The Factuality Status of Chinese Necessity Modals Exploring the Distribution Via Corpus-Based Approach

This paper is intended to test the deontic vs anankastic hypothesis outlined by Sparvoli 2012. The stipulation is that, in past contexts, deontic modals trigger a counterfactual inference, while anankastic modals (here called ‘goal-oriented modals’) either trigger an actuality entailment effects (‘only possibility’ modals) or a generic non-factual reading (‘mere necessity’ modals). The result of this corpus-based study conducted in a Chinese-English parallel corpus confirm the crucial role played by the deontic vs goaloriented contrast in the marking of factuality in Chinese and shows that the factuality value decreases across a cline from goal-oriented to deontic modals.


Introduction
The framework here adopted relies on the differentiation between deontic and anankastic modalities. Based on von Wright (1963), this theory postulates that modals pertaining to duty and necessity are distributed within a semantic domain having two poles (Sparvoli 2012): namely, the deontic, which expresses an obligation (ancient Greek déon) and is related to a moral duty, grounded on a principle, as in (1a); and the anankastic (from anánkē, literally 'rope, wire'), which indicates a practical necessity, linked to a specific purpose, as in (1b).
1. a. 'We should be modest and prudent'.
(translated from Alleton 1984, 200) [deontic] b. To get to the station you have to take bus 66.
( Van der Auwera, Plungian 1998, 80) [anankastic] Anchored in the notion of 'inevitability', the anankastic expresses what 'cannot be done otherwise' and makes it possible to establish a unique and consistent class for expressions which are commonly related to different modalities, such as the necessity depending on natural law, circumstances or a given goal (or wish). Rough equivalents of the anankastic modality are found in the "participant-external non-deontic" (Van der Auwera, Plungian 1998), the "goal-oriented or teleological" (von Fintel, Iatridou 2007) and in the "neutral" or "circumstantial dynamic" modality (Palmer 1990). Importantly, the anankastic domain includes markers of different binding force, ranging from weak to strong anankastic modals (as 'must' and 'cannot but', respectively) (Sparvoli 2012). Along these lines, this paper focuses on the factuality 1 reading triggered by Chinese modals in past contexts. The working hypothesis is that (i) deontic modals such as 应该 yīnggāi 'should' yields counterfactuality, that is, they trigger the inference that "the speaker believes a certain proposition not to hold" (Iatridou 2000, 231) and such meaning is understood via an inference; (ii) the strongest anankastic modals, such as 不得不 bùdébù 'cannot but' or 只好 zhǐhǎo 'can only', trigger an uncancellable inference that the event took place in the actual world, therefore they are implicative, yield actuality entailments (Bhatt 1999;Hacquard 2006) and have a factual reading; (iii) 必须 bìxū 'have to' preferably gets a factual interpretation; (iv) weaker anankastic modals, such as 得 děi and 要 yào 'must', have a distribution similar to imper-2 Background

The Deontic vs Anankastic Contrast
Though interchangeable in a positive context, the classification into deontic or anankastic modality is based on the different interaction with negation (Sparvoli 2012). Namely, the negation of a prominent 3 deontic marker produces a Prohibition, like 'should not', while the negation of the anankastic produces an Exemption, like 'don't have to', 'need not'. In other words, deontic modals scope over negation, while anankastic modals scope under negation (Lü [1942(Lü [ ] 1944. In Chinese, the categorisation into either one of these two modalities, though expressed in different terminology, is already found in the modality in-2 Further details on the corpus are provided in the Bibliography. 3 The underlying principle of the concept of "modal prominence" (Li 2004, 176) is that the different modal meanings of polysemous markers can be ranked into four categories: namely, prominent markers (that is, prototypical, as for 应该 yīnggāi in the deontic and epistemic modalities); frequent but non-prominent; non-frequent; not used. vestigation prior to 1949 (Sparvoli 2012). In this literature, the prominent markers of these two modalities are the deontic (应)该/当 (yīng) gāi/dāng 'should' (2a), and the anankastic 必须 bìxū 'must' and 得 děi 'have to ' (2b); the latter two are positive polarity items, negated via suppletive forms expressing Exemption, like 不必 búbì, 无需 wúxū 'don't have to' or 不用 bùyòng, 甭 béng 'need not '. 4 The classification of 要 yào is more difficult, since it can have the meaning of 必要 bìyào 'must', 需要 xūyào 'need', 想要 xiǎngyào 'would like to', 快要 kuàiyào 'is going to', or 将要 jiāngyào 'will' (Li 2004, 162). In a normative context, following von Wright, who "classified 'must' as anankastic but 'must not' as deontic" (1963, VIII-2, 157), we labelled 要 yào as a weak anankastic and 不要 búyào as a deontic. It must be noted that, in this corpus-based study (see Chart 1), 5 要 yào also occurs as a dynamic marker, indicating some "necessity internal to a participant engaged in the state of affairs" (Van der Auwera, Plungian 1998, 80), as in (2c) (Alleton 1984, 200) [deontic] wǒmen yīnggāi/yīngdāng qiānxū jǐnshèn we should be.modest be.prudent 'We should be modest and prudent'. b. 去火车站得 • 坐第六六路公共汽车。 (Li 2004, 107) [anankastic] qù huǒchē-zhàn děi zuò dìliùliù lù gònggōngqìchē go train-station have.to sit 66 clf bus 'To get to the station you have to take bus 66'. (Van der Auwera, Plungian 1998, 80) c. 鲍里斯每晚要 • 睡十个小时才能正常活动。 (Li 2004, 107) [dynamic] Bàolǐsī měi wǎn yào shuì shí ge xiǎoshí Boris every night need sleep ten clf hour caí néng zhèngcháng huódòng then can normally function 'Boris needs to sleep ten hours every night for him to function properly'. ( Van der Auwera, Plungian 1998, 80) In a cartographic perspective, adjusting our terminology and taxonomy into Tsai's (2015) proposal, the anankastic 必须/要 bìxū/yào are hosted in the inflectional layer, between the outer and the inner subject, while the deontic 应该 yīnggāi is hosted in the complementiser layer, as its epistemic counterpart. Finally, Sparvoli (2012) identified a set of symmetrical traits of the deontic/anankastic contrast. In this context, the more relevant is related to the different behaviour in perfective contexts, where anankastic modals trigger actuality entailment while the deontic get a counterfactual reading. This corpus-based study is therefore aimed at testing this stipulation, but before presenting the method and the results, we need to present the issue related to the factual reading of modalised expression and introduce the notion of 'actuality entailment'.

Modals and Factuality
Since Kiefer (1987) and Chung and Timberlake (1985) and, even before, with Lü Shuxiang ([1942] 1944, modality has been related to the notion of 'non-factuality', implying that when an eventuality is possible or necessary, it is by default non-factual. However, the implicative feature of the semi-modal get and the lexical verb manage to has been identified already by Karttunen (1971), who observed that, in a past environment, sentences like (3a) imply (3b) and express that a given event was actualised; therefore, they are not compatible with a continuation which negates the actualisation of the state of affairs.
3. a. John managed/got/happened to solve the problem, #but he didn't solve it. b. = John solved the problem. (Karttunen 1971, 342, 346 slightly modified) From a typological approach to modality, Van der Auwera and Plungian (1998, underscored that most markers, such as manage, in the perfective form mark the completion of the process. 7 From the possible world semantics, Bhatt (1999) describes this phenomenon as "actuality entailment" (hereafter AE), referred to a modalised proposition whose event holds in the actual world. Hacquard (2006) provided a unified account where AE is inferred contextually through the combination of two ingredients: the scopal properties 7 Van der Auwera and Plungian (1998, classified manage as a demodalised marker expressing participant-internal "actuality" and underscored that most markers of participant-internal actuality, in the perfective form, when paralleled to their imperfective counterparts, mark the completion of the process of the modal and the identity of the event. If the modal scopes below aspect and the event is anchored in a bound interval, then we have AE. In this way, the actuality implication is analysed not only with reference to Ability -that is, considering perfective ability modals as underlyingly implicative, à la Bhatt -but it is also accounted for other root modalities: modal interpretations that did yield actuality entailments were those with a circumstantial modal base (abilities, goal-oriented and pure circumstantials); the ones that didn't were those with an epistemic or a (truly) deontic interpretation. 8 (Hacquard 2006, 113) The circumstantial feature seems to play a crucial role in the actuality reading of modalised expressions in past environment. 9 Moreover, in languages with perfective-imperfective morphology, a deontic modal occurring with an anankastic interpretation, as devoir in (4a), in the perfective form yields AE. In the imperfective form instead (4b), depending on the context and the continuation, it can have a counterfactual, progressive/habitual or generic interpretation (Hacquard 2006, 103 (Hacquard 2006, 14) In Hacquard's framework, the implicative reading arises from the perfective aspect outscoping the modal. More specifically, aspect starts as an argument of the verb and moves out yielding two nodes of type t: TP and VP. This allows a root modal to appear either right above TP or right above VP, with aspect moving right above the modal (Hacquard 2017, 52). 10 When low, the modal is bound by the aspect of the VP event; when high, it is bound by the speech event or, in embedded contexts, by attitude events. This, in turn, implies that 8 Hacquard (2006, 41) uses the label 'real' deontic with reference to someone granting permission or imposing an obligation on someone else.
9 The circumstantial reading is also underscored by Van der Auwera and Plungian (1998, 103-4) with reference to participant-internal actuality.
10 For a cartographic account on the scopal property with respect to aspect of Chinese modals, see Tsai 2015.

Carlotta Sparvoli
The Factuality Status of Chinese Necessity Modals in each configuration, the modal has different relational time: it is anchored, respectively, to the event time, the utterance time and the attitude time. As a result, AE effect is not expected when the modal occurs in embedded sentences. In § 5.2, we will take into account this feature while discussing our results concerning the tokens in embedded position (shown in chart 2).

Counterfactuality and Temporal Orientation
For both Bhatt (1999) and Hacquard (2017), the lack of AEs in imperfective modals, as in (4b), is due to an additional layer of modality associated with the latter. In Reischenbachian terms, the difference between perfective and imperfective aspect is accounted for with reference to the specular relation between reference and event time whereby the perfective locates the event within the reference time, whereas the imperfective locates the reference time within the time of the event, hence its typical features of ongoingness, repetition, and regularity. We do not need to discuss here in more detail the perfective/imperfective contrast, but we should recall that the imperfective morphology can give rise to a number of different readings, such as the progressive and non-progressive continuous interpretations, the habitual (including generic/dispositional meanings), and also the circumstantial habitual. The latter encompasses "a type of discourse in which a type of setting is first introduced, and then sequences of events that typically occur within that setting are enumerated" (Carlson 2012, 838).
Moreover, in modalised expressions, the imperfective can trigger a past counterfactual interpretation. Generated by the opposite inference of AE, the counterfactual reading conveys that "the speaker believes a certain proposition not to hold" (Iatridou 2000, 231); a counterfactual interpretation implies that the situation at stake has already been 'settled', and that such an (unactualised) state of affairs cannot be reversed. In other words, past counterfactual modals tell us how the world should or could have turned out to be, if a state of affairs had obtained (Condoravdi 2002), as in (5): 5. At that point he should/might (still) have won the game but he didn't in the end. (Condoravdi 2002, 62 slightly modified) As emphasised by Condoravdi, (5) conveys that "we are now located in a world whose past included the (unactualised) possibility of his winning the game" (2002,60); in general terms, should have expresses that it is "necessary at the present moment that a certain state of affairs obtained in the past" (60) and is thus compatible with both the epistemic and counterfactual interpretation. The latter reading stems from a future temporal orientation of the modal combined with a past perspective, that is, its reference time is an interval "starting at some past time and extending to the end of time" (75). These elements point to a future-in-the-past orientation of the counterfactual construal. Now that we have set the main coordinates of the theoretical framework, we can turn our attention to the language-specific issues related to counterfactual and AE in Chinese, which will be addressed, respectively, in § § 2.4 and 3.

Counterfactuality in Chinese
Since Bloom (1981), the investigation on the encoding of counterfactuality in Chinese (Nevins 2002;Jiang 2000Jiang , 2019aYong 2016; Jing-Schmidt 2017; Liu 2019, among others) has been primarily focused on counterfactual conditionals, as in (6) While in Indo-European languages the reality status of each proposition is typically signalled through tense morphology, the Chinese encoding of counterfactuality can hardly be captured by a clear-cut syntactic account. The relevant literature has in fact shed light on the role of the combination of hypothetical conjunctions like 要不是 yàobushì 'were it not for' with other markers, such as the aspectual and the sentence final particle 了 le, the temporal marker 早 zǎo 'early', negative operators or discourse markers such as 真的 zhēnde 'really '. 11 Due to the diverse elements at stake, the investigations on Chinese counterfactual conditionals are characterised by a constructionist approach and typically aim at producing a pragmatic or semantic account, without relying on a specific syntactic derivation. This composite scenario is described as a "cluster of unnoticeable weak features or lexical items that contribute, sometimes jointly, to reaching of counterfactual meaning" (Jiang 2019b, 283). For instance, in (7), we have the combination of a conditional conjunction 要是 yàoshi, a past time-reference and the distal 那个 nàge 'that' which contributes to locating the event in a hypothetical past event. As observed by Jiang, by replacing it with the proximal 这个 zhège, the sentence could be interpreted as "if this free-kick is in, the match will go into overtime" (285). The subtle, though essential, contribution of the distal 那个 nàge is thus a good example of what is meant by 'weak feature', that is, a feature which is neither sufficient nor essential but yet contributes to the 'construction' of the counterfactual interpretation.
that-clf free-kick shoot-in sfp hence will kick jiā-shí-sài le extra-time-match sfp 'If that free-kick had been in, the match would have gone into overtime'. NOT: *'if this free-kick is in, the match will go into overtime'.
Despite this 'weak feature', unified accounts are being formulated, especially with reference to past counterfactuals, which, starting from Ziegeler, are considered as the only environment in which the "counterfactual construal can be obtained reliably" (2000,104), as in (6). Similarly, Liu (2019) stressed the role of the combination of the past time reference and the conditional setting, while Jiang (2019a) highlighted the "tense mismatch" which locates the event in a hypothetical past, obtained either by pointing to a relative tense (as in 7) or by the use of time adverbs as 早 zǎo 'early'. 12 It must be emphasised that the proposals above are consistent with Condoravdi's emphasis on the combination between a past perspective and a future temporal orientation of the modal, as the aspectual 了 le in the antecedent, and 会 huì in the consequent, in (6) and (7).
In a corpus-based approach, Yong (2016) shed light on the correlation with past-oriented temporality, negation, emphatic modal adverbs, optative mood, first person pronouns, and demonstratives. Focusing on the pragmatic dimension, Jing-Schmidt (2017) paired a set of discourse functions with five bi-clausal hypothetical constructions and provided an analysis of the co-occurring modality markers, including modal verbs, adverbs, and modal particles. Based on 3,698 tokens of 要不是 yàobushì, she singled out 35 modal items (Jing-Schmidt (2017, 37) wherein the two highest ranked expressions are the futuri-ty markers 不会 búhùi 'won't' and 会 hùi 'will'. 13 Further discussion is in order on the contribution of 会 huì, which can be classified either as a futurity marker or, following Jing-Schmidt, as a speaker stance marker signalling 'epistemic certainty'. In the discussion of current data, we will address this topic in § 5.1. Here we need to recall that Jing-Schmidt observed that those 35 modal combinations uniformly signal speaker stance; thus, she emphasised the evaluative nature of this construal, describing it as the result of the idiosyncratic combination of different counterfactual ingredients.
To conclude, in the study on Chinese counterfactual, the issue of the contribution offered by necessity modals is addressed only peripherally. Importantly, Feng and Yi (2006), following Wu (1994), included 原来应该 yuánlái yīnggāi, glossed as 'should have been', among the markers used to elicit a counterfactual reading by the participants in their study; for two out of three respondents, the deontic modal preceded by 原来 yuánlái proved to be the most productive marker, triggering counterfactual reading in 92% of the 200 statements. This result directly leads us to the working hypothesis of present studies.

Anankastic Strength and Actuality Entailment
We propose that in Chinese, in past contexts, deontic and anankastic modals can be a likely index of the (counter)factual reading (Sparvoli 2012). 14 For outlining our proposal, we will start by focusing on the factuality reading of necessity modals in past contexts. In a formal semantic perspective, Chen (2012) observed a lack of AE of 应该 yīnggāi and 必须 bìxū due to a covert prospective aspect of Mandarin deontic and anankastic (in her terminology, "goal-oriented") modals. From a typological framework and based on the semantic contents of the notional ideas underlying modalities, our working hypothesis is that AE effects are correlated to the modal prominence of the necessity marker: it is high with anankastic markers and it is 13 Jing-Schmidt labels them as "modals that express high epistemic certainty" (2017,36). In the framework entertained here, futurity is a post-modal marker (Van der Awera, Plungian, 1998, 194 ff.), developed from epistemic necessity (Li 2004, 256).
14 As an anticipation of this claim, cf. Alleton 1984 andMyhill, Smith 1995, 266, who underscored the counterfactual value played by 该 gāi. For a diachronic account, cf. Meisterernst 2017. Liu (2019) also suggested the need for more investigation on the role of modality in the making of counterfactual reading.

Sinica venetiana 6 153
Corpus-Based Research on Chinese Language and Linguistics, 143-180 null with pure deontic ones (Sparvoli 2012(Sparvoli , 2015. 15 Our framework suggests that full-fledged AE is typically found with negative forms or forms combined with the exclusive focus marker 只 zhǐ 'only, just' (Sparvoli 2019). Regarding the latter, it must be stressed that: 表示可能的词, 加一"只"字, 如 "只能"、 "只好"、 "只得"、 "只会", 把他的可 能性缩小, 就成为表示必要或必然。 By adding the character 只 zhǐ before words expressing possibility, as in 只能 zhǐnéng, 只好 zhǐhăo, 只得 zhǐdé, 只会 zhǐ huì, their possibility feature is reduced, and they are turned into expressions of necessity or certainty. (Lü Shuxiang [1942] 1944 As emphasised by Li Renzhi, in these cases we do not have a real semantic shift into the necessity domain, but rather the extension of a possibility expression "to its extreme" (2004,190). The underlying principle is that there is a continuum from possibility to necessity. Along the same lines, we propose a cline from deontic to strong anankastic modals, based on their anankastic strength.
Deontic necessity Simple implication, alternatives are available * Typically, bouletic meaning in the antecedent of a conditional period. In the consequent it typically occurs combined with the focus marker 只 zhǐ expressing sufficiency condition. For a more detailed account of the different modal distribution in conditional construction, in combination with 才 cái and 就 jiù, see Sparvoli 2012, 273 ff.

The Working Hypothesis
We have seen that, with a circumstantial reading, the perfective forces the complement to hold in the actual word (Hacquard 2006, 14), and that an imperfective modalised form is typically compatible with a counterfactual, habitual/circumstantial, progressive, and generic reading. In Chinese, morphological tense marking is not available, while anankastic and deontic modalities are lexicalised in two sets of items displaying opposite scopal properties with reference to negation (Lü [1942] 1944; Sparvoli 2012) and aspect (Tsai 2015). The working hypothesis of this paper is that, in such heavily isolating language, the strategy for denoting (counter)factuality could be offered by the shift to a different necessity modal. Practically speaking, a contrast like (4a) and (4b) above would be expressed shifting from a deontic marker, as 应该 yīnggāi, 该 gāi, 应当 yīngdāng, to an anakastic marker, as 不得不 bùdébù, 只好 zhǐhǎo, 必须 bìxū, 得 děi. This paper attempts to verify such an hypothesis through a corpus-based study. If confirmed, this proposal would make it possible to outline a tripartite typological classification of (counter)factual marking: a. in languages perfective/imperfective morphology (French, Italian, Catalan, Bulgarian, Greek, Hindi): mood and tense shift (Hacquard 2006); b. in languages lacking perfective/imperfective morphology but having morphological tense-marking (English): both mood, tense and modal shift; c. in heavily isolating languages like Chinese: modal shift combined with temporal markers.

The Prediction
Along these lines, the predictions are that: (i) the Chinese equivalents of the counterfactual occurrences of should have are marked by pure deontic markers such as (应)当/该 (yīng)dāng/gāi 'should', alone or in combination with the counterfactual marker 本(来) běn(lái); (ii) stronger anankastic markers, such as 不得不 bùdébù 'cannot but' or 只好 zhǐhǎo 'can only', are banned in counterfactual environments; (iii) 必须 bìxū 'have to' preferably gets a factual interpretation; (iv) weaker anankastic modals, such as 得/要 děi/yào 'must', have a distribution similar to imperfective modals in French or Italian, thus they are compatible with both counterfactual and factual environments, without yielding AE.
x * By factual we intend a proposition that can only be understood as actualised, which would typically happen when we have a modal yielding AE effect.

4
The Method To test our predictions, we browsed two subsets of the E-C English-Chinese Parallel Concordancer. More specifically, we consulted the datasets named E-C English Novels (0.807 million words) and the E-C Chinese Novels (0.181 million words), wherein each pair of source and target text is aligned at the sentence level. To facilitate the identification of Chinese modals in past contexts, we selected the most prominent English (counter)factual necessity markers (should have and had to), to then identify their Chinese equivalents in the bilingual tokens thus retrieved. In total, we processed 795 bilingual tokens; after filtering the invalid tokens, the remaining 527 valid ones were tagged against five types of eventualities.  The high rate of invalid tokens (34%, no. 268) is due to the characteristics of the major datasets used in this study. The E-C English Novels Large Corpus includes 13 classics from 19th-century English literature and their Chinese translation (typically conducted just before the turn of this century, see Appendix). In that variety of English, the usage of our first token, should have, encompassed a heterogeneous range of meanings, thus requiring an attentive process of selection for isolating the relevant tokens (as we will clarify below). Moreover, in that repertoire, even when occurring with a counterfactual meaning, should have is often used as an equivalent of would have, as in (11), thus providing data related to conditional counterfactuals rather than modalised counterfactual. However, since conditional counterfactuals attract a conspicuous number of deontic modals (Jing-Schmidt 2017), we also included this type of token in the scope of our analysis. On the other hand, while the sampling size is limited, this repertoire offers the advantage of being easily accessible in full narrative context and in a variety of languages. Focusing on widely translated, easily accessible and relatively familiar classics facilitated the process of disambiguation of the factuality reading. In fact, when necessary, we also double-checked the results of our disambiguation analysing the perfective-imperfective morphology found in the Italian translation of the relevant passage. In this way, we could disambiguate each token in the light of the context of narration, independently from the morphology and the modal classes of the keyword. For instance, (12) was retrieved from the E-C Chinese Novels by selecting had to; in light of the continuation in full narrative context, the token including 该 gāi 'should' was tagged in the counterfactual type.
12. The Kianghsi bus did not cross over, so they had to transfer to the Hunan bus, which departed at noon. 江西公路车不开过去了, 他们该换坐中午开的湖南公路车。 Jiāngxī gōnglùchē bù kāi guo qu le tāmen gāi Jiangxi bus neg drive cross go sfp they should huàn zuò zhōngwǔ kāi de Húnán gōnglùchē transfer sit noon depart de Hunan bus Continuation: The next morning they arrived at Chiehhualung, on the border between the provinces of Kinaghsi and Hunan. The Kianghsi bus did not cross over, so they had to transfer to the Hunan bus, which departed at noon. Of all the buses they had taken on the way, none had arrived at a station so promptly as this one; so rather than quarrel about the short distance they felt that they'd come out a good half-day ahead and decided to take a night's rest instead of catching the bus that day. (Qian Zhongshu, Wei cheng. Engl. transl. Fortress Besieged, 2017, 255) The token visible in (13), instead, has been retrieved with the keyword should have but tagged as factual, given the reading of should have, rendered in Chinese with the evaluative modal 竟然 jìngrán.
13. "It is astonishing […] that my heart should have been so insensible!" (Jane Austen, Sense and Sensibility) 简直令人吃惊, 我的心竟然那么麻木不仁! jiǎnzhí lìngrénchījīng wǒde xīn jìngrán simply shocking my heart unexpectedly name mámùbùrén like.that insensitive = I was insensitive The first step in the disambiguation process was filtering all the invalid segments wherein the Chinese target does not correspond to the English source text or vice versa. When possible, we tried to retrieve the correct target segments. A case in point is (11), repeated in (14), which was already mentioned in the previous section. Such a segment has been classified as counterfactual and tagged as a conditional, namely, a case where should have is rendered in Chinese with the possibility modal 可以 kěyǐ 'can, may' preceded by a hypothetical conjunction. The second step in the disambiguation process was filtering the segments whose reading is not counterfactual. As a point of fact, should have does not necessarily force the counterfactual meaning. It can also have an epistemic reading, as in (16a), and, in embedded claus-es, a deontic meaning (16b). Considering the variety of English offered by the corpus, it also occurs in future-in-the-past interpretations, as in (16c).
16. a. "This wine-shop keeper was a bull-necked, martial-looking man of thirty, and he should have been of a hot temperament, for, although it was a bitter day, he wore no coat, but carried one slung over his shoulder". Moreover, in a substantial group of filtered segments, should have has a purely illocutionary function. In these cases, the Chinese rendering relies on discourse markers, such as 我相信 wǒ xiāngxìn 'I think', as in (17)  The segment with future-in-the-past reading covers 30% of the filtered items [tab. 4], and 14% of the entire 325 tokens retrieved from the E-C English Novels via should have.
18 In order to provide the contextual information needed for the factuality judgement, we included the relevant source text between square brackets.

Keyword 1. Should Have
In this section, we will first present the data retrieved from the E-C English Novels, that is, the English Chinese language combination. The first observation is that the tokens with counterfactual interpretation are embedded in the same environment described in the literature on Chinese counterfactual conditionals (see § 2.4), as 应 该 yīnggāi in the consequent of a conditional construction, in (18) The results of the interrogation show that among the counter-factual tokens retrieved through the keyword should have, the most frequent non-epistemic necessity modal is the deontic (应)该/当 (yīng) gāi/dāng, followed by 要 yào and 最好 zuìhǎo. In the taxonomy, 最好 zuìhǎo is classified as deontic (Sparvoli 2012, 263), and it can safely be said that among the equivalents of should have with counterfactual meaning, anankastic modals are not found.
It also appears that the counterfactual reading is contributed by a number of other markers (see table 5, 'Non-modals') that typically occur in counterfactual conditionals, such as conditional conjunctions, focus markers, and temporal deictics that locate the sentence in a past context (Jiang 2000; Jing-Schmidt 2017; Liu 2019, among others). There are also entries in which the counterfactual meaning is underspecified in Chinese (here signalled with 'nd'), thus confirming a phenomenon already observed by Yong (2016). 20 An example from the present study is (21) The typical scenario of the occurrence of 会 huì is in the consequent of a conditional period. In such an environment, the counterfactual reading is derived by implicature and signalled by a number of weak features described in § 2.3, such as a past temporal orientation combining with a negative or adversative presupposition, typically provided contextually or in the continuation of the narration (as in (22)) and, thus, difficult to capture syntactically. Jing-Schmidt relates Chinese counterfactuals to the prominence of the epistemic stance of the viewer. While agreeing in the epistemic nuance of futurity as conveyed by 会 huì, and in the modal component of the semantic of future in general (Giannakidou, Mari 2016), we prefer to single out the futurity reading from the epistemic certainty. This choice is based on two main reasons. Firstly, 10% of 会 huì occurrenc-20 In a corpus-based study, Yong (2016) used 13 different hypothetical conjunctions as keywords and, after collecting 3,000 conditionals, disambiguated 245 counterfactuals. Yong's investigation also includes data from a parallel corpus, observing a tendency towards "counterfactual cancellation" occurring after being translated into Mandarin (Yong 2016, 909, 912). es are in combination with necessity epistemic markers such as 一定 yídìng and 准 zhǔn, which would confirm classic modal stacking epistemic necessity > futurity (23). Secondly, even though there are contexts in which 会 huì could be interpreted epistemically or even dynamically, as in (23), it could also be argued that without 会 huì the event would be anchored to the time of utterance ("I now know what you meant") rather than to the event time ("at that time, I would have known what you meant"). Paraphrasing Condoravdi (2002), it could be said that 会 huì sets the reference time in an interval "starting at some past time and extending to the end of time". Therefore, in the composite mechanism of Chinese counterfactuality, 会 huì expresses how the world would have turned out to be if a state of affairs had obtained. Moreover, the data also include examples wherein 会 huì cannot be spelled out with any other meaning than futurity. A case in point is (24), which refers to the topic of love commitment. The addressee is telling a third person that, even though Estella's personality had been ruined, had she married him, he would have loved Estella anyway. Our understanding of the sentence in its narrative context is that the speaker's heart here is crying out "I will always love her", without the slightest epistemic weakening (Giannakidou, Mari 2017 In summary, the results suggest that, in past conditionals, 会 huì can be considered as the equivalent of would in future-in-the-past expressions and that the combination with weak features as the past temporal orientation, the negative presupposition and the first person subject (Ziegeler 2000;Yong 2016) trigger a counterfactual inference.

Past Counterfactual of Wish
The data collected selecting the keyword should have in the English-Chinese combination seem to confirm Ziegeler's (2000, 104) claim that: "it is only in past temporal conditionals that a counterfactual construal may be reliably obtained in Chinese". But we also encountered examples where (应)该/当 (yīng)gāi/dāng does not occur in conditional contexts, as in (25). Such examples are labelled as counterfactual wishes, "whereby the subject expresses a desire for things to be different from what they are or were" (Iatridou 2000, 231). Even though it is clear that no linguistic category is independently responsible for the counterfactual interpretation (just as for any other construction, it could be said), the data also show that by adding an appropriate temporal marker such as 那时候 nàshíhòu 'at that time', the shift from counterfactual to factual reading can be obtained by replacing 应该 yīnggāi with 只好 zhǐhǎo; with the latter an AE effect is triggered and the sentence gets a factual reading (26). guānhuái tā more take.care she 'I had been too reserved. At that time, I had to take more care of her'.

Past Counterfactual of Reprimand
More evidence about the contribution of deontic modal in counterfactual environment is found by selecting the keyword should have in the E-C Chinese Novels (0.181 million words). In this way, we collected 60 tokens from texts originally written in Chinese, and then rendered in English via should have. Of the total 60, only 26 have counterfactual interpretation; moreover, in addition to these 26, we also found 5 tokens in which the counterfactual interpretation is present only in the English rendering. Importantly, while processing texts originally written in Chinese and subsequently rendered with the English should have, we found that out of 19 tokens including (应) 该/当 (yīng)gāi/dāng only 2 are in conditional constructions. Moreover, in this repertoire, the prevailing nuance of the deontic tokens is the expression of reproach or reprimand (16 out 20 tokens) that performs the discourse function described by Myhill and Smith, in which "the speaker expresses dissatisfaction with the listener's failure to do something" (1995,266). In a past context, this discourse function obtained a counterfactual reading, as in (27a). Though mostly addressed to second-person subjects, the reprimand can also be referred to a third party, as in (27b).  […] commenting that Hung-chien's father should have insisted that at least one of the two rooms be a large one'. The distribution of modal markers in the tokens from the E-C Chinese Novels attests to the prominence of (应)该/当 (yīng)gāi/dāng, present in 20 out of 26 counterfactual tokens (73%). However, contrary to expectations, there is also one anankastic modal, 须 xū in (28) Other unexpected results found in first-person direct speech will be discussed in § 5.2.2.

Keyword 2. Had to
Selecting had to, 410 tokens were retrieved from the two datasets. Once filtered the invalid and irrelevant entries (83 in total), we obtained 327 segments in which had to occurs with a modal meaning.
The perfective morphology of had to does not necessarily force perfective aspect, being also compatible with habitual, generic, and progressive readings. Moreover, as emphasised by Hacquard (2017), AE is typically neutralised when the modalised proposition is an embedded clause ( § 2.2). Along these lines, each entry was manually tagged as factual, habitual/generic/circumstantial, non-factual, or non-factual (embedded), as in table 7.   Habitual entries also encompass circumstantial habituals (see § 2.3), that is, a sequence of events is enumerated within a setting previously created, as 'cleaning and scraping', introduced by 要 yào with a dynamic necessity meaning, as in (30): The spoons had to be cleaned and the frying-pan scraped, and the mugs and pudding-basin swilled in the lake". (Arthur Ransome, Swallows and Amazons) tāngchí yào qīngxǐ jiān-guō yào guā-xǐ exist spoon need clean frying-pan need scrape-clean hái yǒu bēizi jí bùdīng pán jìnpào zài hú lǐ also exist mugs and pudding basin soak to.be.at lake in We have included in the habitual class also entries like (31), where an episode is depicted as something happening with a certain regularity (有时 yǒushí 'now and then') in a given setting. In languages with rich tense morphology, habitual eventualities are typically rendered with the imperfective; therefore, for double checking the reading, when available, we consulted their Italian translation, and found the indicative imperfective of dovere 'must', which is typically used for expressing a habitual ongoing event in the past, such as doveva in (31) The following is an example of generic habitual, expressing a generalisation which obtained some time in the past, as that for the duty of "a common servant" in (32).  (It. transl.,266) (33) is an example of non-factual reading. Notwithstanding the perfective morphology in English, the full context reveals that the subject hasn't left the island yet (Ransome [1930(Ransome [ ] 2012; therefore, the entry is tagged as non-factual. Another interesting phenomenon is related to the counterfactual reading of 不必 búbì in past contexts, as an equivalent of 'would not have had to'. Just as all the modals triggering AE are possibility markers combined with the negation or with the focus marker 只 zhǐ, in a similar and symmetric way, the anankastic negation 不必 búbì 'there is no need to' seems to yield a counterfactual reading. This is another element pointing to the role of focus-sensitive operators in the expression of factuality and counterfactuality (Sparvoli 2019), a topic that will need to be discussed separately.

Unexpected Data. Backshift in First-Person Narrative
Although the modal distribution in the factual domain meets the prediction, we did find one token in which 要 yào marks the anankastic modality and obtains a factual reading -recall that in our prediction the weak anankastic 要 yào should convey a non-factual meaning, open to both a factual and counterfactual reading, or a habitual reading. The case in point is (37), in which the event, described in a direct speech first-person narrative context, is only compatible with factual interpretation, as it can be inferred by the continuation ('it produced various effects') and confirmed by the perfective indicative (passato remoto) of the Italian dovere 'must' (dovemmo). Similarly, to the unexpected counterfactual reading of 须 xū, (28), it appears that, in first-person direct speech, the reading of necessity modals is elusive. These phenomena, observed in first-person narrative contexts, could be interpreted as a temporal backshift of the speaker viewpoint. More precisely, in a modalised context, the evaluation of necessity is set back at a past time, that is, in (38), before finding the boat. Along these lines, the AE effect stemming from the strong anankastic is neutralised and the event is described as an ongoing state -as also suggested by the imperfective (imperfetto) of the Italian dovere 'must' (dovevamo). 21 21 Two types of backshifts, in the scenarios of justification for a past action and in the narration context, have been described by Hacquard (2017, 59) with reference to the epistemic modals.

Distribution of the 要 yào Tokens
Before presenting our concluding data, we need to focus on the modal distribution of the 要 yào tokens, which surface with five different meanings (see § 2.1). As shown in chart 1, the 要 yaò tokens display a set of related behaviours which are consistent with our predictions for the anankastic and with the account by Bhatt (1999), Hacquard (2006) and Tsai (2015) for the dynamic domain. Firstly, the reality status of the segments including 要 yào is evenly distributed in all the types of eventualities, with the most frequent occurrences in habitual reading (34% in matrix position and 24% including embedded tokens). Secondly, the factual reading is mainly visible in the dynamic domain (8 out of 9, 89%); in the anankastic contexts, we only have one token, shown in (37). Thirdly, given the past contexts of all the tokens, 要 yaò is compatible with the deontic meaning only in embedded position (see § 2.2); finally, 要 yaò gets counterfactual reading only when occurring with a volitional or futurity reading, thus confirming the non-factual feature of this weak anankastic modal.
Chart 1 Distribution of 要 yào: Eventuality types per modal reading (58 tokens) Finally, by aggregating all the data retrieved with the two keywords should have and had to, we obtained a tentative picture of the factuality reading of 386 tokens including Chinese modals, shown in chart 2. 22 By including also modals in embedded position, we could observe that, consistent with what was anticipated in § 2.2, in such an environment strong anankastic modals do not have implicative reading, as in (36), while deontic modals retain their meaning without shift-22 It should be noted that the data displayed in Chart 2 are the result of a filtering process: from the total of 795 tokens, we excluded 268 non-relevant tokens and, from the remaining 567, we also filtered 141 tokens whose Chinese segment does not include a modal marker, thus obtaining 386 tokens including modals in matrix and embedded position. ing to counterfactual reading, as in (35). Finally, to get a clearer picture of the modal distribution per eventuality type, we excluded the tokens in embedded position (41,11%), as seen in chart 3.

Conclusion
The results of the aggregated data for modals in matrix position [chart 3] show a gradient cline in which the two extreme poles obtain a unique reading: past counterfactual for pure deontic and factual for strong anankastic modals. In terms of factuality, the modal categories here observed are not discrete. Each class presents one mark- er that partially overlaps with the adjacent modality. For instance, the distribution of the habitual reading ranges from the dynamic 要 yào (3.14%) to the anankastic 要 yào (11.52%), and can also be seen, albeit less frequently, with other anankastic markers such as 得 děi (4.19%) and 必须 bìxū (2.10%), and even the strong anankastic 非得 fēiděi (1.5%), as seen in (32). Since each modality contains a marker that shares (to a lesser extent) one reading with the adjacent class, the factuality value decreases across a cline from anankastic to deontic modals.
The results confirm our prediction (i): namely, pure deontic markers such as (应)该/当 (yīng)dāng/gāi, alone or in combination with the counterfactual marker 本(来) běn(lái) are the equivalents of counterfactual should have. As shown in chart 2, we can see that, out of all 160 tokens with counterfactual meaning, the deontic is the most prominent full-fledged modality, and it allows for counterfactual reading also when occurring without 本(来) běn(lái). However, the counterfactual distribution is twofold. On the one hand, deontic markers prevail in the Wish and Reprimand Counterfactuals retrieved by browsing the texts originally written in Chinese [tab. 6]. On the other hand, the data retrieved from material originally written in English and then translated into Chinese mainly returned counterfactual conditionals wherein the prominent role is played by the futurity marker 会 huì [tab. 5]. This latter result supports the constructionist view of Chinese counterfactual conditionals and points to the prominent role of futurity markers (Ziegeler 2000;Jiang 2000; Jing-Schimidt 2017; Liu 2019, among others). It also attests to a futurein-the-past orientation of the counterfactual construal, thus confirming Condoravdi's (2002) account. In this sense, we could say that, in the typical makeup of Chinese counterfactual conditional, the choice between a possibility modal (能 néng, 可以 kěyǐ), a deontic necessity modal (应)该/当 (yīng)gāi/dāng or a futurity marker (会 huì) tells us, respectively, how the world could, should or would have turned out to be if only the given state of affairs had obtained.
Prediction (ii) stipulated that stronger anankastic markers, such as 不得不 bùdébù 'cannot but' or 只好 zhǐhǎo 'can only', are banned from counterfactual environments. The data confirm this hypothesis, but we must also mention the occurrence of 非得 fēiděi with a nonfactual reading. The relevant entry occurs in a first-person narrative context, thus it could be interpreted as a backshift, but we also found one token with generic habitual reading; therefore, it appears that, contrary to the predictions, 非得 fēiděi patterns more with the mere necessity markers than with the only-possibility ones.
We obtained a problematic result for prediction (iii), positing that 必须 bìxū 'have to' preferably gets a factual interpretation. We found one token with a counterfactual 须 xū (first-person direct speech), and the data point to a weaker anankastic strength of 必须 bìxū com-pared with 得 děi. Prediction (iv), on the other hand, is confirmed. In general, mere necessity modals have a distribution similar to imperfective markers in Italian since they are compatible and commonly found in habitual and non-factual sentences. In sum, the data show a slightly different order in anankastic strength, namely, 只好 zhǐhǎo > 不得不/不能不 bùdébù/bùnéngbù > 非得 fēiděi > 得 děi > 必 须 bìxū > 要 yào, whereas more data need to be collected for analysing the factuality of 须 xū.
Notwithstanding some minor discrepancies with the prediction, the data confirm the crucial role played by the deontic vs anankastic contrast in the marking of factuality in Chinese. Lastly, some pedagogical implications may be emphasised with reference to the equivalents of the tensed forms of the Italian dovere 'must'. Namely, the two poles getting unique factual (只好 zhǐhǎo, 不得不 bùdébù) and counterfactual ((应)该 (yīng)gāi cluster) readings can be mapped onto, respectively, the past indicative and the past conditional of dovere; a good candidate as an equivalent of the imperfective of dovere can be found in 要 yào (especially for direct speech) or 得 děi. Finally, the data point to the equivalence between the role of the English would and 会 huì in past contexts.