2.1 Distribution of -wán and -diào

The RVC predicates grammatically behave quite similar to normal verbs. For example, they can be passivized:

They can be used in future tense and with deontic modals, in which case -le is not used:

The resultative morphemes can be used with predicates taking NP objects with quantifiers:

Moreover, the resultative morphemes cannot co-occur regardless of -le:

There are many proposals for -le in the literature, including perfective aspect marker, relative past tense marker, verbalizer, neutral resultative marker, quantity marker, etc. The most common view nowadays is that it is a perfective aspect marker. According to Li & Thompson (Reference Li and Thompson1981), -le is a perfective aspect marker which expresses boundedness. It could be temporal boundedness, spatial boundedness, and a kind of boundedness in an abstract sense. However, this analysis makes several incorrect predictions for the data. For example, as pointed out by Klein et al. (Reference Klein, Li and Hendriks2000), if -le expresses boundedness, then we should expect that -le and resultative morphemes like -wán and -diào are incompatible since the resultative morphemes also indicate boundedness for the event. Moreover, the analysis should predict that with -le the accomplishments should entail culmination, and that -le and for- adverbialsFootnote ⁴ are generally incompatible if boundedness entails telicity. But none of these predictions is borne out.

In this study, I follow the typological observation from Comrie (Reference Comrie1976), which says that in many languages, the perfective aspect marker is also a marker of relative past tense (as opposed to absolute past tense) – also see Ross (Reference Ross1995) – for such a dual analysis for -le (see Sybesma Reference Sybesma1997; Wang Reference Wang2018, among others, for alternative proposals), and assume that when used with the resultative morphemes, the suffix -le is a relative past tense marker. This view is also motivated by the fact that without -le, the sentence is non-finite, regardless of the resultative morpheme, as shown in (11), and when -le is used, a past tense interpretation is obtained by default.

So, in this study I assume that -le is a relative past tense marker. However, following the general literature, I gloss it as a perfective marker.

2.2 Termination and culmination

A termination predicate ensures termination of an event, entailing that the event stops progressing at some particular time. It presupposes that the event the verbal predicate denotes has duration, otherwise there would be no event progress to terminate. A culmination predicate ensures completion of an event with respect to the patient, entailing that the patient undergoes a change of state completely. It presupposes a certain quantity of patient, whose complete affectedness defines the delimitation of culmination of an event. The two types of predicates are illustrated below with the data involving -wán and -diào.

First, if a predicate P entails termination of an event, then when put in a temporal sequence with another event, the former must fully precede the latter. Therefore, if -wán expresses termination, then when combining it with an eventive predicate the denoted event must fully precede another event that occurs in temporal sequence. Consider the discourse in (12). It consists of two sequential events, one that Mary ate a certain amount of apples and the other that she wanted to eat a banana.

This discourse gives rise to the inference that the event of Mary eating apples has terminated before she wants to eat a banana. The first event fully precedes the second one. The morpheme -diào shows similar pattern with -wán in this respect, also giving rise to an inference of full precedence. Consider the discourse in (13).

This discourse entails that the event of eating up the apple fully precedes the event of wanting to eat a banana.

Second, if a predicate P entails culmination, then there is a non-cancelable inference that the relevant result state has obtained. Therefore, if -diào expresses culmination, then when it is combined with an eventive predicate, the denoted event must entail that the result state with respect to the patient is obtained. This can be verified by the following discourse.

In this example, the bare noun object píngguǒ ‘apple’ has a definite reading, which is an effect of the meaning of -diào, and it entails that the apple must be consumed entirely. Culmination is also entailed if the object is yī-gè píngguǒ ‘one apple’. The discourse is unacceptable because it is contradictory. The morpheme -wán implies culmination with respect to the patient as well. Consider (15).

This discourse is unacceptable regardless of whether the object is a classifier construction or a bare noun. When the object is yī-gè píngguǒ ‘one apple’, the interpretation is that the apple was consumed entirely, so the discourse is contradictory. When the object is a bare noun píngguǒ ‘apple’, which refers to an unspecified amount of apples, the interpretation is that the amount of apples was consumed entirely. The noun phrase liǎng-kǒu ‘part of some food’ in the second sentence is anaphoric, referring to part of the amount of apples denoted by the bare noun píngguǒ ‘apple’ in the first sentence. So the discourse is contradictory as the first part entails culmination with respect to an unspecified amount of apples while the second part contradicts the culmination inference.

Third, since most events terminate at a particular time point regardless of whether they are denoted by predicates that have an inherent endpoint or not, we should expect that -wán can be combined with eventive predicates that have no inherent endpoints as well. The prediction is borne out. First consider the case of activity verbs. An example is provided in (16) where -wán is combined with the activity verb xiào ‘laugh’.

The morpheme -wán is also compatible with semelfactives, which may refer to a single-event activity or a multiple-event activity (Smith Reference Smith1997: 29–30). However, the interpretation is somewhat coerced into activity. Consider the example in (17), which normally has an iterative interpretation. It also allows an interpretation of a single-event activity. However, in this case, the interpretation is that the predicate qiāo-mén ‘knock on the door’ describes a series of phases surrounding the act of knocking on the door rather than the instantaneous act of knocking.Footnote ⁵ We can see such an effect of coercion from the case where the aspectual expression yíxià ‘once’ is overtly used, as shown in (18). The sentence in (18) is acceptable but it cannot be used to describe the situation where the person rapidly knocked twice on the door.

Fourth, since termination presupposes duration for the event, we may expect that -wán cannot be compounded with achievements since instantaneous events denoted by achievements have no duration. This is also borne out. Consider (19) which involves the achievement verb dào ‘arrive’. The sentence is unacceptable if the verb dào ‘arrive’ is compounded with -wán.

Fifth, a terminative predicate takes a dynamic eventive predicate as its complement, and thus we should expect that it is incompatible with stative predicates.Footnote ⁶ This is largely true with the use of -wán. Consider an example in (20) where -wán is compounded with the stative verb zhōngchéng ‘be loyal to’.

However, it is notable that compounding -wán with a stative predicate is not entirely excluded in Chinese. Such combinations can be licensed by some pragmatic rule. In such a case, the purpose of using such expressions is not to convey the literal meaning that a certain state stops holding at a particular time, though it does convey the literal meaning, instead, it creates certain pragmatic effect that a non-literal meaning is what the speaker intends to convey. An example is provided in (21).

In this example, the speaker is being sarcastic. The sentence literally says the state that John is loyal to this boss stopped holding at a particular time when he became loyal to that boss, and what the speaker is trying to convey is that John is a person who has no loyalty to his boss. To account for the compounding behavior with statives, I assume that -wán does not just require durative but also dynamic property for the predicate it is compounded with, so it is normally incompatible with statives but the compounding can be licensed by some pragmatic condition.

Finally, note that the morpheme -diào is semantically more restricted than -wán in forming RVC constructions. While -wán can be compounded with almost any eventive verb as long as the event in the denotation has duration, -diào is usually restricted to the type of eventive predicates which denote the kind of events in which the patient disappears at the end. For example, other than consumption verbs such as chī ‘eat’ and hē ‘drink’, the verbs that -diào is commonly combined with include transitive verbs such as shāo ‘burn’, cā ‘wipe’, rēng ‘throw’, kǎn ‘cut’, chōng ‘flush (with water)’, mài ‘sell’, shā ‘kill’, and pòhuài ‘destroy, damage’, as well as intransitive verbs such as pò ‘break’, zǒu ‘walk, leave’, and pǎo ‘run’. The range of eventive predicates it may combine with also varies across Chinese dialects (Chao Reference Chao1968: 466). Note that diào can also be used as a contentful intransitive verb which literally means ‘drop’. So when it is used as an RVC morpheme, it seems that the requirement that the patient disappears as the result of the event is a metaphoric use of the literal meaning ‘drop’, for example, the food is conceptualized as having been ‘dropped’ or gone at the end of a consumption event. Also note that -diào is not restricted to the kind of events where a physical change of state occurs, as shown by these examples, but it can also be used in an abstract sense of change of state. In the current study, I limit my concern to the cases where incremental themes are involved in which the patient is physically affected such as a consumption event.

To sum up, in this subsection, I characterize termination and culmination predicates informally and show with Chinese data how they might be attested. However, the purpose of the current study is not to analyze termination and culmination as formal notions. Instead, the purpose is to show that there are two different avenues to telicity, which are revealed to us by the meanings of -wán and -diào, and propose an analysis accordingly. So next we return to telicity.

3.1 Krifka’s model on aspectual composition

Krifka (Reference Krifka, Bartsch, van Benthem and van Emde Boas1989, Reference Krifka, Sag and Szabolcsi1992, Reference Krifka and Rothstein1998) proposed a model to account for the influence of reference types of nominal arguments on temporal properties of verbal predicates. He connected two types of predicates in the nominal domain to the contrast between telic and atelic predicates in the verbal domain by proposing a contrast between two types of predicates, namely, cumulative and quantized. A cumulative predicate is such a predicate that if the predicate can apply to both entities, it can apply to their sum. A quantized predicate is such a predicate that if the predicate applies to x, it cannot apply to a subpart of x. The definitions of the two predicates are provided in (22) and (23) respectively (Krifka Reference Krifka and Rothstein1998: 200).

In the nominal domain, a cumulative predicate can be a mass noun (e.g. beer) or a bare plural noun (e.g. books) since two quantities of beer (or books) are still beer (or books). A nominal quantized predicate can be a count noun (e.g. a book) or a noun phrase that specifies the quantity of the entity (e.g. a glass of beer) since the two predicates cannot apply to a subpart of the entities they denote. This distinction is also reflected in the verbal domain and the cumulative/quantized referential property of the object is correlated with the aspectual property of the eventive predicate. When a verb like eat is combined with a cumulative noun phrase like apples, it yields an atelic predicate as in (24a), which is cumulative since two events of eating apples is still an event of eating apples. When the verb is combined with a quantized noun phrase like an apple, it yields a telic predicate as in (24b), which is quantized since a proper part of an event of eating an apple is not an event of eating an apple.

This correlation between the referential type of the object and the aspectual property of the verbal predicate is explained in terms of an effect of a homomorphic relation between two part structures that formally characterize object and event. The internal arguments of verbs like drink and eat are characterized as bearing a special thematic role called incremental theme (Dowty Reference Dowty1991). The homomorphic θ-relation relates the extent of the incremental theme to the progress of the event by tying each part of the incremental theme with a corresponding part of the event so that the homomorphism allows transferring of mereological properties between the two structures. To have more specific properties for incremental relations, homomorphism further requires the thematic role of incremental theme to have a number of properties, including uniqueness of objects, uniqueness of events, mapping to subevents and mapping to subobjects. These properties are collapsed into two properties mapping to unique subobjects and mapping to unique subevents in Beavers (Reference Beavers, Demonte and McNally2012: 28) and the definitions are repeated in (25). Note that these properties define a strict homomorphism θ that Krifka called strictly incremental relation (SINC), which, as Beavers pointed out, is an isomorphism of subparts that defines being an incremental theme.

The MUSO and MUSE properties ensure a strict one-to-one mapping between the proper parts of e and the proper parts of x. It predicts that the event predicate like in (26) is quantized, or telic.Footnote ⁷

For an event e of drinking a glass of wine x, any proper subpart event e′ ⊂ e is an event of drinking a proper subpart of the glass of wine x′ ⊂ x, by the SINC that holds between e and x. However, a glass of wine has quantized reference, therefore no x′ satisfies this description. This means that no e′ ⊂ e satisfies the description of drink a glass of wine since e′ is an event of drinking less than a glass of wine. So according to the definition of quantized predicate in (23), drink a glass of wine is quantized (and also telic). SINC also predicts that the event predicate like drink wine is cumulative, or atelic.

For an event e of drinking some amount of wine x, any proper subpart event e′ ⊂ e is an event of drinking a proper subpart of that amount of wine x′ ⊂ x by the SINC that holds between e and x. Since wine has cumulative reference, x′ satisfies this description. So e′ ⊂ e satisfies the description of drink wine. Given the definition of cumulative predicate in (22), drink wine is cumulative, or atelic.

The analysis predicts that event predicates like push a cart are not telic, though the nominal predicate is quantized. The explanation provided by this model is as follows: for a subevent of an event of push a cart, there is no proper part of the object a cart that is the patient of a subevent of the event push a cart. Instead, the patient of the subevent is the same as the patient of the event. In other words, the non-quantized property of the event predicate push a cart is due to that the verb push does not assign the thematic role of incremental theme to its internal argument. Therefore, the difference between eat x and push x boils down to the difference in the thematic role each verb assigns to x.

So far, the analysis can provide an adequate account for events where a subpart of the patient is isomorphically related to a unique subpart of the event, for example, eat an apple. However, it is inadequate to account for events such as read a book where some subparts of the patient can be affected iteratively. To deal with this issue, Krifka made a distinction between two types of homomorphism, namely the strict incremental relation (SINC) and the incremental relation (INC). The SINC is an isomorphism of subparts which consists of the two properties defined in (25). In this case, progress of an event is isomorphically related to the extent of the incremental theme, so each subpart of event corresponds to a unique subpart of the theme, and event ends when the theme is entirely affected. By contrast, in the case of INC, an event is incrementally related to the theme in such a way that some subparts of the theme can be affected more than once, so some subparts of an event may correspond to the same subparts of the theme of some other subparts of the event. In the former case, each subpart of the object is a theme of a unique subpart of the event; in the latter case, a subpart of the object can be mapped to more than one subpart of the event.

In Krifka (Reference Krifka and Rothstein1998), he further extended the analysis to account for motion events such as walk from the university to the capitol. He treated paths of motion as incremental themes as well and defined a θ-relation called strict movement relation (SMR) which is isomorphic in subparts, relating the event e to the path p in their subparts. SMR also preserves the spatial/temporal adjacency: two subparts of e in temporal adjacency corresponds to two subparts of p in spatial adjacency, and vice versa.Footnote ⁸

Krifka’s model has received a number of criticisms as it is insufficient to account for a number of empirical linguistic phenomena, and subsequent analyses have been proposed to tackle these issues. Below I will review one of these studies, which will lead to the analysis I propose for the telicizing morphemes of -wán and -diào.

3.2 Zucchi & White’s (Reference Zucchi and White2001) maximal participants

Zucchi & White (Reference Zucchi and White2001) noted that Krifka’s account for telicity is problematic if the object is an indefinite noun phrase like a sequence, a twig, and some Ns. According to Krifka’s definition of quantization, such nominal predicates are not quantized since, for example, a subpart of a sequence is still a sequence and a subpart of some Ns is still some Ns. However, these nominal predicates yield quantized verbal predicates. For example, write a sequence is compatible with in- adverbs but not for- adverbs.

They argued that the assumption that the quantizing effect of NPs of the form an N follows from the fact that the predicate N itself is quantized is problematic. It is not just that it cannot explain why NPs like a sequence yield the quantizing effect but also it ignores our intuition that the fact that plural indefinites of the form some Ns (as well as some other forms of NPs such as most Ns and less than n Ns) yield the same effect should be explained by the same reason.

In their solution to the problem of Krifka’s analysis, they still assumed the model and maintained the idea that quantization leads to telicity.Footnote ⁹ The intuition that motivates their analysis is that an event of writing a particular object x, be it a sequence or a letter, does not have events of writing x as proper parts. In other words, the referent of the object is all the relevant patients involved in the event that the speaker refers to. For example, for an event of John’s writing a sequence, the reference of the object is for all intents and purposes a kind of specific reference, i.e. John wrote a specific thing at a reference time t_r that is a list of ordered numbers. Since no proper subpart of a specific sequence involved in a particular writing event is the same sequence, then the predicate write a sequence is quantized because given the property of mapping to unique subobjects and mapping to unique subevents defined in (25), no proper subpart of an event of writing a given sequence is the same event of writing that sequence at the reference time t_r. In this analysis, the noun phrase is treated like a definite noun phrase which denotes the maximal entity involved in the event.

They modified the definition of quantized predicate and included an assignment function to keep the assignment of individuals fixed. The definition is presented below, where the individuals include both events and ordinary individuals (Zucchi & White Reference Zucchi and White2001: 236).

According to this definition, nominal predicates like a sequence and a letter are quantized in the sense that the specific individual, a sequence or a letter, for a single assignment, has no proper part that the predicate can apply to. They also defined a Max relation, which is encoded in the meaning of quantifiers, to handle the specific individuals involved in an event, which they call maximal participants (Zucchi & White Reference Zucchi and White2001: 254):

Now consider the example of write a letter. The translation provided by Zucchi & White (Reference Zucchi and White2001: 259) is presented in (31).Footnote ¹⁰ The Max operator is introduced by the indefinite quantifier.

According to Zucchi & White (Reference Zucchi and White2001), there might be more than one maximal element in the denotation of Max(λz∃e′[write(e′) ⋀ ag (y, e′) ⋀ pat (z, e′) ⋀ letter′(z) ⋀ τ(e′)⊆t_r], x) since any singular letter that was written during the interval t_r is counted as a maximal element. But the denotation of the predicate write a letter as in (31) is restricted to a writing event whose patient is a singular letter at t_r. Given that the object role of write has the property of mapping to objects, a proper subevent e′ of the event of writing a given letter is not an event of writing that letter since a proper subpart of a given letter is not itself. This means that e′ is not in the denotation of write a letter. Therefore, according to the definition of quantization, write a letter is quantized.

Zucchi & White (Reference Zucchi and White2001) also provided an account for the quantization puzzle. For example, for the semantics of DPs like most Ns, they assume that they denote a generalized quantifier that takes the verb as an argument and the verb’s patient argument is saturated by a variable that picks the maximal participants with respect to the reference time t_r, which is conditioned by the cardinality being greater than one half of the total number. The representation of most letters they provided is repeated as follows (Zucchi & White Reference Zucchi and White2001: 254):

Thus the nominal predicate most letters introduces a set of letters which are the maximal participants in some event described by its first argument P. Translation of the event predicate write most letters they provided is repeated as follows (Zucchi & White Reference Zucchi and White2001: 254):

This analysis predicts that write most letters is quantized. Assuming that the object of write is an incremental theme which has the property of mapping to objects, the maximal sum of letters written by an agent during a given reference time has no proper part which is also the maximal sum of letters written during the reference time, and thus the event of writing such a maximal sum of letters during the reference time does not have a proper part that is an event of writing the maximal sum of letters during the reference time. Therefore, the predicate write most letters is quantized.

Zucchi & White (Reference Zucchi and White2001) also extended their analysis to account for activity predicates such as rule most countries in terms of maximal participants. The atelicity of such an activity predicate is accounted for as follows: the patient of an event of ruling most countries is the sum of all the countries ruled at reference time t_r. But since rule does not have the property of mapping to objects, a subevent may have as its patient the same sum of countries that are ruled at reference time t_r, therefore the predicate rule most countries is not quantized.

However, Rothstein (Reference Rothstein2004: 152–154) pointed out that this analysis may fail to predict atelic readings for activity predicates which have maximalization as part of the meaning of the object. One of her illustrating sentences is provided as follows (Rothstein Reference Rothstein2004: 153).

Zucchi & White’s (Reference Zucchi and White2001) analysis makes the incorrect prediction that this sentence is telic. In a possible context where John has been buying up houses on this street incrementally, the event of owning 30 out of 40 houses during the reference time has a subevent of owning 29 houses, both of which can be described as owning more than half the houses but have different maximal sum of participants. Therefore, according to Zucchi & White’s (Reference Zucchi and White2001) analysis, it is a telic predicate. Yet it is atelic. Thus Rothstein (Reference Rothstein2004) concluded that quantization of the theme argument does not determine telicity of accomplishment predicates. However, Beavers (Reference Beavers, Demonte and McNally2012) noted that this conclusion is too strong. He pointed out that what seems to be relevant for quantized theme arguments calculating telicity is whether the verb introduces incrementality, and own does not.

In the next section, I first provide an analysis for the two telicizing RVC morphemes -wán and -diào under the framework defined by Krifka and assuming the remedy provided by Zucchi & White (Reference Zucchi and White2001), and then present a short account for the non-culmination reading of non-RVC accomplishments in Chinese.

4.1 Analyzing -wán

The proposed analysis for -wán is based on the assumption that event time is a semantic argument of an eventive predicate. It is reasonable to treat event time as one of the semantic arguments of a verbal predicate, though it is apparently different from a regular semantic argument. As pointed out by Krifka (Reference Krifka and Rothstein1998), a predicate establishes a relation of a specific type between some number of semantic arguments, and the number and types of the semantic arguments involved in a predication may vary in different cases. For example, the sentence John slept establishes a sleep-type relation between the individual John and some event; Mary ate the apple establishes an eat-type relation between Mary, a particular apple, and some event; and John walked from the campus to the capitol establishes a walk-type relation among John, some event, and some path in space between the campus and the capitol. A semantic argument might be expressed by a syntactic argument such as the subject and the object, and it might also be expressed by a syntactic adjunct such as from the campus to the capitol. Krifka did not consider event time as a semantic argument; however, for the purpose of the current study, I propose that we may take event time as a semantic argument.

In the semantic representation, we may treat event time as a special semantic argument like the semantic argument of event e we normally assume for a verbal predicate in the (neo-)Davidsonian approach to verb meaning, that is, it is saturated by existential closure at the end of composition. For example, the translation of the verb chī ‘eat’ is represented as follows:

In this representation, the eventive predicate chī ‘eat’ is analyzed as a four-place relation that relates a patient x, an agent y, and an event time t to an event e. Event time is defined as the run time of the denoted event, which is the output of the temporal trace function τ mapped onto the domain of event.

The proposed analysis for -wán is an extension of the maximal participant account proposed by Zucchi & White (Reference Zucchi and White2001) from the domain of entity of patient to the domain of entity of time. I propose that -wán presupposes the predicate it applies to is durative and dynamic, and it denotes a function that maps the event time onto a maximal set of times, which I call the maximal time participant. The representation of -wán that I propose is presented as follows:Footnote ¹¹

The translation says that -wán is a function that takes a durative, eventive predicate as its argument and saturates the predicate’s time argument with a variable that picks out the maximal time interval involved in the event at reference time t_r.

I propose that -wán structurally applies at the level of VP denotation. The structure is shown in (38) where I assume certain movements occur in PF, giving rise to the observed word order at the surface level.

The reason why I assume -wán applies at the VP level rather than the V level is that it makes a right prediction about the data. If we assume it applies at the VP level, it predicts that -wán cannot co-occur with the progressive formative (zhèng)zài, provided that -wán is an aspectual marker (‘outer aspect’), which moves to the functional projection of AspP in PF. This is because formal expressions of members that belong to the same category should be in complementary distribution (see Filip & Rothstein Reference Filip, Rothstein, Lavine, Franks, Filip and Tasseva-Kurktchieva2005 for the same reasoning for the aspectual expressions in Slavic languages). Both the progressive formative (zhèng)zài and -wán belong to the category of outer aspect, and thus they should not co-occur. This prediction is borne out. Consider (39).

By contrast, as shown below, -diào applies at the V level (or ‘inner aspect’), and the analysis successfully predicts that it is compatible with the progressive form.

The analysis of -wán makes another valid prediction about the data. It predicts that we cannot apply -wán to the VP telicized by -diào because it would amount to telicizing what already is a telic predicate, but this kind of aspectual operation is generally excluded, for example, the application of progressive to a progressive form generally results in ungrammatical expressions: *John was being running (Filip & Rothstein Reference Filip, Rothstein, Lavine, Franks, Filip and Tasseva-Kurktchieva2005). This prediction is borne out. Consider (10), which is repeated in (40).

As mentioned above, I assume that -le is largely a relative past tense marker when used with RVC predicates. I adopt the tense rule formulated by Zucchi & White (Reference Zucchi and White2001: 250) as the denotation for -le, which is presented as follows.

The representation says that past tense is a precedence relation held between the reference time t_r, which contains the runtime of the denoted event, and the speech time. Note that Zucchi & White (Reference Zucchi and White2001) used the same variable t_r for the reference time introduced by the tense node as the one introduced in the Max operator. This follows the common treatment of tense in DRT, that is, using the same variable for the reference time at various stages when constructing the semantic representation of the sentence. In a simple case where the sentence refers to a particular event such as (38), the variable t_r introduced by -le and the variable t_r are bound by the same existential quantifier. In the derivations presented below, for the space, I will only present the composition of -le for the first derivation in (42) and skip for the rest.

A derivation of the sentence in (38) is provided below. Following Krifka (Reference Krifka, Carlson and Pelletier1995), I assume classifiers denote a nu (natural unit) function which measures the number of objects. I treat the classifier construction like a normal indefinite noun phrase, and assume the analysis that the variable introduced by it is existentially bound immediately as opposed to the Kamp–Heim analysis for English indefinite NPs which says such a variable is bound at the discourse level.

According to this translation, combining an event predicate chī yī-ge píngguǒ ‘eat one apple’ with -wán gives rise to a quantized predicate. Specifically, given the homomorphic relation between the event structure and the time structure, a proper part e′ of an event e in the denotation of chī-wán yī-ge píngguǒ ‘finish eating one apple’ can only correspond to a proper part of the time interval during which the event progresses at the reference time t_r. But this means that e′ is not in the denotation of chī-wán yī-ge píngguǒ ‘finish eating one apple’ since by the definition of quantization provided in (29), events in this denotation must have the entire time interval at t_r as the time participant. So the resulting predicate is quantized.

When -wán combines with atelic predicates like chī píngguǒ ‘eat apples’, which do not specify for the quantity of patient, the resulting predicate is still telic. The final representation of a sentence that contains such a complex predicate is provided as follows:

According to this translation, combining the atelic predicate chī píngguǒ ‘eat apples’ with -wán also gives rise to a quantized predicate with respect to the time participant. The reason is the same as the one above. A proper part e′ of an event e in the denotation of chī-wán píngguǒ ‘finish eating apples’ only corresponds to a proper part of the time interval during which the event progresses at the reference time t_r. This means that e′ is not in the denotation of chī-wán píngguǒ ‘finish eating apples’ since by definition events in this denotation must have the entire time interval at t_r as the time participant.

As noted above, expressions with -wán always entail termination for the denoted event, which is shown by the entailment of full precedence when two events are put in a temporal sequence. Consider (12), which is repeated in (44). As mentioned above, the discourse entails that the event of eating apples fully precedes the event of wanting to eat a banana.

In the current analysis, the termination entailment is explained as follows. The function of maximalization over time that -wán denotes necessarily takes the entire run time of the event as the input, which includes the initial and the final points of the event time. This gives rise to an effect such that we can infer that the event reaches some specific final point, which is the point at which the event terminates. So -wán entails termination of the event. To account for the full precedence entailment in (44), we may postulate that terminated events are treated like units and by default they prohibit an overlapping interpretation with other events expressed in discourse.

We also noted above that the morpheme -wán does not just entail termination for the denoted event but also culmination with respect to the patient, regardless of whether the patient is expressed by a classifier construction yī-ge píngguǒ ‘one apple’, which specifies the quantity, or a bare noun píngguǒ ‘apple’, which does not specify the quantity. The example is presented in (45), which is repeated from (15).

The culmination reading in this case comes as a surprise at first thought since we normally would expect quantization over time should be effective only in the temporal domain. However, this effect in the nominal domain follows naturally in the current framework. I first assume that the two noun phrases are just normal noun phrases in the sense that they have the properties that we normally assume noun phrases have, such as referentiality, definiteness, and specificity. Given the definition of the framework we assume here, transferring mereological properties from one structure to another via homomorphism would have an effect that maximalization over one argument also obtains for the other. In the case of (45), maximalization over time, a function of -wán, puts a constraint on the time structure, whose mereological properties are then transferred to the event structure by the homomorphic relationship between them. But since the event is in turn homomorphically related to the patient, this will in turns ensures that we get constraints on the patient such that it will have a kind of maximal reading of the patient as well. If the noun phrase is yī-ge píngguǒ ‘one apple’, it is one apple that is picked out as the maximal patient. If it is a bare noun píngguǒ ‘apple’, it is a contextually specific amount of apples that is picked out as the maximal patient. In either case, the patient is maximal, which means all parts of it are affected in the event, and the event culminates with respect to it.

The proposed analysis of -wán also allows it to be compounded with atelic predicates such as activities e.g. xiào ‘laugh’ and yóu-yǒng ‘swim’, and semelfactives e.g. qiāo ‘knock’ and késòu ‘cough’. In this case, the patient structure is irrelevant as there is no patient involved in those types of events or the patient is not an incremental theme (e.g. qiāo ‘knock’). Such a predicate compounded with -wán is quantized because, for example, a proper part e′ of an event of swimming e can only correspond to a proper part of the time interval during which the swimming event e progresses at reference time, which means e′ is not in the denotation of the predicate yóu-wán-yǒng ‘finish swimming’ as it does not have the entire time interval at reference time as the time participant.

4.2 Analyzing -diào

As mentioned above, -diào is restricted to the type of eventive predicates which denote the kind of events in which the patient undergoes change of state and disappears as a natural ending. So I assume that -diào presupposes the verb it compounds with is a verb that takes an object of incremental theme. The entire compound depicts two stages of a dynamic event: a process subevent, in which the patient undergoes gradual change of state as the event progresses, and a result subevent, in which the patient’s state of not existing is obtained. What -diào specifically describes is the transition of the patient from being in the state of existing to the state of being not existing.Footnote ¹² For the semantics of telicity that -diào contributes to the entire compound, I assume it arises from maximalization over patient, following Zucchi & White (Reference Zucchi and White2001). Specifically, I propose that it denotes a function that also contains such a Max operator that maps the patient involved in the event at reference time t_r onto a maximal entity, which I call the maximal patient participant. The formalization for -diào, as presented in (46), is derived from Zucchi & White’s (Reference Zucchi and White2001) translation of maximal patients (see Section 3.2). It is decomposed from their translation by introducing a λ-abstraction over the predicate while remaining the Max operator that picks out the maximal patient participant.

The definition says that -diào is a function that takes the verb for the process subevent as an argument and saturates the verb’s patient argument with a variable that denotes the maximal patient involved in the event at reference time t_r. The structure is presented in (47) where I also assume movements occur in PF.

This is different from the syntactic representation for the corresponding sentence with -wán as I assume that the maximalization operator introduced by -diào applies at the V level rather than the VP level. This is motivated by the fact that different from predicates with -wán, the predicates with -diào can co-occur with the progressive form, as shown in (48).Footnote ¹³

As argued above, if -diào applied at the VP level, like -wán, then we would expect that it was such kind of aspectual marker (‘outer aspect’) that could not co-occur with the progressive formative since they belonged to the same category and should be in complementary distribution. However, this prediction is not valid as (48) shows.

For the composition, I assume the same denotations for the components Mǎlì ‘Mary’, chī ‘eat’, and yī-ge píngguǒ ‘one apple’ as those in the -wán sentence. The composition of the rest is presented as follows:

According to this translation, the derived event predicate chī-diào yī-ge píngguǒ ‘eat up one apple’ is quantized. Specifically, given that the thematic role of the object assigned by the verb chī ‘eat’ has the property of mapping to object, a proper part e′ of an event e in the denotation of chī-diào yī-ge píngguǒ ‘eat up one apple’ corresponds to a proper part of the object, which, however, is not the maximal participant of the event e with respect to the reference time. This means that e′ is not in the denotation of chī-diào yī-ge píngguǒ ‘eat up one apple’, so by the definition of quantization, the predicate is quantized.

When the object is a bare noun, it receives a specific or definite interpretation. We may explain this interpretation as an effect of the maximalization over patient introduced by the meaning of -diào. The final representation of the sentence is presented as follows.

According to the translation, the predicate chī-diào píngguǒ ‘eat up some/the apple(s)’ is quantized. This is because a proper part e′ of an event e in the denotation of chī-diào píngguǒ ‘eat up some/the apple(s)’ corresponds to a proper part of the object, which is not the maximal patient participant of the event e at the reference time. So e′ is not in the denotation of chī-diào píngguǒ ‘eat up some/the apple(s)’ and thus the predicate is quantized.

As mentioned above, culmination is always entailed when the expression is compounded with -diào, regardless of whether the object is a classifier construction yī-ge píngguǒ ‘one apple’ or a bare noun píngguǒ ‘apple’. In the former case, it entails that the event culminates with respect to a certain apple. In the latter case, the bare noun receives a specific or definite interpretation owing to maximalization of the patient and the sentence entails culmination with respect to the patient. The culmination entailment in the two cases is illustrated by the contradiction of the discourse in (51), which is repeated from (14).

The culmination entailment in this case, as opposed to the culmination entailment in the case when -wán is compounded with an accomplishment (see above), is explained as follows: The function of maximalization over patient that -diào denotes necessarily takes all parts of the patient as the input, entailing that all parts of whatever the contextually defined patient at t _r is are affected. This gives rise to an effect such that we can infer that the event culminates with respect to the entire patient. In a consumption event, it entails that all parts of the food are consumed. So we can infer that the event culminates with respect to (all parts of) the patient.

We also noted above that expressions compounded with -diào entail termination as well, which is shown by the entailment of full precedence when two events are put in a temporal sequence. The example from (13) is repeated in (52). As mentioned above, the discourse entails that the event of eating an apple fully precedes the event of wanting to eat a banana.

Our model of the ternary framework can provide an account for the entailment of full precedence in this discourse. Given the homomorphic relation between the three structures of event, patient, and time, maximalization over the patient would cause a transfer of mereological properties from the patient structure to the event structure, picking out the maximal event, and then a transfer of mereological properties from the event structure to the time structure, picking out the maximal time of the event, which is a time stretch that includes the initial and final points of the event, therefore event termination is entailed. So by using -diào, which directly expresses culmination, the speaker indirectly expresses termination. This explains why (52) entails the event of eating an apple terminates before Mary wanted to eat a banana.

4.3 Accounting for the non-culmination reading of non-RVC accomplishments

Recall that the non-RVC accomplishments do not entail culmination when used with -le. This is explained as follows: The culmination reading arises due to an effect of maximalization, which is contributed by an external source such as the RVC morphemes -wán and -diào; since -le is a relative past tense marker which contains no maximal relation, it cannot provide any maximalization and thus cannot give rise to culmination. But note that such accomplishments do not exclude culmination interpretations. When the context and world knowledge provide certain clues, they may allow culmination interpretations, which, however, are conversational implicatures and are cancelable.Footnote ¹⁴