constructions a. Step 1: Reconstruct the preposed object back to the base position. Formally: P(b), where P is an unsaturated proposition excluding the preposed object and b the preposed object b b. Step 2: Form a polar question from the object preposing construction. Formally: {P(b)} c. Step 3: Form a set of polar questions from the result of step 2 by replacing the CT-marked object with some alternative to it. Formally: {{P(x)} | x ∈ D}, where x is a variable ranging over alternative entities.

The meaning of (81a) can now be obtained as follows. First, reconstructing the object to its base position yields the proposition in (83a). Second, a polar question can be formed out of this proposition by turning it into a singleton set, as in (83b). Finally, replacing the object phrase with one or more alternatives leads to a set of polar questions, as in (83c), namely the CT-value of (81a).

Long description

(83) Deriving the CT-value of (82a) a. ‘I like this paper.’ (Step 1) b. {‘I like this paper’} = ‘Do I like this paper?’ (Step 2) c. {{‘I like this paper’}, {‘I like that paper’}} = {‘Do I like this paper?’, ‘Do I like that paper?’} = ‘For every entity x in {‘this paper’, ‘that paper’}, do I like x?’ (Step 3).

Under this analysis, an object preposing construction in Mandarin has a contrastive reading and requires a conjunct clause to be complete because the object is CT-marked and triggers a set of subquestions. Since the construction itself only responds to one of the subquestions, the former would not be complete without another clause.

As for object preposing constructions in which the object appears in the initial position, CT-marking on the object is optional and can be triggered if the preposed object is given stress or if the current QUD introduces at least one alternative to the object referent, as shown in (84), due to a reviewer.

Long description

(84) (What did you give to whom?) Gei gege, wo gei-le yi-ben shu. Gei jiejie, wo gei-le yi-liang zixingche. Gloss line: to elder.brother 1SG give-ASP one-CL book to elder.sister 1SG give-ASP one-CL bike ‘To the elder brother, I gave one book. To the elder sister, I gave one bike.’.

Otherwise, as two reviewers remark, an OSV sentence does not require a continuing clause and the preposed object can be interpreted as a discourse topic, as with (86a) below, unlike the SOV version of the same sentence. Example (85), provided by a reviewer, further shows that the OSV order is compatible with a simple topic-comment construction; compare (9).

Long description

(85) a. Li ni bu xihuan, pingguo ne? pear 2 superscript SG NEG like apple PRT 'As for pears, you don’t like them. How about apples?' b. Pingguo wo xihuan. apples 1 superscript SG like 'As for apples, I like them.'.

However, if (part of) the initial object is stressed, as in (86a), incompleteness emerges; if the copula shi is also inserted, as in (86b), an adversative continuation is expected.

Long description

(86) (What do you think about these students? Do you like Yijun?) a. ZHEI-ge xueshengcomma wo xihuan . . . this-CL student 1SG like ‘This studentcomma I like . . .’ b. ZHEI-ge xueshengcomma wo shi xihuan . . . this-CL student 1SG COP like ‘This studentcomma I do like . . .’.

This can be explained if shi in (86b) is just ${shi}_{{\scriptsize{\text{VDC}}}}$, which presupposes that an alternative question to the CQ, such as ‘Do you like Yijun and have you taught her?’, has a negative answer.