1 Introduction

For decades, the Taiwanese Southern Min sentence like (1a), in contrast to its non-u counterpart (i.e., (1b)), has attracted many scholars’ attention by virtue of the following syntactic and semantic properties (Li 1950; Zhang 1983; Yang 1991; Lai 2007; Lien 2010) (For ease of exposition, I use the term TSM to represent ‘Taiwanese Southern Min’).1

    1. (1)
    1. a.
    1. Tsit-khuan
    2. this-CL
    1. sann
    2. clothing
    1. (*tsang)
    2.     yesterday
    1. tsin
    2. very
    1. u-tshing.
    2. have-wear
    1. ‘For anyone to wear it, this kind of clothing is very durable/lasts quite long.’
    1.  
    1. b.
    1. Yi
    2. s/he
    1. (tsang)
    2. yesterday
    1. (*tsin)
    2.     very
    1. tshing
    2. wear
    1. tsit-khuan
    2. this-CL
    1. sann.
    2. clothing
    1. ‘S/He wore this kind of clothing (yesterday).’

First, as Lien (2010: 1276) points out, “putting the morpheme u with the literal meaning have or its negative counterpart bo ‘not-have’ before a transitive activity verb” like tshing ‘wear’ in (1a) “brings about a change in the argument structure of the verb”. Namely, the external agent argument of the verb is syntactically deleted and the internal argument is syntactically externalized as subject bearing the role of theme.2

Second, “the u/bo-V predicate”, for example u-tshing ‘have-wear’ in (1a), “denotes a stative scalar predicate that can be modified by a degree adverb”; however, in (1b), the predicate tshing tsit-khuan sann ‘wear this-CL clothing’, being non-gradable, cannot be modified by a degree adverb (Lien 2010: 1278).

Third, “an implicit argument carrying the agent role is a necessary, but not sufficient, condition for a sentence” like (1a), but, in (1b), the agent role must overtly occur as subject (Lien 2010: 1279).

Fourth, “the implicit agent in sentences” like (1a) “is construed as ANY (i.e., an arbitrary or free choice item fed by pragmatic information)” (Lien 2010: 1278).

Fifth, a sentence like (1a), having stative but not punctual aspect, expresses a generic/characterizing rather than episodic/particular state, but (1b) can express an episodic event (Lien 2010: 1278).

Sixth, a sentence like (1a) conveys that the entity denoted by the subject NP (i.e., tsit-khuan sann ‘this-CL clothing’) has “the property of being washed many times over”, but (1b) does not (Lien 2010: 1277).

These properties lead Lien (2010: 1285) to analyze the TSM sentence like (1a), which denotes a pluractional event, as a type of middles and dub it the pluractional middle. According to his analysis, which consists of the following major points, (1a) has a syntactic structure like (2), in which the binding of the arguments is established through theta-identification.3 (The asterisk is used to indicate an argument that is closed.)

(2) [S [NP tsit-khuan sann]i … [VP<*1, *2> pro [V’<1, 2*> [Adv tsin] [Adv u<(1, 2, e), tui 1 lai-kong>] tshing<1, 2> ti]]]

First, the adverb of intensifier u ‘have’ with an internal structure like <(1, 2, e), tui 1 lai-kong>, as (2) shows, takes an event (i.e., e) as its argument, the experiencer 1 becomes an adjunct in conjunction with the circumfix tui … lai-kong ‘as far as … is concerned’, and, then, the experiencer 1 of the adverb u ‘have’ is theta-identified with the agent 1 of the verb tshing ‘wear’.

Second, the activity verb tshing ‘wear’ is changed by the converter u ‘have’ into a stative scalar predicate and loses the ability to assign the accusative case to the object NP.

Third, the strong feature of the obligatory adverb of intensifier u ‘have’ triggers the object-to-subject movement to fulfill the condition of EPP in the sentence (Lien 2010: 1283).

However, after closely scrutinizing, it is found that the syntactic and semantic properties shown by the TSM construction like (1a) are much more complex than what Lien (2010) and other previous studies have pointed out.

First, as Lien (2010) argues, in the pluractional middle, the transitive activity verb changed into a stative scalar predicate by the converter u ‘have’ loses the ability to assign the accusative case to the object NP. So, the internal argument is syntactically externalized as subject bearing the theme role. However, what occurs as subject in the pluractional middle, as Lien (2010: 1276) himself notices but does not provide any remark, actually can be an instrument or a location adjunct, as illustrated by (3b) and (4b), respectively (To note the valency change function and the degree introducing function associated with the morpheme u in expressions like u-tshing ‘have-wear’, in the following, I use ‘uVD’ to gloss it).

    1. (3)
    1. a.
    1. Yi
    2. he
    1. yonn
    2. use
    1. tsit-khuan
    2. this-CL
    1. pi
    2. pen
    1. sia
    2. write
    1. gi.
    2. word
    1. ‘He writes words by this kind of pens.’
    1.  
    1. b.
    1. Tsit-khuan
    2. this-CL
    1. pi
    2. pen
    1. kha
    2. more
    1. u-sia.
    2. uVD-write
    1. ‘This kind of pens is more durable for writing.’
    1. (4)
    1. a.
    1. Yi
    2. he
    1. ti
    2. at
    1. tshan-lin
    2. field-inside
    1. tsing
    2. plant
    1. tshai.
    2. vegetable
    1. ‘He plants vegetables in the field.’
    1.  
    1. b.
    1. Tsit-khu
    2. this-CL
    1. tshan
    2. field
    1. kha
    2. more
    1. u-tsing.
    2. uVD-plant
    1. ‘The planting capacity of this field (or the harvest from this field) is larger.’

If the transitive activity verb’s dysfunction in assigning the accusative case, as Lien (2010) argues, induces the externalization of the theme role of the verb in the pluractional middle, what occurs as subject in (3b) and (4b) should be the theme role rather than an adjunct of the verb. However, neither does (3b) have a theme subject, nor does (4b).

Second, in addition to the internal theme argument or the adjunct of an transitive verb, the external agent argument of a transitive verb can also occur as subject of a pluractional middle, as attested by (5), where the u-V expression u-lim ‘uVD-drink’ is modified by the agent-oriented adverb thiaukang ‘intentionally’.

    1. (5)
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. u-lim
    2. uVD-drink
    1. kapi.
    2. coffee
    1. ‘Recently, he intentionally drinks coffee more frequently.’

Third, as (5) further indicates, in the pluractional middle, the agent role of the transitive verb (i.e., yi ‘he’) can be overtly realized. Thus, the agent role is not necessary to occur as an implicit one construed as an arbitrary individual fed by pragmatic information.

Fourth, a pluractional middle actually can express an episodic event or a temporary state, as (6a–b) illustrate.

    1. (6)
    1. a.
    1. Yi
    2. he
    1. kinalit
    2. today
    1. tsai
    2. morning
    1. kha
    2. more
    1. u-lim
    2. uVD-drink
    1. kapi.
    2. coffee
    1. ‘This morning, he drank coffee more frequently.’
    1.  
    1. b.
    1. Tshaikue
    2. loofah
    1. tshang
    2. yesterday
    1. kai
    2. very
    1. u-siau.
    2. uVD-sell/consume
    1. ‘Yesterday, the loofah sold well/people consumed many loofahs.’

Given these, I will call the TSM sentence like (1a) the TSM u-V construction in the rest of this paper.

The purpose of this paper is to study the syntax and semantics of the TSM u-V construction. The main themes I am going to argue for are as follows. First, the TSM u-V construction, in which the V of the u-V compound verb can be a non-gradable lexical verb or an aspectual verb, is not a middle construction because (A) an aspectual verb does not bear any theta roles and (B) the u-V construction is not necessary to carry a generic reading. Second, the morpheme u ‘uVD’, which only induces a change in the valency of V in cases where the V is a lexical verb by introducing (a) generic operator(s) to bind the unsaturated argument(s), contributes a structure-preserving map from events, states or time containment relations to their measures along various dimensions (Wellwood 2015). Third, the morpheme u ‘uVD’ compositionally changes the denotation of V into a set of events (or time containment relations). This proposal has the following empirical and theoretical implications. First, the fact that the TSM morpheme u ‘uVD’ cannot introduce degrees for gradable adjectives implies that the degree-theoretic approach for comparatives is still needed (Wellwood 2015). Second, TSM also adopts the possessive morphosyntactic strategy for predicating gradable properties, but, unlike languages like English and German, the nominal involved is not necessary to be an abstract property concept nominal (Francez & Koontz-Garboden 2015; 2017; Li to appear).

The organization of this paper is as follows. In Section 2, I discuss the syntactic and semantic properties of the TSM u-V construction in depth, and, then, end this section by pointing out the empirical and theoretical questions raised by this construction; among these questions, the discussion in Section 4 and 5 will center around the following five.

  1. Is the TSM u-V construction a middle construction?

  2. Is the TSM u-V expression a compound adjective as what Yang (1991) and Lien (2010: 1276) suggest?

  3. Depending on whether the V of the u-V sequence involves a valency change, the TSM u-V constructions can be divided into the u-Vvc type, where the V involves a valency change, and the u-Vnvc type, where the V does not involve a valency change. Behind this empirical fact is the question of what makes the u-Vvc construction different from the u-Vnvc construction in that the former involves a valency change in the V while the latter does not.

  4. How and where does the TSM u-V construction get its degree meaning?

  5. The dimension of measurement shown by the TSM u-V construction might involve the property of the theme subject, the quantity of the event denoted by the V or an aspect of the event denoted by the V. So, what could be the exact measure function of the TSM u-V construction?

Section 3 includes the theoretical foundations of my proposal. In Section 4, a nutshell of my proposal is provided first; then, I demonstrate how my proposal accounts for the syntax and semantics of the TSM u-V construction. Then, I go back to the question of whether the TSM u-V construction is a middle construction in Section 5, where some remarks on Francez & Koontz-Garboden (2015; 2017) and Wellwood (2015) will be provided. Section 6 includes the concluding remarks.

2 The syntactic and semantic properties of the TSM u-V Construction

The TSM u-V constructions can be divided into two types in terms of whether the V of the u-V expression involves a valency change or not, as shown by (7a–b), respectively.

    1. (7)
    1. a.
    1. Tsit-khuan
    2. this-CL
    1. sann
    2. clothing
    1. kha
    2. more
    1. u-tshing.
    2. uVD-wear
    1. ‘For anyone to wear it, this kind of clothing is more durable for wearing/lasts longer.’
    1.  
    1. b.
    1. Yi
    2. s/he
    1. tsuekin
    2. recently
    1. kha
    2. more
    1. u-tshing
    2. uVD-wear
    1. tsit-khuan
    2. this-CL
    1. sann.
    2. clothing
    1. ‘Recently, s/he wears this kind of clothing more frequently.’

In (7a), the external agent argument of the verb tshing ‘wear’ is syntactically deleted and semantically construed as an arbitrary individual; however, in (7b), the argument structure of the verb tshing ‘wear’ is intactly retained by having the external agent argument yi ‘s/he’ occur as subject and the internal theme argument tsit-khuan sann ‘this-CL clothing’ occur as object. So, in the following, I use ‘the u-Vvc construction’ to represent a TSM construction like (7a), and ‘the u-Vnvc construction’ to represent a TSM construction like (7b).

Thus, in Section 2.1, I will discuss the syntactic and semantic properties of the u-Vvc construction and, then, the properties of the u-Vnvc construction will be discussed in Section 2.2. Then, I end this section by highlighting the questions raised by the TSM u-V construction.

2.1 The syntactic and semantic properties of the u-Vvc construction

The TSM u-Vvc construction has the following characteristics. First, the verb able to form an u-Vvc ‘uVD-Vvc’ expression with the morpheme u ‘uVD’ can be ditransitive, transitive or intransitive, as illustrated by (8a–b)–(10a–b), respectively (Marelj 2004; Fagan 2009; Xiong 2018).

    1. (8)
    1. a.
    1. Bikim
    2. dollar
    1. kha
    2. more
    1. u-tsio.
    2. uVD-lend
    1. ‘The amount of dollars lent by a lender to borrowers is larger.’
    1.  
    1. b.
    1. Tionn
    2. medium
    1. sio
    2. small
    1. khigiap
    2. enterprise
    1. kha
    2. more
    1. u-tsio.
    2. uVD-lend
    1. ‘The number of small and medium enterprises to which a lender lends money is larger.’
    1. (9)
    1. Tsit-khuan
    2. this-CL
    1. sann
    2. clothing
    1. kha
    2. more
    1. u-tshing.
    2. uVD-wear
    1. ‘This kind of clothing is more durable for wearing.’
    1. (10)
    1. a.
    1. Bitpo
    2. bat
    1. long
    2. all
    1. kangkhuan,
    2. the-same
    1. amsi-a
    2. night-PRT
    1. kha
    2. more
    1. u-tshuthen.
    2. uVD-show-up
    1. ‘All kinds of bats are the same in that the night is more susceptible to their showing up.’
    1.  
    1. b.
    1. Tsit-ting
    2. this-CL
    1. phonntshng
    2. spring-mattress
    1. kha
    2. more
    1. u-thiau.
    2. uVD-jump
    1. ‘This spring mattress is more durable for jumping on it.’

As (10a–b) further indicate, the intransitive verbs involved can be an unaccusative or unergative verb.

Second, as the grammaticality of (11a–b) shows, the V of the u-Vvc ‘uVD-Vvc’ expression can be a non-volitional or mental verb, but, as (12a–b) show, cannot be modified by a degree adverb (Marelj 2004; Fagan 2009; Xiong 2018).4

    1. (11)
    1. a.
    1. Tsit-khuan
    2. this-CL
    1. hosuann
    2. umbrella
    1. kha
    2. more
    1. u-phangken.
    2. uVD-lose
    1. ‘This kind of umbrella is more susceptible to getting lost.’
    1.  
    1. b.
    1. Tsit-khuan
    2. this-CL
    1. thiang
    2. pain
    1. kha
    2. more
    1. u-kamkak.
    2. uVD-feel
    1. ‘This kind of pain is more perceivable.’
    1. (12)
    1. a.
    1. Yi
    2. s/he
    1. (*kha)
    2.     more
    1. phangken
    2. lose
    1. tsit-ki
    2. one-CL
    1. hosuann.
    2. umbrella
    1.  
    1. b.
    1. Gua
    2. I
    1. (*tsiok)
    2.     very
    1. kamkak
    2. perceive
    1. kha
    2. leg
    1. le
    2. ASV
    1. thiang.
    2. painful

Third, depending on the inner aspects of verbs, verbs able to form an u-Vvc ‘uVD-Vvc’ expression with the morpheme u ‘uVD’ can be an activity, a stative, an achievement or a semelfactive verb, but cannot be an accomplishment verb, as the grammatical contrast between (13a–d) and (13e) illustrates (Smith 1997).5

    1. (13)
    1. a.
    1.   Tsit-khuan
    2.   this-CL
    1. sann
    2. clothing
    1. kha
    2. more
    1. u-tshing.
    2. uVD-wear
    1.    ‘This kind of clothing is more durable for wearing.’
    1.  
    1. b.
    1.   Yihak
    2.   medicine
    1. tsinpo,
    2. progress
    1. lang
    2. people
    1. e
    2. E
    1. singbiann
    2. life
    1. kha
    2. more
    1. u-potsiong.
    2. uVD-guarantee
    1.    ‘Given the progress of medicine, the life of people is more guaranteed.’
    1.  
    1. c.
    1.   Bitpo
    2.   bat
    1. long
    2. all
    1. kangkhuan,
    2. the-same
    1. amsi-a
    2. night-PRT
    1. kha
    2. more
    1. u-tshuthen.
    2. uVD-show-up
    1.    ‘All kinds of bats are the same in that the night is more susceptible to their showing up.’
    1.  
    1. d.
    1.   Tsit-ting
    2.   this-CL
    1. phonntshng
    2. spring-mattress
    1. kha
    2. more
    1. u-thiau.
    2. uVD-jump
    1.    ‘This spring mattress is more durable for jumping on it.’
    1.  
    1. e.
    1. *Tsit-khuan
    2.   this-CL
    1. uann
    2. bowl
    1. kha
    2. more
    1. u-konnphua.
    2. uVD-hit-break

Fourth, in the TSM u-Vvc construction, the argument syntactically suppressed as an implicit one and construed as an arbitrary item fed by pragmatic information can be the agent, theme or experiencer role of V, as the interpretation of (14a–d) illustrates (Lien 2010: 1278).

    1. (14)
    1. a.
    1. Tsit-khuan
    2. this-CL
    1. sann
    2. clothing
    1. kha
    2. more
    1. u-tshing.
    2. uVD-wear
    1. (agent)
    2.  
    1. ‘For anyone to wear it, this kind of clothing is more durable for wearing.’
    1.  
    1. b.
    1. Tsit-te
    2. this-CL
    1. satbun
    2. soap
    1. kha
    2. more
    1. u-se.
    2. uVD-wash
    1. (agent and theme)
    2.  
    1. ‘For anyone to wash anything by it, this piece of soap is more durable for washing.’
    1.  
    1. c.
    1. Oobinlapue,
    2. Platalea-minor
    1. tsit-khuan
    2. this-CL
    1. tsiau-a
    2. bird-PRT
    1. kha
    2. more
    1. bo-khuanntioh.
    2. not-uVD-see
    1. (experiencer)
    2.  
    1. ‘As is generally recognized, the Platalea minor, this kind of birds is rarer.’
    1.  
    1. d.
    1. Tshiu-a
    2. tree-PRT
    1. hioh
    2. leaf
    1. long
    2. all
    1. kangkhuan,
    2. the-same
    1. kuannthinn
    2. winter
    1. kha
    2. more
    1. u-lak.
    2. uVD-fall
    1. (theme)
    2.  
    1. ‘All kinds of leaves are the same in that the winter is more susceptible to having fallen leaves.’

Moreover, the subject of the TSM u-Vvc construction is not necessary to be the internal theme role of V. It can be an instrument or location adjunct of V or the goal role of a ditransitive V, as illustrated by (15a–c), respectively (Lai 2007; Lien 2010: 1276).6

    1. (15)
    1. a.
    1. Tsit-tai
    2. this-CL
    1. tsia
    2. car
    1. kha
    2. more
    1. u-tsai.
    2. uVD-load
    1.              (instrument)
    2.  
    1. ‘For anyone to pick up anything by it, the loading capacity of this car is larger.’
    1.  
    1. b.
    1. Tsit-king
    2. this-CL
    1. tshngkho
    2. storehouse
    1. kha
    2. more
    1. u-khng.
    2. uVD-store
    1.       (location)
    2.  
    1. ‘For anyone to store anything in it, the storing capacity of this storehouse is larger.’
    1.  
    1. c.
    1. Tionn
    2. medium
    1. sio
    2. small
    1. khigiap
    2. enterprise
    1. kha
    2. more
    1. u-tsio.
    2. uVD-lend
    1. (goal)
    2.  
    1. ‘The number of small and medium enterprises to which a lender lends money is larger.’

Fifth, based on the interpretation of (16a), Lien (2010: 1277) suggests that a TSM u-Vvc construction always conveys the property of pluractionality accrued to the entity denoted by the subject NP.

    1. (16)
    1. a.
    1.   Tsit-khuan
    2.   this-CL
    1. sann
    2. clothing
    1. kha
    2. more
    1. u-se.
    2. uVD-wash
    1.    ‘This kind of clothing is more durable for washing.’
    1.  
    1. b.
    1.   Tsit-liap
    2.   this-CL
    1. iu-a
    2. pomelo-PRT
    1. kha
    2. more
    1. u-khng.
    2. uVD-preserve
    1.    ‘This pomelo can be preserved longer.’
    1.  
    1. c.
    1. *Tsit-liap
    2.   this-CL
    1. iu-a,
    2. pomelo-PRT
    1. gua
    2. I
    1. khng
    2. preserve
    1. sann
    2. three
    1. pai.
    2. time

And, “pluractionality is taken here in the sense that the property (e.g., of durability) that accrues to something (e.g., clothing) is based on the observed result of a set of repeated actions (e.g., washing)” (Lien 2010: 1277).

However, Lien’s (2010) observation is not without exceptions. For example, as the ungrammaticality of (16c) shows, an u-Vvc construction like (16b) can only convey the property of ‘monoactionality’ accrued to the entity denoted by the subject NP. And, from the property of monoactionality, the implicature that this pomelo can be preserved longer is implicated.

Sixth, the whole predicate of the TSM u-Vvc construction, as Lien (2010) suggests, looks like a dispositional construed as attributing a stative scalar property to the derived subject in question, and the dimension of measurement is the property of the theme subject (e.g., the amount of money), as the interpretation of (17a) shows.

    1. (17)
    1. a.
    1. Bikim
    2. dollar
    1. siunn
    2. too
    1. u-tsio.
    2. uVD-lend
    1. ‘The amount of dollars lent by a lender to borrowers is too large.’
    1.  
    1. b.
    1. Tsit-liap
    2. this-CL
    1. iu-a
    2. pomelo-PRT
    1. tsin
    2. very
    1. u-khng.
    2. uVD-preserve
    1. ‘This pomelo can be preserved very long.’

However, as the interpretation of (17b) shows, the dimension of measurement can also be the quantity (i.e., the temporal duration) of the event denoted by the V. So, the dimension of measurement can be the property of the subject NP or the quantity of the event denoted by the V.

Seventh, a TSM u-Vvc expression might allow one or more than one dimension of measurement to measure the relevant degrees, which makes the sentence ambiguous, as the interpretations of (18) illustrate.

    1. (18)
    1. Tsit-tiunn
    2. this-CL
    1. yi-a
    2. chair-PRT
    1. kha
    2. more
    1. u-tse.
    2. uVD-sit
    1. a. ‘This chair is more durable than that chair for sitting.’
    2. b. ‘The seating capacity of this chair is larger than the seating capacity of that chair.’

As reading (18a) shows, the dimension of measurement is ‘the durableness for sitting’; however, as reading (18b) shows, the dimension of measurement is ‘the seating capacity’.

Eighth, the TSM u-Vvc construction can describe a temporary state or an episodic event, as the interpretation of (19a–b) shows.

    1. (19)
    1. a.
    1. Tshaikue
    2. loofah
    1. tsang
    2. yesterday
    1. kai
    2. very
    1. u-siau.
    2. uVD-sell/consume
    1. ‘Yesterday, the loofah sold well/people consumed many loofahs.’
    1.  
    1. b.
    1. Li
    2. you
    1. kinalit
    2. today
    1. tsai
    2. morning
    1. kha
    2. more
    1. u-lim
    2. uVD-drink
    1. kapi.
    2. coffee
    1. ‘This morning, you drink coffee more frequently.’

Ninth, as Lien (2010: 1285) points out, the u-Vvc construction “involves subjectivity, or subjective judgment or evaluation based on personal experience or direct evidence on the part of a sentient being”.

Tenth, Yang (1991: 234, 236) as well as Lien (2010: 1276) analyzes the TSM u-Vvc expression as a compound adjective because, whenever occurring as predicate, it syntactically behaves the same as the TSM adjective.

    1. (20)
    1. a.
    1. Tsit-le
    2. this-CL
    1. gin-a
    2. child-PRT
    1. kha
    2. more
    1. laosit.
    2. honest
    1. ‘This child is more honest.’
    1.  
    1. b.
    1. Tsit-le
    2. this-CL
    1. gin-a
    2. child-PRT
    1. laosit
    2. honest
    1. o!
    2. SFP
    1. ‘This child is honest!’
    1. (21)
    1. a.
    1. Tsit-khuan
    2. this-CL
    1. sann
    2. clothing
    1. kha
    2. more
    1. u-tshing.
    2. uVD-wear
    1. ‘This kind of clothing is more durable.’
    1.  
    1. b.
    1. Tsit-khuan
    2. this-CL
    1. sann
    2. clothing
    1. u-tshing
    2. uVD-wear
    1. o!
    2. SFP
    1. ‘This kind of clothing is durable!’

However, the TSM u-Vvc expression differs from the TSM adjective in that the former cannot undergo adjectival reduplication but the latter can.

    1. (22)
    1. a.
    1.   Tsit-le
    2.   this-CL
    1. gin-a
    2. child-PRT
    1. laolaositsit.
    2. honest-honest
    1.    ‘This child is honest.’
    1.  
    1. b.
    1.   Tsit-le
    2.   this-CL
    1. gin-a
    2. child-PRT
    1. gongtitgongtit.
    2. honest-straightfoward-honest-straightfoward
    1.    ‘This child is honest and straightfoward.’
    1.  
    1. c.
    1. *Tsit-khuan
    2.   this-CL
    1. sann
    2. clothing
    1. u-u-tshing-tshing.
    2. uVD-uVD-wear-wear
    1.  
    1. d.
    1. *Tsit-khuan
    2.   this-CL
    1. sann
    2. clothing
    1. u-tshing-u-tshing.
    2. uVD-wear-uVD-wear

2.2 The syntactic and semantic properties of the u-Vnvc construction

The TSM u-V construction not involving a change in the valency of V (i.e., the u-Vnvc construction) has the following characteristics. First, the V of the u-Vnvc ‘uVD-Vnvc’ expression can be ditransitive, transitive or intransitive, as illustrated by (23)–(25a–b), respectively (Marelj 2004; Fagan 2009; Xiong 2018).

    1. (23)
    1. Taiuan
    2. Taiwan
    1. ginhann
    2. bank
    1. kha
    2. more
    1. u-tsio
    2. uVD-lend
    1. bikim
    2. dollar
    1. hoo
    2. to
    1. tionn
    2. medium
    1. sio
    2. small
    1. khigiap.
    2. enterprise
    1. ‘Bank of Taiwan lends dollars to small and medium enterprises more frequently.’
    1. (24)
    1. Yi
    2. he
    1. tsit
    2. this
    1. kui
    2. several
    1. kang
    2. day
    1. sinthe
    2. body
    1. kha
    2. more
    1. hoo,
    2. good
    1. kha
    2. more
    1. u-tsia
    2. uVD-eat
    1. binnkiann.
    2. thing
    1. ‘During these days, he feels better and eats things more frequently.’
    1. (25)
    1. a.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. u-tshuthen.
    2. uVD-show-up
    1. (unaccusative)
    2.  
    1. ‘Recently, he intentionally shows up more frequently.’
    1.  
    1. b.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. u-tsau.
    2. uVD-run
    1.               (unergative)
    2.  
    1. ‘Recently, he intentionally runs more frequently.’

And, the intransitive verbs, as (25a–b) show, can be an unaccusative or unergative verb.

Second, as the grammaticality of (26a–b) shows, the V of the u-Vnvc ‘uVD-Vnvc’ expression can be a non-volitional or mental verb, but, as (27a–b) show, cannot be modified by a degree adverb (Marelj 2004; Fagan 2009; Xiong 2018).

    1. (26)
    1. a.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. kha
    2. more
    1. u-phangken
    2. uVD-lose
    1. hosuann.
    2. umbrella
    1. ‘Recently, he lost umbrellas more frequently.’
    1.  
    1. b.
    1. Gua
    2. I
    1. tsuekin
    2. recently
    1. kha
    2. more
    1. u-kamkak
    2. uVD-feel
    1. kha
    2. leg
    1. le
    2. ASV
    1. thiang.
    2. painful
    1. ‘Recently, I feel my legs painful more frequently.’
    1. (27)
    1. a.
    1. Yi
    2. s/he
    1. (*kha)
    2.     more
    1. phangken
    2. lose
    1. tsit-ki
    2. one-CL
    1. hosuann.
    2. umbrella
    1.  
    1. b.
    1. Gua
    2. I
    1. (*kha)
    2.     more
    1. kamkak
    2. perceive
    1. kha
    2. leg
    1. le
    2. ASV
    1. thiang.
    2. painful

Third, depending on the types of the inner aspects, the V of the u-Vnvc ‘uVD-Vnvc’ expression can be an activity, a stative, an achievement, an accomplishment or a semelfactive verb, as shown by (28a–e), respectively.

    1. (28)
    1. a.
    1. Yi
    2. he
    1. kha
    2. more
    1. u-tshing
    2. uVD-wear
    1. tsit-khuan
    2. this-CL
    1. sann.
    2. clothing
    1. ‘He wears this kind of clothing more frequently than someone.’
    1.  
    1. b.
    1. Gua
    2. I
    1. tsuekin
    2. recently
    1. kha
    2. more
    1. u-kamkak
    2. uVD-feel
    1. kha
    2. leg
    1. le
    2. ASV
    1. thiang.
    2. painful
    1. ‘Recently, I feel my legs painful more frequently.’
    1.  
    1. c.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. bo-tshuthen.
    2. not-uVD-show-up
    1. ‘Recently, he intentionally shows up less frequently.’
    1.  
    1. d.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. kha
    2. more
    1. u-konnphua
    2. uVD-hit-break
    1. uann.
    2. bowl
    1. ‘Recently, he breaks bowls more frequently.’
    1.  
    1. e.
    1. Pennlang
    2. patient
    1. kinalit
    2. today
    1. kha
    2. more
    1. bo-sau.
    2. not-uVD-cough
    1. ‘Today, the patient coughs less frequently.’

Fourth, the subject of the u-Vnvc construction can be the agent argument of V and the V can be a ditransitive verb, a transitive verb or an intransitive verb (e.g., an unergative or an unaccusative verb), as attested by (29a–d).

    1. (29)
    1. a.
    1. Taiuan
    2. Taiwan
    1. ginhann
    2. bank
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. u-tsio
    2. uVD-lend
    1. tsing
    2. money
    1. hoo
    2. to
    1. tionn
    2. medium
    1. sio
    2. small
    1. khigiap.
    2. enterprise
    1. ‘Recently, Bank of Taiwan intentionally lends money to small and medium enterprises more frequently.’
    1.  
    1. b.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. u-lim
    2. uVD-drink
    1. kapi.
    2. coffee
    1. ‘Recently, he intentionally drinks coffee more frequently.’
    1.  
    1. c.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. u-khau.
    2. uVD-cry
    1. ‘Recently, he intentionally cries more frequently.’
    1.  
    1. d.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. bo-tshuthen.
    2. not-uVD-show-up
    1. ‘Recently, he intentionally shows up less frequently.’

Fifth, the whole predicate of the TSM u-Vnvc construction might look like a dispositional construed as a stative scalar property about how frequently the event or state denoted by the predicate occurs.

    1. (30)
    1. a.
    1. Yi
    2. He
    1. tsuekin
    2. recently
    1. nae
    2. why
    1. tsia
    2. so
    1. u-tshing
    2. uVD-wear
    1. tsit-khuan
    2. this-CL
    1. sann?
    2. clothing
    1. ‘Why does he recently wear this kind of clothing so frequently?’
    1.  
    1. b.
    1. Li
    2. you
    1. tsuekin
    2. recently
    1. nae
    2. why
    1. tsia
    2. so
    1. u-kamkak
    2. uVD-perceive
    1. kha
    2. leg
    1. le
    2. ASV
    1. thiang?
    2. painful
    1. ‘Why do you recently feel legs painful so frequently?’
    1.  
    1. c.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. nae
    2. why
    1. tsia
    2. so
    1. u-phangken
    2. uVD-lose
    1. binnkiann?
    2. thing
    1. ‘Why does he recently lose things so frequently?’
    1.  
    1. d.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. nae
    2. why
    1. tsia
    2. so
    1. u-konnphua
    2. uVD-hit-break
    1. uann?
    2. bowl
    1. ‘Why does he recently break bowls so frequently?’
    1.  
    1. e.
    1. Pennlang
    2. patient
    1. kinalit
    2. today
    1. nae
    2. why
    1. tsia
    2. so
    1. u-sau?
    2. uVD-cough
    1. ‘Why does the patient cough so frequently today?’

Sixth, the TSM u-Vnvc construction can describe temporary states or episodic events.

    1. (31)
    1. a.
    1. Gua
    2. I
    1. kinalit
    2. today
    1. tsai
    2. morning
    1. kha
    2. more
    1. u-kamkak
    2. uVD-feel
    1. kha
    2. leg
    1. le
    2. ASV
    1. thiang.
    2. painful
    1. ‘This morning, I felt my legs painful more frequently.’
    1.  
    1. b.
    1. Li
    2. you
    1. kinalit
    2. today
    1. tsai
    2. morning
    1. kha
    2. more
    1. u-lim
    2. uVD-drink
    1. kapi.
    2. coffee
    1. ‘This morning, you drank coffee more frequently.’

Seventh, the TSM u-Vnvc ‘uVD-Vnvc’ expression differs from the TSM adjective in that the former can take an NP object while the latter cannot.

    1. (32)
    1. a.
    1.   Yi
    2.   he
    1. tsuekin
    2. recently
    1. kha
    2. more
    1. u-lim
    2. uVD-drink
    1. kapi.
    2. coffee
    1.    ‘Recently, he drinks coffee more frequently.’
    1.  
    1. b.
    1. *Lausu
    2.   teacher
    1. tsin
    2. very
    1. giam
    2. severe
    1. haksing.
    2. student

Thus far, the syntactic and semantic properties shown by the two types of the TSM u-V construction bring us the following empirical and theoretical questions that any study on the TSM u-V construction has to address.

First, is the TSM u-V construction a middle construction? If it is, then the following sequential questions related to the first question need to be well addressed.

  1. Why does the TSM u-Vnvc construction not involve a valency change in the V?

  2. How can the TSM u-V construction get an episodic event or a temporary state reading?

  3. How can the V of the u-Vvc expression be an intransitive verb, either unaccusative or unergative?

  4. How can the V of the u-Vvc expression be a stative or mental verb?

  5. How can the goal role of a ditransitive verb like tsio ‘lend’ occur as the subject of the u-Vvc construction?

Second, is the TSM u-V expression a compound adjective?

Third, what causes the u-Vvc construction different from the u-Vnvc construction in that the former involves a valency change in the V while the latter does not? Namely, what makes the external argument of V able to occur as subject in the u-Vnvc construction but unable to occur as subject in the u-Vvc construction?

Fourth, how and where does the TSM u-V construction get its degree meaning?

Fifth, why can the V of the u-Vnvc expression be an activity, a stative, an achievement, an accomplishment, or a semelfactive verb? And, why is the V of the u-Vvc expression unable to be an accomplishment verb?

Sixth, what could be the exact measure function of the TSM u-V construction?

For ease of exposition, before going into the details of my proposal for the syntax and semantics of the TSM u-V construction, I will briefly introduce as the theoretical foundation Wellwood’s (2015) unified account for comparative constructions.

3 The theoretical foundation

Among the properties shown by the TSM u-V construction, the following two provide us a good starting point to investigate the semantic nature of the morpheme u ‘uVD’.

First, the presence of the morpheme u ‘uVD’ distinguishes a TSM u-V construction (e.g., (33a)) from its non-u ‘non-uVD’ counterpart (i.e., (33b)) in that the former expresses a degree reading while the latter does not.

    1. (33)
    1. a.
    1. Tsit-nia
    2. this-CL
    1. sann
    2. clothing
    1. kha
    2. more
    1. u-se.
    2. uVD-wash
    1. ‘This article of clothing is more durable for washing.’
    1.  
    1. b.
    1. Yi
    2. he
    1. (*kha)
    2.     more
    1. se
    2. wash
    1. tsit-nia
    2. this-CL
    1. sann.
    2. clothing
    1. ‘He (*more) washes this article of clothing.’

Second, neither can the morpheme u ‘uVD’ independently determine the dimension of measurement, nor can the V of the u-V expression do so by itself. It is the interaction between the lexical meaning of V and the relevant contextual factor that determines the dimension of measurement. For example, in (34a), the interaction between the lexical meaning of the verb tse ‘sit’ and the relevant contextual factor leads the speaker to select ‘the durableness for sitting’ as the dimension of measurement.

    1. (34)
    1. Tsit-tiunn
    2. this-CL
    1. yi-a
    2. chair-PRT
    1. pi
    2. than
    1. hit-tiunn
    2. that-CL
    1. yi-a
    2. chair-PRT
    1. kha
    2. more
    1. u-tse.
    2. uVD-sit
    1. a. ‘This chair is more durable than that chair for sitting.’
    2. b. ‘The seating capacity of this chair is larger than the seating capacity of that chair.’

In contrast, in (34b), the collaboration of the same verb tse ‘sit’ with a different contextual factor leads the speaker to select ‘the seating capacity’ as the dimension of measurement. So, the morpheme u ‘uVD’ should not lexically specify the dimension of measurement (See Section 5.2 for how the pragmatic effect is constrained).

These two semantic features of the TSM u-V construction, especially the degree introducing function of the morpheme u ‘uVD’, remind us of the following three semantic properties of the English much pointed out by Cresswell (1977) and von Stechow (1984).

First, the presence of the semantically vacuous much distinguishes (35a) from (35b) in that the former expresses an entity reading while the latter expresses a degree reading.

(35) a. John buys this coffee.
  b. John buys this much coffee.

Second, the English much may occur in a variety of contexts, at least including an adjectival, nominal and verbal domain.

(36) a. much alike/different
  b. Much water is left in the bucket.
  c. I much prefer wine to beer.

Third, the dimension of measurement of the English much is not lexically specified.

In addition to these, Cresswell (1977) further suggests it is the interaction between the predicate and the context that determines the measure function introduced by the English much in a given case. And, the dimensions allowed, as Schwarzschild (2002; 2006) argue, have to respect strict part-whole relations, as (37a–c) illustrate (Wellwood et al. 2012; Wellwood 2015; Solt 2015; Dunbar & Wellwood 2016: 16).

(37) a. Al drank as much coffee as Bill did. volume/*temperature
  b. Al ran as much as Bill did. time/distance/*speed
  c. We look so much alike. alikeness/*volume

In (37a), larger portions of coffee have greater measures by volume than smaller portions; however, this is not generally the case with measures by temperature. In (37b), larger ‘quantity’ of running event has greater measures by time or distance than smaller ‘quantity’ of running event; however, the same does not obtain in cases with measures by speed. In (37c), larger ‘quantity’ of alikeness state has greater measures by alikeness than smaller ‘quantity’ of alikeness state; however, this is not generally the case with measures by volume.

Further developing these ideas, Wellwood (2015: 68–69) proposes a unified account for comparative constructions, either adjectival, nominal or verbal, by claiming that “degrees are (i) introduced compositionally, (ii) introduced by much, which semantically contributes a structure-preserving map from entities, events or states to their measures along various dimensions, and (iii) introduced not by any other expression”.

In contrast with the degree-theoretic approaches which assume gradable adjectives lexically specify measure functions while nouns and verbs do not, Wellwood (2015: 69) suggests that “which dimensions are possible across domains is a consequence of what is measured, rather than which expressions measure”. So, the interpretations for coffee in (37a), run in (37b), and alike in (37c) can be represented as in (38a–c), where x, y range over elements of the domain of individuals De, and e, e’, …, s, s’, … range over elements of the eventive and stative subsets of the domain of eventualities Dv.

(38) a. ⟦coffee⟧A = λx.coffee(x)
  b. ⟦run⟧A = λe.run(e)
  c. ⟦alike⟧A = λs.alike(s)

Namely, a noun like coffee introduces individuals, a verb like run introduces events, and an adjective like alike introduces states for being measured.

Hence, the English much, as Wellwood (2015: 69) suggests, has a semantic interpretation as in (39), relative to any assignment of values to variables, A.

(39) muchμA = A(μ)

Here, the type of measure function over which the variable m ranges can be <e, d> or <v, d>, and d is the type of degrees. Assuming this, (38a–c) correspondingly have (40a–c) as their potential value for the variable m (Wellwood 2015: 69).

(40) a. A(μ) = VOLUME
  b. A’(μ) = TEMPORAL DURATION/DISTANCE
  c. A’’(μ) = ALIKENESS

Wellwood (2015: 74) further sets the following restriction on A(μ) to exclude a telic verb phrase from being a possible domain to which the measure function A(μ) applies in any given context or on any assignment A: the domain to which A(μ) applies must be non-trivially structured ones. Namely, for any two entities properly ordered in a part-of relation, their measurements are similarly ordered in Schwarzschild’s (2002; 2006) sense.

Accordingly, as (41b) shows, (41a) is true just in case Al is the agent of a running event, the A(μ)-measure of which is greater than that of a running event by Bill. If A(μ) is ‘temporal duration’ or ‘distance’, the result will be interpretable. If it is ‘speed’, it will not be (Wellwood 2015: 78).

(41) a. Al ran more than Bill did.
  b. ⟦Al ran more than Bill did⟧A = T iff
    e[Agent(e)(a) & run(e) & A(μ)(e) > max(λd.∃e’[Agent(e’)(b) & run(e’) & A(μ)(e’) ≥ d])]

4 The proposal

Taking Wellwood (2015) as the theoretical foundation, in this section, a nutshell of my proposal will be provided first; then, I demonstrate how my analysis accounts for the syntax and semantics of the TSM u-V construction, the u-Vvc and the u-Vnvc type.

4.1 A nutshell of the analysis

Following Li (1950: 158), Yang (1991: 236), Lai (2007) and Lien (2010), I assume that the TSM u-V expression is a compound word; however, instead of treating it as a compound adjective, I analyze the TSM u-V expression as an intransitive compound verb denoting a stative scalar property because of the following reasons. First, the TSM u-V expression cannot undergo adjectival reduplication, but the TSM adjective can, as shown by the contrast below.

    1. (42)
    1. a.
    1. *Tsit-khuan
    2.   this-CL
    1. sann
    2. clothing
    1. u-u-tshing-tshing.
    2. uVD-uVD-wear-wear
    1.  
    1. b.
    1. *Tsit-khuan
    2.   this-CL
    1. sann
    2. clothing
    1. u-tshing-u-tshing.
    2. uVD-wear-uVD-wear
    1. (43)
    1. a.
    1. Tsit-le
    2. this-CL
    1. gin-a
    2. child-PRT
    1. laolaositsit.
    2. honest-honest
    1. ‘This child is honest.’
    1.  
    1. b.
    1. Tsit-le
    2. this-CL
    1. gin-a
    2. child-PRT
    1. gongtitgongtit.
    2. honest-straightfoward-honest-straightfoward
    1. ‘This child is honest and straightfoward.’

Second, a TSM adjective cannot take a theme object NP unless it is introduced by a PP adjunct occurring before the adjective, as the grammatical contrast between (44a–b) and (44c–d) shows.

    1. (44)
    1. a.
    1. *Tsit-le
    2.   this-CL
    1. lausu
    2. teacher
    1. tsiok
    2. very
    1. [AP[[A
    2.  
    1. giam]
    2. severe
    1. [NP
    2.  
    1. haksing]]].
    2. student
    1.  
    1. b.
    1. *Yi
    2.   s/he
    1. tsiok
    2. very
    1. [AP [[A
    2.  
    1. sennso]
    2. unfamiliar
    1. [NP
    2.  
    1. inngi]]].
    2. English
    1.  
    1. c.
    1.   Tsit-le
    2.   this-CL
    1. lausu
    2. teacher
    1. [[PP [[P
    2.  
    1. tui]
    2. to
    1. [NP
    2.  
    1. haksing]]]
    2. student
    1. [DegP
    2.  
    1. tsiok
    2. very
    1. giam]].
    2. severe
    1.    ‘This teacher is very severe to students.’
    1.  
    1. d.
    1.   Yi
    2.   s/he
    1. [[PP
    2.  
    1. [[P
    2.  
    1. tui]
    2. with
    1. [NP
    2.  
    1. inngi]]]
    2. English
    1. [DegP
    2.  
    1. tsiok
    2. very
    1. sennso]].
    2. unfamiliar
    1.    ‘S/He is very unfamiliar with English.’

However, a TSM u-Vnvc ‘uVD-Vnvc’ expression can take an NP or a VP complement, as shown by (45a–b), respectively (henceforth, I use the term u-V compound verb to represent the u-V expression).78

    1. (45)
    1. a.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. kha
    2. more
    1. [VP [V
    2.  
    1. u-lim]
    2. uVD-drink
    1. [NP
    2.  
    1. kapi]].
    2. coffee
    1. ‘Recently, he drinks coffee more frequently.’
    1.  
    1. b.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. kha
    2. more
    1. [VP [V
    2.  
    1. u-le]
    2. uVD-ASV
    1. [VP
    2.  
    1. lim
    2. drink
    1. kapi]].
    2. coffee
    1. ‘Recently, he drinks coffee more frequently.’

After assuming that the TSM u-V expression is an intransitive compound verb denoting a stative scalar property, I will define the morphosyntactic function of the morpheme u ‘uVD’ in 4.1.1 and the degree introducing function of the morpheme u ‘uVD’ in 4.1.2. (For ease of exposition, I will use the term ums when discussing the morphosyntactic function of u ‘uVD’, and us when discussing the degree introducing function of u ‘uVD’.)

4.1.1 The morphosyntactic function of Ums

In the TSM u-V construction, the morpheme u ‘uVD’ and a verb (i.e., the V of u-V) form an intransitive compound verb denoting a stative scalar property at the level of lexicon. The V of the u-V compound can be a non-gradable lexical verb bearing theta roles or an aspectual verb which encodes aspectual information about events but never bears theta roles.

On one hand, if the V is a lexical verb bearing theta roles, the morpheme u ‘uVD’ has the following morphosyntactic functions:

First, in order to stativize the V, the morpheme ums changes the valency of V by introducing a generic operator (or generic operators) to bind the unsaturated external argument (or the unsaturated external and the unsaturated internal argument) of V in Chierchia’s (1989) sense of argument saturation (Reinhart 1996).9

(46) y P<x, y>) (a) → (λy OPx P<x, y>) (a) (Argument Saturation)

Second, if the unsaturated external argument and internal argument(s) of V are all bound by a generic operator, the morpheme ums will lead a non-thematic argument (in the semantic term ‘a property of an event’ or in the syntactic term ‘an adjunct of the verb’) into the structure which, then, syntactically occurs as the subject of the sentence.

Third, according to the ambiguity approach proposed by Wilkinson (1991) and Gerstner-Link & Krifka (1993) for the interpretations of English bare plurals, the denotational ambiguity of a verb between a disposition (or a habit) (e.g., bark in (47a)) and an episodic event (e.g., bark in (48a)) results from how the eventuality argument s contained in the valency of the verb is quantified (Dayal 2011: 1091).

(47) a. Dogs bark.
  b. GEN s, x [dogs(s, x)] [bark(s, x)]
(48) a. Dogs are barking.
  b. s, x [dogs(s, x) ∧ are-barking(s, x)]

As (47b) shows, when the eventuality argument s is bound by a generic operator (i.e., GEN), the verb denotes a disposition (or a habit); however, as (48b) shows, when the eventuality argument s is bound by an existential operator, the verb denotes an episodic event. As Lien (2010: 1277) points out, the TSM u-Vvc construction always expresses the disposition of the subject based on the pluractionality of events. So, assuming that the valency of a verb contains an eventuality argument v, I suggest that the morpheme ums changes the denotation of the V of the u-V compound verb by having all the arguments and adjuncts bound by the generic operator, except one which is not the external argument or internal argument of an unaccusative verb, and, after this unbound variable takes the subject as its argument, it will return to a set of events (i.e., <v, t> with the symbol v as the type of event).10 And, the number of element events of the set of events, depending on the lexical meaning of V and the relevant contextual factor, might be one or more than one.

Depending on the types of lexical verbs that can occur as the V of the TSM u-Vvc compound verb, the interpretation of the morpheme ums can be represented as follows.11

(49) Ditransitive verbs (e.g., tsio ‘lend’)
  a. P<v, <e, <e, <e, t>>>>A = λxλyλzλv.P(z, y, x, v)
  b. umsA = (i) λPλxλvOPyOPz.P(v)(x)(y)(z)
      (ii) λPλyλvOPxOPz.P(v)(x)(y)(z)
      (iii) λPλwλv[OPxOPyOPz.P(v)(x)(y)(z) ∧ Property(v, w)]11
    P is a ditransitive verb, OP is a generic operator, z is the external argument, y and x are the internal arguments, w is a non-thematic argument, and v is the eventuality argument of P.
(50) Transitive verbs (e.g., se ‘wash’)
  a. P<v, <e, <e, t>>>A = λxλyλv.P(y, x, v)
  b. umsA = (i) λPλxλvOPy.P(v)(x)(y)
      (ii) λPλwλv[OPxOPy.P(v)(x)(y) ∧ Property(v, w)]
    P is a transitive verb, OP is a generic operator, y is the external argument, x is the internal arguments, w is a non-thematic argument, and v is the eventuality argument of P.
(51) Unergative verbs (e.g., thiau ‘jump’)
  a. P<v, <e, t>>A = λyλv.P(y, v)
  b. umsA = λPλwλv[OPy.P(v)(y) ∧ Property(v, w)]
    P is an intransitive verb, OP is a generic operator, y is the external argument, w is a non-thematic argument, and v is the eventuality argument of P.
(52) Unaccusative verbs (e.g., tshuthen ‘appear’)
  a. P<v, <e, t>>A = λxλv.P(x, v)
  b. umsA = λPλwλv[OPx.P(v)(x) ∧ Property(v, w)]
    P is an intransitive verb, OP is a generic operator, x is the internal argument, w is a non-thematic argument, and v is the eventuality argument of P.

On the other hand, in TSM, there are two preverbal aspectual verbs (i.e., u ‘the realization aspect’ and le ‘the progression aspect’), as shown by (53a–b), respectively (Chappell 1989; Yang 1991: 235–236).12

    1. (53)
    1. a.
    1. Yi
    2. he
    1. u
    2. ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘He drank coffee.’
    1.  
    1. b.
    1. Yi
    2. he
    1. le
    2. ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘He is drinking coffee.’

An aspectual verb simply functions to encode aspectual information about events but never bears theta roles, as attested by the data below (Fukuta 2012).

    1. (54)
    1. a.
    1. Yi
    2. he
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘He drinks coffee.’
    1.  
    1. b.
    1. Yi
    2. he
    1. u
    2. ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘He has drunk coffee.’

In (54a), the lexical verb lim ‘drink’ assigns one of its theta roles (i.e., the agent role) to the subject NP yi ‘he’ and the other (i.e., the theme role) to the object NP kapi ‘coffee’. In addition to the lexical verb lim ‘drink’, (54b) also contains the aspectual verb u ‘the realization aspect’. The grammaticality of (54b) implies that all theta roles of the predicate are assigned and all the NPs inside receive one and only one theta role. Since (54b) has as many NPs as (54a) has, it can be said that the aspectual verb u ‘the realization aspect’ does not assign any theta role of its own. The aspectual verb u ‘the realization aspect’, therefore, does not bear any theta roles. The same also happens to the aspectual verb le ‘the progressive aspect’ in (55b).

    1. (55)
    1. a.
    1. Yi
    2. he
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘He drinks coffee.’
    1.  
    1. b.
    1. Yi
    2. he
    1. le
    2. ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘He is drinking coffee.’

Adopting Lin’s (2003: 271) definition of the realization aspect and the progressive aspect, I suggest that the aspectual verb u ‘the realization aspect’ and le ‘the progressive aspect’ have (56a–b) as their corresponding semantic representation (Bohnemeyer & Swift 2001). (In (56a–b), τ(e’), in which t is the temporal trace function, can be equivalent to the event time and t is the topic time.)13

(56) a. uASV⟧ = λP<v, t>λtλee’[P(e) ∧ P(e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]
  b. leASV⟧ = λP<v, t>λtλee’[P(e) ∧ P(e’) ∧ e’ ≤E e ∧ τ(e’) ⊇ t]

Applying the meaning of the aspectual verb u ‘the realization aspect’ to the sentence yi lim kapi ‘he drink coffee’ (i.e., P in (56a–b)), the meaning of (57a) can be derived as follows: there is an event e of yi lim kapi ‘he drink coffee’, this event has a subpart (i.e., e’) and τ(e’) is contained within the topic time (i.e., t).

    1. (57)
    1. a.
    1. Yi
    2. s/he
    1. u
    2. ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘S/He drank coffee.’
    1.  
    1. b.
    1. Yi
    2. s/he
    1. le
    2. ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘S/He is drinking coffee.’

Likewise, applying the meaning of the aspectual verb le ‘the progression aspect’ to the sentence yi lim kapi ‘he drink coffee’, we can get the meaning of (57b) (i.e., there is an event e of yi lim kapi ‘he drink coffee’, this event has a subpart (i.e., e’), and τ(e’) (i.e., the event time) contains the topic time (i.e., t)).

So, the denotation of an aspectual verb can be regarded as a containment relation between the topic time (i.e., t) and the event time (i.e., τ(e’)). Since an aspectual verb does not bear any theta roles, the valency change function of the morpheme ums ‘uVD’ is nullified. However, ums ‘uVD’ still retains the ability of compositionally changing the denotation of an aspectual verb into a set of containment relations between the topic time and the event time. (In the following, I will use the term VASVms to represent the aspectual verb derived from applying the morphosyntactic function of u ‘uVD’ to the aspectual verb VASV.)

Assuming these, I suggest that, after applying the morphosyntactic function of the morpheme u ‘uVD’ to the TSM aspectual verb, the derived aspectual verb uASVms has an interpretation like (58a) and the derived aspectual verb leASVms has an interpretation like (58b).14

(58) a. uASVmsA = λP<v, t>λtkE<v, t>ev[(P(e) ∧ eE) → ∃ev[P(e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]]
    ‘After the combination with an argument P, which denotes a set of events, and a topic time t, uASVms derives a set of events (i.e., E<v, t>) such that for its every element event e which describes P, e has a subpart e’ which describes the same P and whose running time is contained within the topic time.’
  b. leASVmsA = λP<v, t>λtkE<v, t>ev[(P(e) ∧ eE) → ∃ev[P(e’) ∧ e’ ≤E e ∧ τ(e’) ⊇ t]]
    ‘After the combination with an argument P, which denotes a set of events, and a topic time t, leASVms derives a set of events (i.e., E<v, t>) such that for its every element event e which describes P, e has a subpart e’ which describes the same P and whose running time contains the topic time.’

4.1.2 The degree semantics of Us

Partially along the line of Wellwood (2015), I suggest that the morpheme us, being a component of a compound verb, functions to introduce degrees for the V of the u-V intransitive compound verb and, depending on whether the V is a non-gradable lexical verb or an aspectual verb, has a semantic interpretation as in (59a–b), with μ a variable over measure function-types, whose value is determined by the assignment function A. (In the following, I will use the term us of type μ when discussing the degree introducing function of the morpheme u ‘uVD’.)

(59) a. If α is a non-gradable lexical verb, the morpheme us has a semantic interpretation like:
    usμA = λxλα.A(μ)(α(x))
    α(x) denotes a set of events related to the lexical verb and x is not an eventuality argument. The dimension of measurement selected by A(μ) is the number of element events of the set of events or the temporal duration of the event denoted by α.
  b. If α is an aspectual verb, the morpheme us has a semantic interpretation like:
    usμA = λαλQλy.A(μ)(α(Q(y)))
    α(Q(y)) denotes a set of containment relations between the event time and the topic time. The dimension of measurement selected by A(μ) is the number of element containment relations of the set of time containment relations.

Whether a measure function is permissible or not is determined by the sort of thing that α(x) or α(Q(y)) is. For the TSM u-V construction, the type of measure function over which the variable m ranges is <<v, t>, d> or <<<v, t>, <k, t>>, d>, depending on whether the sort of thing measured is α(x) or α(Q(y)), and d is the type of degrees. So, for the TSM u-V construction, degrees are (i) introduced compositionally, and (ii) introduced by the morpheme u ‘uVD’, which semantically contributes a structure-preserving map from events, states or time containment relations to their measures along various dimensions in Wellwood’s (2015) sense. The domain to which A(μ) applies, as Wellwood (2015) suggests, is subject to the condition: for any two entities properly ordered in a part-of relation, their measurements are similarly ordered (Schwarzschild 2002; 2006).

As I have argued, the TSM u-V constructions can be divided into two types (i.e., the u-Vvc and the u-Vnvc type) in terms of whether the V of the u-V compound verb has undergone a valency change.

Given this, the discussion below will proceed in a way as follows. I first show how my proposal accounts for the syntax and semantics of the u-Vvc construction, and, then, I deal with the syntax and semantics of the u-Vnvc construction.

4.2 The application of the analysis

4.2.1 The u-Vvc construction

As I have suggested, the TSM u-V intransitive compound verb formed by the morpheme u ‘uVD’ and a non-gradable verb (i.e., V) denotes a stative scalar property.

If the V is a lexical verb, the morpheme ums, depending on the types of lexical verbs (i.e., the ditransitive, the transitive, the unergative or the unaccusative verb), has seven different application ways, as shown by (60a–d), respectively.

(60) a. Ditransitive verbs: λPλxλyλzλv.P(z, y, x, v) (e.g., tsio ‘lend’)
    umsA = (i) λPλxλvOPyOPz.P(v)(x)(y)(z)
      (ii) λPλyλvOPxOPz.P(v)(x)(y)(z)
      (iii) λPλwλv[OPxOPyOPz.P(v)(x)(y)(z) ∧ Property(v, w)]
  b. Transitive verbs: λPλxλyλv.P(y, x, v) (e.g., se ‘wash’)
    umsA = (i) λPλxλvOPy.P(v)(x)(y)
      (ii) λPλwλv[OPxOPy.P(v)(x)(y) ∧ Property(v, w)]
  c. Unergative verbs: λPλyλv.P(y, v) (e.g., tsau ‘run’)
    umsA = λPλwλv[OPy.P(v)(y) ∧ Property(v, w)]
  d. Unaccusative verbs: λPλxλv.P(x, v) (e.g., lak ‘fall’)
    umsA = λPλwλv[OPx.P(v)(x) ∧ Property(v, w)]

These seven different application ways can be exemplified by (61a–c), (62), (63), (64) and (65), respectively.

    1. (61)
    1. a.
    1. Tionn
    2. medium
    1. sio
    2. small
    1. khigiap
    2. enterprise
    1. kha
    2. more
    1. u-tsio.
    2. uVD-lend
    1. ‘The number of small and medium enterprises to which a lender lends money is larger.’
    1.  
    1. b.
    1. Bikim
    2. dollar
    1. pi
    2. than
    1. auguan
    2. euro
    1. kha
    2. more
    1. u-tsio.
    2. uVD-lend
    1. ‘The amount of dollars lent by a lender to borrowers is larger than the amount of euros is.’
    1.  
    1. c.
    1. Tsuekin
    2. recently
    1. kha
    2. more
    1. u-tsio.
    2. uVD-lend
    1. ‘The recent days are with more cases of a lender’s lending money to a borrower.’
    1. (62)
    1. Tsit-nia
    2. this-CL
    1. sann
    2. clothing
    1. pi
    2. than
    1. hit-nia
    2. that-CL
    1. sann
    2. clothing
    1. kha
    2. more
    1. u-se.
    2. uVD-wash
    1. ‘For anyone to wash it, this article of clothing is more durable than that article of clothing.’
    1. (63)
    1. Tsit-te
    2. this-CL
    1. satbun
    2. soap
    1. pi
    2. than
    1. hit-te
    2. that-CL
    1. satbun
    2. soap
    1. kha
    2. more
    1. u-se.
    2. uVD-wash
    1. ‘For anyone to wash anything by it, this piece of soap is more durable for washing than that piece of soap.’
    1. (64)
    1. Tsit-khuan
    2. this-CL
    1. e
    2. shoe
    1. pi
    2. than
    1. hit-khuan
    2. that-CL
    1. e
    2. shoe
    1. kha
    2. more
    1. u-tsau.
    2. uVD-run
    1. ‘For anyone to run by wearing it, this kind of shoes is more durable than that kind of shoes.’
    1. (65)
    1. Tshiu-a
    2. tree-PRT
    1. hioh
    2. leaf
    1. long
    2. all
    1. kangkhuan,
    2. the-same
    1. kuannthinn
    2. winter
    1. pi
    2. than
    1. zuanthinn
    2. summer
    1. kha
    2. more
    1. u-lak.
    2. uVD-fall
    1. ‘All kinds of leaves are the same in that the winter is more susceptible to having fallen leaves than the summer.’

However, due to space limit, I will only demonstrate how my proposal accounts for the syntax and semantics of (61b), (62), (63), (64) and (65), respectively.

First, in (61b), the ditransitive verb tsio ‘lend’ forms the intransitive compound verb u-tsio ‘uVD-lend’ with the morpheme u ‘uVD’ and the unsaturated agent argument and the unsaturated goal argument of it, as (67c) shows, are bound by a generic operator at the level of lexicon. So, at the syntactic level, (61b) has a structure like (66), where the theme argument bikim ‘dollar’ of intransitive compound verb u-tsio ‘uVD-lend’, which can be understood as the theme argument of the verb tsio ‘lend’, occurs in the specifier position of VP projected by the compound verb u-tsio ‘uVD-lend’ and, then, moves to the subject position.

    1. (66)
    1. [IP [bikim]i
    2. dollar
    1. [DegP [[PP
    2.  
    1. pi
    2. than
    1. auguan]
    2. euro
    1. [Deg’ [Deg
    2.  
    1. kha]
    2. more
    1. [VP ti [V’ [V
    2.  
    1. u-tsio]]]]]]]
    2. uVD-lend
    1. ‘The amount of dollars lent by a lender to borrowers is larger than the amount of euros is.’

Based on this syntactic structure, the semantic composition of (61b) can be demonstrated by (67a–j). For readership, the English gloss is added behind the slash, ⟦umsA represents the morphosyntactic function of u ‘uVD’, ⟦tsioms/lendmsA, for example, represents the set of lending events denoted by the verb tsio ‘lend’ after it undergoes the morphosyntactic process induced by u ‘uVD’, ⟦usA represents the semantic function of u ‘uVD’, and ⟦us-tsioms/us-lendmsA is the denotation of the intransitive compound verb u-tsio ‘uVD-lend’.15

(67) a. tsio/lendA = λxλyλzλv.tsio(z, y, x, v)
  b. umsA = λPλyλvOPxOPz.P(v)(x)(y)(z)
  c. tsioms/lendmsA = λyλvOPxOPz.tsio(z, y, x, v)
  d. usA = λαλy.A(μ)(α(y))
  e. ⟦[V us-tsioms/us-lendms]⟧A = λy.A(μ)(λvOPxOPz.tsio(z, y, x, v))
  f. ⟦[Deg kha/more]⟧A = λαλdλg.g(α) > d
  g. ⟦[DegP kha us-tsioms/more us-lendms]⟧A = λdλy.A(μ)(λvOPxOPz.tsio(z, y, x, v)) > d
  h. ⟦[PP pi auguan/than euro]⟧A = dauguan
  i. ⟦[DegP pi auguan kha us-tsioms/than euro more us-lendms]⟧A = λy.A(μ)(λvOPxOPz.tsio(z, y, x, v)) > dauguan
  j. ⟦[IP bikim pi auguan kha us-tsioms/dollar than euro more us-lendms]⟧A
    = A(μ)(λvOPxOPz.tsio(z, bikim, x, v)) > dauguan
    = T iff ∃E<v, t>[E<v, t> = λvOPxOPz.tsio(z, bikim, x, v) ∧ A(μ)(E<v, t>) > dauguan]
    A(μ) is the number of element events of the set of lending events.

Thus, (61b) is true just in case there is a set of lending events in which bikim ‘dollar’ is lent in each lending event, and the number of element events of this set of lending events is larger than the number of element events of the set of lending events in which auguan ‘euro’ is lent in each lending event.

From this ‘core’ meaning, a native speaker can obtain the implicature that the amount of dollars lent by a lender to borrowers is more than the amount of euros is.16 So, the dimension of measurement ‘the amount of money lent’, perceived from (61b) by the native speaker and related to the property of the theme subject (i.e., bikim ‘dollar’), can be regarded as an implicature implicated from the exact measure function (i.e., the number of element events of the set of lending events).

Second, in (62), the transitive verb se ‘wash’ of the intransitive compound verb u-se ‘uVD-wash’, as (69c) shows, has its unsaturated external argument bound by a generic operator at the level of lexicon. So, at the syntactic level, (62) has a structure like (68), where the theme argument of the intransitive compound verb u-se ‘uVD-wash’ (i.e., tsit-nia sann ‘this-CL clothing’) occurs in the specifier position of VP projected by the compound verb u-se ‘uVD-wash’ and, then, moves to the subject position.

    1. (68)
    1. [IP [tsit-nia
    2. this-CL
    1. sann]i
    2. clothing
    1. [DegP [[PP
    2.  
    1. pi
    2. than
    1. hit-nia
    2. that-CL
    1. sann] [Deg’ [Deg
    2. clothing
    1. kha] [VP ti [V’ [V
    2. more
    1. u-se]]]]]]]
    2. uVD-wash
    1. ‘This article of clothing has the property of being washed more times than that article of clothing.’

Based on (68), the semantic composition of (62) can be represented by (69a–j).

(69) a. se/washA = λxλyλv.se(y, x, v)
  b. umsA = λPλxλvOPy.P(v)(x)(y)
  c. sems/washmsA = λxλvOPy.se(y, x, v)
  d. usA = λαλx.A(μ)(α(x))
  e. ⟦[V us-sems/us-washms]⟧A = λx.A(μ)(λvOPy.se(y, x, v))
  f. ⟦[Deg kha/more]⟧A = λαλdλg.g(α) > d
  g. ⟦[DegP kha us-sems/more us-washms]⟧A = λdλx.A(μ)(λvOPy.se(y, x, v)) > d
  h. ⟦[PP pi hit-nia sann/than that-CL clothing]⟧A = dhns
  i. ⟦[DegP pi hit-nia sann kha us-sems/than that-CL clothing more us-washms]⟧A = λx.A(μ)(λvOPy.se(y, x, v)) > dhns
  j. ⟦[IP tsit-nia sann pi hit-nia sann kha us-sems/this-CL clothing than that-CL clothing more us-washms]⟧A = A(μ)(λvOPy.se(y, tsit-nia sann, v)) > dhns
    = T iff ∃E<v, t>[E<v, t> = λvOPy.se(y, tsit-nia sann, v) ∧ A(μ)(E<v, t>) > dhns]
    A(μ) is the number of element events of the set of washing events.

As (69j) shows, (62) is true just in case there is a set of washing events in which tsit-nia sann ‘this-CL clothing’ is washed in each washing event, and the number of element events of this set of washing events is larger than the number of element events of the set of washing events in which hit-nia sann ‘that-CL clothing’ is washed in each washing event.

From this ‘core’ meaning, a native speaker can obtain the implicature that this article of clothing is more durable for washing than that article of clothing is. So, the dimension of measurement ‘the durableness for washing’ related to the property of the theme subject tsit-nia sann ‘this-CL clothing’ can be regarded as an implicature implicated from the exact measure function of (i.e., the number of element events of the set of washing events).

Third, in (63), the morpheme ums, at the level of lexicon, (A) introduces generic operators to bind the unsaturated external argument and the unsaturated internal argument of the transitive verb se ‘wash’ of the intransitive compound verb u-se ‘uVD-wash’, (B) leads a non-thematic argument w (i.e., the instrument adjunct tsit-te satbun ‘this-CL soap’) into the structure, and (C) compositionally changes the denotation of the verb se ‘wash’ into a set of washing events. So, the verb derived (i.e., sems ‘wash’) has a semantic representation as in (70).

(70) sems/washmsA = λwλv[OPxOPy.se(y, x, v) ∧ Instrument(v, w)]

Assuming this, I suggest that, at the syntactic level, (63) has a structure like (71), where the theme argument of the intransitive compound verb u-se ‘uVD-wash’ (i.e., tsit-te satbun ‘this-CL soap’), which can be understood as the instrument adjunct of the verb se ‘wash’, occurs in the specifier position of VP projected by the compound verb u-se ‘uVD-wash’ and, then, moves to the subject position.

    1. (71)
    1. [IP [tsit-te
    2. this-CL
    1. satbun]i [DegP [[PP
    2. soap
    1. pi
    2. than
    1. hit-te
    2. that-CL
    1. satbun] [Deg’ [Deg
    2. soap
    1. kha] [VP ti [V’
    2. more
    1. [V u-se]]]]]]]
    2. uVD-wash
    1. ‘This piece of soap has the property of being washed more times than that piece of soap.’

Based on (71), the semantic composition of (63) can be demonstrated by (72a–j).

(72) a. se/washA = λxλyλv.se(y, x, v)
  b. umsA = λPλwλv[OPxOPy.P(v)(x)(y) ∧ Property(v, w)]
  c. sems/washmsA = λwλv[OPxOPy.se(y, x, v) ∧ Instrument(v, w)]
  d. usA = λwλα.A(μ)(α(w))
  e. ⟦[V us-sems/us-washms]⟧A = λw.A(μ)(λv[OPxOPy.se(y, x, v) ∧ Instrument(v, w)])
  f. ⟦[Deg kha/more]⟧A = λαλdλg.g(α) > d
  g. ⟦[DegP kha us-sems/more us-washms]⟧A = λdλw.A(μ)(λv[OPxOPy.se(y, x, v) ∧ Instrument(v, w)]) > d
  h. ⟦[PP pi hit-te satbun/than that-CL soap]⟧A = dhts
  i. ⟦[DegP pi hit-te satbun kha us-sems/than that-CL soap more us-washms]⟧A = λw.A(μ)(λv[OPxOPy.se(y, x, v) ∧ Instrument(v, w)]) > dhts
  j. ⟦[IP tsit-te satbun pi hit-te satbun kha us-sems/this-CL soap than that-CL soap more us-washms]⟧A = A(μ)(λv[OPxOPy.se(y, x, v) ∧ Instrument(v, tsit-te satbun)]) > dhts
    = T iff ∃E<v, t>[E<v, t> = λv[OPxOPy.se(y, x, v) ∧ Instrument(v, tsit-te satbun)] ∧ A(μ)(E<v, t>) > dhts]
    A(μ) is the number of element events of the set of washing events.

Thus, (63) is true just in case there is a set of washing events in which tsit-te satbun ‘this-CL soap’ is washed in each washing event, and the number of element events of this set of washing events is larger than the number of element events of the set of washing events in which hit-te satbun ‘that-CL soap’ is washed in each washing event. From this ‘core’ meaning, the implicature that this piece of soap is more durable for washing than that piece of soap comes out naturally.

Fourth, according to my proposal, the grammaticality of (64) repeated as (73), is also under expectation.

    1. (73)
    1. Tsit-khuan
    2. this-CL
    1. e
    2. shoe
    1. pi
    2. than
    1. hit-khuan
    2. that-CL
    1. e
    2. shoe
    1. kha
    2. more
    1. u-tsau.
    2. uVD-run
    1. ‘For anyone to run by wearing it, this kind of shoes is more durable than that kind of shoes.’

In (73), the morpheme ums ‘uVD’ first stativizes the event denoted by the verb tsau ‘run’ by introducing a generic operator to bind the unsaturated external argument at the level of lexicon, then compositionally changes the denotation of it into a set of running events by having the eventuality argument v bound by a lambda operator, and finally leads a non-thematic argument w (i.e., the instrument adjunct tsit-khuan e ‘this-CL shoe’) into the structure. So, the derived verb tsaums ‘wash’ has an interpretation as in (74).

(74) tsaums/runmsA = λwλv[OPy.tsau(y, v) ∧ Instrument(v, w)]

Thus, (73) has a syntactic structure like (75), based on which the semantic composition of (73) can be demonstrated by (76a–j).

    1. (75)
    1. [IP [tsit-khuan
    2. this-CL
    1. e]i [DegP [[PP
    2. shoe
    1. pi
    2. than
    1. hit-khuan
    2. that-CL
    1. e] [Deg’ [Deg
    2. shoe
    1. kha] [VP ti [V’ [V
    2. more
    1. u-tsau]]]]]]]
    2. uVD-run
    1. ‘This kind of shoes is more durable for one to run by wearing it than that kind of shoes is.’
(76) a. tsau/runA = λyλv.tsau(y, v)
  b. umsA = λPλwλv[OPy.P(v)(y) ∧ Property(v, w)]
  c. tsaums/runmsA = λwλv[OPy.tsau(y, v) ∧ Instrument(v, w)]
  d. usA = λwλα.A(μ)(α(w))
  e. ⟦[V us-tsaums/us-runms]⟧A = λw.A(μ)(λv[OPy.tsau(y, v) ∧ Instrument(v, w)])
  f. ⟦[Deg kha/more]⟧A = λαλgλd.g(α) > d
  g. ⟦[DegP kha us-tsaums/more us-runms]⟧A = λdλw.A(μ)(λv[OPy.tsau(y, v) ∧ Instrument(v, w)]) > d
  h. ⟦[PP pi hit-khuan e/than that-CL shoe]⟧A = dhke
  i. ⟦[DegP pi hit-khuan e kha us-tsaums/than that-CL shoe more us-runms]⟧A = λw.A(μ)(λv[OPy.tsau(y, v) ∧ Instrument(v, w)]) > dhke
  j. ⟦[IP tsit-khuan e pi hit-khuan e kha us-tsaums/this-CL shoe than that-CL shoe more us-runms]⟧A = A(μ)(λv[OPy.tsau(y, v) ∧ Instrument(v, tsit-khuan e)]) > dhke
    = T iff ∃E<v, t>[E<v, t> = λv[OPy.tsau(y, v) ∧ Instrument(v, tsit-khuan e)] ∧ A(μ)(E<v, t>) > dhke]
    A(μ) is the number of element events of the set of running events.

From the ‘core’ meaning of (73), a native speaker can obtain the implicature that this kind of shoes is more durable for one to run by wearing it, and this implicature has ‘the durableness for running’ as the dimension of measurement.

Fifth, in (65) (repeated as (77a)), the V of the intransitive compound verb u-lak ‘uVD-fall’ is an unaccusative verb (i.e., lak ‘fall’) and the TSM u-V construction involved has the NP kuannthinn ‘winter’, which can be thematically understood as the temporal adjunct of the verb lak ‘fall’, as subject. This u-V construction has a syntactic structure like (77b), based on which the semantic composition of (77b) can be demonstrated by (78a–j).

    1. (77)
    1. a.
    1. Tshiu-a
    2. tree-PRT
    1. hioh
    2. leaf
    1. long
    2. all
    1. kangkhuan,
    2. the-same
    1. kuannthinn
    2. winter
    1. pi
    2. than
    1. zuathinn
    2. summer
    1. kha
    2. more
    1. u-lak.
    2. uVD-fall
    1. ‘All kinds of leaves are the same in that the winter is more susceptible to having fallen leaves than the summer.’
    1.  
    1. b.
    1. [IP [kuannthin]i
    2. winter
    1. [DegP [[PP
    2.  
    1. pi
    2. than
    1. zuathinn]
    2. summer
    1. [Deg’ [Deg
    2.  
    1. kha]
    2. more
    1. [VP ti [V’ [V
    2.  
    1. u-lak]]]]]]]
    2. uVD-fall
    1. ‘The winter is more susceptible to having fallen leaves than the summer.’
(78) a. lak/fallA = λxλv.lak(x, v)
  b. umsA = λPλwλv[OPx.P(v)(x) ∧ Property(v, w)]
  c. lakms/fallmsA = λwλv[OPx.lak(x, v) ∧ Time(v, w)]
  d. usA = λwλα.A(μ)(α(w))
  e. ⟦[V us-lakms/us-fallms]⟧A = λw.A(μ)(λv[OPx.lak(x, v) ∧ Time(v, w)])
  f. ⟦[Deg kha/more]⟧A = λαλgλd.g(α) > d
  g. ⟦[DegP kha us-lakms/more us-fallms]]⟧A = λdλw.A(μ)(λv[OPx.lak(x, v) ∧ Time(v, w)]) > d
  h. ⟦[PP pi zuathinn/than summer]⟧A = dzuathinn
  i. ⟦[DegP pi zuathinn kha us-lakms/than summer more us-fallms]⟧A = λw.A(μ)(λv[OPx.lak(x, v) ∧ Time(v, w)]) > dzuathinn
  j. ⟦[IP kuannthin pi zuathinn kha us-lakms/winter than summer more us-fallms]⟧A = A(μ)(λv[OPx.lak(x, v) ∧ Time(v, kuannthin)]) > dzuathinn
    = T iff ∃E<v, t>[E<v, t> = λv[OPx.lak(x, v) ∧ Time(v, kuannthin)] ∧ A(μ)(E<v, t>) > dzuathinn]
    A(μ) is the number of element events of the set of leaf-falling events.

So, (77b) is true just in case there is a set of leaf-falling events in each of which the leaf falls in winter, and the number of element events of this set of leaf-falling events is larger than the number of element events of the set of leaf-falling events in each of which the leaf falls in summer.

From this ‘core’ meaning, the native speaker obtains the implicature that winter is more susceptible to having fallen leaves.

4.2.2 The u-Vnvc construction

My proposal for the syntax and semantics of the TSM u-Vnvc construction can be exemplified as follows. On one hand, an u-Vnvc construction like (79a), which involves no change in the valency of V and conveys a meaning about the occurrence frequency of the event denoted by the predicate (i.e., lim kapi ‘drink coffee’), has a syntactic structure like (79b).

    1. (79)
    1. a.
    1. Yi
    2. he
    1. pi
    2. than
    1. li
    2. you
    1. kha
    2. more
    1. u-lim
    2. uVD-drink
    1. kapi.
    2. coffee
    1. ‘He drinks coffee more frequently than you.’
    1.  
    1. b.
    1. [Yii
    2. he
    1. [DegP [[PP
    2.  
    1. pi
    2. than
    1. li]
    2. you
    1. [kha
    2. more
    1. [ASVP t’i [ASV
    2.  
    1. [u-[ASV
    2. uVD
    1. u]][VP 
    2. ASV
    1. ti
    2.  
    1. lim
    2. drink
    1. kapi]]]]]]].
    2. coffee
    1. ‘He drinks coffee more frequently than you.’

Namely, what forms the u-V compound verb with the morpheme u ‘uVD’ in (79a) is the aspectual verb u ‘the realization aspect’ rather than the lexical verb lim ‘drink’. Then, at the phonetic level, one of the two consecutive u’s (i.e., the morpheme u ‘uVD’ and the aspectual verb u ‘the realization aspect’) is haplologically eliminated due to their phonetic identity, as attested by the fact that (79a) is almost identical to (80) in semantic interpretation.

    1. (80)
    1. Yi
    2. he
    1. pi
    2. than
    1. li
    2. you
    1. kha
    2. more
    1. u-le
    2. uVD-ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘He drinks coffee more frequently than you.’

That is, in (80), it is the aspectual verb le ‘the progressive aspect’ that forms the u-V compound verb with the morpheme u ‘uVD’. So, the argument structure of the lexical verb lim ‘drink’ is not affected by the morpheme ums. This explains why the valency change does not happen in (80).

As the same reasoning, I suggest that what forms the u-Vnvc compound verb with the morpheme ums in (79a) is the aspectual verb u ‘the realization aspect’ and, given this, the lexical verb lim ‘drink’ does not undergo the valency change induced by ums.

On the other hand, adopting Lin’s (2003: 271) definition of the realization aspect and the progressive aspect, I suggest that the TSM aspectual verb u ‘the realization aspect’ and le ‘the progressive aspect’ have (81a–b) as their corresponding semantic representation (Bohnemeyer & Swift 2001).

(81) a. uASV⟧ = λP<v, t>λtλee’[P(e) ∧ P(e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]
  b. leASV⟧ = λP<v, t>λtλee’[P(e) ∧ P(e’) ∧ e’ ≤E e ∧ τ(e’) ⊇ t]

So, the denotation of an aspectual verb can be regarded as a containment relation between the topic time (i.e., t) and the event time (i.e., τ(e’)). Since an aspectual verb does not bear any theta roles, the valency change function of the morpheme ums is nullified. However, ums still retains the ability of compositionally changing the denotation of an aspectual verb into a set of time containment relations.

Assuming these, the aspectual verb derived by having the aspectual verb u ‘the realization aspect’ undergone the morphosyntactic process induced by the morpheme ums (i.e., uASVms) has an interpretation as in (58a), repeated as (82).

(82) uASVmsA = λP<v, t>λtkE<v, t>ev[(P(e) ∧ eE) → ∃ev[P(e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]]

Namely, after the combination with an argument P, which denotes a set of events, and a topic time t, uASVms derives a set of events (i.e., E<v, t>) such that for its every element event e which describes P, e has a subpart e’ which describes the same P and whose running time is contained within the topic time.

Thus, assuming that (79a) has a syntactic structure like (79b), the semantic composition of (79a) can be demonstrated by (83a–l).

(83) a. ⟦[V lim/drink]⟧A = λxλyλev.lim(y, x, e)
  b. ⟦[VP lim kapi/drink coffee]⟧A = λyλev.lim(y, kapi, e)
  c. ⟦[ASV uASV]⟧A = λP<v, t>λtkλevev[P(e) ∧ P(e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]
  d. uASVmsA = λP<v, t>λtkE<v, t>ev[(P(e) ∧ eE) → ∃ev(P(e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t)]
  e. usA = λαλQλy.A(μ)(α(Q(y)))
  f. ⟦[ASV us-uASVms]⟧A = λQλy.A(μ)(λP<v, t>λtkE<v, t>ev[(P(e) ∧ eE) → ∃ev[P(e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]](Q(y)))
    = λQλy.A(μ)(λtkE<v, t>ev[(Q(y)(e) ∧ eE) → ∃ev[Q(y)(e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]])
  g. ⟦[ASVP us-uASVms lim kapi/us-uASVms drink coffee]⟧A = λy.A(μ)(λtkE<v, t>ev [(lim(y, kapi, e) ∧ eE) → ∃ev[lim(y, kapi, e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]])
  h. ⟦[Deg kha/more]⟧A = λαλdλg.g(α) > d
  i. ⟦[DegP kha us-uASVms lim kapi/more us-uASVms drink coffee]⟧A = λdλy.A(μ)(λtkE<v, t>ev[(lim(y, kapi, e) ∧ eE) → ∃ev [lim(y, kapi, e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]]) > d
  j. ⟦[PP pi li/than you]⟧A = dli
  k. ⟦[DegP pi li kha us-uASVms lim kapi/than you more us-uASVms drink coffee]⟧A = λy.A(μ)(λtkE<v, t>ev[(lim(y, kapi, e) ∧ eE) → ∃ev[lim(y, kapi, e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]]) > dli
  l. ⟦[IP yi pi li kha us-uASVms lim kapi/he than you more us-uASVms drink coffee]⟧A = A(μ)(λtkE<v, t>ev[(lim(yi, kapi, e) ∧ eE) → ∃ev[lim(yi, kapi, e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]]) > dli
    = T iff ∃E<k, t>[E<k, t> = λtkE<v, t>ev [(lim(yi, kapi, e) ∧ eE) → ∃ev[lim(yi, kapi, e’) ∧ e’ ≤E e ∧ τ(e’) ⊆ t]] ∧ A(μ)(E<k, t>) > dli]
    A(μ) is the number of element containment relations of the set of containment relations between the topic time and the event time.

As (83l) shows, (79a) is true just in case there is a set of containment relations in each of which the event time (i.e., τ(e’)) of s/he drank coffee is contained within the topic time (i.e., t). Since the measure function selected by A(μ) is the number of element containment relations of the set of containment relations between the topic time and the event time in each of which the event time (i.e., τ(e’)) of s/he drank coffee is contained within the topic time (i.e., t). So, the interpretation of (79a) is derived as follows: the number of element containment relations of the set of time containment relations between the topic time and the event time in each of which the event time (i.e., τ(e’)) of s/he drank coffee is contained within the topic time (i.e., t) is larger than the number of element containment relations of the set of time containment relations between the topic time and the event time in each of which the event time (i.e., τ(e’)) of you drank coffee is contained within the topic time (i.e., t). From this ‘core’ meaning, a native speaker can obtain the implicature that s/he drinks coffee more frequently than you because ‘frequency’ is essentially an aspectual notion related to the number of containment relations between the topic time and the event time.17 In other words, the dimension of measurement shown by this implicature is related to the aspect of the event denoted by the predicate.

As the same reasoning, example (84a) has a syntactic structure like (84b) and its semantic interpretation can be represented by (85).

    1. (84)
    1. a.
    1. Yi
    2. he
    1. pi
    2. than
    1. li
    2. you
    1. kha
    2. more
    1. u-le
    2. uVD-ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘He drinks coffee more frequently than you.’
    1.  
    1. b.
    1. [Yii
    2. he
    1. [DegP [[PP
    2.  
    1. pi
    2. than
    1. li]
    2. you
    1. [kha
    2. more
    1. [ASVP t’i [ASV
    2.  
    1. [u-[ASV
    2. uVD
    1. le]][VP
    2. ASV
    1. ti
    2.  
    1. lim
    2. drink
    1. kapi]]]]]]].
    2. coffee
    1. ‘He drinks coffee more frequently than you.’
(85) ⟦[IP yi pi li kha us-leASVms lim kapi/he than you more us-leASVms drink coffee]⟧A = T iff ∃E<k, t>[E<k, t> = λtkE<v, t>ev [(lim(yi, kapi, e) ∧ eE) → ∃ev [lim(yi, kapi, e’) ∧ e’ ≤E e ∧ τ(e’) ⊇ t]] ∧ A(μ)(E<k, t>) > dli]
  A(μ) is the number of element containment relations of the set of containment relations between the event time and the topic time.

Namely, (84a) has a semantic interpretation as follows: the number of element containment relations of the set of time containment relations in each of which the topic time (i.e., t) is contained within the event time of s/he is drinking coffee is larger than the number of element containment relations of the set of time containment relations in each of which the topic time is contained within the event time of you are drinking coffee. From this ‘core’ meaning, a native speaker can obtain the implicature that s/he drinks coffee more frequently than you.

After exemplifying how my proposal accounts for the syntax and semantics of the TSM u-V construction, I will discuss some consequences and implications of my proposal before going into the concluding remarks.

5 Consequences and implications

In this section, I first highlight the consequences of my proposal by showing how the questions raised by the TSM u-V construction are dealt with, and, then, some implications concerning the possessive morphosyntactic strategy for predicating gradable properties and Wellwood (2015) will be addressed.

5.1 Middles or not middles

As for the questions raised by the TSM u-V construction, first things first, is the TSM u-V construction a kind of middle constructions? To answer this question, I will use Ackema & Schoorlemmer’s (2006: 132–138) widely-accepted definition of the middle construction as in (86) and a much less strict definition proposed by Yoshimura & Taylor (2004: 303) (i.e., (87)) as criterion to judge whether the TSM u-V construction is a middle construction.

(86) a. The external argument of the non-middle counterpart of the middle verb cannot be expressed as a regular DP-argument in the middle.
  b. If the non-middle counterpart of the middle verb has a direct internal argument role, the subject of the middle sentence carries this role.
  c. The middle verb is stative, non-episodic. The middle sentence is a generic statement.
  d. In a middle, the logical subject argument of the underlying verb is semantically present.
(87) A middle expression presents a non-Agent participant as possessing certain inherent properties which significantly facilitate, enable (or, as the case may be, impede) the unfolding of the kind of process designated by the verb phrase; at the same time, the contribution of the Agent to the process, though not erased, is backgrounded.

The answer we get is quite clear. The TSM u-V construction is not a middle construction because of the following reasons. (A) The subject of the TSM u-V construction (i.e., the TSM u-Vnvc construction) can be an NP bearing an agent role, (B) in the TSM u-Vnvc construction, the V of the u-V compound verb can be one without an argument structure, and (C) the TSM u-V construction might describe an episodic event or a temporary state, as illustrated by (88a), (88b) and (89a–b), respectively.

    1. (88)
    1. a.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. u
    2. uVD-ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘Recently, he intentionally drinks coffee more frequently.’
    1.  
    1. b.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. u-le
    2. uVD-ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘Recently, he intentionally drinks coffee more frequently.’
    1. (89)
    1. a.
    1. Li
    2. you
    1. kinalit
    2. today
    1. tsai
    2. morning
    1. kha
    2. more
    1. u
    2. uVD-ASV
    1. lim
    2. drink
    1. kapi.
    2. coffee
    1. ‘This morning, you drank coffee more frequently.’
    1.  
    1. b.
    1. Tshaikue
    2. loofah
    1. tsang
    2. yesterday
    1. kai
    2. very
    1. u-siau.
    2. uVD-sell/consume
    1. ‘Yesterday, the loofah sold well/people consumed many loofahs.’

On one hand, the fact that the NP subject of the TSM u-V construction can be an entity bearing the agent role (e.g., yi ‘s/he’ in (88a)) makes the TSM u-V construction unable to fit into the definition of the middle construction provided by Ackema & Schoorlemmer (2006) or Yoshimura & Taylor (2004).

On another hand, the subject of a middle sentence, as Ackema & Schoorlemmer (2006) and Yoshimura & Taylor (2004) suggest, must be a non-agent participant of the middle verb. However, in a TSM u-Vnvc construction, the V, being an aspectual verb, does not bear any theta roles. Hence, it is impossible to get a non-agent participant from this V. So, it is hard to assign the TSM u-V construction to the category of middle constructions under Ackema & Schoorlemmer’s (2006) or Yoshimura & Taylor’s (2004) definition.

On the other hand, neither Ackema & Schoorlemmer’s (2006) nor Yoshimura & Taylor’s (2004) definition can accommodate the fact that the TSM u-V construction might describe an episodic event or a temporary state.

Since the TSM u-V construction is not a middle construction, there is no reason to exclude (A) an intransitive verb (e.g., an unaccusative verb like tshuthen ‘appear’ in (25a) or an unergative verb like tsau ‘run’ in (25b)) or (B) a mental or stative verb like kamkak ‘feel’ in (26b) from being the V of the u-V compound verb. Of course, the possibility of having the goal role of a ditransitive verb as the subject of a TSM u-V construction like (15c) cannot be excluded, either.

Besides, contra Lien (2010: 1283), which assumes that, in the pluractional middle, the internal argument has to be externalized as subject bearing the theme role, the type of the u-V constructions with a non-theme NP subject, for example (90), should not be a problem to my analysis.

    1. (90)
    1. Tsit-khuan
    2. this-CL
    1. pi
    2. pen
    1. kha
    2. more
    1. u-sia.
    2. uVD-write
    1. ‘This kind of pens is more durable for writing.’

Namely, no object-to-subject movement is assumed under my proposal.

5.2 Consequences

My proposal for the syntax and semantics of the TSM u-V construction has the following empirical and theoretical consequences. First, the analysis proposed well explains the question of why the TSM u-V constructions can be divided into two types in terms of whether the V of the u-V compound verb involves a valency change or not. On one hand, if the V of the u-V compound verb is an aspectual verb, the valency change does not occur because an aspectual verb does not bear any theta roles. So, the external argument of the lexical verb following the aspectual verb, regardless of its inner aspect, can occur as subject of the sentence, as shown by (91a–e), respectively.18

    1. (91)
    1. a.
    1. Yi
    2. he
    1. kha
    2. more
    1. u
    2. uVD-ASV
    1. tshing
    2. wear
    1. tsit-khuan
    2. this-CL
    1. sann.
    2. clothing
    1. ‘He wears this kind of clothing more frequently.’
    1.  
    1. b.
    1. Gua
    2. I
    1. tsuekin
    2. recently
    1. kha
    2. more
    1. u
    2. uVD-ASV
    1. kamkak
    2. feel
    1. kha
    2. leg
    1. le
    2. ASV
    1. thiang.
    2. painful
    1. ‘Recently, I feel my legs painful more frequently.’
    1.  
    1. c.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. thiaukang
    2. intentionally
    1. kha
    2. more
    1. bo-le
    2. not-uVD-ASV
    1. tshuthen.
    2. show-up
    1. ‘Recently, he intentionally shows up less frequently.’
    1.  
    1. d.
    1. Yi
    2. he
    1. tsuekin
    2. recently
    1. kha
    2. more
    1. u
    2. uVD-ASV
    1. konnphua
    2. hit-break
    1. uann.
    2. bowl
    1. ‘Recently, he breaks bowls more frequently.’
    1.  
    1. e.
    1. Pennlang
    2. patient
    1. kinalit
    2. today
    1. kha
    2. more
    1. bo
    2. not-uVD-not-ASV
    1. sau.
    2. cough
    1. ‘Today, the patient coughs less frequently.’

On the other hand, if the V of the u-V compound verb is a lexical verb, the morpheme ums will cause the lexical verb to undergo a valency change by introducing a generic operator (or generic operators) to bind the unsaturated external argument (or the unsaturated external argument and the unsaturated internal argument) at the level of lexicon. If the external argument and internal argument(s) of V are all bound by a generic operator at the lexical level, the morpheme ums will lead a non-thematic argument of V into the structure, and this non-thematic argument, then, occurs as the subject of the sentence at the syntactic level. So, the external argument of the lexical verb is impossible to occur as the subject of the sentence at the syntactic level.

Second, assuming that, in the TSM u-V construction, degrees are (i) introduced compositionally and (ii) introduced by the morpheme u ‘uVD’, which semantically contributes a structure-preserving map from events, states or time containment relations to their measures along various dimensions, measure functions allowed must be those that can only be applied to non-trivially structured domains in Schwarzschild’s (2002; 2006) sense. This well explains why an accomplishment verb, which is not homogeneous, cannot form an u-V compound verb with the morpheme u ‘uVD’, as attested by the ungrammaticality of (13e), repeated as (92).

    1. (92)
    1. *Tsit-khuan
    2.   this-CL
    1. uann
    2. bowl
    1. kha
    2. more
    1. u-konnphua.
    2. uVD-hit-break

Third, the ambiguity of (93) can be well explained by having the core dimension of measurement (i.e., the number of element events of the set of sitting events) associated with the implicature ‘the durableness for sitting’ in a context like (93a) or ‘the seating capacity’ in a context like (93b).

    1. (93)
    1. Tsit-tiunn
    2. this-CL
    1. yi-a
    2. chair-PRT
    1. pi
    2. than
    1. hit-tiunn
    2. that-CL
    1. yi-a
    2. chair-PRT
    1. kha
    2. more
    1. u-tse.
    2. uVD-sit
    1.  
    1. a.
    1. ‘Assuming other things being equal, this chair has been used for sitting for ten years until it is broken, and that chair has been used for sitting for nine years until it is broken. So, it can be said that this chair is more durable than that chair for sitting.’
    1.  
    1. b.
    1. ‘Assuming other things being equal, this chair allows ten persons, one by one, to sit on it adjacently until its space is fully occupied, and that chair allows nine persons, one by one, to sit on it adjacently until its space is fully occupied. So, it can be said that the seating capacity of this chair is larger than the seating capacity of that chair.’

And, the ‘derivation’ of these two implicatures must be subject to Grice’s (1975) conversational maxims.

Fourth, as I have argued, in the TSM u-Vvc construction, the morpheme ums compositionally changes the denotation of V into a set of events. The element number of a significant set can be one or more than one. So, we might expect there to be a TSM u-Vvc construction where the set of events generated by the morpheme ums contains only one element. The fact bears out this expectation. Example (94a) is such a case because it does not make sense for one to preserve a pomelo more than one time, as the ungrammaticality of (94b) attests.

    1. (94)
    1. a.
    1. Tsit-liap
    2. this-CL
    1. iu-a
    2. pomelo-PRT
    1. kha
    2. more
    1. u-khng.
    2. uVD-preserve
    1. ‘This pomelo is more durable for preserving.’
    1.  
    1. b.
    1. *Tsit-liap
    2.   this-CL
    1. iu-a,
    2. pomelo-PRT
    1. gua
    2. I
    1. khng
    2. preserve
    1. san
    2. three
    1. pai.
    2. time

Given this, A(μ) selects ‘the temporal duration of this single preserving event’ as the dimension of measurement; (94a), therefore, has its core meaning as follows: this pomelo has the property of undergoing a preserving event with a temporal duration longer than that pomelo has. Implicated from this core meaning is the implicature that this pomelo is more durable for preserving than that pomelo.

Fifth, the many different dimensions of measurement intuitively perceived by native speakers from the TSM u-V construction, for example, the property of the entity denoted by the subject NP (e.g., the durableness for washing or the seating capacity) and the occurrence frequency of an event (i.e., the aspect of the event denoted by the predicate), actually are all implicatures derived from the core dimension of measurement selected by A(μ). So, the exact measure function of the TSM u-V construction is the number of element events or element containment relations of a set of events or time containment relations.

5.3 Implications

After answering the questions raised by the TSM u-V construction, I want to have the attention shifted to the following two implications of my proposal. One is related to the possessive morphosyntactic strategy for predicating gradable properties, and the other is concerning Wellwood’s (2015) unified theory for comparative constructions.

5.3.1 The possessive morphosyntactic strategy

According to Francez & Koontz-Garboden (2015; 2017), many languages (e.g., English and German) have two types of Property Concept (PC) lexemes: PC adjectives, and PC nominals. The former is used in canonical PC constructions that, in most cases, involve the copula verb, and the latter often triggers ‘the possessive strategies of predication’, in which PC nominals form a PC predicate with a possessive or an existential morpheme, as illustrated by (95a–b), respectively.

    1. (95)
    1. Property Concept Adjectives
    1.  
    1. a.
    1. John is knowledgeable.           (English)
    1.  
    1. b.
    1. Ich
    2. I
    1. bin
    2. am
    1. hungrig.
    2. hungry
    1.          (German)
    2.  
    1. ‘I am hungry.’
    1. (96)
    1. Property Concept Nominals
    1.  
    1. a.
    1. John has (a lot of) knowledge.                      (English)
    1.  
    1. b.
    1. Er
    2. he
    1. hatte
    2. had
    1. mehr
    2. more
    1. Hunger
    2. hunger
    1. als
    2. than
    1. ich.
    2. I
    1. (German)
    2.  
    1. ‘He was hungrier than me.’

As Francez & Koontz-Garboden (2017: 548) further notice, only abstract-substance-denoting nominals are allowed in the PC predicate. So, they argue that PC nominals (e.g., knowledge) are semantically distinct from other mass nouns (e.g., water). That is, PC nominals denote a set of ‘portions’ of substances; for instance, knowledge denotes a set of portions of knowledge, as (97) shows.

(97) knowledge⟧ = λpp.knowledge(p)

As they argue, portions, being a primitive entity (of type p), are subject to a total preorder ≤ (smaller than or equal to). Hence, the denotation of knowledge differs from that of a concrete substance noun like water in that water denotes a set of water substance partially ordered by a mereological part-whole relation (Link 2002).

(98) water⟧ = λxe.water(x)

Given this semantic distinction, the PC nominal knowledge of type <p, t> alone cannot serve as a predicate of an individual. So, it has to combine with the possessive verb have with an interpretation as in (99) to form a Possessive PC predicate by having the possessive verb have function to relate individuals to portions.

(99) have⟧ = λP<p, t>λxλD.∃Dz[P(z) ∧ π(x, z)]

Namely, P is a variable over (abstract) substances, and p is a possessive relation. D, being a variable over sets of portions, provides a domain restriction for the existential quantifier such that the value of z is restricted to portions that count as ‘big enough’ in the context. Thus, combining have with the quality NP knowledge and the subject John yields the truth-conditions for (100a), as shown below.

(100) a. John has knowledge.
  b. John has knowledge⟧ = ∃Dz[knowledge(z) ∧ π(John, z)]

Namely, (100a) is true in case there is a portion of knowledge that counts as ‘big enough’ in the context and John possesses it.

According to Zhang (2019) and Li (to appear), such a morphosyntactic strategy for predicating gradable properties is also found in Chinese, and the nominal involved is also limited to property concept nominals. For instance, (101a), which contains a property concept noun (i.e., zhihui ‘wisdom’), is grammatical with a gradable property reading but the gradable property reading is not allowed for (101b), which contains a concrete substance noun (i.e., shui ‘water’).

    1. (101)
    1. a.
    1.   Zhangsan
    2.   Zhangsan
    1. hen
    2. very
    1. you
    2. have
    1. zhihui.
    2. wisdom
    1.    ‘Zhangsan has a lot of wisdom.’
    1.  
    1. b.
    1. *Zhangsan
    2.   Zhangsan
    1. hen
    2. very
    1. you
    2. have
    1. shui.
    2. water
    1.    ‘Intended: Zhangsan has a lot of water.’

Relevantly here, according to the previous studies on the TSM u-V construction (e.g., Yang 1991; Lai 2007; Lien 2010), the morpheme u has the literal meaning have or possess. So, the grammaticality of (102a–b) implies that TSM also adopts the possessive morphosyntactic strategy for predicating gradable properties (henceforth, I use the term ‘the TSM u-N construction’ to represent a TSM construction like (102a–b)).

    1. (102)
    1. a.
    1. Tsit-le
    2. this-CL
    1. lang
    2. person
    1. kha
    2. more
    1. u-siuiong.
    2. have-self-cultivation
    1. ‘This person has more self-cultivation.’
    1.  
    1. b.
    1. Yi
    2. he
    1. kha
    2. more
    1. u-gankong.
    2. have-vision
    1. ‘He has more vision.’

However, contra Francez & Koontz-Garboden (2015; 2017), Zhang (2019) and Li (to appear), it is found that the nominal allowed in the TSM u-N construction is not necessary to be an abstract property concept noun, as attested by (103a–d), where I still use the term uVD to gloss the morpheme u of the TSM u-N expression.

    1. (103)
    1. a.
    1. Kin
    2. this
    1. ni
    2. year
    1. kha
    2. more
    1. u-hootshui.
    2. uVD-rainwater
    1. ‘This year is more rainy than last year was.’
    1.  
    1. b.
    1. Kin
    2. this
    1. ni
    2. year
    1. yi
    2. s/he
    1. be
    2. sell
    1. kha
    2. more
    1. u-tshia.
    2. uVD-car
    1. ‘This year, s/he sells more cars.’
    1.  
    1. c.
    1. Tsit-le
    2. this-CL
    1. gin-a
    2. child-PRT
    1. kinalit
    2. today
    1. sia
    2. read
    1. kha
    2. more
    1. u-gi.
    2. uVD-word
    1. ‘Today, this child writes more words than he did yesterday.’
    1.  
    1. d.
    1. Ti
    2. on
    1. Autsiu
    2. Europe
    1. e
    2. E
    1. kosokkonnlo
    2. freeway
    1. khuann
    2. see
    1. kha
    2. more
    1. bo-TOYOTA.
    2. not-uVD-TOYOTA
    1. ‘People see fewer Toyota’s on the freeway in Europe.’

Thus, the relevant TSM data empirically challenges Francez & Koontz-Garboden’s (2017) proposal for the construction adopting the possessive morphosyntactic strategy for predicating gradable properties in the following aspects.

First, how does Francez & Koontz-Garboden (2017) account for the syntax and semantics of the TSM u-V construction, in which what follows the morpheme u with the literal meaning have is a verb rather than a PC nominal?

Second, can the semantic distinction between the PC nominals and other mass nouns be maintained?

My proposal for the TSM u-V construction can be further applied to the TSM u-N construction by making the following adjustments which clearly distinguish my proposal from Francez & Koontz-Garboden’s (2017) analysis.

First, in the TSM constructions adopting the possessive morphosyntactic strategy for predicating gradable properties (i.e., the TSM u-V construction and the TSM u-N construction), what occurs after the morpheme u with the literal meaning have is not limited to a nominal.

Second, assuming Chierchia’s (1998) claim that all nouns in Chinese and Chinese dialects are all mass nouns, elements measured by the measure function in the TSM constructions adopting the possessive morphosyntactic strategy for predicating gradable properties, including verbs and nouns, must be contained within a non-trivially structure domain.

Third, the u-N sequence in the TSM u-N construction is a compound noun.

Fourth, in the TSM u-N construction, the morpheme us ‘uVD’ has a semantic interpretation as in (104), in which α(x) is a set of entities denoted by the nominal, μ is a variable over the measure function of type <<e, t>, d> and A(μ) is the amount/quantity of the entities.

(104) usμA = λαλx.A(μ)(α(x))

Assuming these, a TSM u-N construction like (105a) has a syntactic structure like (105b), and its semantic composition can be demonstrated by (106a–j).

    1. (105)
    1. a.
    1. Tsit-le
    2. this-CL
    1. gin-a
    2. child-PRT
    1. pi
    2. than
    1. hit-le
    2. that-CL
    1. gin-a
    2. child-PRT
    1. sia
    2. write
    1. kha
    2. more
    1. u-gi.
    2. uVD-word
    1. ‘This child writes more words than that child.’
    1.  
    1. b.
    1. [S [NP Tsit-le
    2. this-CL
    1. gin-a] [[PP
    2. child-PRT
    1. pi
    2. than
    1. hit-le
    2. that-CL
    1. gin-a] [VP [V
    2. child-PRT
    1. sia] [NP [[Deg
    2. write
    1. kha]
    2. more
    1. [N u-[N gi]]]]]]].
    2. uVD-word
    1. ‘This child writes more words than that child.’
(106) a. ⟦[N gi/word]⟧A = λx.gi(x)
  b. usA = λαλx.A(μ)(α(x))
  c. ⟦[N us-gi/uVD-word]⟧A = λx.A(μ)(gi(x))
  d. ⟦[Deg kha/more]⟧A = λαλdλg.g(α) > d
  e. ⟦[NP kha us-gi/more uVD-word]⟧A = λdλx.A(μ)(gi(x)) > d
  f. ⟦[V sia/write]⟧A = λxλy.sia(y, x)
  g. ⟦[VP sia kha us-gi/write more uVD-word]⟧A = λdλy.sia(y, (єx[gi(x) & A(μ)(gi(x)) > d]))19
  h. ⟦[PP pi hit-le gin-a/than that-CL child]⟧A = dhlg
  i. ⟦[[PP pi hit-le gin-a] [VP sia kha us-gi]]/[[PP than that-CL child] [VP write more uVD-word]]⟧A = λy.sia(y, (єx[gi(x) & A(μ)(gi(x)) > dhlg]))
  j. ⟦[S tsit-le gin-a pi hit-le gin-a sia kha us-gi/this-CL child than that-CL child write more uVD-word]⟧A = sia(tsit-le gin-a, (єx[gi(x) & A(μ)(gi(x))> dhlg]))
    A(μ) is the quantity of gi ‘word’.

Simply put, the semantic distinction between the PC nominals and other mass nouns is not necessary for the TSM u-N construction. Why does this difference exist? Perhaps, what matters is the cross-linguistic parameter.19

5.3.2 Remarks on Wellwood (2015)

One important feature of Wellwood’s (2015) theory for comparative constructions is that “degrees are introduced by much, which semantically contributes a structure-preserving map from entities, events or states to their measures along various dimensions”. Assuming this, coffee in (107a), run in (107b) and hot in (107c) have (108a–c) as their corresponding interpretation.

(107) a. Al bought more coffee than Bill did.
  b. Al ran more than Bill did.
  c. Al’s soup is hotter than Bill’s is.
(108) a. ⟦coffee⟧A = λx.coffee(x)
  b. ⟦run⟧A = λe.run(e)
  c. ⟦hot⟧A = λs.hot(s)

Namely, in (108a), x ranges over elements of the domain of individuals; in (108b), e ranges over elements of the domain of events; in (108c), s ranges over elements of the domains of states.

Partially along the line of Wellwood (2015), I suggest that, in the TSM u-V construction, “degrees are (i) introduced compositionally, (ii) introduced by u ‘uVD’, which semantically contributes a structure-preserving map from events, states or time containment relations to their measures along various dimensions, and (iii) introduced not by any other expression”. This, then, makes my proposal for the syntax and semantics of the TSM u-V construction imply that the TSM morpheme us ‘uVD’ cannot introduce degrees for individuals (i.e., the denotation of nouns). However, as I have argued in Section 5.3.1, after making some adjustments, the analysis proposed for the TSM u-V construction can also be applied to the TSM u-N construction, in which the morpheme us ‘uVD’ introduces degrees for individuals. Nevertheless, the following empirical fact from TSM clearly indicates that the morpheme us ‘uVD’ cannot introduce degrees for some specific type of state (i.e., the state denoted by a gradable adjective), as the ungrammaticality of examples in (109) shows.

    1. (109)
    1. a.
    1. Hit-tsang
    2. that-CL
    1. tshiu-a
    2. tree-PRT
    1. kha
    2. more
    1. (*u)
    2.     uVD
    1. kuan.
    2. tall
    1.  
    1. b.
    1. Hit-le
    2. that-CL
    1. tsabogin-a
    2. girl-PRT
    1. kha
    2. more
    1. (*u)
    2.     uVD
    1. sui.
    2. beautiful
    1.  
    1. c.
    1. Tsang
    2. yesterday
    1. kha
    2. more
    1. (*u)
    2.     uVD
    1. kuann.
    2. cold

This distinction between the TSM morpheme us ‘uVD’ and the English much provides a good point to distinguish my proposal for the syntax and semantics of the TSM morpheme us ‘uVD’ from Wellwood’s (2015) proposal for the syntax and semantics of much.

First, Wellwood (2015) proposes the interpretation of much as in (110a), but the interpretation I propose for us ‘uVD’ is as in (110bi–ii), depending on whether the V of the u-V ‘uVD-V’ compound verb is a lexical or an aspectual verb.

(110) a. muchμA = A(μ)
  b. usμA = i. λxλα.A(μ)(α(x))
      ii. λαλQλy.A(μ)(α(Q(y)))

Namely, the denotation of the morpheme us ‘uVD’ I propose differs from the denotation of much suggested by Wellwood (2015) in the additional argument α(x) or α(Q(y)). This difference might result from the fact that the morpheme u ‘uVD’ occurs as a component of a compound verb.

Second, since TSM gradable adjectives do not need the morpheme us ‘uVD’ to introduce degrees for them, it is not implausible to say that (A) a TSM gradable adjective intrinsically carries a degree argument, and (B) the morpheme us ‘uVD’ cannot co-occur with a gradable adjective or verb.20 Thus, TSM, in some sense, provides empirical evidence in support of the degree-theoretic approach according to which gradable adjectives lexically specify measure functions while nouns and verbs do not.

Third, the ‘composition’ between the English much and a noun/verb/adjective is done at the level of syntax, but the ‘composition’ between the TSM morpheme u ‘uVD’ and a noun/verb is done at the level of lexicon.

Fourth, the TSM morpheme u ‘uVD’ differs from the English much in that the former triggers a valency change for the lexical verb with which it forms a stativized intransitive compound verb but the latter does not.

6 Concluding remarks

This paper investigates the syntax and semantics of the TSM u-V construction in depth. The main themes I have reached are as follows. First, the V of the u-V compound verb can be an aspectual verb or a non-gradable lexical verb. An aspectual verb does not bear any theta roles; therefore, there might not be a valency change for the V of the TSM u-V compound verb. Thus, the TSM u-V construction should not belong to the category of middles.

Second, in TSM, the morpheme us ‘uVD’ introduces degrees for concrete substance and property concept nouns and non-gradable verbs by contributing a structure-preserving map from entities, events, states or time containment relations to their measures along various dimensions; however, it does not introduce degrees for gradable adjectives. So, contra Wellwood (2015), I suggest that the degree-theoretic approach for comparatives is still needed.

Third, TSM also adopts the possessive morphosyntactic strategy for predicating gradable properties; however, the nominals involved can be a property concept nominal or other mass nouns. This makes TSM different from other languages in how to apply the possessive morphosyntactic strategy for predicating gradable properties (Francez & Koontz-Garboden 2017).

Abbreviations

ASP = aspect marker, ASV = aspectual verb, CL = classifier, E = marker for modifying phrases, PRT = particle, QILAI = directional complement, SFP = sentence final particle. Besides, nasalization of vowels is signaled by –nn, and will be left unspecified if it is predicted by nasal initials.

Notes

  1. Seven native speakers of TSM, with their ages ranging from thirty-eight to eighty-eight, are consulted about the grammaticality of the data discussed. [^]
  2. As Lien (2010) points out, except the semantic distinction between affirmation and negation, the u-V ‘have-V’ expression and its negative counterpart (i.e., the bo-V ‘not-have-V’ expression) are parallel to each other in morphosyntax and semantics. Hence, I assume my proposal for the syntax and semantics of the morpheme u ‘have’ can be applied to that of its negative counterpart. So, examples with a bo-V ‘not-have-V’ expression will not be discussed in the rest of this paper. [^]
  3. Lien (2010: 1283), without providing any supporting evidence, simply claims that the marker u ‘have’ in examples like (2) is an adverb of intensifier. [^]
  4. Xiong (2018) claims that mental and stative verbs are not allowed in the Chinese qilai middle (Fagan 2009: 97).
      1. (i)
      1. *Xiaohaizi
      2.   child
      1. ai
      2. love
      1. qilai
      2. QILAI
      1. hen
      2. very
      1. rongyi.
      2. easy
      1.    ‘Intended: Children love easily.’
    [^]
  5. As Fagan (2009) and Xiong (2018) argue, stative and achievement verbs are banned from middle formation. Besides, example (i) is a case where potsiong ‘guarantee’ is used as a stative verb.
      1. (i)
      1. Hualut
      2. law
      1. potsiong
      2. guarantee
      1. ginbin
      2. people
      1. e
      2. E
      1. singbiann
      2. life
      1. ka
      2. and
      1. tsaisan.
      2. property
      1. ‘The law protects people’s life and property.’
    [^]
  6. Marelj (2004) as well as Xiong (2018) claims that the source/goal role of distransitive verbs cannot occur as subject in a middle construction. [^]
  7. One of the features that distinguish the compound u-V from the phrasal u-V, as Yang (1991: 234, 236) argues, is that the former expresses a degree reading while the latter expresses the aspectual meaning of event realization. [^]
  8. In Section 4.2.2, I will argue that example (45a) actually has a syntactic structure like (i), in which one of the two consecutive u’s (i.e., the morpheme u ‘uVD’ and the aspectual verb u ‘the realization aspect’) is haplologically eliminated at the phonetic level due to their phonetic identity.
      1. (i)
      1. Yi
      2. he
      1. tsuekin
      2. recently
      1. kha
      2. more
      1. [ASVP [[ASV
      2.  
      1. u-[ASV u]]
      2. uVD-ASV
      1. [VP [[V
      2.  
      1. lim]
      2. drink
      1. [NP
      2.  
      1. kapi]]]]].
      2. coffee
    So, in (45a), the u-Vnvc expression actually takes a VP complement rather than an NP complement. [^]
  9. According to Chierchia (1989) and Reinhart (1996), two operations on unbound semantic argument variables are available. That is, the unbound semantic argument variables can be bound by a semantic operator (i.e., OP) or completely removed from the semantic representation. The former operation is called argument saturation while the latter is called argument reduction, as shown by (i) and (ii), respectively.
    (i) y P<x, y>) (a) → (λy OPx P<x, y>) (a) (Saturation)
    (ii) y P<x, y>) (a) → (λy P<y>) (a) (Reduction)
    they further suggest, argument saturation yields the middle interpretation, whereas argument reduction is responsible for the anticausative and inherent reflexive interpretations. [^]
  10. As one anonymous reviewer reminds me, in order not to create (ontological) confusion, it would be better to state things in terms of events here. So, I assume the valency of a verb contains an eventuality argument v with the type of event. [^]
  11. I assume there is only one ums, which compositionally changes the denotation of V of the u-V compound verb into a set of events. So, (49bi–iii) are allomorphs of the morpheme ums, and they only differ from each other in which argument or adjunct is selected as the syntactic subject. Besides, I use the term ‘Property’, which means ‘a property of an event’ in the semantic term or ‘an adjunct’ in the syntactic term to represent the predicate modification relation between the eventuality argument v and the non-thematic argument variable w. This predicate modification relation is subject to Beck’s (2005: 34) Generalized Predicate Modification:
    (i) If α = [β γ] and β’ is of type <e, <i, t>> and γ’ is of type <e, <i, t>>, then α’ = λxλe.β’(x) & γ’(x)(e)
    [^]
  12. The TSM aspectual verb u ‘the realization aspect’ and the TSM morpheme u ‘uVD’ of the u-V compound verb are two morphemes with different properties in syntax and semantics. [^]
  13. Here, I use the notion of event time rather than situation time to avoid ontological confusion. [^]
  14. In (58a–b), the capital E represents a set of events, the subscript v is the type of event and the subscript k is the type of topic time (i.e., t). [^]
  15. I treat the morpheme kha ‘more’ as the TSM counterpart of the English comparative morpheme -er because the obligatory element kha ‘more’ provides the ‘explicit comparison’ meaning for a TSM comparative construction, as (i) shows.
      1. (i)
      1. Yi
      2. s/he
      1. (pi
      2. than
      1. li)
      2. you
      1. *(kha)
      2.     more
      1. kuan.
      2. tall
      1. ‘S/He is taller (than you).’
    Bartsch & Vennemann (1972) and Kennedy (1999), I further suggest kha ‘more’ has an interpretation like (ii), where γ ranges over measure functions, d is provided by the standard of comparison and a may be an individual of type e.
    (ii) λαλdλg.g(α) > d
    However, as (67e) shows, the denotation of [V us-tsioms] already contains a measure function (i.e., A(μ)). So, kha ‘more’ that occurs in the TSM u-V construction has a denotation like (iii).
    (iii) λαλd.a > d
    [^]
  16. Thanks to one anonymous reviewer for reminding me that the ‘amount of money lent’ reading is at best an implicature. The ‘implicature’ status of the ‘amount of money lent’ reading can be verified by its cancellability, as shown below.
      1. (i)
      1. Bo
      2. not
      1. m-tio,
      2. incorrect
      1. bikim
      2. dollar
      1. pi
      2. than
      1. auguan
      2. euro
      1. kha
      2. more
      1. u-tsio,
      2. uVD-lend
      1. m-ko
      2. but
      1. sanntsap
      2. thirty
      1. pi
      2. sum
      1. bikim
      2. dollar
      1. e
      2. E
      1. sohbok
      2. amount
      1. pi
      2. compare
      1. be
      2. not
      1. kue
      2. cross
      1. gitsap
      2. twenty
      1. pi
      2. sum
      1. auguan
      2. euro
      1. e
      2. E
      1. sohbok.
      2. amount
      1. ‘Yes, the number of the events of lending dollars to someone is larger than the number of the events of lending euros to someone; however, the amount of the thirty sums of dollars lent is less than the amount of the twenty sums of euros lent.’
    And, the ‘derivation’ of the implicature must be subject to Grice’s (1975) conversational maxims. [^]
  17. Thanks to one of the anonymous reviewers for reminding me of this. [^]
  18. Example (91a), (91b), (91d) and (91e) all involve haplology at the phonetic level because the morpheme u/bo ‘uVD/neg-uVD’ and the aspectual verb are phonetically identical. [^]
  19. Along the line of Wellwood (2015: 75), here I suggest there exists a Hilbert’s є operator to bind the variable x in (106g). [^]
  20. Example (109a–c) seem to provide evidence for the assumption that u ‘uVD’ is the TSM counterpart of English much in that they both cannot directly precede an adjective (Bresnan 1973).
    (i) *John is so much intelligent.
    However, it would be too hasty to claim that the morpheme u ‘uVD’ is the TSM counterpart of the English much simply based on the ungrammaticality of (i) and (109a–c). As (ii) shows, much, when directly preceding a so-pronominal, can be modified by a degree adverb like too (Corver 1997).
    (ii) John is fond of Mary. Maybe he is too much so.
    However, the same does not happen to the TSM u ‘uVD’, as (iii) illustrates.
      1. (iii)
      1. Thaoke
      2. boss
      1. tui
      2. to
      1. guankang
      2. employee
      1. tsiok
      2. very
      1. tangsng
      2. stingy
      1. e,
      2. SFP
      1. tampetkong
      2. frankly-speaking
      1. thaoke
      2. boss
      1. siu
      2. too
      1. (*u)
      2.     uVD
      1. hit-le.
      2. that-CL
      1. ‘Intended: The boss is very stingy with his employees. Frankly speaking, the boss is too much so.’
    [^]

Acknowledgements

I am indebted to Chin-Fa Lien, Ying-Hsiung Chou, Chung-Hao Ku and Ting-Chi Wei for crosschecking the data used in this study for grammaticality judgments, and Hsiu-Chen Liao and Yi-Hsun Chen for their timely and helpful consultation which significantly improves the semantic part of this study. Parts of this paper have been presented in Guangdong University of Foreign Studies and National Tsing Hua University. I would like to thank the audiences there, especially Wei-Wen Roger Liao, Chin-Fa Lien, Tzong-Hong Lin, Hongyong Liu, Haihua Pan, Dingxu Shi, Sze-Wing Tang, Yang Yang and Qingwen Zhang, for their stimulating questions and suggestions. Moreover, I want to express my immense gratitude to the three Glossa reviewers for their rigorous but constructive comments and inspiring suggestions at various stages of this study which bring the paper into a more readable state than it otherwise would have been. I have learned a lot from them. The thoughtful comments and editorial help from Glossa, especially Waltraud Paul, also improved the content and presentation of this work considerably. Added to these, I gratefully acknowledge the research Grant MOST108-2410-H-009-004 from the Ministry of Science and Technology, Taiwan. Finally, any errors or inconsistencies that have persisted, of course, are my responsibility.

Competing Interests

The author has no competing interests to declare.

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