Contextual bias and the landscape of Mandarin polar questions

Chapter 6 Contextual bias and the landscape of Mandarin polar questions Yurie Hara Hokkaido University Mengxi Yuan Jinan University Mandarin Chinese has at least three kinds of polar questions, positive ma questions, negative ma questions and A-not-A questions, which have similar semantics but are not totally interchangeable. In particular, they carry different bias connotations. We show that their bias meanings and distribution are best characterized by the notion of contextual bias, which is formalized in terms of the subjective probability distribution within the framework of Farkas & Bruce’s (2010) Table model. Our analysis offers a simple lexical semantics for ma questions by employing pragmatic competition, and supports the idea that prosodic contours like the Final Fall in Anot-A questions are intonational morphemes that carry semantic contents. 1 Introduction According to Hamblin’s (1958, 1973) seminal theory of questions, a question denotes a set of propositions that count as possible answers to it, which predicts that there is no semantic difference between English positive polar questions, negative polar questions and alternative questions of the form ‘𝑝or not 𝑝?’. However, a number of subsequent studies present evidence that these questions have different properties and are not always interchangeable (Bolinger 1978, Ladd 1981, Büring & Gunlogson 2000, Van Rooy & Šafářová 2003, Romero & Han 2004, Biezma 2009, Roelofsen & van Gool 2010, Biezma & Rawlins 2012, Sudo 2013, Krifka 2015, Domaneschi et al. 2017, Farkas & Roelofsen 2017, a.o.). Yurie Hara & Mengxi Yuan. 2025. Contextual bias and the landscape of Mandarin polar questions. In Tue Trinh, Anton Benz, Daniel Goodhue, Kazuko Yatsushiro & Manfred Krifka (eds.), Biased questions: Experimental results and theoretical modelling, 175–205. Berlin: Language Science Press. DOI: 10.5281/zenodo.17158186 Yurie Hara & Mengxi Yuan Mandarin Chinese also has three types of polar questions that are not interchangeable: positive ma questions (+maq), negative ma questions (−maq) and A-not-A questions (anaq). Ma-questions, henceforth maqs, are formed by attaching a question particle ma at the end of the sentence as in (1–2). As we will see below, positive and negative ma questions are in complementary distribution. (1) Xia fall yu rain le perf ma? q ‘Did it rain?’ (+maq) (2) Mei not xia fall yu rain ma? q ‘Did it not rain?’ (−maq) A-not-A questions, henceforth anaqs, conjoin the verb and its negative counterpart and end with an obligatory final boundary low tone L% (henceforth the final Low tone is indicated by as ‘↓’) and an optional question particle ne: (3) Xia fall mei not xia fall yu rain (ne)?↓/L% q ‘Did it rain or not rain?’ (anaq) While intuitively (1–3) are asking the same question of whether it rained, they are used in different contexts. This naturally raises the following question: What determines the distribution of the three kinds of questions? Yuan & Hara (2019) discuss the syntactic and prosodic differences among the three constructions as well as the differences in compositional semantics. The current paper focuses on the bias profile/type of bias that arise from these constructions. 2 Data This section presents the main empirical observation regarding Mandarin polar questions. In particular, we show which constructions are available in what kind of contexts. 2.1 Positive ma question Let us first take a look at positive ma questions (+maq). A +maq can be used in out-of-blue contexts where no conversation participants have expressed any bias: 176 6 Contextual bias and the landscape of Mandarin polar questions (4) A researcher uses a questionnaire to investigate the relationship between the weather and people’s mental states. The first question in the questionnaire is: Ni you de gen chengshi city zuotian yesterday xia fall yu rain le perf ma? ma ‘Did it rain yesterday in your city?’ (+maq) It can also be used in positively biased contexts. In (5), Speaker A’s assertion of 𝑝renders the context biased towards 𝑝. (5) A: Zuowan last-night (henkeneng) probably xia fall yu rain le. perf ‘(Probably,) It rained last night.’ B: Xia fall yu rain le perf ma? ma ‘Did it rain?’ (+maq) +maq are also felicitous in contexts that are non-verbally biased towards p: (6) B enters A’s windowless room wearing a dripping wet raincoat. A: Xia fall yu rain le perf ma? ma ‘Did it rain?’ (+maq) In contrast, when the context is biased toward ¬𝑝, a +maq cannot be used: (7) A and B open the window and find the ground dry. A speaks to B, who stayed up all night. A: #Zuowan last-night xia fall yu rain le perf ma? ma ‘Did it rain last night?’ (+maq) As summarized in Table 1, +maqs are felicitous when the context is neutral or positively biased. 2.2 Negative ma questions Negative ma questions (−maqs) are in complementary distribution with +maqs. Thus, they cannot be used in an out-of-the-blue context like (8). 177 Yurie Hara & Mengxi Yuan Table 1: Distribution of positive maqs Neutral biased towards 𝑝biased towards ¬𝑝 positive maqs 3 3 # (8) A researcher uses a questionnaire to investigate the relationship between the weather and people’s mental states. The first question in the questionnaire is: # Ni you de gen chengshi city zuotian yesterday mei neg xia fall yu rain ma? ma ‘Did it not rain yesterday in your city?’ (−maq) Negative maqs are also disallowed in positively biased contexts as in (9–10). (9) A: Zuowan last-night (henkeneng) probably xia fall yu rain le. perf ‘It (probably) rained last night.’ B: #Mei neg xia fall yu rain ma? ma ‘Did it not rain?’ (−maq) (10) B enters A’s windowless room wearing a dripping wet raincoat. A: #Mei neg xia fall yu rain ma? ma ‘Did it not rain?’ (−maq) This raises the questions of when -MAQs can be used. The answer is that they can be used in contexts that exclude +MAQs when the context is biased towards ¬𝑝. The bias can arise verbally as in (11) or non-verbally as in (12). (11) A: Zuowan last-night mei neg xia fall yu. rain ‘It did not rain last night.’ B: Mei neg xia fall yu rain ma? ma ‘Did it not rain?’ (−maq) 178 6 Contextual bias and the landscape of Mandarin polar questions (12) B leaves A’s windowless room carrying a raincoat. When B returns, A notices that B’s raincoat is dry. A: Mei neg xia fall yu rain ma? ma ‘Did it not rain?’ (−maq) Table 2 summarizes the distribution of maqs. Positive and negative maqs are in complementary distribution. Negative maqs are uttered when the context is biased towards ¬𝑝while positive maqs are uttered elsewhere, i.e., when the context is neutral or biased towards 𝑝.1 Table 2: Distribution of maqs Neutral biased towards 𝑝biased towards ¬𝑝 positive (+) maqs 3 3 # negative (-) maqs # # 3 2.3 A-not-A question A-not-A questions are used only in neutral contexts as in (13). 1In Mandarin, there is another type of polar questions that contains a negation morpheme bushi.Bu-shi questions, like English inner high negation questions, are used when the speaker has a prior bias toward the positive answer but the utterance context is biased toward the negative one as in (i). This example was suggested by the reviewer, and the reviewer pointed out that this example is a high negative polar question. We clarify that this paper only discusses the semantics of unmarked negative ma questions which are comparable to low negative polar questions in English, and we don’t discuss the semantics of bu-shi questions (which are comparable to high negative polar questions in English). (i) B told A that he was married. On the next day, A found B at a bachelor party. A: ni you bu-shi not-shi jiehun-le married-asp ma? q ‘Aren’t you married?’ bu-shi questions are distinct from (negative) maqs. Bu-shi questions are comparable to high negative polar questions in English and unmarked negative maqs are comparable to low negative polar questions in English. See Fu (2021) for an analysis that uses Romero & Han’s (2004) VERUM operator. 179 Yurie Hara & Mengxi Yuan (13) A researcher uses a questionnaire to investigate the relationship between the weather and people’s mental states. The first question in the questionnaire is: A: Ni you de gen chengshi city zuotian yesterday xia fall mei not xia fall yu?↓ rain ‘Did it rain or not rain yesterday in your city?’ (anaq) Once the context is biased towards either answer, questioning with an anaq becomes infelicitous. In (14–15), the context is positively biased and the anaq is ruled out: (14) A: Zuowan last-night xia fall yu rain le. perf ‘It rained last night.’ B: #Xia fall mei neg xia fall yu?↓ rain ‘Did it rain or not rain?’ (anaq) (15) B enters A’s windowless room wearing a dripping wet raincoat. A: #Xia fall mei neg xia fall yu?↓ rain ‘Did it rain or not rain?’ (anaq) Likewise, in (16–17), the context is negatively biased and the anaq is infelicitous. (16) A: Zuowan last-night mei neg xia fall yu. rain ‘It did not rain last night.’ B: #Xia fall mei neg xia fall yu?↓ rain ‘Did it rain or not rain?’ (anaq) (17) B leaves A’s windowless room carrying a raincoat. When B returns, A notices that B’s raincoat is dry. A: #Xia fall mei neg xia fall yu?↓ rain ‘Did it rain or not rain?’ (anaq) 180 6 Contextual bias and the landscape of Mandarin polar questions Table 3: Distribution of maqs and anaqs neutral biased towards p biased towards ¬𝑝 positive maqs 3 3 # negative maqs # # 3 anaqs 3# # Table 3 summarizes the distribution of +/−maqs and anaqs. The next question we will address is what kind of bias is involved. Put another way, what exactly does it mean to say ‘the context is biased/neutral’? 3 Question bias in traditional grammar Traditional grammarians attempted to analyze the meanings of maqs and anaqs with regard to the speaker’s bias. On the one hand, most traditional linguists conclude that the speaker of a anaq is neutral between a positive and a negative answer. On the other hand, the nature of the bias expressed by maqs was controversial. According to Wang (1943: 168), for instance, maqs are confirmationseeking questions that encode the speaker’s bias towards the prejacent proposition 𝑝, whereas Chao (1968: 356) and Shao (1996: 72) claim that maqs signify the speaker’s bias towards the negation of the prejacent proposition ¬𝑝. We regard these traditional approaches as problematic in several respects. First, the semantics of maqs and anaqs and their biases are not compositionally derived but stipulated (see Yuan & Hara 2019 for compoisitional semantics of these questions). Second, empirical data shows that the bias is not lexically encoded in maqs. To illustrate, the speaker of the +maq in (6) seems to be biased towards the positive answer while the speaker in (4) seems to be neutral. As shown in (18), furthermore, the same +maq can be uttered in various contexts with different speaker biases. If a +maq were a lexically biased question, that is, if a +maq obligatorily denoted the speaker’s bias towards the positive answer, then (18a) and (18c) would be unacceptable since the continuations contradict the semantic content of the +maq . (18) Xia fall yu rain le perf ma? ma ... ‘Did it rain? ...’ 181 Yurie Hara & Mengxi Yuan a. ... Wo I bu neg juede. think ‘... I don’t think so.’ b. ... Wo I cai guess xia fall le. perf ‘... I guess it rained.’ c. ... Wo I wanquan totally bu neg qingchu. clear ‘... I totally have no idea.’ (+maq) Furthermore, the speaker does not need to be neutral about the answers when she utters an anaq. The speaker in (4) is probably neutral regarding the answers, while she can hold a private bias toward either answer in some other contexts. For instance, A in (19) can felicitously utter an anaq even though she is privately biased towards the positive alternative You have questions: (19) A believes that his audience usually have questions to raise after his speech: A: Nimen you you have mei not you have wenti?↓ questions ‘Do you have or not have questions?’ (anaq) Similarly in (20), A is only privately biased towards the proposition He looks like you, that is, the other discourse participant does not know that A is biased towards p.2 (20) A and B are in the museum. A finds a portrait that looks like B. A: (Kan!) look Ta he xiang resemble bu not xiang resemble ni? you ‘(Look!) Does he look like you or not like you?’ Finally, the notion of the speaker bias seems too strong to characterize the bias that arises from −maqs. That is, the speaker does not need to have a strong belief that ¬𝑝in uttering a −maq. In (21), for instance, speaker A only considers a (slight) possibility of ¬𝑝or just reports that someone else other than the speaker mentioned ¬𝑝, yet the context licences the use of the −maq. 2We owe example (20) to an anonymous reviewer. 182 6 Contextual bias and the landscape of Mandarin polar questions (21) A1: Zuowan last-night keneng maybe mei neg xia fall yu. rain ‘Maybe it did not rain last night.’ A2: Wo I bu neg juede think zuowan last-night xia fall yu rain le. perf ‘I don’t think that it rained last night.’ A3: John John shuo say zuowan last-night mei neg xia fall yu. rain ‘John said that it did not rain last night.’ B: Mei neg xia fall yu rain ma? ma ‘Did it not rain?’ (−maq) In summary, the speaker bias is not in the lexical specification of either maqs or anaqs. As we argue below, the notion of ‘contextual bias’ is more appropriate to characterize the semantics and pragmatics of maqs and anaqs. 4 Proposals To derive the distribution of the polar questions sketched in Section 2, we make the following proposals. (22) a. The bias meaning involved in Mandarin polar questions are best characterized by the notion of contextual bias (‘evidential bias’ in Sudo 2013) b. As for maqs, only the negative maq lexically encodes the bias meaning. c. The contextual neutrality of anaq is derived by the exhaustivity operator denoted by the final low tone ↓/L%. When the context is biased toward ¬𝑝, a −maq is the most optimal. Accordingly, a +maq is used elsewhere, i.e., in neutral and positively biased contexts as we have seen in Table 2, repeated here as Table 4. In Section 7.1, we show how the elsewhere condition explains the complementary distribution of positive/negative maqs. As for anaqs, we argue that the exhaustive interpretation that arises from the final low tone ↓/L% is the source of the neutrality requirement. In a nutshell, ↓ expresses that the Hamblin alternatives presented by the A-not-A construction, 183 Yurie Hara & Mengxi Yuan (43) B enters A’s windowless room wearing a wet raincoat. A: Wo I jiu part zhidao know (hui can zheyang). this-like ‘This is what I expected.’ A′: Bu neg keneng, possible wo I bu neg xiangxin believe (hui would zheyang). this ‘No way, I don’t believe this (would happen).’ As can be seen from (40) and (43), as long as some individual publicly entertains the possibility of 𝑝,𝑝becomes an issue that is on the Table for discussion. To implement this intuition, we propose that as long as some individual’s consideration of the possibility of 𝑝is made public in a context 𝑐, the issue {𝑝}is pushed onto the Table at 𝑐: (44) Pushing an issue onto the Table: If cg(𝑐′)=cg(𝑐)∪(∃𝑥.𝑥∈𝐴(𝑐)&Cred𝑥(𝑝)>0), Then 𝑇(𝑐′)=push({𝑝},𝑇(𝑐)). where 𝑐′and 𝑐are the output context and input context respectively and 𝐴(𝑐)is the set of epistemic agents at 𝑐. Now that (44) allows an issue {𝑝}to be on the Table as long as some individual considers 𝑝possible, the definitions of assert and cce are simplified as below: (45) ccp of assert (final version): assert(𝑝)(𝑐)=c′such that cg(𝑐′)=cg(𝑐)∪(Credspkr(𝑝)⩾0.98) (46) ccp of cce (final version): Let 𝑝,𝑞be propositions and 𝑎be a discourse participant, a. cce𝑎(𝑝)(𝑐)is defined iff ∃𝑞.𝑃(𝑝|Dox𝑎∩𝑞)>𝑃(𝑝|𝐷𝑜𝑥𝑎)∧𝑃(𝑝|Dox𝑎∩𝑞)>0.5 b. If defined, cce𝑎(𝑝)(𝑐)=c′such that cg(𝑐′)=cg(𝑐)∪(Cred𝑎(𝑝)>0.5) Finally, we can formalize the contextual bias and neutrality. First, A context 𝑐 is biased towards a proposition 𝑝if the issue {𝑝}, but not {¬𝑝}, is on the Table in 𝑐: (47) Contextual bias (final version) A context 𝑐is biased towards a proposition 𝑝iff {𝑝}⊆⋃𝑛𝑥=1𝑇(𝑐)[𝑥]and {¬𝑝}⊈⋃𝑛𝑥=1𝑇(𝑐)[𝑥], where 𝑛=|𝑇(𝑐)|. 190 6 Contextual bias and the landscape of Mandarin polar questions We also define context neutrality as follows: The context is neutral with respect to 𝑝if no issue is on the Table or if both 𝑝and ¬𝑝are on the Table. More precisely, the context is neutral when the union of all the issues at each stack member of the Table amount to an empty set or contains the issue {𝑝,¬𝑝}: (48) The context c is neutral with respect to 𝑝iff ⋃𝑛𝑥=1𝑇(𝑐)[𝑥]=∅or {𝑝,¬𝑝}⊆⋃𝑛𝑥=1𝑇(𝑐)[𝑥], where 𝑛=|𝑇(𝑐)|. To sum up, we formalize the notion of contextual bias using the subjective probability and the Table model. A context is biased towards 𝑝when the proposition that someone entertains the possibility of 𝑝becomes an issue of the Table. 6 Semantics of Mandarin polar questions Before looking at how our notion of contextual bias derives the pattern summarized in Section 2, we briefly review the semantics of maq and anaq given by Yuan & Hara (2019). Furthermore, this paper adds felicity conditions on the semantics of −maq. 6.1 Ma Questions Yuan & Hara (2019) claim that a maq like (49) has the syntactic structure given in (50). (49) Li Li he drink jiu alcohol ma? q1 ‘Does Li drink alcohol?’ (50) ForceP TP Li VP he jiu Force ma/q1 191 Yurie Hara & Mengxi Yuan The semantics of the particle ma/q1is defined as in (51). The particle takes its sister proposition 𝑝as an argument, creates a Hamblin alternative {𝑝,¬𝑝}as an issue and pushes the issue onto the Table: (51) ccp of q1: q1(𝑝)(𝑐)=𝑐′such that 𝑇(𝑐′)=push({𝑝,¬𝑝},𝑇(𝑐)) Now, we claim that −maqs have a felicity condition (Searle 1965) in addition to the usual felicity condition of questions that +maqs also have.7In a nutshell, a¬𝑝-ma is felicitous only when the context is biased towards ¬𝑝, i.e., {¬𝑝}⊆ ⋃𝑛𝑥=1𝑇(𝑐)[𝑥]and {𝑝}⊈⋃𝑛𝑥=1𝑇(𝑐)[𝑥]: (52) Felicity condition of −maq: The use of a negative maq, i.e., a maq containing NegP as the maximal I-projection which denotes ¬𝑝, is felicitous in a context c only if c is biased towards ¬𝑝. 6.2 A-not-A questions Turning to anaqs, Yuan & Hara (2019) propose that an anaq like (53) has the structure in (54), adopting Huang’s (1991) analysis. The feature r represents the reduplication of the predicate with the negative marker bu. The optional particle ne is the phonological realization of another question operator q2. (53) Li Li he drink bu not he drink jiu alcohol (ne)?↓ q2 ‘Does Li drink or not drink alcohol?’ 7See Trinh (2014) for an alternative analysis of the felicity conditions for positive and negative polar questions. Trinh (2014) makes two generalizations about the felicitous use of polar questions: 1. A polar question is felicitous only if its prejacent does not contradict the answer implied by contextual evidence; 2. In contexts where there is neither evidence for p nor evidence for ¬𝑝, the question denoting {𝑝,¬𝑝}is felicitous only if it is an inverted positive question. Trinh (2014) explains the first generalization by adopting the Principle of Maximize Presupposition and explains the second one by adopting the Maxim of Manner: in a neutral context where there is neither evidence for p nor evidence for ¬𝑝, the speaker will choose a positive polar question instead of a negative one because the former is simpler in syntactic form. 192 6 Contextual bias and the landscape of Mandarin polar questions (54) ForceP TP NP1 Li T′ T r VP V he NP2 jiu Force q2/ne The reduplication feature r is responsible for creating a Hamblin set: (55) Semantics of reduplication r JrK=𝜆𝑃.𝜆𝑥.{𝑃(𝑥),¬𝑃(𝑥)} The particle q2/ne pushes the Hamblin set created by r to the Table: (56) ccp of the operator q2: q2(𝑄)(𝑐)=c′such that 𝑇(c′)=push(𝑄,𝑇(𝑐)) Finally, an anaq has to be uttered with a final L% boundary tone (↓). Following Biezma & Rawlins’s (2012) analysis of English final falling tone of alternative questions, Yuan & Hara (2019) argue that the Mandarin final ↓/L% is a closure operator which indicates that there is no issue on the Table or the issue presented by the anaq is the only issue on the Table. The current paper proposes the following semantics for ↓:8 8An anaq followed by the particle ne can be uttered with final H%, as pointed out by an anonymous reviewer. We speculate that when an anaq containing ne is uttered with H% tone, the L% tone is overridden by H%. Thus, the source of neutrality is still L%. Our intuition is that when an anaq containing ne is uttered with H% tone, the speaker is more anxious to know the answer, compared with anaqs without ne. This is why Shao (1996) argues that the semantics of ne reinforces the interrogative force. We believe that this reinforcing meaning is not due to ne, but due to the H% boundary tone. Following Bartels (1997) and Hara & Davis (2013), the H% tone indicates that the utterance is directed at the addressee and the speaker expects the addressee to resolve the issue. Thus, when uttering anaqs containing ne with H% tone, the speaker sounds more anxious in seeking an answer. Another complexity is that whether the 193 Yurie Hara & Mengxi Yuan (57) Semantics of ↓ J↓K=𝜆𝜑.𝜆𝑐.⋃𝑛𝑥=1𝑇(𝑐)[𝑥]=𝜑or ∅, where 𝑛=|𝑇(𝑐)| Thus, when an anaq (i.e., 𝑝-or-not-𝑝) is uttered with ↓, it expresses that the Table has no issue or that only issue on the Table is {𝑝,¬𝑝}. 7 Deriving the distribution Let us illustrate how our notion of contextual bias (47), repeated here as (58), together with the notion ‘pushing an issue on the Table’ (44), repeated here as (59), correctly predicts the felicity of maqs and anaqs in different contexts. (58) Contextual bias (final version) A context c is biased towards a proposition 𝑝iff {𝑝}⊆⋃𝑛𝑥=1𝑇(𝑐)[𝑥]and {¬𝑝}⊈⋃𝑛𝑥=1𝑇(𝑐)[𝑥], where 𝑛=|𝑇(𝑐)|. (59) Pushing an issue onto the Table: If cg(𝑐′)=cg(𝑐)∪(∃𝑥.𝑥∈𝐴(𝑐)&Cred𝑥(𝑝)>0), Then 𝑇(𝑐′)=push({𝑝},𝑇(𝑐)). where 𝑐′and 𝑐are the output context and input context respectively and 𝐴(𝑐)is the set of epistemic agents at 𝑐. 7.1 Positive/Negative ma questions As summarized in Section 2, +maqs and −maqs are in complementary distribution. Recall that a ¬𝑝-ma has a specific felicity condition (52) that dictates that the Table must contain the issue {¬𝑝}. On the other hand, positive maqs do not have such a contextual requirement. maqs. That is, 𝑝-ma is unacceptable when the context is biased towards ¬𝑝while it is acceptable when the context is neutral or biased towards 𝑝. We show in this section that the distribution is straightforwardly explained in terms of pragmatic competition. particle ne carries the final H% or L% depends on the lexical tone of the previous syllable. Thus, in (i) when the previous syllable carries a high level lexical tone (55), the particle ne cannot carry a H%. (i) Kai55 open bu not kai55 open chuang55 window ne? ne ‘Shall we open the window or not?’ 194 6 Contextual bias and the landscape of Mandarin polar questions 7.1.1 Neutral context In (60), there is no issue on the Table, thus −maq is ruled out, while +maq, which does not have such an extra condition, is okay: (60) The first question in a questionnaire investigating the relationship between weather and people’s mental states is: Q: Ni you de gen chengshi city zuotian yesterday xia fall yu rain le perf ma? ma ‘Did it rain yesterday in your city?’ (+maq) Q′: # Ni you de gen chengshi city zuotian yesterday mei neg xia fall yu rain ma? ma ‘Did it not rain yesterday in your city?’ (−maq) 7.1.2 positively biased context As shown in (31), repeated here as (61), A has asserted the proposition 𝑝It rained. That is, cg(𝑐′)=cg(𝑐)∪(CredA(𝑝)⩾0.98), hence the issue {𝑝}is pushed onto the Table and the context is biased towards 𝑝. A default +maq is felicitous in such a positively biased context. In contrast, ¬𝑝-ma is infelicitous since unlike +maqs, −maqs have a contextual requirement that the context needs to be negatively biased. (61) A: Zuowan xia yu le. ‘It rained last night.’ B: Xia fall yu rain le perf ma? ma ‘Did it rain?’ (+maq) B’: # Mei neg xia fall yu rain ma? ma ‘Did it not rain?’ (−maq) The assertion of bare 𝑝is not the only way to mark the context as biased towards 𝑝, but a modalized or embedded 𝑝as in A1–A3 of (62) is enough to make the context 𝑝-biased. Recall from the definition of ‘pushing an issue onto the Table’ (44) that 𝑝is pushed onto the Table as long as there is some individual 𝑥, who is not necessarily a conversation participant, that entertains the possibility of 𝑝(∃𝑥.𝑥∈𝐴(𝑐)&Cred𝑥(𝑝)>0). Thus, since all the A-utterances in (62) make the context biased towards 𝑝, only the +maq is felicitous: 195 Yurie Hara & Mengxi Yuan (62) A1: Zuowan yesterday keneng possible xia fall yu rain le. perf ‘Maybe it rained last night.’ A2: Wo I juede think zuowan last.night xia fall yu rain le. perf ‘I think that it rained last night.’ A3: John John shuo said zuowan last.night xia fall yu rain le. perf ‘John said that it rained last night.’ B: Xia fall yu rain le perf ma? ma ‘Did it rain?’ (+maq) B’: # Mei neg xia fall yu rain ma? ma ‘Did it not rain?’ (−maq) Similarly, in (63) the contextually compelling evidence pushes 𝑝onto the Table (see (46) and (59)), thus the context is biased towards 𝑝and 𝑝-ma is okay while ¬𝑝-ma is unacceptable: (63) B enters A’s windowless room wearing a wet raincoat. A: Xia fall yu rain le perf ma? ma ‘Did it rain?’ (+maq) A′: # Mei neg xia fall yu rain ma? ma ‘Did it not rain?’ (−maq) In short, a −maq cannot be used in neutral nor positively biased contexts as it has a felicity condition that requires negatively biased contexts. A +maq does not have such a requirement, thus it is a default polar question that can be used in both neutral and positively biased contexts. 7.1.3 negatively biased contexts Now, let us look at the contexts where −maqs are used. As long as the context suggests that someone entertains the possibility of ¬𝑝as in the following, ¬𝑝 is pushed onto the Table and the context is biased towards 𝑝. Since this is the 196 6 Contextual bias and the landscape of Mandarin polar questions context that the felicity condition of ¬𝑝-ma (52) requires, −maq wins over +maq as a result of pragmatic competition: (64) A1: Zuowan last-night (keneng) possible mei neg xia fall yu. rain ‘(Maybe) it did not rain last night.’ A2: Wo I bu neg juede think zuowan last-night xia fall yu rain le. perf ‘I don’t think that it rained last night.’ A3: John John shuo say zuowan last-night mei neg xia fall yu. rain ‘John said that it did not rain last night.’ B: Mei neg xia fall yu rain ma? ma ‘Did it not rain?’ (−maq) B′: # Xia fall yu rain le perf ma? ma ‘Did it rain?’ (+maq) Similarly, when the contextually compelling evidence supports ¬𝑝,¬𝑝is pushed onto the Table, thus the context is biased towards ¬𝑝. Thus, ¬𝑝-ma is acceptable, while 𝑝-ma is not: (65) B leaves A’s windowless room carrying a raincoat. When B returns, A notices that B’s raincoat is dry. A: Mei neg xia fall yu rain ma? ma ‘Did it not rain?’ (−maq) A′: # Xia fall yu rain le perf ma? ma ‘Did it rain?’ (+maq) Furthermore, the felicity condition of −maq (52) accounts for the availability of the negative maq in (66), which is translated from the English example used by Romero & Han (2004) to show that English low negative questions can convey the speaker’s epistemic neutrality towards answers. 197 Yurie Hara & Mengxi Yuan (66) The speaker is organizing a party and she is in charge of supplying all the non-alcoholic beverages for teetotalers. The speaker is going through a list of people that are invited. She has no previous belief or expectation about their drinking habits. A: Jane Jane he and Mary Mary bu neg hejiu. drink-alchol ‘Jane and Mary do not drink.’ S: Haode. good-attr Bill Bill ne? ne? Ta 3sg (ye) too bu neg hejiu drink-alchol ma? ma ‘OK. What about Bill? Does he not drink (either)?’ (−maq) In (66), the goal of the discourse is to ‘[supply] non-alcoholic beverages’ and A has asserted ‘Jane and Mary do not drink’, thus we can infer that the current question under discussion is a negative wh-question ‘Who does not drink?’. This means that what is on the Table is the issue, {¬drink(j),¬drink(m),¬drink(b)}. Then, A’s assertion pushes ¬drink(j)and ¬drink(m)onto the Table. Therefore, ⋃3𝑥=1𝑇(𝑐)[𝑥]=𝑇(𝑐)[1]∪𝑇(𝑐)[2]∪𝑇(𝑐)[3]={¬drink(m)}∪{¬drink(j)}∪ {¬drink(j),¬drink(m),¬drink(b),...}={¬drink(j),¬drink(m),¬drink(b),...}.9The resulting Table contains ¬drink(b)but not drink(b). Thus, the context is biased towards ¬drink(b), even though the speaker does not have any epistemic bias. Since our definition only requires the context, not the spaker, to be biased, it correctly predicts the use of the negative maq in (66) to be felicitous. In contrast, a negative maq is infelicitous in (67), where the goal of the conversation is now to find out who drinks. The context is biased towards 𝑝rather than ¬𝑝, thus a −maq cannot be used. (67) The speaker is organizing a party and she is in charge of supplying all the alcoholic beverages for (alcoholic) drinkers. The speaker is going through a list of people that are invited. She has no previous belief or expectation about their drinking habits. S: # John John bu neg hejiu drink-alchol ma? ma ‘ Does John not drink?’ (−maq) In summary, we explain the complementary distribution of positive and negative maqs summarized in Table 5 in terms of pragmatic competition. 9We could also treat S’s utterance of Haode ‘OK’ as an acceptance of A’s assertion, thus ¬drink(j) and ¬drink(m)may be already removed from the Table. 198 6 Contextual bias and the landscape of Mandarin polar questions Table 5: Distribution of positive and negative maqs neutral biased towards 𝑝biased towards ¬𝑝 positive maqs 3 3 # negative maqs # # 3 The felicity condition of −maqs (52) plays a crucial role. A −maq has a more specific condition that the context has to be negatively biased. Thus, whenever this rule applies, −maqs win over +maqs, which are uttered elsewhere, i.e., in neutral and positively biased contexts. We do not need to stipulate any contextual requirement for +maqs, which are default polar questions. Note also that our definition allows us to uniformly deal with bias arising from default assertions, contextual compelling evidence and possibility claims. 7.2 A-not-A questions Let us finally turn to anaqs. As summarized in Table 6, anaqs are only available in neutral contexts. Table 6: anaqs in neutral contexts neutral biased towards 𝑝biased towards ¬𝑝 anaqs 3# # In Section 5.2, we define contextual neutrality as in (68). The context is neutral with respect to 𝑝when the Table is empty or the Table contains the issue {𝑝,¬𝑝}. (68) The context c is neutral with respect to 𝑝iff ⋃𝑛𝑥=1T(𝑐)[𝑥]=∅or {𝑝,¬𝑝}⊆⋃𝑛𝑥=1T(𝑐)[𝑥], where 𝑛=|𝑇(𝑐)|. Now as discussed in Section 6.2, an anaq is always uttered with the boundary tone ↓/L%, which denotes that all the issues on the Table amount to the Hamblin set denoted by the A-not-A construction or that an empty set: (69) Semantics of ↓ J↓K=𝜆𝜑.𝜆𝑐.⋃𝑛𝑥=1𝑇(𝑐)[𝑥]=𝜑or ∅, where 𝑛=|𝑇(𝑐)| 199