Bidirectional grammaticalization: Chinese modal and conditional

Using a constructional approach to morphosyntax, this study describes a triclausal construction (a type of anankastic conditional construction) and related constructions in the history of Chinese. It demonstrates that the triclausal construction constitutes a context of morphosyntactic vagueness where category boundaries between modals and conditional protasis connectives are underdetermined; consequently, bidirectional rather than unidirectional developments occur. Morphosyntactic vagueness is defined by properties shared between two morphosyntactic categories: distributional and functional similarities. Therefore, changes enabled by morphosyntactic vagueness are argued to be regular processes of change mediated by grammatical equivalence. If grammaticalization is defined as the development of morphosyntactic categories, but not in terms of non-equivalence such as unidirectionality or increased grammaticality, grammaticalization may be systematically bidirectional when enabled by morphosyntactic vagueness.


INTRODUCTION
This paper is concerned with a triclausal construction and related constructions in the history of Mandarin Chinese.Using corpus data and a constructional approach to morphosyntax (e.g.Croft 2001;Bybee 2010;Diessel 2019), it shows that modals and conditional protasis connectives (henceforth, conditionals, not to be confused with the conditional mood) may occur in a particular position of the triclausal construction.The implications of this phenomenon are then considered.
Example (1) schematizes the form and meaning of the triclausal construction.Formally, IF, WANTS, MODAL, and THEN represent positions filled by conditionals, verbs of desire, modals, and apodosis connectives, respectively.P 1 , Q, and P 2 refer to clauses.
(1) IF WANTS P 1 MODAL Q THEN P 2 'If you want P 1 you must Q; then P 2 .' Functionally, the speaker uses IF WANTS P 1 to presuppose the addressee's goal (represented by P 1 ) and MODAL to propose Q as the necessary means to achieve P 1 .THEN P 2 describes the consequence of Q, refers anaphorically to P 1 , and reinforces (somewhat redundantly) the connection between P 1 , P 2 , and Q.The construction is a directive speech act (Searle 1979: viii), used to direct the addressee to do Q, assuming that P 1 is the goal.It is also a special type of anankastic conditional construction, e.g. if you want P you must Q, where Q is a necessary means to achieve P (Condoravdi & Lauer 2016).
(3) 若要做見幾而諫, 除非就本文添一兩字始得 Ruò yào zuò jiàn jī ér jiàn chúfēi jiù if want take see chance and remonstrate must to běn wén tiān yì liǎng zì shǐ dé original text add one two word only.thenpossible 'If you want to take it to mean 'remonstrate when there is a chance', you must add one or two words to the original text; only then is it possible (to derive the meaning).' 2 (1270; Yǔlèi) The MODAL position is proposed to be a morphosyntactically vague context.Vagueness is a well-known concept in lexical semantics (e.g.Tuggy 1993).In morphosyntax, a context is vague when the morphosyntactic category of an item is underdetermined and has multiple compatible morphosyntactic analyses but does not require a precise one (Denison 2017(Denison , 2018;;Kuo 2021Kuo , 2022a)).As a vague context is where boundaries are blurred, an item in a vague context may change its morphosyntactic category (Denison 2017: 305).
This paper argues that bidirectionality between modals and conditionals in Chinese is neither unconstrained nor unprincipled.It is conditioned by morphosyntactic vagueness, which is only observed under specific, yet systematic, conditions where distributional and functional similarities exist between morphosyntactic categories, such that the morphosyntactic status of an item is underdetermined and not at issue.Therefore, even though not unidirectional, bidirectional changes, when enabled by morphosyntactic vagueness, are regular processes that are mediated by grammatical equivalence.If grammaticalization is defined as the development of grammatical categories, but not in terms of grammatical non-equivalence, e.g.unidirectionality and increased grammaticality, grammaticalization may be systematically bidirectional when enabled by morphosyntactic vagueness.
Unless otherwise stated, all data were drawn from the Academia Sinica Corpora of Ancient Chinese and Modern Mandarin Chinese, particularly the Corpus of Early Mandarin Chinese (seventh-nineteenth centuries CE).These corpora are relatively modest in size but contain quality data that are fully tagged and segmented into words.The methodology used in this paper is predominantly qualitative, but some quantitative evidence and analysis are provided.
The paper is structured as follows.Section 2 introduces the constructional approach to morphosyntax, the notion of morphosyntactic vagueness, and its instantiation in Chinese modals and conditionals.Section 3 describes the triclausal construction.Section 4 describes the histories of chúfēi and xūshì as bidirectional and attributes their bidirectionality to occurrences within the triclausal construction.Section 5 discusses implications.Section 6 concludes.

MORPHOSYNTACTIC VAGUENESS IN CONSTRUCTION GRAMMAR AND CHINESE
Section 2.1 introduces Radical Construction Grammar (Croft 2001) and its approach to morphosyntax.Section 2.2 interprets Denison's (2017) notion of morphosyntactic vagueness in terms of Radical Construction Grammar.Section 2.3 proposes that Modal and Conditional in Chinese are vague.Henceforth, morphosyntactic categories are capitalized.

Constructions and morphosyntax
As in other constructional theories (e.g.Goldberg 1995;Bybee 2010;Traugott & Trousdale 2013;Diessel 2019), constructions in Radical Construction Grammar are learned and conventionalized form-meaning pairings.They consist of syntax, morphology, and phonology on the formal side and semantics, pragmatics, and discourse functions on the meaning side.Non-predictability is frequently used to define constructions: something is a construction iff some aspect of its form or meaning 'is not strictly predictable from [a construction]'s component parts or from other previously established constructions' (Goldberg 1995: 4).Distributional preferences of the components of a construction, an aspect of nonpredictability, can also be a criterion (Hilpert 2014).The reasoning is that if something is non-predictable, users must learn and store its form and meaning.Sufficient frequency can lead to storage and hence constructions, too, but proposing a frequency threshold for constructions is problematic (Goldberg 2019: 54).
A construction may be specific or schematic.A word like cake is a specific construction because its form is fully specified and arbitrarily (i.e.non-predictably) associated with its meaning.A bound morpheme, e.g.plural -s, is part of a schematic construction, as it abstracts over more specific constructions, e.g.cats, cakes, etc.The plural -s construction can be represented as [COUNT_NOUN-s].Brackets indicate that it is a construction, while small caps indicate a 'slot', or a position within a construction, which represents an abstraction over expressions that may occur there.For example, cat and cake may fill in the COUNT_NOUN slot in the plural -s construction.A construction may be more complex than a word.The ditransitive construction has the form [SUBJECT VERB OBJECT 1 OBJECT 2 ] with the meaning 'X causes Y to receive Z' (Goldberg 1995).See Zhan & Traugott (2015), Zhan (2017), Peng (2017), and Kuo (2020, 2021, 2022a) for complex constructions in Chinese.
In Radical Construction Grammar, morphosyntactic categories are generalizations over items in particular slots and result from cross-constructional associations.An item is an adjective in the unfilled slots of the comparative construction ([ADJECTIVE-er]) and the superlative one ([ADJECTIVE-est]), because both slots are associated with the prototypical adjectival property of gradability and similar items may occur in both.For example, red is as an adjective in redder and reddest.However, this does not mean that red may not be something else.It is a noun in red is my favorite because it is in the subject position, a nominal slot.In other words, constructions are used as categorization tools for morphosyntax.The traditional category of an expression may be reconceptualized as derived from the most typical kind of slot that it occurs in.

Morphosyntactic vagueness in Radical Construction Grammar
Vagueness is a well-known concept in lexical semantics (e.g.Tuggy 1993).For example, cousin is vague with respect to gender.Typically, this kind of underspecification does not hamper communication (unless specification is required contextually).This contrasts with ambiguity, where deciding on precisely which one of the possible meanings is intended by a speaker is typically at stake (e.g. bank 'financial institution; river edge').Recently, Denison (2017Denison ( , 2018) ) has extended vagueness to morphosyntax: the category status of an expression may be underdetermined.
Whereas Denison does not distinguish between types of morphosyntactic vagueness, two are proposed here: item-level and slot-level.An item is vague if it has multiple compatible analyses.A slot is vague if it generalizes over multiple compatible analyses of items in it.Slot-level vagueness is by definition schematic, as it generalizes over various similar instances, whereas item-level vagueness is lexically specific in the sense that it is associated with particular items.Distributional and functional similarities characterize both types. 3 Some English words display item-level vagueness between Noun and Adjective in some contexts.For example, most nouns and adjectives may occur in a pair of constructions with similar slots: the compounding construction [NOUN NOUN] and the attributive adjective construction [ADJECTIVE NOUN], where the slots in bold are prenominal modifier slots.The category of a word in a prenominal modifier slot is vague between Noun and Adjective if the word may be attributed to [NOUN NOUN] and [ADJECTIVE NOUN].Such attribution is possible if there is no distributional pattern specific to Noun or Adjective (e.g.very preceding the slot renders it adjectival) and the word is functionally similar to Noun, in being referential, and Adjective, in being gradable.See Croft (2001: Ch. 2) for Noun, Verb, and Adjective in Radical Construction Grammar.
For example, Denison (2017: 304) observes that expert is an adjective in (4a) and a noun in (4b), but in (4c), where expert is a prenominal modifier, 'AD/R [addressee/reader] cannot know whether expert is noun or adjective here… the choice makes no difference to interpretation and no difference to constituent structure.'(4) (a) Naihe from Ka'u on the Big Island was so expert a surfer that his fellow chiefs grew jealous… (b) An expert's decision is usually final and binding.(c) You could do it yourself or get expert help.(Denison 2017: 304; originally from the British National Corpus) That is, expert help may be interpreted as NOUN NOUN or ADJECTIVE NOUN.Yet it is not at issue which one it is because expert is similar to Noun and Adjective functionally (in being potentially referential and gradable) and distributionally (in occurring without category-specific morphosyntax, e.g.Noun-specific possessive 's and Adjective-specific very).This type of vagueness that Denison discusses is more likely item-level than slot-level.For example, the prenominal items in expert advice, killer punches, and powerhouse songs are identified as vague by Denison, and such vagueness is more likely associated with the items and the phrases that they occur in, rather than with one schematic slot.In fact, most prenominal items are consistently nominal or adjectival.For example, bread in bread rolls is not vague, as it is not construed as gradable (cf.bready).
Lexically specific contexts where item-level vagueness is observed may be contexts of change.For example, Denison (2017: 305) suggests that, after occurring frequently before nouns, such as punch, killer may become vague and then adjectival (by acquiring gradable semantics).He thus likens lexically specific contexts of morphosyntactic vagueness to Heine's (2002) bridging contexts, where original and innovative analyses overlap and enable morphosyntactic change.By the same token, as a vague slot generalizes over multiple vague items, it may also be a bridging context.The multiple analyses available in a vague context by definition have low saliency, a general enabler of change (De Smet 2012); this is because in such a context 'the matter of which exact interpretation one selects is of little or no consequence' (Traugott 2017: 100). 4 In sum, morphosyntactic vagueness is observed in contexts where distributional and functional similarities between multiple categories neutralize any possible distinction between such categories.Without distributional similarity, there will be category-specific cues (e.g.very cues Adjective).Without functional similarity, even given distributional similarity, morphosyntactic categories by hypothesis will serve distinct functional purposes that keep them conceptually apart, assuming a conceptual view on morphosyntax (e.g.Croft 2001;Diessel 2019).

Morphosyntactic vagueness between Chinese Modal and Conditional
Sections 2.3.1-2.3.2 discuss distributional and functional similarities that characterize vagueness between Chinese Modal and Conditional, in order to show that a slot may be vague between Modal and Conditional.

Distributional similarities between Modal and Conditional
Modal in Chinese may be pre-or post-verbal.The post-verbal subtypes (Li & Thompson 1981: Chs.7 & 22) will not be discussed, as their distributions are clearly distinct from Conditional, which is pre-verbal.The pre-verbal subtypes are [4] Bridging contexts are originally conceptualized as ambiguous.However, Traugott (2017: 99-100) observes: 'Such structures [analyses available in bridging contexts] need not be pragmatically or semantically ambiguous, strictly-speaking, but need to allow multiple analyses (see Harris and Campbell 1995: 70-72)'.
Auxiliary and Adverb.Being distributionally more specialized than Adverb (Li & Thompson 1981: Ch. 5), Auxiliary is more sharply distinguished from Conditional.Auxiliary and its distributional properties proposed by Li & Thompson (1981) will be examined vis-à-vis Conditional, to show that even assuming many and even stringent distributional criteria cannot reliably distinguish Auxiliary from Conditional.Henceforth, Modal exclusively refers to Auxiliary.This subsection is based on Kuo (2022aKuo ( , 2022b)).Li & Thompson (1981: Ch. 5) propose eight distributional criteria for Modal, summarized and renumbered in (5). 5   ( (h) cannot be pre-subject.
Criteria (5a, b) distinguish Modal from Conditional, but many verbs also occur in those constructions (Li & Thompson 1981: 173).As no modal appears exclusively in these constructions, (5a, b) alone cannot reliably differentiate between Modal and Conditional.Like Modal, Conditional also does not occur in the constructions described in (5c-f).Criteria (5g-h) deserve more discussion.A conditional takes a clausal complement and can be pre-subject or post-subject (Li & Thompson 1981;Eifring 1995).Therefore, (5g) may distinguish Modal from Conditional.However, in null-subject contexts or when it is post-subject, a conditional immediately precedes the predicate, which would appear as if it took a verbal complement.Similarly, (5h) may distinguish between Modal and Conditional, but the latter is not consistently presubject and in null-subject contexts this criterion is ineffective.To provide evidence for the distribution of Conditional and its subject, 5,000 instances of ruò 'if', the most frequent Early Mandarin conditional, were sampled from the corpus.Assuming that a proper name, a common noun, or a pronoun immediately before or after ruò is the subject of the ruò-marked protasis, most instances of such protases are modal-like in being null-subject (4,244 instances) or post-subject (349).This means that in null-subject contexts, a modal may resemble a pre-subject or post-subject conditional, and a conditional a modal; (6) illustrates this possibility by describing Modal and Conditional (represented by IF) word orders.
(6) (a) (SUBJECT) MODAL… (b) IF (SUBJECT)… (c) (SUBJECT) IF… Some have argued that the criteria in (5) are too stringent (Tang 1988: 228-235;Li 2004: Ch. 4;Peng 2007: Ch. 2).Others have relaxed (5h) by defining Modal as possibly pre-subject (Tsao 1996), which blurs the distinction between Modal and Conditional even further.Nevertheless, the criteria in (5) are assumed here to show that even stringent criteria cannot reliably distinguish between Modal and Conditional.Eifring (1995: 54-55) proposes three distributional properties for Conditional and some (non-modal) adverbs, but they are not effective at distinguishing between Modal and Conditional.According to him, a conditional may immediately precede ne (a pause-marking particle similar to um), shuō 'say', and shì 'be'.Shì may even be a bound component of a conditional (Yu 1998;Hsu et al. 2015;Zhan 2017).However, a modal can take shuō and shì as its complements and collocation between ne and conditionals is rare.Ne is not attested in the corpora until Early Mandarin, where no conditional precedes ne immediately.In Modern Mandarin, only one instance does: rúguǒ ne 'if um', whose mutual information value of -1.84 (calculated by the corpus' built-in function) suggests that rúguǒ and ne do not tend to co-occur.
Finally, a modalized protasis, which is marked by a modal and a conditional simultaneously, distinguishes between the two, e.g.(SUBJECT) IF MODAL and IF (SUBJECT) MODAL.Nevertheless, such occurrences are rare panchronically.A simple collexeme analysis (Stefanowitsch & Gries 2003) shows that throughout the history of Chinese, only possibility modals néng and nénggòu 'be able to; can' are significantly attracted to protases (i.e. they occur statistically more frequently than expected in protases), while the other modals are not.Tables 1 and 2 summarize the results of the analysis, by dividing modals into two kinds: whether they are attracted to or repelled from protases marked by ruò in Old Chinese (eighth-first centuries Attracted Repelled Table 1 Collostructional strength (CS) between modals and ruò in Old Chinese.

370
Y U E H H S I N K U O BCE) and rúguǒ in Modern Mandarin, both of which are the most frequent conditionals in their respective periods.Attraction (or repulsion) indicates that they occur more (or less) frequently than expected.Collostructional strength > 1.30, a logtransformed number here, indicates p < .05(Fisher's exact test), i.e. attraction or repulsion is significant.'n' is the raw frequency of a modal in protases .
Tables 1 and 2 suggest that néng and nénggòu are overwhelmingly represented in protases throughout the history of Chinese, but most modals are not significantly attracted.Therefore, although modals and conditionals have distinct distributions in modalized protases, such sequences are generally rare. 6 In sum, Chinese Modal and Conditional share distributional properties.One may be distinguished from the other in some distributional contexts (e.g.[IF SUBJECT MODAL…]), but neither is uniquely associated with such contexts or occurs there consistently.

Functional similarities between Modal and Conditional
Both modals and conditionals represent propositions as non-factual (Narrog 2012), share similar types of readings (Sweetser 1990), and have speech act uses (Akatsuka 1992;Akatsuka & Clancy 1993).These similarities are shared between most modals and conditionals, unlike English Noun and Adjective, where shared similarities such as referentiality and gradability are more lexically specific.One formal semantic tradition especially highlights the interconnection between modals and conditionals.Kratzer (2012), building her analysis of conditionals on that of Table 2 Collostructional strength (CS) between modals and rúguǒ in Modern Mandarin.
[6] Modern Mandarin modals are assumed to be those identified by Li & Thompson (1981) and Old Chinese ones are those identified as canonical modals by Li (2016: 174) and Wu (2018).The precise meanings of the modals are irrelevant here, as the purpose is to show that they are statistically infrequent in protases.However, note that the meanings of néng and nénggòu, the only highly attracted ones, are mostly dynamic (Kuo 2022b), while the modal meaning of the triclausal construction is teleological.
modals, proposes that conditionals function like modals: they restrict modal meanings by specifying what would otherwise be left inferred by modals.Kratzer (2012: 108) thus remarks: 'There is no two-place if… then connective in the logical forms for natural languages.If-clauses are devices for restricting the domains of operators'.See Condoravdi & Lauer (2016) for a review.Speech acts are central to Radical Construction Grammar: what speakers intend to do linguistically is the building block of grammar such that the three basic crosslinguistic categories, Noun, Verb, and Adjective, are hypothesized to originate from the communicative acts of referring, predicating, and modifying, respectively (Croft 2001: 66).Following Radical Construction Grammar and on the basis of the dataset considered here, the most prominent functional similarity between Modal and Conditional is their speech act uses (i.e.performativity): both can be the heads of constructions that perform similar speech acts.That is, they are 'performatively equivalent'.For example, (7a, b) are responses to the addressees' questions about what to read.Both responses can be understood as directives, which, by Searle's (1979: viii) definition, 'get [people] to do things'; or specifically, as a speech act of advice (Searle 1979: 13), in that they advise on what course of action to take.Given that a modal utterance like (7a) and a conditional one like (7b) can be understood directively, an utterance without any morphosyntax specific to Modal or Conditional may thus sometimes be interpreted modally or conditionally in performative contexts.This is illustrated in the performative context of (8a), where xū can be understood as either a modal or a conditional; (8a) is where the pre-subject, conditional use of xū in (8b) originated (Kuo 2022a Performative uses of modal and conditional constructions are well known (e.g.Akatsuka 1992;Akatsuka & Clancy 1993;Verstraete 2001;Kaltenböck 2016).Such uses are typically labelled as indirect, in that they are less direct ways of performing speech acts.Performative verbs (I request that you do it) and imperatives (do it!)may perform more direct acts.Performative equivalence between two expressions does not necessarily suggest that there is no functional distinction between them, as there are multiple ways of performing the same act, each of which likely has its own functional motivations.The distinction between directive and indirective acts also reflects the idea that the same act can be performed differently.For issues regarding variation and (in)direct acts, see Frajzyngier & Jirsa (2006) and Mauri & Sansó (2011).
Performative equivalence, in combination with distributional similarities, enables Modal and Conditional to be vague.A slot is vague between Modal and Conditional if it may be assigned both modal and conditional statuses and yet no difference in distribution or performativity suggests one status over the other.Other non-performative functional similarities may play a role, but, as far as the triclausal construction is concerned, performativity will be shown to be the most prominent function that provides the shared background against which its MODAL slot may be understood as morphosyntactically vague.

THE TRICLAUSAL CONSTRUCTION
Section 3.1 introduces the triclausal construction.Sections 3.2-3.4describe THEN P 2 , MODAL Q, and IF WANTS P 1 , respectively.The MODAL slot and items in it will be shown to be morphosyntactically vague.Section 3.5 discusses the distribution of the construction and its constructional status.Section 3.6 summarizes.
The Early Mandarin Corpus was queried for words that typically function as connectives, modals, and verbs of desire.The results were manually examined to identify instances of the triclausal construction.A particularly thorough examination of (Zhūzǐ) Yǔlèi, a collection of Zhūzǐ's (1130-1200) conversations compiled in 1270, was undertaken, for the following reasons.First, the colloquial nature and the size of Yǔlèi make it a crucial source of Early Mandarin (Sun 1996: 4-8).Second, the construction is particularly frequent in Yǔlèi. 7Third, as will be shown in Section 4, Yǔlèi is the transitional period for the bidirectional developments of two items in the construction.

Introduction
In the following, (1), reproduced as (9), is a snapshot of the construction.
(9) IF WANTS P 1 MODAL Q THEN P 2 'If you want P 1 you must Q; then P 2 .'P 1 is some goal that the speaker assumes someone (typically the addressee) wants to achieve.Q is modalized as the necessary means to achieve P 1 .MODAL is a teleological modal, which marks a proposition as necessary with respect to some goal (Narrog 2012: 8).THEN anaphorically refers to Q, signaling that P 2 temporally follows or conditionally depends on Q; Q THEN P 2 may be paraphrased as 'after/if Q, P 2 '.This polysemy between temporality and conditionality is a general property of Chinese connectives (Li & Thompson 1981: Ch. 23;Eifring 1995: Ch. 4) and typologically widespread (Traugott 1985).P 2 describes the result of Q and anaphorically refers to the goal described by P 1 , by containing one or more lexical items from P 1 and/or a modal expressing the possibility of P 1 .P 2 can be paraphrased as 'P 1 is possible' and understood as referring to the same goal as P 1 does.For example, in ( 10 The construction functions as a directive.First, it assumes the addressee's goal (IF WANTS P 1 'if you want P 1 '); second, it indicates to the addressee what is to be done (MODAL Q 'one must Q'), if P 1 is the goal; and third, it expresses what happens after/ if Q is achieved (THEN P 2 ), which anaphorically refers to P 1 .It is more specifically an indirect directive: it does not categorically direct the addressee to do Q but phrases it as contingent on one's desire to achieve P 1 .
The construction is a special type of the anankastic conditional construction (Condoravdi & Lauer 2016), which has a desire predicate within its protasis (IF WANTS P) and an apodosis modalized by a teleological modal (MODAL Q).The modal expresses the necessary precondition and means through which P comes true.The anankastic conditional construction, as in (11), typically directs the addressee to do Q, if they want P. A typical anankastic conditional construction is represented as (11) If you want to go to Harlem, you have to take the A train.(Condoravdi & Lauer 2016: 2) The form IF WANTS P MODAL Q does not always have the anankastic conditional function.Consider ( 12), where Q is not the necessary means for P and the speaker does not direct the addressee to achieve P.
(12) If you want to eat chocolate, you should try thinking about something else.(Condoravdi & Lauer 2016: 2) The triclausal construction resembles the anankastic conditional construction: IF WANTS P 1 presupposes the addressee's desire and MODAL Q expresses how to achieve P 1 .Unlike the anankastic conditional construction, the triclausal construction has THEN P 2 , which refers anaphorically to P 1 .
( As P 2 refers to P 1 without exception and THEN pertains to the condition or time established by Q, the function of THEN P 2 is likely to emphasize Q as being the precondition and the necessary means to achieve P 1 /P 2 .The connection between P 1 and P 2 is non-predictable and qualifies the triclausal construction as a construction in the sense of Goldberg (1995) and Hilpert (2014); see Section 3.5 for more discussion.

MODAL Q
MODAL marks Q as teleologically necessary with respect to the realization of P 1 ; (13)-( 18) show that xū and xūshì occur in MODAL.Bì 'must' is another but rarer possibility.He et al. (1985: 639) note that the strength of xū varies between bì 'must' and yīng 'should' and presumably so does its derivative xūshì.For consistency, xū(shì) is translated into 'must'.
The status of xū þ shì in (2), ( 13), ( 18), and ( 19) deserves particular attention.Etymologically shì is a copula.Depending on the context, xū þ shì may be interpreted as a disyllabic modal (xūshì) or a sequence where xū modalizes the focus-marking copula shì that introduces a focalized element. 8For example, following a subject and preceding a predicate, xū þ shì is xūshì 'must', e.g. ( 20).Preceding a subject, xū þ shì is xū shì 'must be (the case that)'.Because no modal is assumed to be pre-subject, the subject suggests that shì is not part of a modal, e.g. ( 19). ( 20 21b).Yet no morphosyntax suggests which one is to be preferred and whichever it is does not alter the intended message: the whole construction constitutes a directive that advises 'going and asking…' (= Q), if one wants to 'capture this demon' (= P 1 ).Both translations can perform this directive.Similarly, the intended speech acts in (2), (13), and ( 18 While Translations (b) are the most plausible original interpretations, chúfēi in this context is vague.It can be assigned a modal status, as an item in the MODAL slot in the triclausal construction (IF… chúfēi MODAL Q…) or a conditional status, as an item in the IF slot in the conditional construction [IF Q THEN P] preceded by another protasis (IF…chúfēi IF Q…).No morphosyntax specific to Modal or Conditional indicates which analysis to select and whichever construction it is, there is no significant difference in the speech act being performed.The speaker (or the addressee) presumably does not need to choose an analysis to perform (or understand) the intended directive that they must do Q, if they want P 1 /P 2 .
In sum, xū þ shì exhibits item-level vagueness between xū shì 'must be (the case that)' and xūshì 'must'; and chúfēi, between 'only if' and 'must'.One interpretation is performatively equivalent to the other and no category-specific morphosyntax suggests one over the other.Only when xū þ shì in MODAL Q is pre-subject is it not vague, in which case it is xū shì.This non-vagueness is at the level of xū MODAL shì… Q .On the whole, the MODAL slot is morphosyntactically vague: both modal and conditional analyses are allowed and neither is enforced, due to distributional and functional similarities to Modal and Conditional.Crucially, the very first use of chúfēi in MODAL, (23), may be hypothesized as the source of subsequent modal uses.Furthermore, as chúfēi is vague between a modal and a conditional, in principle non-pre-subject xū þ shì in the same slot may be vague, too.This will be explored in Section 4.

IF WANTS
Some examples lack an explicit IF.Clauses without any connective in Chinese may signal conditional or temporal relationships between clauses, the first one of which typically expresses the precondition or the temporally earlier event (e.g.Li & Thompson 1981;Eifring 1995).WANTS P 1 is also found in a clause marked by a temporal connective like shí 'when' alone, as in ( 16), or by both temporal and conditional connectives, e.g. ( 15).All cases but one contain WANTS.Yào consistently means 'want' in WANTS, but may be a modal 'will/have to' or a conditional 'if' elsewhere (Yu 1998;Hsu et al. 2015).

Distribution and non-predictability of the construction
Table 3 describes the distribution of IF, WANTS, MODAL, THEN, and whether P 2 contains lexical similarity to P 1 or no similarity but a possibility modal in Yǔlèi.Lexical similarity is defined as identity of form between parts or all of P 1 and P 2 .Shí under IF is an instance of shí 'when' without rú or ruò.Ránhòu under THEN includes the only one instance where multiple connectives mark P 2 .
Rather than a construction with its own form and function, the triclausal construction could be a sequence of two independent constructions: an anankastic conditional construction [IF WANTS P 1 MODAL Q] and [THEN P 2 ]; or an 'insubordinate' protasis [IF WANTS P 1 ] (i.e. a protasis used as a main clause) and a typical conditional [IF Q THEN P 2 ].If true, two consequences follow.First, any triclausal sequence would result from the interaction of the two constructions, which supposedly could be predicted from elsewhere (e.g.general pragmatic principles).Second, possible multiple analyses of the MODAL slot would arise from the possibility that the sequence might be [IF WANTS P 1 MODAL Q] and [THEN P 2 ] or [IF WANTS P 1 ] and [IF Q THEN P 2 ].However, the independent constructional status of the construction will be argued for.
Functionally, THEN P 2 emphasizes Q as being the precondition and necessary means to achieve P 1 /P 2 (Section 3.2).By hypothesis, lexical similarity between P 1 and P 2 , in addition to the possibility modal, is instrumental in this emphatic function, as it explicitly creates coherence between P 1 and P 2 .Such similarity is an aspect of the distributional preferences of the slots, which, if non-predictable, suggests the independent status of the construction.
Corpus work was undertaken to compare lexical similarity between P 1 and P 2 with a similar sequence from which lexical similarity presumably could be predicted, WANTS P x MODAL Q y THEN P z .If the difference in likelihood of similarity was significant, similarity between P 1 and P 2 was assumed to be non-predictable.Instances of MODAL (xū, xū þ shì, bì, and chúfēi) were examined if one of the ten preceding words was WANTS (yào or yù); ten is the limit of the filter function.The remaining 210 instances were then manually examined.An instance was counted as WANTS P x MODAL Q y THEN P z if it was not the triclausal construction and if THEN referred to Q y (to delimit the search range between MODAL and THEN; otherwise, any number of words could intervene); 16 were identified, out of which only two showed lexical similarity, e.g. ( 26)-( 27).Compare 17 out of 32 in Table 3 Lexical similarity between P 1 and P 2 is significantly more likely than between P x and P y (p = .011,φ = 0.392, using Fisher's exact test), suggesting that it is nonpredictable and construction-specific.A similar procedure was used to compare WANTS P x (…) THEN P z .73 out of 287 showed similarity.Lexical similarity between P 1 and P 2 is again significantly more likely (p = .002,φ = 0.185, using Fisher's exact test).

Summary
The components of the triclausal construction are summarized in ( 28)-( 30).
(28) IF WANTS P 1 (a) It specifies that the following clauses are about the desire to achieve P 1 .(b) P 1 refers to some goal that the speaker assumes the addressee wants to achieve. ( It expresses what must be done, given WANTS P 1 . (b) Q refers to the means through which the goal P 1 is to be achieved.(c) MODAL is teleological, as it marks Q as necessary with respect to the achievement of P 1 .(d) MODAL is filled by bì, xū, xūshì or chufēi, typically a connective.
(30) THEN P 2 (a) It refers to the temporal and/or conditional consequence of Q, reiterates the goal, P 1 and emphasizes Q as the means to achieve P 1 /P 2 .(b) P 2 refers to P 1 through lexical similarity to P 1 and/or a modal implying the possibility of P 1 .
The construction is an indirect directive: it frames the illocutionary act as contingent on the addressee's desire.The directive function and the absence of morphosyntax specific to Modal or Conditional around the MODAL slot provide the background against which the slot is vague: it may be modal or conditional, the determination of which is not at issue, as both analyses are performatively equivalent.One communicative explanation for the vagueness is that the slot need not be specified, as the construction already specifies the relevant function: directivity.

BIDIRECTIONALITY BETWEEN MODAL AND CONDITIONAL: CHÚFĒI AND XŪSHÌ
Sections 4.1-4.2examine the histories of chúfēi and xūshì to illustrate bidirectionality between Modal and Conditional.The vague morphosyntactic status of the triclausal MODAL slot is proposed as an enabling factor, as it allows one category to become the other.Since morphosyntactic vagueness highlights distributional and functional similarities, the analysis draws on analogy-based accounts (e.g.Fischer 2008;Noël 2017).Change is hypothesized to proceed 'on the basis of similarity relations between environments' that trigger 'analogically induced recategorization' (De Smet 2012: 601-604).Section 4.3 considers coercion as an alternative explanation.Section 4.4 discusses similar cases.

Chúfēi: from Conditional to Modal
Section 4.1.1introduces construction types involving chúfēi and Eifring's (1995) analysis of chúfēi as a non-conditional connective.Section 4.1.2proposes that the pattern that motivates Eifring's analysis is an anankastic conditional construction where chúfēi is a teleological modal.Section 4.1.3proposes a diachronic account of modal chúfēi.
In Type 1, 'only if Q, P', the apodosis connective is typically cái 'only then' or one of its near-synonyms.This is the type that ( 22) instantiates.In Type 2, 'unless Q, P', the apodosis connective is fǒuzé 'or; otherwise', or one of its near-synonyms.Both types are illustrated in (31a, b). ( 31  Chúfēi occurs in more patterns than Table 4 suggests; for example, the chúfēi-marked protasis may be post-posed (Wang et al. 2014).Despite its incompleteness, Table 4 captures the primary focuses of the literature on chúfēi: the meanings of 'only if' and 'unless' and its protasis-marking function.
A construction where chúfēi neither means 'only if; unless' nor marks the protasis is [IF WANTS P chúfēi Q], as in ( 32), where WANTS is filled by verbs of desire (Eifring 1995).
(32) Ruò yào rén bù zhī chúfēi jǐ mò wèi if want people not know chúfēi self not do 'If (you) do not want people to know your wrongdoing, you yourself should not do it.'(Wang et al. 2014: 42) Because chúfēi heads the apodosis in this construction, it is problematic for accounts treating it as exclusively a conditional.In the literature, this construction is either neglected or downplayed (Yang 2007;Wang et al. 2014), likely due to its low frequency in Modern Mandarin.According to Wang et al. (2014: 46) To propose one function and one morphosyntactic label for chúfēi across the whole gamut of patterns, Eifring (1995) proposes that chúfēi is a 'necessity clause connective' that marks its clausal complement as necessary (but not conditional) and any conditional meaning associated with chúfēi-marked patterns is attributed to the neighboring connective.Therefore, (31a, b) mean literally that Q is necessary ('that you go is necessary') and the conditionality originates from THEN and OR (respectively, 'only then will I go' and 'otherwise he will not go').For Eifring, this analysis is not the same as analyzing chúfēi as a modal or a conditional protasis connective.First, chúfēi cannot be a modal, as it can be pre-subject, e.g.(31a, b).Second, chúfēi does not mark protases because IF already does so in [IF WANTS P chúfēi Q], e.g. ( 32).Because under Eifring's analysis chúfēi is not a conditional protasis connective, (32) is not problematic.Instead, it means 'if you do not want people to know, that you do not do it yourself is necessary'.
In sum, Eifring assumes chúfēi as functionally and morphosyntactically invariant across distributional contexts, which is a 'no redundancy in representation' linguistic analysis (Croft 2001: 121).This leads to the conclusion that chúfēi is a necessity clause connective, not a modal or a conditional protasis connective.

Chúfēi as a teleological modal
Eifring's analysis is problematic.No study seems to have uncovered any comparable non-conditional necessity clause type cross-linguistically.The analysis is thus ad hoc, positing a novel category based on a specific distributional pattern with no cross-linguistic near-equivalent.Furthermore, from a usage-based perspective, a non-redundancy analysis is not necessarily preferable or psychologically real (Croft 2001: Ch. 3).Although chúfēi does not mark the protasis or mean 'only if; unless' in [IF WANTS P chúfēi Q], it does not mean that it does not do so elsewhere; cf.Yang's (2007) constructional approach to chúfēi.
To explain [ in the literature are anankastic conditional constructions: they direct someone to do Q if they want P and chúfēi marks Q as teleologically necessary for P. Lü (1999: 125) describes [IF WANTS P chúfēi Q] as '(if) one wants to obtain a certain result ([i.e.result = P]), one must do so ([i.e.do so = Q]).Wang et al. (2014: 42)  Assuming modals as strictly post-subject, chúfēi in this construction, when presubject, is not a prototypical modal but a modal-conditional hybrid.Its pre-subject syntax suggests a conditional status; yet, by analogy with the anankastic conditional construction [IF WANTS P MODAL Q], it resembles modals and expresses teleological modality.Analyzing something as a modal or conditional may be important in some theories, but presumably a user would only need to know that any instance of [IF WANTS P chúfēi MODAL Q] constitutes a directive where Q is the teleologically necessary means to achieve P. A precise analysis of chúfēi is not necessary.Furthermore, chúfēi in [IF WANTS P chúfēi MODAL Q] is not consistently pre-subject: only 34.6% (9/26) of the time is it so, based on texts between the fourteenth and eighteenth centuries.This means that most of the time, by analogy with [ In sum, chúfēi is a teleological modal when in the MODAL position of the anankastic conditional construction, i.e. [IF WANTS P chúfēi MODAL Q].This analysis is more desirable.First, it proposes no ad hoc clause type but draws on the anankastic conditional construction.Second, unlike Eifring's analysis, it upholds the established analysis of chúfēi as a conditional in constructions described in Table 4.Only chúfēi in [IF WANTS P chúfēi MODAL Q] is a teleological modal.

The morphosyntactic history of chúfēi
Teleological modal chúfēi likely develops from its use in the triclausal construction, [IF WANTS P 1 MODAL Q THEN P 2 ], which ultimately originates from its use in the Type 1 construction [IF Q THEN P] 'only if Q, P', described in Table 4.It is hypothesized as a series of analogy-based changes, as instances of chúfēi in the following constructions are formally similar and performatively equivalent (the slots that chúfēi occurs in are in bold): First, chúfēi in [IF Q THEN P] is attested earlier than the other two uses.There are 5 such instances of chúfēi that are earlier than or contemporaneous with the earliest triclausal use of chúfēi, i.e. ( 23).All 5 are used directively, as in ( 22) and ( 34), where the speaker directs the addressee to do Q by saying that Q is the teleologically necessary precondition for the addressee's goal, referred to by P.
(34) 除非首尾熟背得方得 Chúfēi shǒu wěi shú bèi dé fāng dé chúfēi head tail familiar memorize can only.thenget 'Only if you can commit to memory the whole thing from start to finish can you get it (you must commit it to memory to get it).' (1270; Yǔlèi) Chúfēi in [IF Q THEN P] up to and including Yǔlèi thus resembles the last two clauses in the triclausal construction (i.e.[…MODAL Q THEN P 2 ]), formally and functionally.This resemblance reflects the item-level vagueness of chúfēi in the triclausal construction (Section 3.3): a sequence like IF WANTS P 1 chúfēi Q THEN P 2 can be interpreted as the triclausal construction (IF… chúfēi MODAL Q…) or a protasis and Second, chúfēi is attested in the triclausal construction earlier than in the anankastic conditional construction [IF WANTS P MODAL Q], cf. ( 23) and (33).Because the first two clauses of the triclausal construction constitute the anankastic conditional construction, the occurrences of chúfēi in the latter are likely to have been motivated analogically by the former.Moreover, the MODAL positions in both constructions are teleological, so it is not unexpected that chúfēi started behaving like a modal after occurring in the triclausal construction, as in analogy 'An item's new syntactic behavior can be modeled on its behavior under a different syntactic status' (De Smet 2012: 604).
Finally, whereas neither pre-Yǔlèi texts nor Yǔlèi contains chúfēi in the anankastic conditional construction, in post-Yǔlèi texts between the fourteenth and eighteenth centuries, 32.9% (26/79) of chúfēi occur in the anankastic conditional construction.This suggests chúfēi to have become more clearly modal after its occurrences in the triclausal construction.
The formal similarities between the constructions that chúfēi occurs in are visualized in (35).In ( 36)-( 38), their semantics are summarized in (a), directive meanings in (b), and earliest attestations in (c).
(a) 'Q is teleologically necessary for P.' e.g. ( 22) and ( 34 In sum, a series of 'analogically induced recategorization' has likely led chúfēi to become a teleological modal.This change is likely enabled by the underdetermined morphosyntactic status of the triclausal MODAL slot, because chúfēi in the slot may be assigned a conditional status, in keeping with its origin, or a modal one, by analogy with other modals, which then gives rise to the teleological modal use.
4.2 Xūshì: from modal to conditional Section 4.2.1 describes the history of xūshì.Section 4.2.2 summarizes the histories of xūshì and chúfēi and considers relevant details.

The morphosyntactic history of xūshì
Xū þ shì originates from xū shì 'must be', e.g. ( 39) (Wu 2004).Before Yǔlèi, xū þ shì may be xū shì 'must be', xūshì 'must' or focus-marking xū shì 'must be (the case that)'.It may be vague between the latter two, e.g. ( 40).These uses persist into Yǔlèi, e.g. ( 19), (20), and ( 41 Furthermore, in Yǔlèi xū þ shì occurs in the triclausal MODAL slot for the first time and is vague in a way similar to (41), if not pre-subject (Section 3.3).As suggested at the end of Section 3.3, xūshì 'only if' is another possible interpretation, for which there are two supporting arguments.The primary one is that both xū þ shì and chúfēi occur in MODAL.Therefore, if chúfēi may be analyzed as a modal or conditional, e.g. ( 23), so may xū þ shì.The secondary one is that, although collocation with shì is not specific to Modal or Conditional, shì may be a bound component of a conditional (Section 2.3.1),which may nudge the status of the otherwise vague xū þ shì towards that of a conditional.Reproduced from ( 18), ( 42 In terms of performativity, not much seems to depend on the analysis of xū þ shì.To understand (42), the addressee presumably would only need to know that the speaker intends to direct them to realize Q.The multiple analyses are also enabled by lack of category-specific morphosyntax (except if regarding shì as part of a conditional).One of the earliest instances of xū þ shì as potentially xūshì 'only if' is (42); so are (2) and ( 13), all contemporaneous with the earliest vague instance of chúfēi, e.g. ( 23).Note that pre-subject xū þ shì in the triclausal construction, e.g. ( 19), is not considered vague here, as such instances are xū shì 'must be (the case that)', assuming that no modal is pre-subject.If assuming otherwise, this means that the triclausal MODAL slot can be pre-subject and more cases of xū þ shì will be vague between xūshì 'must' and xūshì 'only if'. 11 After Yǔlèi, xū þ shì occurs in more conditional constructions, likely by analogy with chúfēi.Chúfēi in [IF Q THEN P] is exemplified in ( 43)-( 44 For example, speakers may start using chúfēi in the triclausal construction and xūshì in the anankastic conditional construction to exploit their difference in illocutionary force (xūshì varies between 'must' and 'should'; Section 3.3).For the emergence of directives across languages, see Mauri & Sansó (2011).

Coercion as an alternative
Coercion, whereby 'the meaning of the lexical item conforms to the meaning of the structure in which it is embedded' (Michaelis 2004: 25) due to semantic incompatibility, may provide an alternative account.A conditional might be 'coerced' into having a modal meaning in the slot and by accommodating the conditional, the slot then became morphosyntactically vague.However, this assumes semantic incompatibility and an a priori morphosyntactic distinction that became vague only after coercion.This is problematic given, first, similarities between modality and conditionality (Section 2.3.2;especially Kratzer 2012); second, the panchronic lack of consistent distributional distinctions between the categories; and third, the absence of category-specific morphosyntax in the triclausal construction.Ziegeler (2007Ziegeler ( : 1023Ziegeler ( -2014) also remarks 'the need to posit an a priori syntactic frame with which certain lexical items may be in conflict' undermines the concept of coercion; see also Traugott & Trousdale (2013: 206-207).
Most changes reviewed here have not been attributed to morphosyntactic vagueness, but they support the likelihood of bidirectionality, including the morphosyntactic development of chúfēi, CONDITIONAL > MODAL. 13

IMPLICATIONS FOR (DE)GRAMMATICALIZATION
Under the unidirectionality hypothesis, the development of morphosyntactic categories as typically unidirectional would be expected (Kuteva et al. 2019).
Therefore, one of the processes, MODAL > CONDITIONAL and CONDITIONAL > MODAL, should be grammaticalization and the other should not.Which one is it?The answer depends on how grammaticalization is defined.
First, UNIDIRECTIONALITY may be characterized as 'a core property of grammaticalization', as done in 'most of the literature' (Börjas & Vincent 2011: 164).Simplifying somewhat, what is not unidirectional may therefore be considered as degrammaticalization (Norde 2009).This proposal leads to the conclusion that MODAL > CONDITIONAL and CONDITIONAL > MODAL cannot be grammaticalization simultaneously; only one of them is and it should be more frequent than the other, because grammaticalization is typical and degrammaticalization is highly restricted (Trousdale & Norde 2013: 34).This proposal, a frequency-based heuristic, is described in (55).
(55) Associate unidirectionality with cross-linguistic prevalence: The process that is cross-linguistically more prevalent is grammaticalization; the other could be degrammaticalization.
This proposal requires a balanced sample of languages, which is beyond the scope of this study.
Second, INCREASES IN GRAMMATICALITY may be assumed to define grammaticalization (i.e.something grammaticalizes if it becomes more grammatical).Specific frameworks may be used to define and compare degrees of grammaticality.As far as the dataset is concerned, this proposal is not unlike (55).Building either unidirectionality or increased grammaticality into the definition of grammaticalization leads to the same conclusion that both processes cannot be grammaticalization simultaneously.Compared with (55), this proposal, described in (56), is qualitative.
(56) Associate one category with more grammaticality: The process leading to an increase in grammaticality is grammaticalization.
In hierarchical models of clause structure, conditionals may be more grammatical than modals, as the former is at clause periphery (e.g.Narrog 2012).Therefore, MODAL > CONDITIONAL may be grammaticalization.CONDITIONAL > MODAL may be degrammaticalization, or something else, such as insubordination (Evans 2007;Kaltenböck 2016), whereby a subordinate clause and its marker (e.g.IF P) become a main clause (e.g.MODAL P).Lehmann's (1995) grammaticalization parameters and Norde's (2009) degrammaticalization counterparts produced inconclusive results (Kuo 2020), partially because the parameters are biased towards grammatical affixes, which neither Modal nor Conditional is in Chinese.Fischer (2008: 356) also remarks 'not all of Lehmann's parameters seem to be at work' in clausecombining.Third, clause-combining or other processes could be assumed not to be grammaticalization because they are qualitatively different, as in (57).
(57) Assume one of the processes is not grammaticalization.For example, Norde (2009: 26), following Fischer (2008), thinks that 'clause combining is too different from other types of grammaticalization to be subsumed under it'.MODAL > CONDITIONAL thus lies outside grammaticalization and CONDI-TIONAL > MODAL may or may not be (de)grammaticalization.
In ( 55)-( 57), or in any similar proposals aiming to differentiate between the processes, such processes are presupposed as NON-EQUIVALENT; (55)-( 56) also assume grammatical NON-EQUIVALENCE (or 'asymmetry';Börjas & Vincent 2011: 164) between the source and outcome.As far as changes enabled by morphosyntactic vagueness are considered, both processes and their sources and outcomes are mediated by EQUIVALENCE: the grammatical contrast between Modal and Conditional is not at stake due to shared properties in some contexts, where one analysis is as plausible as the other.An alternative proposal is to highlight their equivalence by disassociating grammaticalization from unidirectionality and increased grammaticality.This is not a radical idea.Even though they regard unidirectionality as an important aspect of grammaticalization elsewhere (2003: Ch. 5), Hopper & Traugott's (2003: xv) definition of grammaticalization does not include unidirectionality or increased grammaticality: 'the change whereby lexical items and constructions come in certain linguistic contexts to serve grammatical functions and, once grammaticalized, continue to develop new grammatical functions'.The second half of the definition applies to MODAL > CONDITIONAL and CONDITIONAL > MODAL.Company (2018), assuming a similar definition, also proposes that grammaticalization may be non-unidirectional and involve no change in grammatical status.Given a definition of grammaticalization free from unidirectionality and increased grammaticality, both MODAL > CONDITIONAL and CONDITIONAL > MODAL are grammaticalization because both modality-marking and clause-combining are grammatical functions; (58) then follows.
The histories of two grammatical categories in one language do not falsify but only slightly weaken the unidirectionality hypothesis.After all, it has been shown to be a tendency (Norde 2009).Therefore, bidirectionality between Modal and Conditional in Chinese (and potentially elsewhere) should only be considered as a regular exception to unidirectionality in grammaticalization, provided that both directions are enabled by morphosyntactic vagueness and grammaticalization is not defined in terms of non-equivalence.REGULAR is the operative word: bidirectional grammaticalization, although by definition an exception to unidirectionality, is not unconstrained or unprincipled.It is constrained: to change, it is necessary for an item to occur in specific contexts where morphosyntactic vagueness is at play.It is principled: morphosyntactic vagueness is tied to two specific conditions, distributional and functional similarities, neither of which is exceptional.The former is a distributional fact about Chinese and the latter is a cross-linguistic functional fact about modals and conditionals.This systematicity of vagueness-enabled bidirectionality aligns it with how grammaticalization is typically conceptualized: a regular process (Kuteva et al. 2019).
In sum, if grammatical equivalence rather than non-equivalence defines grammaticalization, morphosyntactic vagueness may enable grammaticalization to be bidirectional.

CONCLUSION
This paper has described the triclausal construction and observed that its MODAL slot constitutes a context of morphosyntactic vagueness where a modal or a conditional protasis connective can occur and its precise analysis (as a conditional or a modal) is underdetermined, which enables bidirectional changes.
Changes enabled by morphosyntactic vagueness are characterized by grammatical equivalence, as by definition morphosyntactic vagueness pertains to neutralized grammatical contrast that is not at stake.Proposing one direction of change to be non-equivalent or distinct from the other therefore undermines morphosyntactic vagueness.Consequently, both directions of change are proposed as regular processes of grammaticalization, if defined as the development of grammatical categories, but not in terms of non-equivalence (i.e.unidirectionality or increased grammaticality).In other words, bidirectionality is a possible feature of grammaticalization, when enabled by morphosyntactic vagueness between minor morphosyntactic categories.
Even though only Chinese Modal and Conditional have been examined, if two minor morphosyntactic categories are morphosyntactically vague, bidirectionality is by hypothesis possible.As isolating languages may be particularly rich in morphosyntactic vagueness (or 'soft boundaries'; Berg 2014: 521), due to lack of inflectional morphology, future research may concentrate on such languages to uncover more cases of morphosyntactic vagueness and bidirectionality and provide alternative accounts.
(7) (a) 須先看大學 Xū xiān kàn dàxué must first read Dàxué 'You must read Dàxué first.'(b) 非讀不可 Fēi dú bù kě unless read not possible 'Unless you read them, it is not good (i.e.you must read them).' (1270; Yǔlèi) 379 B I D I R E C T I O N A L G R A M M A T I C A L I Z A T I O N : C H I N E S E M O D A L A N D C O N D I T I O N A L I R E C T I O N A L G R A M M A T I C A L I Z A T I O N : C H I N E S E M O D A L A N D C O N D I T I O N A L 393 B I D I R E C T I O N A L G R A M M A T I C A L I Z A T I O N : C H I N E S E M O D A L A N D C O N D I T I O N A L ).
if you one.by.onego look understand PFV only.thencan 'Only if you have looked at it one by one and understood it is it possible.'(1270; Yǔlèi) ) 若要可行, 須是酌古之制, 去其重複, 使之簡易, 然後可 Connectives in THEN anaphorically refer to the condition or time established by Q.Apodosis connectives alone may signal temporal or conditional relations without protasis connectives, so Q THEN P 2 may mean '(only) after/if Q, P 2 '.
must early go only.thenobtain/possible'If you want to go, you must go early; only then is it possible (to go).' (1270;  Yǔlèi) 須用鉤鎌鎗可破 Yù pò zhèn shí xū yòng gōulián qiāng kě pò want break formation when must use Gōulián spear can break 'When you want to break up the enemy's tactical formation, you must use Gōulián spears; then one can break it up.' (fourteenth century; If you want to distinguish one from the other, one must go to the Buddha of Léiyīn Temple; only then can you do so.' (sixteenth century; Xīyóujì) 18) 要去所在, 須是去到, 方得 Yào qù suǒzài xūshì qù dào fāng dé want go where.it.is must go arrive only.thenobtain/possible'If you want to go where it is, one must get there; only then is it possible (to go there).' (1270; Yǔlèi) If you want to get it, it must be the case that your daily zhuāngjìng kungfu (the way one conducts oneself) has reached a certain level; only then can you get it.'(1270; Yǔlèi) 'If you want to capture this demon, you must go and ask Guānyīn Bodhisattva; only then is it possible.'(b) 'If… it must be the case that you go and ask…' (sixteenth century; Xīyóujì) Xū þ shì in MODAL Q, when not pre-subject, exhibits item-level vagueness.Using subscripts to indicate the types of filled slots, xū þ shì can be assigned a modal analysis, IF… xūshì MODAL Q, as in (21a); or a modalized copula one, IF… xū MODAL shì… Q , as in ( ) 學者須是學顏子 Xuézhě xūshì xué yánzǐ scholar must learn Yánzǐ 'A scholar must learn from Yánzǐ.' (1270; Yǔlèi)In null-subject contexts, the distinction between xū shì and xūshì is less clear, e.g.(2), (13), and (18); (21) illustrates the possible distinction in the triclausal construction when null-subject.Translation (21a) assumes xūshì.(21b) assumes xū shì, where xū fills in MODAL, shì qù qǐng… fills in Q '(it) is (the case that) you go…; lit.be go ask' and MODAL Q means 'it must be the case that you go…'.
) do not require a precise analysis of xū þ shì; they essentially mean 'Do Q, if you want P 1 /P 2 '.Readings of xū þ shì in MODAL Q are thus performatively equivalent and their morphosyntactic statuses are vague, if no subject follows. 9Furthermore, chúfēi, typically a conditional 'only if', also occurs in MODAL; (22) exemplifies a conditional construction [IF Q THEN P] 'only if Q, P' with chúfēi in the IF slot.The order of P and Q is reversed to highlight similarities to the corresponding triclausal slots (see Section 4.1 for more details).Only if you follow the Fǎhuā scripture can you avoid disasters.'(seventhtenth centuries; Dūnhuáng biànwén) Reproduced from (3), (23) illustrates the earliest instance of chúfēi in MODAL; (24)-(25) are later attestations.Translations (a) are modal readings of chúfēi analogically based on modals in the slot.Translations (b) are conditional readings modeled on chúfēi in the IF slot of [IF Q THEN P], where the sequence IF WANT P 1 MODAL Q THEN P 2 is interpreted as IF WANT P 1 chúfēi IF Q THEN P 2 'if you want P 1 only if Q then P 2 '. 'If you want to interpret what this sign means and do not understand Diéshī (a method of divination), you must use Dàliùrén (another method of divination); only then can you accurately interpret it.'(b) 'If… only if you… can you…' (1791; Hónglóumèng)

Table 3
Distribution of the triclausal construction in Yǔlèi.
[10] Unlike the triclausal construction, P x in (26) does not refer to the same goal as P z and contains an apodosis; (27) is not performative and WANTS is negated.
, 1.9% of chúfēi in Spoken Chinese and 0.5% in Written Chinese are [IF WANTS P chúfēi Q].But it is more frequent in Early Mandarin: in texts between the fourteenth and eighteenth centuries in the corpus (from Shuǐhǔzhuàn to Qílùdēng), 32.9% (26/79) of chúfēi appears in [IF WANTS note that (32) is a common saying and translate chúfēi into 'should'; (33) is another example.
'If you want to obtain worldly glory, you must do good this lifetime.'(b) 'If… it must be the case that you …' (seventh-tenth centuries; 'If you want to practice it, you must practice Jǐngtián (a feudal system).'(b) 'If… it must be the case that you…' (1270; Yǔlèi) ) considers the possible interpretations of xū þ shì: xū shì 'must be (the case that)', xūshì 'must' and xūshì 'only if'.(42) Yào qù suǒzài xūshì qù dào fāng dé want go where.it.is must(.be)/only.ifgo arrive only.thenobtain/possible (a) 'If you want to go where it is, it must be the case that you get to that place; only then is it possible (to go there).'(b) 'If… you must … is it possible.'(c) 'If… only if you… is it possible.'(1270; Yǔlèi) ); (45)-(46) are instances of xūshì in [IF Q THEN P] that parallel chúfēi in (43)-(44).Xūshì in (45)-(46) is pre-subject, suggesting a clear conditional status.Xūshì IF and chúfēi IF are not as pragmatically specialized as pre-Yǔlèi chúfēi IF , i.e. (34), as shown in (44)-(45).In (44), P is not the speaker's assumption of the addressee's goal; (45) does not direct the addressee.Yǔlèi that inferences of conditionality (or modality) are invited in local contexts, particularly the triclausal MODAL slot.Third, pragmatic motivations likely underlie the changes.Directives are interactional and sensitive to interpersonal dynamics and vary in strength and other nuances; therefore, their origins are inherently pragmatic.
(47)IF WANTS P xūshì MODAL Q (a) 'Q is teleologically necessary for P.' e.g.(41) (b) 'Do Q to achieve P if you want P.' (c) Pre- (Akatsuka & Clancy 1993) is not good (i.e.you must read them).' (1270; Yǔlèi) Japanese and Korean use conditionals to express modal meanings(Akatsuka & Clancy 1993), some types of which have turned into modals, especially in the spoken languages, exemplifying CONDITIONAL > MODAL.