4.1.1 The morphosyntactic function of U_ms

In the TSM u-V construction, the morpheme u ‘u_VD’ 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 ‘u_VD’ has the following morphosyntactic functions:

First, in order to stativize the V, the morpheme u_ms 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

Second, if the unsaturated external argument and internal argument(s) of V are all bound by a generic operator, the morpheme u_ms 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).

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-V_vc 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 u_ms 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-V_vc compound verb, the interpretation of the morpheme u_ms can be represented as follows.¹¹

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

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

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).

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

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).

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 u_ms ‘u_VD’ is nullified. However, u_ms ‘u_VD’ 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 V_ASVms to represent the aspectual verb derived from applying the morphosyntactic function of u ‘u_VD’ to the aspectual verb V_ASV.)

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

4.1.2 The degree semantics of U_s

Partially along the line of Wellwood (2015), I suggest that the morpheme u_s, 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 u_s of type μ when discussing the degree introducing function of the morpheme u ‘u_VD’.)

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 ‘u_VD’, 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-V_vc and the u-V_nvc 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-V_vc construction, and, then, I deal with the syntax and semantics of the u-V_nvc construction.

4.2.1 The u-V_vc construction

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

If the V is a lexical verb, the morpheme u_ms, 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.

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

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 ‘u_VD-lend’ with the morpheme u ‘u_VD’ 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 ‘u_VD-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 ‘u_VD-lend’ and, then, moves to the subject position.

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, ⟦u_ms⟧^A represents the morphosyntactic function of u ‘u_VD’, ⟦tsio_ms/lend_ms⟧^A, for example, represents the set of lending events denoted by the verb tsio ‘lend’ after it undergoes the morphosyntactic process induced by u ‘u_VD’, ⟦u_s⟧^A represents the semantic function of u ‘u_VD’, and ⟦u_s-tsio_ms/u_s-lend_ms⟧^A is the denotation of the intransitive compound verb u-tsio ‘u_VD-lend’.¹⁵

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 ‘u_VD-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 ‘u_VD-wash’ (i.e., tsit-nia sann ‘this-CL clothing’) occurs in the specifier position of VP projected by the compound verb u-se ‘u_VD-wash’ and, then, moves to the subject position.

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

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 u_ms, 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 ‘u_VD-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., se_ms ‘wash’) has a semantic representation as in (70).

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 ‘u_VD-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 ‘u_VD-wash’ and, then, moves to the subject position.

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

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.

In (73), the morpheme u_ms ‘u_VD’ 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 tsau_ms ‘wash’ has an interpretation as in (74).

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

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 ‘u_VD-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).

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-V_nvc construction

My proposal for the syntax and semantics of the TSM u-V_nvc construction can be exemplified as follows. On one hand, an u-V_nvc 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).

Namely, what forms the u-V compound verb with the morpheme u ‘u_VD’ 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 ‘u_VD’ 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.

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

As the same reasoning, I suggest that what forms the u-V_nvc compound verb with the morpheme u_ms 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 u_ms.

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).

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 u_ms is nullified. However, u_ms 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 u_ms (i.e., u_ASVms) has an interpretation as in (58a), repeated as (82).

Namely, after the combination with an argument P, which denotes a set of events, and a topic time t, u_ASVms 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).

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).

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.

5.3.1 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.

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.

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).

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.

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.

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’).

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)).

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 u_VD to gloss the morpheme u of the TSM u-N expression.