Derive the biased reading of A-not-A questions in Mandarin

. Among many forms of A-not-A questions in Mandarin Chinese, the shi-not-shi question is found to be unique in that it obligatorily gives rise to a biased reading toward its prejacent, so-called positive bias. The previous pragmatic approach by Ye (2020) establishes a link between focus in polar questions and question bias to explain this biased reading. However, the current study finds that two other A-not-A questions formed by epistemic modals, hui-not-hui and keneng-not-keneng which are not focus markers, obligatorily produce positively biased readings as well. I propose that biased A-not-A questions are a type of high-negation questions with A-not-A residing outside of TP. shi , hui and keneng should all be analyzed as epistemic modals which are the overt realization of Goodhue’s (2019) epistemic operator scoped by the negator. The positively biased reading is derived from the resulting unbalanced partition based on general pragmatic principles. This analysis from the semantic aspect provides new evidence for the argument that the first A has reality only in PF. Furthermore, the Mandarin Chinese data lends evidence to Goodhue’s (2019) argument that there exists a doxastic speech operator between NegP and TP in high negation questions. The paper also provides explanations for previously remaining questions on bias cancelation by the stress marker daodi and factive predicates like zhidao (“know”).

(1) a.It was observed that among various forms of A-not-A questions, the shi-not-shi question is rather unique in that it entails the questioners bias toward the answer entailed by the prejacent of shi-not-shi, while other A-not-A questions do not.As shown by (2), Zhangsan as the questioner obtained the clue that Lisi likes painting.To find out if his guess is correct, Zhangsan can use either the shi-not-shi or the V-not-V polar question to ask Wangwu.But it is only under the shinot-shi question can Wangwu felicitously responds with a confirmative expression.This example indicates that the shi-not-shi but not V-not-V question entails the questioners bias toward the truth of its prejacent.
(2) Context: Zhangsan saw Lisi bought many paintbrushes yesterday.Wangwu knows Lisi very well.Today, Zhangsan asks Wangwu: a. Lisi Lisi shi-bu-shi painting Does Lisi like painting?Wangwu replies: #How do you know that!However, I find that the shi-not-shi is not the only type of biased A-not-A question.Under the same context as described in (2), the confirmative response is also felicitous under both (3a) and (3b), which suggests that the A-not-A questions formed by Mandarin epistemic modals, hui ('probably') and keneng ('probably')1 , are positively biased as well.
(3) Zhangsan asks Wangwu: a.The current paper provides a unified analysis that explains the facts mentioned above by treating Mandarin A-not-A questions as a type of high-negation question and adopting Goodhue's (2019) epistemic operator and deriving the positively biased reading from the resulted unbalanced partitions.
In addition, there are two situations where the positive bias is canceled.First, as Ye (2020) points out, when biased A-not-A has an intonational stress on the first A under the scope of the optional stress marker daodi, the bias is canceled and the question becomes neutral.(4a) shows that the stressed question is felicitous to use under the context where the questioner has equal amounts of prior expectations for the positive and the negative answer.But if the questioner lacks prior evidence for either answer, stressed questions are never licensed, as illustrated by (4b).To explain this, I propose that daodi is an exhaustive partition operator with the semantics of partitioning a set of worlds into sets of balanced cells.
(4) a.Secondly, Ye (2020) leaves a puzzle that the positive bias is concealed when the A-not-A question is embedded under a responsive predicate but not when under a rogative predicate, as shown by (5).I argue know is a factive verb that selects DPs as its complement.To turn the question into a DP, there is an implicit THE ANSWER TO operator which partitions a set of worlds into sets of balanced cells.
In the remainder of the paper, Section 2 argues against Ye's (2020) focus account.Section 3 displays the syntactic and pragmatic properties of A-not-A questions and high negation questions in English.I argue that the Mandarin biased A-not-A question is a type of high negation question.Section 4 reviews previous accounts for high negations and discusses their application to Mandarin.Section 5 shows how Goodhue's (2019) operator and pragmatic principles can successfully apply to the Mandarin data.This section also provides explanations for bias cancelations.Section 6 discusses the implications of the analysis and concludes the paper.
2. Against the focus account.Ye (2020) proposes that in the shi-not-shi question, shi is a focus marker which presupposes its prejacent p is a possible complete answer to the current Question Under Discussion (QUD), that is, no other true answer entails p. shi-not-shi questions are treated as the same focus marker, so the same presupposition projects out of shi-not-shi questions.shinot-shi questions are used to check the truth of possible complete answers to the current QUD, so-called F(ocus)-stategy of inquiry, while other A-not-A questions are used to check the truth of possible partial answers, so-called C(ontrastive)T(opic)-strategy of inquiry.The difference between the two strategies is that when using F-strategy, the yes answer to the polar question closes the QUD; while using CT-srategy, the QUD will not be closed until the questioner has gone through all the subquestions.This can be illustrated by the following example in (6).Ye further assumes that the F-strategy of inquiry indicates the questioners intention to close the current QUD, and to achieve this goal, they expect a positive answer.As shi-not-shi question is part of the F-strategy, it is expected to bias toward a positive answer.In short, Ye's approach establishes a link between focus in polar questions and question bias and predicts that shi-not-shi questions are forced to have a positively biased reading.
However, based on a simple survey of native Mandarin speakers that I conducted, shi-not-shi questions without salient focus are still felicitous to induce a positively biased reading while followed by other subquestions, as shown by ( 7).This suggests that shi-not-shi does not necessarily presuppose a possible complete answer set.Thus, to assume shi-not-shi questions as part of the F-strategy of inquiry seems dubious.Subquestion: How about syntax?Wangwu: Yes, that's also his interest.
Furthermore, it is unclear how Ye's proposal works for the current new observation of huinot-hui and keneng-not-keneng biased questions as they do not function as focus markers.As (8a) illustrates, the focused constituent is required to appear within the scope of shi, otherwise, the sentence is unacceptable.Yet, the focus is felicitous when appears above the epistemic modals2 in (8b).In fact, Mandarin shi can be used in more than one way.Besides the focus marker function mentioned above, it is also widely accepted to be a copula.However, the copula meaning also fails to apply to the analysis of shi in shi-not-shi questions.( 9) shows that in a situation where Zhangsan lacks prior bias toward the prejacent, the COPULA-not-COPULA question is felicitous to use.I propose to treat shi in the positively biased shi-not-shi question as an epistemic modal.It is widely agreed that epistemic modals vary in the degree of certainty toward the proposition in its scope, based on the amount of evidence accumulated within the epistemic state in support of that proposition.For example, in English, Q believes For a fact p if and only if (iff) Q has direct evidence for p; Q believes Must p iff Q has at least indirect evidence for p and no evidence against p; Q believes Probably p iff Q has much more evidence for p than against p; etc., ⟨ for a fact, must, probably, ...⟩.Similarly, Mandarin Chinese has a set of epistemic modals scaled on the same basis, in which shi is the strongest one for a speaker to use if they have direct evidence: ⟨ shi, hui/keneng, ...⟩.As (10) shows, when Zhangsan has direct evidence, it is natural to use shi instead of a less probable hui or keneng.The following section displays more evidence for this argument by showing that shi both syntactically and pragmatically resembles canonical epistemic modals when forming biased A-not-A questions. 3. Compare properties of A-not-A question to high negation question.In the literature, biased questions are observed in English and many other languages such as Greek, Spanish, German, and Korean as well (e.g., Romero & Han 2004;Sudo 2013;AnderBois 2019).In this section, I take the English high-and low-negation polar question pair as an example to compare with Mandarin A-not-A questions in terms of their syntactic and pragmatic properties.
3.1.SYNTACTIC PROPERTIES.Previous studies argue that the biased A-not-A is triggered by an outer A-not-A above TP, while the neutral counterpart is licensed by an inner A-not-A morpheme situated below TP (e.g., Law 2006;Liu 2004Liu , 2010;;Tsai & Yang 2015).Law (2006) proposes an adverbial test to evidence this argument.(11a) shows the neutral A-not-A, here formed by V-not-V, is typically blocked by sentential frequency adverbials like often, whereas shi-not-shi is not (11b-c).Observe that hui-not-hui and keneng-not-keneng pass the tests as well.{shi-bu-shi/hui-bu-hui/ke-bu-keneng} {SHI-not-SHI/probably-not-probably} kan watch dianshi?TV Int.: Is it the case that Lisi often watches TV? Goodhue (2019) proposes several tests for English to support the argument that the negation operator in high negation questions is above the matrix TP as well.For example, the word again triggers the presupposition that the proposition denoted by its complement has happened before.When negation is within the prejacent of again, negation is part of the presupposition (12a).Applying again to high negation questions as in (12b), we find the question does not presuppose the negative proposition.again here is in the scope of the negator, and its presupposition projects out of it.Another example, until-adverbial only combines with clauses that have durative rather than punctual aspect (13a), and negating a verb with punctual aspect creates durative aspect (13b-c).However, high negation questions do not (13d).Both tests show that again and until-adverbial cannot scope above negation in high negation questions, indicating the negator is outside of TP.
(12) a. Did John not come to class again?
⇝ John did not come to class before.
b. Didn't John come to class again?⇝ John came to class before.
b. Lily didn't discover the thief until 9.
c. Did Lily not discover the thief until 9? d. #Didn't Lily discover the thief until 9?
3.2.PRAGMATIC PROPERTIES.As discussed above, Mandarin outer A-not-A questions are biased in that they necessarily require the speaker to have a prior expectation that the proposition embedded is true.By contrast, inner A-not-As do not have such a requirement.English negation questions parallel the same property: English high negation questions necessarily convey that the speaker is epistemically biased, but low negation questions do not have biased readings.As shown by ( 14) taken from Goodhue (2019), in the context of (14a) where the questioner Lucy lacks expectations toward Kate's being home or not, the low negation question is perfect but the high negation question is unacceptable; while in the context of (14b) where Lucy has a prior expectation that the proposition embedded under negation is true, the high negation question becomes felicitous.
( Given the similarity between A-not-A questions and negation questions, I propose to analyze Mandarin A-not-A questions as a type of negation question that have been cross-linguistically observed, outer A-not-A questions resembling high negation questions, and inner A-not-A questions resembling low negation questions.

Previous accounts for high negation questions.
To analyze high negation questions, previous theories propose an operator scoped by the negator in high negation questions.The meaning defined for such an operator differs among various proposals.Romero & Han (2004) observe that both high negation questions and questions with polarity focus convey the speaker's epistemic bias, as shown by (15).They thus relate the two questions and argue that high negation scopes above an epistemic, conversational operator in the form of a VERUM focus, which can be overtly spelled out with the English adverb really and relates to the strength with which a proposition should be added to the common ground.VERUM(p) reads as it is for sure that p should be added to the common ground.Following Hamblin's set denotation for questions, with the application of VERUM to high negation questions, we get an unbalanced partition, {¬VERUM(p), VERUM(p)}.¬VERUM(p) represents a larger set of worlds in which it is not for sure that p should be added to the CG or it is for sure that p shouldn't be added to the CG.The questioner using high negation questions to asks whether p can be assumed with a high degree of certainty, thus, a pragmatic bias toward p.It is also argued that VERUM can apply above the negator, thus creating an ambiguous high negation question.However, this theory does not apply to Mandarin A-not-A questions.As (4) in Section 1 illustrates, when A-not-A is focused, the question does not obtain the biased reading anymore.Relating outer A-not-A to polarity focus thus seems dubious.Moreover, Goodhue (2019) points out that polarity focus but not high negation requires the sort of antecedent needed to license prosodic prominence shifts more generally.A unified account of high negation and polarity may not be appropriate even for other languages.
⇝ The speaker believes that Kate is home.
b.Is F Kate home?⇝ The speaker believes that Kate is not home.
Repp ( 2013) is against Romero & Han (2004) and argues that high negator is a conversational epistemic operator itself, supported by the evidence for the parallel behavior of high negation and negation in denials concerning their syntax and scope behavior in negative gapping sentences.She assumes high negation expresses an additional operator FALSUM that states the degree of strength with which the proposition should be added to the common ground is zero.This operator allows answers with a reduced degree of certainty such as Yes, I think there is a station, but I'm not sure.While applying this account to Mandarin can account for the biased reading of outer A-not-As, since it is the negator that plays an important role in deriving the bias, it remains unclear why only epistemic modals form outer A-not-As with the negator.
By contrast, Goodhue (2019) proposes high negation scopes over an epistemic operator as defined in ( 16).He further develops a pragmatic analysis based on the general pragmatic principles in (17-18).( 16) Epis = λp.λw.∀w ′ ∈ Dox x (w)[p(w ′ ) = 1] Dox x (w) is the set of worlds compatible with x's beliefs in w. x is a free variable for individuals whose value is contextually determined.In high-negation questions, x is the addressee.In plain English, (15) simply states that the addressee believes p.
(17) a. Felicity Condition for the use of questions: A question Q is felicitous only if Q is at least as useful as other questions Q'.

b. The lemma:
Outer A-not-A questions are at least as useful as other Qs only if the speaker is biased for p.

c. Conclusion:
Outer A-not-A questions are felicitous only if the speaker is biased for p.
(18) Strategies for comparing the utility of questions a. Gain information strategy: Q 1 is more useful than Q 2 iff Q 1 partitions cells produce epistemic states that are more informed relative to p than the cells of Q 2 do.
b. Determine agreement strategy: Q 1 is more useful than Q 2 iff Q 1 partitions cells make it easier to determine whether the addressee agrees with the speaker about p than the cells of Q 1 do.
Since Mandarin only allows for epistemic modals to form an outer A-not-A, plus the parallel between A-not-A and high negation questions, I propose that the epistemic operator in ( 16) is spelled out with the Mandarin epistemic modals, and the biased reading of A-not-A questions should be derived in the same way as for negation questions.In the next section, I show how the positive bias of A-not-A questions is obtained based on Goodhue's theory.
5. Analysis.The syntactic structure for outer A-not-A questions is displayed below.I assume that the first A in the PolarP head has only phonological reality, thus, I treat the denotation of it as an identity function.Note that it is plausible the second A in the EpisP head lacks realization in LF, which I will discuss later.Moreover, I assume the denotation for Q is a Hamblin's set (19).The semantics of the outer A-not-A question is computed in ( 20).
In plain English, the resulting answer set in (20d) is {the addressee does not believe p, the addressee believes p}, schematically {¬□p, □p}.This is an unbalanced partition in that not believing p includes a wider range of situations where the addressee lacks belief either way or the addressee believes not p.
If the questioner lacks belief about p either way, their goal will be to gain information about p from the addressee, thus adopting the gain information strategy (18a).Either p or ¬p would be a perfect answer to increase the questioners information.Therefore, under such situations, the questioner would prefer to ask a question with balanced partition {p, ¬p}, such as the neutral polar question with an inner A-not-A structure, Lisi like-not-like painting?On the other hand, if the questioner has a prior expectation toward one answer, their goal will be to determine whether or not they and the addressee agree on p, thus adopting the determine agreement strategy (18b).If the questioner biases toward p, that the addressee believes p will agree with them, while that the addressee does not believe p will indicate disagreement.In this case, the questioner would rather ask a question with an unbalanced partition {□p, ¬□p}.By contrast, if the questioner biases toward ¬p, that the addressee believes ¬p will agree with them, while that the addressee does not believe ¬p will indicate disagreement.Again, the questioner would prefer to ask a question with an unbalanced partition {□¬p, ¬□¬p}.This explains why outer A-not-A questions always have a biased reading toward its prejacent proposition.
As mentioned earlier, it is plausible that the first A has reality in LF while the second A is realized only in PF, as shown by the structure below.In such cases, we obtain the resulting answer set {the addressee believes not p, the addressee does not believe not p} (21), schematically, {□¬p, ¬□¬p}.
As discussed above, according to the determine agreement strategy, the questioner only uses questions with such a partition when they are biased toward the negative answer.However, a negative bias toward p is not attested in Mandarin outer A-not-A questions with the form of A-not-A p.It is only attested when the prejacent is negated, A-not-A ¬p.Therefore, I conclude that the high position A only has reality in PF while the lower position A is realized in LF.This analysis from the semantic aspect thus provides new evidence for the argument that the first A is realized by phonological processes such as reduplication or syllable copy and deletion.Furthermore, the Mandarin Chinese data lends additional language evidence to Goodhue's 2019 argument that there exists an epistemic operator between NegP and TP in high negation questions and this structure is not ambiguous.
Since no epistemic operator is available for inner A-not-A questions, whose structure is presented below, the resulting partition of the question is a balanced one by default ( 22).The inner A-not-A questions are predicted to have the same answer set as that of canonical polar questions.Pragmatically, since the questioner lacks belief either way, the gain information strategy requires the most informative answer set {p, ¬p}.Now let's turn to the two bias cancelation cases.First, when the outer A-not-A is stressed with an optional stress marker daodi, the speaker's prior positive bias toward the prejacent is canceled, and they become neutral toward the answer.The example is repeated in (23).Notice that the prior positive bias is a presupposition for using the stressed A-not-A question, as it is infelicitous to ask such a question when the context does not entail the initial positive bias (23b).( 23 Thus, I treat daodi as an exhaustive partition operator that takes a partition as input and produces a balanced partition.It presupposes the input partition is unbalanced.The definition is given in ( 23). (24 is a function that partitions a question under discussion into non-overlapping sets of worlds, so-called cells.This proposal is endorsed by independent evidence from wh-questions.For instance, in (25), Zhangsan's first response is blurred by hiding the other two detailed answers, that Zhangsan had hotpot and that Zhangsan ate ice cream.The doctor believed that Zhangsan didn't tell the whole story because her question "what did you eat?" can denote an unbalanced answer set.To gain more information, the doctor needs a complete and detailed answer, thus, she continued with a daodi-question that requires an obligatorily balanced partition.
(25) Context: Zhangsan had hotpot, cakes, and ice cream.After a few minutes, the pain started in his stomach.He then went to the hospital.Notice there is a parallel pattern in terms of positive bias inferences and presuppositions.( 27) shows that wh-questions embedded under zhidao ('know') have existential presupposition projected to the matrix level, while the no existential presupposition projects when embedded under xiangzhidao ('wonder').Based on the comparison above, I propose it is the contrast between being factive or nonfactive matters, instead of being responsive or rogative.According to Kastner (2015), the complements of factive attitudes have a definite DP-like behavior, while complements of non-factives do not necessarily.I assume that factives can embed DPs via a silent THE ANSWER TO operator, as shown in ( 28).
(28) Zhangsan knows [the answer to] who went to the meeting.I further assume the semantics of THE ANSWER TO operator is similar to that of daodi which takes a partition as input and produces a balanced partition, but it does not have any presupposition requirement (29).This proposal is evidenced by examples like (30): when the answer to is overtly stated in the response, we expect a complete and exhaustive answer instead of a vague one.?"The answer to your question is that he had cakes and something else that I'm not sure about."

Conclusion.
This paper provides a unified analysis for Mandarin positively biased A-not-A questions.It is observed that only those formed by shi-not-shi, hui-not-hui, and keneng-notkeneng can derive positive bias.I argue that the previous focus theory is not able to account for the data and propose to analyze these three A-not-As are epistemic modals.Based on the similarity shared by Mandarin A-not-A questions and English negation questions in syntactic and pragmatic properties, I argue that A-not-A question is a type of high negation question.I further adopt Goodhue's epistemic operator and pragmatic principles to derive the positively biased reading based on the resulting unbalanced partition.This analysis from the semantic aspect provides new evidence for the argument that the first A has reality only in PF.Furthermore, the Mandarin Chinese data lends evidence to Goodhue's (2019) argument that there exists an epistemic operator between NegP and TP in high negation questions.In addition, I argue that the positive bias can be canceled by exhaustive partition operators.In stressed A-not-A, the operator is surfaced as the stress marker daodi, while in factive embeddings, the operator is surfaced as the DP convertor THE ANSWER TO.
(6) QUD: Which branches of linguistics does Lisi like?a.Is it pragmatics F that Lisi likes?Answer: Yes (close the QUD) b.CT-strategy of inquiry: Subquestion: Does Lisi like pragmatics?Answer: Yes (move to the next subquestion, such as How about syntax?) that Lisi likes?Wangwu replies: How do you know that! b.Cont.Zhangsan: who probably likes painting.
Zhangsan thought Lisi likes painting.But Lisi dropped the painting class yesterday.Now Zhangsan is not sure if Lisi likes painting or not.Zhangsan asks Wangwu: {shi-bu-shi/hui-bu-hui/keneng-bu-keneng} F {SHI-not-SHI/probably-not-probably} 14) a. Lucy is looking for her roommate Kate.She has no idea whether Kate is home or not.
She looks around and can't find her.But Lucy sees Grace, so she asks Grace: (i) Is Kate not home?(ii) #Isn't Kate home?b.Lucy is looking for her roommate Kate.She expects Kate to be home.But Lucy can't find her anywhere.Lucy asks Grace: (i) Is Kate not home?(ii) Isn't Kate home?
) a. Zhangsan thought Lisi likes painting.But Lisi dropped the painting class yesterday.Now Zhangsan is not sure if Lisi likes painting or not.Zhangsan asks Wangwu: OK...I had cakes, hotpot, and ice cream.Finally, Ye (2020) leaves a puzzle that the bias of outer A-not-A is survived when embedded under rogative verbs like xiangzhidao ('wonder') but concealed when embedded under responsive verbs such as zhidao ('know'), repeated in (26).