On the syntax-semantics interface of focus particles: the additive particle 還 hai “HAI” in Mandarin Chinese

Abstract

This paper investigates the syntax-semantics interface of the focus particle 還 hai 'HAI' in Mandarin Chinese. In particular, this paper argues that the various interpretations of hai observed in the previous studies can be explained by the syntactic positions where it occurs. Based on the word order of hai and adverbials that occupy fixed positions, I map out the typography of hai: Hai occurring in the CP periphery is associated with the additive meaning. Hai that adjoins to AspP has the additive or temporal meaning. Hai adjoining to DegP is associated with the comparative or marginal meaning. I propose that hai only has one core sense, which is the additive reading (König 1991). By adopting the theory of alternative semantics (Rooth 1992), I propose that the various interpretations of hai result from the interaction between the additive sense, and the focus associate and the focus domain, which are restricted by the syntactic positions of hai.

1 Introduction

In many languages, aspectual adverbs can be associated with several readings, such as still in English and noch 'still' in German (Kӧnig 1991; Michaelis 1993). A similar phenomenon has also been observed in Mandarin Chinese (henceforth MC) (Yeh 1998; Liu 2000). As shown by the following examples, the particle hai can have many interpretations^{1 , 2 , 3}.

(1) a. (李四煮了飯,) 他還洗了碗。 [additive]

(lisi__zhu-le__fan,)__ta__hai__xi-le__wan

Lisi__cook-PERV__rice__he__HAI__wash-PERV__bowl

Lisi cooked, and he also did the dishes.

b. (李四剛剛在洗碗,) 他現在還在洗。 [temporal]

(lisi__ganggang__zai__xi__wan,)__ta__xianzai__hai__zai__xi

Lisi__just.now__PROG__wash__bowl__he__now__HAI__PROG__wash

Lisi was doing dishes just now, and he is still doing now.

c. 張三的房間還(算){乾淨/好/可以}。 [marginal]

zhangsan-de__fangjian__hai__(suan)__{ganjing/hao/keyi}

Zhangsan-DE__room__HAI__count__clean/good/okay

Zhangsan’s room is still {clean/good/okay}.

d. 張三比李四還高。 [comparative]

zhangsan__bi__lisi__hai__gao

Zhangsan__than__Lisi__HAI__tall

Zhangsan is even taller than Lisi.

First, hai in 1a asserts that the housework denoted by the predicate (i.e., 洗了碗 wash-PERV bowl 'washed the dishes') is not the only thing that the subject (i.e., 李四 lisi 'Lisi') did, but another related work (e.g., 煮了飯 zhu-le fan 'cooked') must have been done before (henceforth, the additive hai). Second, in 1b, hai requires an extension of the state 在洗碗 zai xi wan 'washing dishes' through the topic time 現在 xianzai 'now' (henceforth, the temporal hai). Third, 1c suggests that a sentence containing hai can indicate that the subject (i.e., 張三 zhangsan 'Zhangsan') only meets the standard of the property denoted by the predicate (e.g., 乾淨 ganjing 'clean') in a marginal way (henceforth, the marginal hai). Finally, 1d shows that hai, when used in comparatives, can imply that the standard of comparison (i.e., 李四 lisi 'Lisi') and the subject (i.e., Zhangsan) have a positive sense of the property denoted by the predicate 高 gao 'tall' (henceforth, comparative hai). That is, both are considered tall.

The observation that hai can be associated with various meanings raises two interesting questions: (1) What is the semantics of hai? (2) How likely are these meanings derived from one core sense? Instead of treating hai simply as a polysemous word, previous studies on the semantics of hai (Liu 2000; also see Kay 1990; Michaelis 1993) propose that hai only has one core sense, namely, the scalar sense, which requires the proposition in question to be more informative than propositions in the context (Fillmore et al. 1988). In other words, the various meanings of hai are derived from the composition of the core sense and different semantic dimensions that are provided by the context.

Along this line, this paper sets out to explore the restriction on what meanings hai may have in a sentence. The previous analyses suggest that the context plays the major role in the meaning of hai. However, this paper argues that the context is not the only factor. The syntax of hai, particularly the syntactic position, also restricts the meaning in an interesting way. Following alternative semantics (Rooth 1985, 1992), I propose that there are three subparts that comprise the meaning of hai: (i) the core sense, in particular, an additive sense (König 1991); (ii) the denotation of the focus domain; and (iii) the focus associate (i.e., the element which is in focus in a sentence) and the alternatives induced by them. Importantly, the latter two are, in fact, conditioned by the syntactic position of hai: the focus domain refers to the projection immediately c-commanded by hai, and the focus associates must be located within the focus domain (i.e., within the scope of hai). By using hai as a case study, this paper argues that one needs to take the syntactic position into consideration when accounting for the multiple meanings of a lexical item, and that the various meanings usually result from the cooperation between syntactic positions and semantic interpretations. In fact, this idea is not new; it has also been strongly advocated by the cartographic approach (Rizzi 1997; Cinque 1999; among others).

This paper is organized as follows. Section 1.1 investigates the distribution of hai associated with the meanings mentioned in 1 and maps out the topography of hai. In Section 2.1, I briefly introduce the theory of alternative semantics (Rooth 1992), and then argue that hai is an additive particle (König 1991). Then, to derive the various meanings of hai, I combine the core sense, namely, the additive meaning, with the denotation of the focus domain and the alternatives. Section 3.1 reviews an alternative analysis proposed by Liu (2000). Section 4 is the conclusion.

2 The distribution of hai

This section examines the distribution of hai in terms of its relative position with respect to aspect markers and certain adverbials. Based on this, I propose that the additive hai adjoins to AspP, IP, or CP; the temporal hai adjoins to AspP; the marginal hai and the comparative hai are DegP adjuncts.

2.1 On the additive hai

As Example 2 shows, the additive hai conveys that, in addition to the housework that the subject already did (i.e., cooking), he did other housework (e.g., doing the dishes).

(2) (張三煮了飯,) 他還洗了碗。 [additive]

(zhangsan__zhu-le__fan,)__ta__hai__xi-le__wan

Zhangsan__cook-PERV__rice__he__HAI__wash-PERV__bowl

Zhangsan cooked, and he also did the dishes.

Syntactically, the additive hai occurs above AspP because it must precede AspP adjuncts, such as 已經 yijing 'already' in 3. Besides, the reading shows that hai scopes over the perfect aspect marker 了 –le 'PERF', which denotes a sense of becoming (Lin 2003; Shen 2004; among others).

(3) 李四在工作了, 他(*已經)還(已經)有房子了。

(lisi__zai__gongzuo-le,)__ta__(*yijing)__hai__(yijing)__you__fangzi-le

Lisi__in__work-PERF__he__already__HAI__already__have__house-PERF

Lisi has a job, and he also has already owned a house.

#Lisi has a job, and it has become the case that he also owns a house.

Moreover, CP-level adverbials can be used to examine the syntactic position of the additive hai. According to Cinque (1999, 2004) (also see Rizzi 1997; Tsai 蔡維天 2010), there are four functional projections in the CP layer, as shown in 4 (Cinque 2004: 133). What is crucial here is that the additive hai can only occur after evidential adverbials, such as 好像 haoxiang 'seemingly', as in 5, suggesting that the additive hai occurs below MoodP_evidential ⁴. Thus, the additive hai adjoins to projections below MoodP_evidential but not lower than AspP.

(4) MoodP_{speech act} > MoodP_evaluative > MoodP_evidential > ModP_epistemic > TP…

(5) 李四在工作了, 他(好像)還(??好像)有房子。

lisi__zai__gongzuo-le,__ta__(haoxiang)__hai__(??haoxiang)__you__fangzi

Lisi__in__job-PERF__he__seemingly__HAI__seemingly__have__house

Lisi has a job, and it seems that he also owns a house.

Therefore, there are three possible adjunction positions for the additive hai: AspP, IP, and ModP_epistemic (henceforth, MP^Epi), as illustrated in Examples 2, 6a, and 6b⁵. In 6a, the additive hai adjoins to IP because it occurs to the right of the epistemic modal 或許 huoxu 'perhaps'. By contrast, the additive hai in 6b occurs to the left of the modal, so it adjoins to MP^EPi.

(6) a. 這次颱風, 北部地區已經淹水了, 晚點南部地區或許還會停電。

zhe-ci__taifeng__beibu__diqu__yijing__yanshui-le.__wandian__nanbu__diqu

__ huoxu__ hai__hui__tingdian

this-CL__typhoon__north__area__already__flood-PERF__later__south__area

__maybe__HAI__will__blackout

Due to this typhoon, northern Taiwan has already been flooded. Perhaps people in southern Taiwan will also experience a blackout later.

b. 這次颱風來勢洶洶, 北部地區一定會淹水, 南部地區還或許會停電。

zhe-ci__taifeng__laishixiongxion__beibu__diqu__yiding__hui__yanshui,__

nanbu__diqu__hai__huoxu__hui__tingdian

this-CL__typhoon__violent__north__area__must__will__flood-PERF__

later__south__area__HAI__maybe__will__blackout

The super typhoon is approaching. It must be the case that northern Taiwan will be flooded, and it is also possible that people in southern Taiwan will experience a blackout.

Interestingly, the meaning which the additive hai contributes to a sentence seems to differ with respect to the syntactic positions to which it adjoins. First, when adjoining to AspP as in 2, the additive hai indicates that the subject Zhangsan not only did the work denoted by the predicate (i.e., doing the dishes) but also did other related work, like cooking. Second, if attached to IP, the additive hai has the meaning that the proposition denoted by the IP (i.e., “people in southern Taiwan will experience a blackout later”) is true, and the other propositions related to the topic 這次颱風 zhe-ci taifeng 'this typhoon' are also true, such as the proposition that northern Taiwan has already been flooded. However, there is a mismatch between the surface position of hai and its meaning. That is, the meaning of 6a suggests that the additive hai scopes over the whole IP, but the surface structure of this sentence shows that the subject 南部地區 nanbu diqu 'southern area' is out of the scope of hai. To explain this mismatch, I assume that the subject is topicalized to the position before the additive hai in the surface structure. Since MC is a topic-prominent language (Tsao 1979; Huang 1984; Tsai 2015b), it is plausible to make this assumption⁶. Finally, when the additive hai adjoins to MP^Epi, as in 6b, it indicates that the possibility denoted by MP^Epi exists (i.e., it is possible that people in southern Taiwan will experience a blackout), in addition to other relevant possibilities provided by the context. For example, it must be the case that northern Taiwan will be flooded.

In sum, the additive hai can adjoin to AspP, IP, or MP^Epi. The exact adjunction position of the additive hai can be determined by its relative position with epistemic modals and the meanings it indicates (i.e., the addition of actions, propositions or possibilities).

2.2 On the temporal hai

As exemplified by 7, the temporal hai expresses that the denoted state (e.g., washing the dishes) extends from a salient temporal point in the context, 剛剛 ganggang 'just now', to the topic time 現在 xianzai 'now', resulting in a sense of persistence.

(7) (李四剛剛在洗碗,) 他現在還在洗。

(lisi__ganggang__zai__xi__wan,)__ta__xianzai__hai__zai__xi

Lisi__just.now__PROG__wash__bowl__he__now__HAI__PROG__wash

Lisi was washing the dishes just now, and he is still doing now.

The word order of the temporal hai and some delimitators helps identify the syntactic position where it occurs. First, the temporal hai must precede the aspect marker 在 zai 'PROG', which is treated as the head of AspP (Tsai 2008). See the contrast between 7 and 8. Thus, the temporal hai is located above AspP.

(8) *(李四剛剛在洗碗,) 他現在在還洗。

*(lisi__ganggang__zai__xi__wan,)__ta__xianzai__zai__hai__ xi

Lisi__just.now__PROG__wash__bowl__he__now__PROG__HAI__wash

Second, the temporal hai cannot occur to the left of the subject and epistemic modals, as in 9a,b⁷. This means that the temporal hai is located below IP.

(9) a. *剛剛還{李四/很少學生}在讀書。

*ganggang__hai__{lisi/henshao__xuesheng}__zai__dushu

just.now__HAI__Lisi/few__student__PROG__study

{Lisi/Few students} are still studying just now.

b. ??(李四剛剛在洗碗,) 他現在還或許在洗。

??(lisi__ ganggang__zai__xi__wan,)__ta__xianzai__hai__huoxu__zai__xi

Lisi__just.now__PROG__wash__bowl__he__now__HAI__maybe

__PROG__wash

Lisi was doing dishes just now, and maybe he is still doing now.

The examples discussed above suggest that the temporal hai is adjoined to AspP because it occurs above AspP but below IP.

2.3 On the comparative hai

The comparative hai occurs between a gradable predicate and the bi phrase in bi-comparatives (Kennedy 2007; Liu 2010b, 2011; among others), as in Example 10. Comparatives denote a superiority relation (e.g., Zhangsan is taller than Lisi). On top of that, hai implies that both Zhangsan and Lisi are tall.

(10) 張三比李四還高。 [comparative]

zhangsan__bi__lisi__hai__gao

Zhangsan__than__Lisi__HAI__tall

Zhangsan is even taller than Lisi.

Since the comparative hai appears in bi-comparatives, it is important to examine the word order of hai and the other components in this construction. According to Liu (2011), bi-comparatives are composed of a gradable predicate, the covert comparative morpheme geng inducing the sense of superiority, a bi phrase introducing the standard of comparison, and the subject referring to the compared individual. These components are structured as in 11. Geng and the overt counterpart 更 geng 'GENG' are treated as the head of DegP preceding AP, and the bi phrase is adjoined to the DegP⁸.

(11) [_S [_NP 張三] [_DegP [_PP 比 [_NP 李四]] [_DegP {geng /更} [_AP高]]]

zhangsan__bi__lisi__geng/geng__gao

Zhangsan__than__Lisi__geng/GENG__tall

Zhangsan is taller than Lisi.

Building from the analysis in 11, I propose that the comparative hai occurs above DegP that contains the comparative morpheme and AP. One piece of evidence that supports this analysis comes from the fact that hai must precede geng, as in 12.

(12) 張三比李四(*更)還(更)高。

zhangsan__bi__lisi__(*geng)__hai__(geng)__gao

Zhangsan__than__Lisi__GENG__HAI__GENG__tall

Zhangsan is even taller than Lisi.

In addition, Example 12 shows that hai occurs to the right of the bi phrase, which is an adjunct of DegP. So this means that the comparative hai cannot occur higher than DegP. Accordingly, I suggest that hai is adjoined to DegP.

2.4 On the marginal hai

When immediately preceding gradable predicates, hai can have a sense of marginality, namely, indicating that the subject only meets the standard of the property denoted by the predicate in a marginal way. For example, 13a (also see Liu 2000: 42) denotes that Zhangsan’s room is considered marginally clean⁹. Example 13b also illustrates the similar idea: Zhangsan can slightly walk¹⁰.

(13) a. 張三的房間還乾淨。 [marginal]

zhangsan-de__fangjian__hai__ganjing

Zhangsan-DE__room__HAI__clean

Zhangsan’s room is still clean.

b. 張三還{能/可以}走路。 [marginal]

zhangsan__hai__{neng/keyi}__zoulu

Zhangsan__HAI__can/can__walk

Zhangsan is still able to walk.

Based on this reading, the marginal hai seems to regulate the degrees of the property denoted by the gradable predicate (e.g., ganjing in 13a), so hai must directly operate on degrees. Accordingly, I suggest that the marginal hai is adjoined to DegP.

Unfortunately, it is not an easy task to prove the syntactic position of the marginal hai proposed above because the sense of marginality is incompatible with many adverbials and aspect markers. The only type of adverbial that can interact with the marginal hai is the locative adverbial, which occurs in the scope of AspP headed by the perfect aspect marker –le. Consider 14.

(14) 連續殺人犯在台北殺了人了。

lianxu__sharenfan__zai__taibei__sha-le__ren-le

serial__killer__in__Taipei__kill-PERV__person-PERF

It has become the case that the serial killer killed someone in Taipei.

In 14, the speaker presupposes that the serial killer killed people in some places and asserts that it becomes the case that he killed people in Taipei. To obtain this reading, the locative adverbial 在台北 zai taibei 'in Taipei' should be in the scope of –le. Therefore, if an element occurs after locative adverbials, it is also located below AspP.

As an adjunct of DegP below AspP, the marginal hai should occur after locative adverbials. As shown in 15, the prediction is borne out. The marginal hai can only follow the locative adverbial 在小公司 zai xiao gonsi 'in small companies'. Otherwise, the sentence would become ungrammatical.

(15) 這樣的做法(在小公司)還(*在小公司)可以, 但在大公司就不行了。

zhe-yang-de__zuofa__(zai__xiao__gongsi)__hai__(*zai__xiao__gongsi)

__keyi,__dan__zai__da__gongsi__jiu__buxing-le

this-CL-DE__behavior__in__small__company__HAI__in__small__company

__okay__but__in__big__company__then__not.permit-PERF

It is still fine to deal with things like this in small companies, but you cannot behave like this in big companies.

2.5 Syntacticizing the diverse senses of hai

The syntactic positions of hai associated with different meanings are summarized as follows: The additive hai adjoins to AspP, IP or MP^Epi; the temporal hai is an AspP adjunct; the comparative hai and the marginal hai are DegP adjuncts, as sketched in 16.

The syntactic positions of hai with different meanings, as in Example 16, present a transparent mapping between syntax and semantics. More interestingly, this typography can be further supported by the word order of modals and hai. According to Tsai (2015a), who adopts the cartographic approach (Cinque 1999; Rizzi 1997), modals appear in specific positions: epistemic, deontic, and dynamic modals (e.g., 或許 huoxu 'maybe', 必須 bixu 'must', 肯 ken 'willing') are, respectively, located in the complementizer layer, the inflectional layer, and the lexical layer, as in 17¹¹.

Thus, I take 16 and 17 as the basis and propose that hai and modals can be linearized as follows. First, the additive hai, which can be an adjunct of MP^Epi, IP, or AspP, may occur either before or after epistemic modals, but should precede deontic and dynamic modals, as in 18. Second, the temporal hai, which adjoins to AspP, occurs between epistemic modals and deontic modals, as in 19. Third, the comparative hai and the marginal hai, which are DegP adjuncts, occur between deontic modals and dynamic modals, as in 20–21, respectively.

(18) additive hai > MP^Epi > additive hai > MP^Deo > MP^Dyn

a. (除了煮飯,) 李四(或許)還(或許)洗了碗。

(chule__zhufan,)__lisi__(huoxu)__hai__(huoxu)__xi-le__wan

in.addition__cook__Lisi__maybe__HAI__maybe__wash-PERV__bowl

(In addition to cooking a meal,) it is also possible that Lisi did the dishes.

(In addition to cooking a meal,) Lisi may also do the dishes.

b. (除了打針,) 李四(*必須)還(必須)吃藥。

(chule__dazhen,)__lisi__(*bixu)__hai__(bixu)__chi__yao

in.addition__injection__lisi__must__HAI__must__eat__medicine

(In addition to having an injection,) Lisi also must take medicine.

c. (除了會跳舞,) 李四(*會^Dyn)還(會^Dyn)彈鋼琴。

(chule__hui__tiaowu,)__lisi__ (*hui^Dyn)__hai__(hui^Dyn)__tan__gangqin

in.addition__can__dance__Lisi__can__HAI__can__play__piano

(In addition to dancing,) Lisi also can play piano.

(19) MP^Epi > temporal hai > MP^Deo > MP^Dyn

a. (李四之前喜歡瑪麗,) 他(或許)還(*或許)喜歡她。

(lisi__zhiqian__xihuan__mali,)__ta__(huoxu)__hai__(*huoxu)__xihuan__ta

Lisi__before__like__Mary__he__maybe__HAI__maybe__like__she

(Lisi has liked Mary.) Perhaps, Lisi still likes her.

b. (李四還在生病,) 他(*必須)還(必須)吃藥。

(lisi__hai__zai__shengbing,)__ta__(*bixu)__hai__(bixu)__chi__yao

Lisi__HAI__PROG__sick__he__must__HAI__must__eat__medicine

Lisi is still sick. He still needs to take medicine.

c. (李四小時候會^Dyn游泳,) 他現在(*會^Dyn )還(會^Dyn )游。(lisi__xiaoshihou__hui^Dyn__youyong,)__ta__xianzai__(*hui^Dyn)__hai__ (hui^Dyn)__you

Lisi__childhood__can__swim__he__now__can__HAI__can__swim

Lisi can swim when he was a child, and now he still can swim.

(20) MP^Epi > MP^Deo > comparative hai > MP^Dyn

a. 張三(*還)或許比李四(還)高。

zhangsan__(*hai)__huoxu__bi__lisi__(hai)__gao

Zhangsan__HAI__maybe__than__Lisi__HAI__tall

Zhangsan may be even taller than Lisi.

b. (要進校隊,) 張三(*還)必須比李四(還)高。

(yao__jin__xiaodui,)__zhangsan__(*hai)__bixu__bi__lisi__(hai)__gao

want__enter__varsity__Zhangsan__HAI__must__than__Lisi__HAI__tall

(In order to be on the varsity team, Zhangsan must be even taller than Lisi.

c. 張三比李四(還)會^Dyn (*還)游泳。

zhangsan__bi__lisi__(hai)__hui^Dyn__(*hai)__youyong

Zhangsan__than__Lisi__HAI__can__HAI__swim

Zhangsan even swims better that Lisi.

(21) MP^Epi > MP^Deo > marginal hai > MP^Dyn

a. 這個地方昨天(或許)還(*或許)安全。

zhe-ge__difang__zuotian__(huoxu)__hai__(*huoxu)__anquan

this-CL__place__yesterday__maybe__HAI__maybe__safe

This place may be still safe yesterday.

b. 我們對住宿的要求嘛, 交通必須還方便, 價格(必須)還(*必須)便宜。

wome__dui__zhusu-de__yaochiu-ma,__jiaotong__bixu__hai__fangbian,__jiage__ (bixu)__hai__(*bixu)__pianyi

we__to__accommodation-DE__request-TOP__traffic__must__HAI__ convenient__price__must__HAI__bixu__cheap

As for our request of accommodations, the transportation must be still convenient, and the price must be still low.

c. 張三(*能^Dyn/*可以^Dyn)還(能^Dyn/可以^Dyn)走路。

zhangsan__(*neng^Dyn/*keyi^Dyn)__hai__(neng^Dyn/keyi^Dyn)__zoulu

Zhangsan__can/can__HAI__can/can__walk

Zhangsan is still able to walk.

Moreover, since hai is an adjunct, there can be multiple hais in a sentence. Following the Linear Correspondence Axiom (Kayne 1994), which states that the asymmetrical c-command relation is mapped to the precedence relation at PF, the hierarchy of hai in 16 predicts that hai with distinct meanings can be ordered as in 22.

(22) hai _additive > hai _temporal /hai _additive > hai _comparative /hai _marginal

The additive hai asymmetrically c-commands the temporal hai, which in turn asymmetrically c-commands the others. Accordingly, the additive hai precedes the temporal hai, and the temporal hai occurs to the left of the marginal hai and the comparative hai. As shown by the following examples, the prediction is borne out. Perhaps due to the difficulties in processing, sentences with multiple hais are less preferred, but still some can be found on the Internet and the corpus.

(23) [additive > temporal/marginal]

請不要再送收容所了, 在野外還或許還可以活下來。

qing__bu-yao__zai__song__shourongsuo-le,__zai__yewai__hai__huoxu__hai__keyi__huo-xiaqu

please__not-want__again__send__shelter-PERF__in__wild__HAI__maybe__ HAI__can__survive

Don’t send stray dogs to shelters anymore, please. It is also possible that they are still able to survive in the wild, (in addition to other possibilities) ¹².

(24) [additive > comparative]

如果收費就算了, 竟然還比果汁還貴。

ruguo__shoufei__jiu__suan-le,__jingran__hai__bi__guozhi__hai__gui

if__charge__just__fine-PERF__surprisingly__HAI__than__juice__HAI__expensive

It’s barely acceptable to pay for hot water. Surprisingly, it is also the case that hot water is even more expensive than juice ¹³.

(25) [additive > additive]

不但能舒解壓力, 還或許還能更專心在工作上。

budan__neng__shujie__yali,__hai__huoxu__hai__neng__geng__zhuanxin__zai__gongzuo-shang

not.only__can__relieve__stress__HAI__maybe__HAI__can__even__ concentrate__in__work-up

This way helps you relieve stress, and it is also possible that it can help you concentrate on your work ¹⁴.

Examples 23–24 show that the additive hai occurs to the left of hais associated with the temporal, marginal, and comparative meanings. More interestingly, there can be two additive hais in a sentence, as in 25. This co-occurrence of two additive hais also follows from my proposal because they occur in different positions: the first hai adjoins to MP^Epi in the CP layer and the second hai occurs in the IP layer. The word order of hais in 23–25 cannot be reversed; otherwise, the sentences above would become ungrammatical.

In this section, I propose the topography of hai and provide two pieces of evidence to support this analysis. I will use the proposed syntactic analysis of hai to account for its various meanings in the next section.

3 The semantics of hai

This section argues that hai only has one core sense, namely, the additive meaning (König 1991). Following the theory of alternative semantics (Rooth 1985, 1992), I propose that the various interpretations of hai result from the interactions between the additive meaning and different focus domains and the alternatives evoked by the focus associate. In Section 2.1.1, I briefly introduce the theory of alternative semantics. Then, I argue that the core meaning of hai is the additive meaning in Section 2.1.2. Finally, I show how these various readings of hai are derived in Section 2.1.3. I will present the idea in a relatively informal way, leaving the formalization of hai’s meaning for further research.

3.1 Alternative semantics

What a focus particle contributes to a sentence is influenced by the focus associate (i.e., the focused phrase) in the scope of the particle, which is known as association with focus (Jackendoff 1972; Rooth 1985, 1992; Krifka 1992, 2006; among others). Consider 26.

(26) a. John only [_VP introduced [BILL]_F to Sue].

b. John only [_VP introduced Bill to [SUE]_F].

These sentences only differ in the focus associate. It is Bill in 26a and Sue in 26b. Interestingly, this distinction causes 26a and 26b to have different meanings. 26a indicates that, except for Bill, John introduced no one else to Sue; 26b means that John introduced Bill to nobody else but Sue.

Rooth (1985, 1992) propose the theory of alternative semantics to explain this phenomenon. In addition to ordinary semantic values (i.e., the denotation of phrases or sentences), there is another type of semantic value, namely, focus semantic values. To state it more clearly, the focus semantic value refers to the set of elements “obtainable from the ordinary semantic value by making a substitution in the position corresponding to the focused phrase” (Rooth 1992: 76). The elements that can be the replacement are determined by the context. For example, in 26a, the focus associate is Bill, and the ordinary semantic value of the syntactic sister of only (i.e., [_VP introduced [BILL]_F to Sue]) is the property of introducing Bill to Sue. To obtain the focus semantic value, the focus associate Bill is replaced by other individuals salient in the context, like Matt, Tom, or Bill himself, resulting in the set of properties {introduce Bill to Sue, introduce Matt to Sue, introduce Tom to Sue}. This set is the focus semantic value of the sister of only. Then, the focus particles only asserts that all properties in the set are excluded (i.e., introducing Matt to Sue, introducing Tom to Sue) except the property that has the same meaning as the ordinary semantic value (i.e., introducing Bill to Sue). Thus, 26a has the meaning that John introduced Bill to Sue and he did not introduce other people to Sue.

For ease of exposition, I call the sister of focus particles “the focus domain” (e.g., [_VP(=FD) introduced [BILL]_F to Sue] in 26a)¹⁵. The ordinary semantic value and focus semantic value of the focus domain are called “the focused denotation” and “the alternatives,” respectively. Besides, I assume that the alternatives include only members with different meanings from the focused denotation (e.g., {introduce Matt to Sue, introduce Tom to Sue} for the alternatives of 26a). Based on this, the focus particle only asserts that the focused denotation (i.e., introducing Bill to Sue), but not alternatives (i.e., introducing Matt to Sue, introducing Tom to Sue), participates in the following semantic computation. This results in the meaning that the subject John possesses the focused denotation, namely introducing Bill to Sue, but not the alternatives.

Now, let us turn to 26b. Adjoining to the same position, only in 26b has the same focus domain and focused denotation as it does in 26a. However, the focus associate in the focus domain is different (i.e., [_VP(=FD) introduced Bill to [SUE]_F]), so different alternatives are induced (i.e., {introduce Bill to Jane, introduce Bill to Mary}), given that the salient individuals in the context are Jane and Mary. Then, only asserts that the focused denotation (i.e., introducing Bill to Sue) can be composed with the subject (i.e., John), but not the alternative properties (i.e., introducing Bill to Jane, introducing Bill to Mary). Accordingly, 26b indicates that John introduced Bill to Sue, but not the others.

The contrast between 26a and 26b shows that what focus particles contribute to sentences varies with the focus associate. This is because the focus associate serves to identify the alternatives of the focused denotation by specifying the element which can be substituted by other salient elements in the context. Therefore, distinct focus associates lead to different alternatives. Since excluding different alternatives from further semantic computation, the focus particle only contributes different meanings to the sentence.

This paper adopts the theory of alternative semantics to derive the various meaning of hai. In the next section, I will show that hai only has one core sense, the additive sense. The various meanings hai contributes actually result from different focus domains, different focus associates, and the alternatives the focus associates induced.

3.2 Hai as an additive particle

Focus particles are divided into exclusive (i.e., restrictive) and additive (i.e., inclusive) particles depending on whether the alternatives are excluded from (exclusive particles; cf. 26) or included (additive particles) in further computation (König 1991: 55; also see Sudhoff 2010: 53). Besides, according to whether the alternatives must be arranged on scales, additive particles are further divided into simple inclusion additive particles (henceforth, additive particles) and scalar additive particles (henceforth, scalar particles). Additive particles (e.g., also) “do not induce an ordering, but operate over an unordered set of contextually relevant values” (König 1991: 63; also see Krifka 1999: 1; Sudhoff 2010). For example, also in 27 asserts that the focused property met Mary applies to the subject Jenny (i.e., Jenney has the property of meeting Mary) and presupposes that at least one alternative property, such as met Bill, is possessed by Jenny. Therefore, 27 indicates that Jenny met Mary and someone else. Crucially, also does not induce any scale to rank the properties. That is, Jenny is just as likely to meet Mary as to meet other people salient in the context.

(27) Jenny also [_VP=FD met [MARY]_F]. [additive particle]

Jenny met Mary (and she met someone else).

By contrast, scalar particles (e.g., even) arrange the focused denotation and its alternatives on a scale and assign the latter an extreme position (Sudhoff 2010: 53; also see König 1991: 38 and 68). In many contexts, this scale is based on the likelihood of an event (Karttunen and Peters 1979; Krifka 1999: 1). As shown in 28, even asserts that the focused property met Mary is less likely to be applied to the subject than the alternatives, as met Bill. Therefore, scalar particles induce a scale of likelihood and require the focused denotation to have a lower value (i.e., less likely) than the alternatives.

(28) Jenny even [_VP=FD met [MARY]_F]. [scalar particle]

Jenny met Mary (and Mary is an unlikely person for Jenny to meet with).

Interestingly, with appropriate contexts, additive particles can be associated with scalar interpretations, as shown by the contrast of the German examples in 29 (König 1991: 64).

(29) a. Mein Sohn ist auch [EIN GUTER SCHWIMMER]_F. [additive sense]

My son is also a good swimmer.

b. Auch [IN HANNOVER]_F wird eine U-Bahn gebaut. [scalar sense]

In Hanover, too, a subway is being built.

Example 29b can have the scalar sense that a subway can be built even in Hanover. König (1991) suggests that the focus particle auch only contributes the additive meaning to the sentence. That is, in addition to other places, a subway is built in Hanover. Instead, the meaning that Hanover is an unlikely place to have a subway is provided by the context, such as the landform of Hanover. In other words, it is the context that induces a scale of likelihood and the ordering of the focused denotation and alternatives, which are instead encoded in the semantics of scalar particles. Therefore, in 29b, the scalar sense is derived from combining the additive meaning of auch with the scale and ordering induced by the context¹⁶.

Accordingly, additive particles intrinsically convey an additive sense, and they do not induce scales or rank the focused denotation and alternatives on the scale. By contrast, scalar particles are only associated with the scalar sense. That is, they induce a scale of likelihood and rank the focused denotation in a lower position of the scale. Therefore, one way to distinguish these two types of particles is to see if they can impose a restriction of the ordering of the focused denotation and the alternatives. If they do not, the particle is an additive particle.

With this in mind, let us turn to hai. I suggest that hai is an additive particle because, unlike scalar particles, it does not induce scales or orderings for the focused denotation and the alternatives. As shown in 30, these two semantic components may be unordered. Hai only asserts that Xiaoying has the focused property of eating chocolate, in addition to other alternative properties (i.e., ate cookies, drank black tea)¹⁷. Crucially, hai does not assert that it is less likely for Xiaoying to eat chocolate than to have other sweets. That is, hai can have a sense of simple inclusion.

(30) Context: Xiaoying loves sweets. As usual, she had some after dinner today.

(除了吃了餅乾,喝了茶,) 小英還[_VP=FD吃了巧克力]_F。 [additive sense]

(chule__chi-le__binggan,__he-le__cha)__xiaoying__hai__chi-le__qiaokeli

in.addition__eat-PERV__cookie__drink-PERV__tea__Xiaoying__HAI__ eat-PERV__chocolate

Xiaoying ate cookies and drank tea. She also ate chocolate.

Interestingly, if the sentence in 30 is uttered in a different context, like the context where Xiaoying is on the diet, the focused action (i.e., eating chocolate) is less likely to be done by Xiaoying than the alternative actions. Therefore, hai can occur in a sentence in which the focused denotation is less likely than the alternatives.

Moreover, 31 shows that hai can even allow the focused denotation (i.e., 偷了一台 BMW tou-le yi-tai BMW 'stole a BMW') to be ranked in the higher position than the alternative in the context (i.e., 殺了人 sha-le ren 'killed people').

(31) (李四殺了人,) 他還[_VP=FD偷了一台BMW]_F。 [additive sense]

(lisi__sha-le__ren,)__ta__hai__tou-le__yi-tai__BMW

Lisi__kill-PERV__people__he__HAI__steal-PERV__one-CL__BMW

Lisi killed someone and he also stole a BMW.

Stealing and murder are crimes committed by the subject Lisi in 31. With regard to crimes, the latter is more serious than the former. This means that the alternative crime (i.e., murder) is less likely to be committed than the focused crime (i.e., stealing).

The discussion above suggests that hai does not impose any scale and ordering on the focused denotation and the alternatives because they can be unranked or ranked in either order. This flexible ordering strongly argues that hai is an additive particle.

3.3 The multiple senses of hai

So far, hai is proposed to be an additive particle. The various meanings of hai are derived by the interaction of the additive sense and different focused denotations and distinct focus associates, which are restricted by the syntactic positions of hai. In particular, the focus domain is immediately c-commanded by hai, and the focus associate must be in the scope of the focus particle (Bayer 1996; Büring and Hartmann 2001; Jacob 1983; Sudhoff 2010). Therefore, to derive the meanings of hai, one needs to consider its relative syntactic positions. On the basis of the typography proposed in Section 1.1 (cf. 16), in this section, I identify the focused denotation and the alternatives induced by the focus associate, combining them with the core sense of hai, namely, the additive sense, and thereby derive the semantic contribution of hai in different environments.

3.3.1 The additive sense

Let us start with the additive hai. Syntactically, the additive hai is an adjunct of MP^Epi, IP, or AspP, as in 32. Constituents below the position of hai can be the focus associate, namely, DP, VP, AspP, IP, and MP^Epi, as presented by 33a–e, respectively.

(32) [_CP … [_MP ^Epi (hai _additive)… [_IP (hai _additive)…[_AspP …(hai _additive) [_AspP…[_VP…]]]]]]

(33) a. (除了餅乾,) 她_i 還 [ _MP ^Epi _(=FD) 或許 [_TP t_i [_VP 吃了 [ _DP 巧克力] _F ]]]。

(chule__binggan,)__ta_i__hai__huoxu__t_i__chi-le__qiaokeli

in.addition__cookie__she__HAI__maybe__t_i__eat-PERV__chocolate

In addition to some cookies, it is also possible that she ate chocolate.

b. (除了喝了茶,) 她_i 還[ _MP ^Epi _(=FD) 或許[_TP t_i [ _VP 吃了巧克力] _F ]]

(chule__he-le__cha,)__ta_i__hai__huoxu__t_i__chi-le__qiaokeli

in.addition__drink-PERV__tea__she__HAI__maybe__t_i__eat-PERV__ chocolate

She drank some tea, and it is also possible that she ate chocolate.

c. (除了一直在抱怨,) 她_i 還[ _MP ^Epi _(=FD) 或許[_TP t_i [ _AspP 哭了] _F ]]。

(chule__yizhi__zai__baoyuan,)__ta_i__hai__huoxu__t_i__ku-le

in.addition__continuously__PROG__complain__she__HAI__

maybe__t_i__cry-PERF

She was complaining continuously, and it is also possible that she cried.

d. 這次颱風, 北部地區已經淹水了, 晚點南部地區_i 還 [ _MP ^Epi _(=FD) 或許

[ _TP t _i 會停電] _F ]。

zhe-ci__taifeng__beibu__diqu__yijing__yanshui-le.__wandian__nanbu__ diqu__hai__huoxu__t _i __hui__tingdian

this-CL__typhoon__north__area__already__flood-PERF__later__south

__area__HAI__maybe__t _i __will__blackout

Northern Taiwan has already been flooded due to this typhoon, and it is also possible that southern Taiwan will experience a blackout later.

e. 這次颱風來勢洶洶, 北部地區一定會淹水, 南部地區_i 還[ _MP ^Epi _(=FD)

或許[ _TP t _i 會停電]] _F

zhe-ci__taifeng__laishixiongxiong,__beibu__diqu__yiding__hui__yanshui,__

nanbu__diqu_i__hai__huoxu__t _i __hui__tingdian

this-CL__typhoon__violent__north__area__must__will__flood-PERF__

south__area__HAI__maybe__t _i __will__blackout

The super typhoon is approaching. It must be the case that northern Taiwan will be flooded, and it is also possible that southern Taiwan will experience a blackout.

In the examples in 33, hais adjoin to MP^Epi, so they have the same focus domains, namely, MP^Epi. However, the focus associates in the sentences are different, and hence the alternatives cannot be the same. In particular, the alternatives of the focused denotation (i.e., the denotation of the focus domain) (henceforth, fd) in 33a–e are obtained by substituting the correspondent focus associate with other salient elements in the context, as in 34a–e, respectively.

(34) a. the alternatives of fd in 33a: { it is possible that she ate cookies, …}

b. the alternatives of fd in 33b: {it is possible that she drank green tea, …}

c. the alternatives of fd in 33c: {it is possible that she was crying, …}

d. the alternatives of fd in 33d: {it is possible that northern Taiwan has already been flooded, … }

e. the alternatives of fd in 33e: {it is possible that northern Taiwan will be flooded, …}

What hai contributes here is a simple inclusion additive sense. It asserts that the focused denotation will continue to participate in the computation of a sentence, in addition to the alternatives. No scale or ordering is induced. Take 33a as an example, hai asserts that it is possible that she ate chocolate (i.e., the focused denotation) and it is possible that she ate cookies (i.e., the alternatives). Hai does not indicate that the focused denotation is less likely than the alternatives, or vice versa.

Recall that in Section 2.1.2, I have mentioned that hai can be associated with the scalar meaning if the context induces scales and orderings of the focused denotation and the alternatives. Consider 35.

(35) Context: Xiaomei has been going on a diet recently, so she has to keep sweets away. However, she terribly desired sweets today, and unfortunately had some.

(除了吃了餅乾, 喝了茶,) 小美還[ _AspP=FD 吃了巧克力] _F [scalar sense]

(chule__chi-le__binggan,__he-le__cha,)__xiaomei__hai__chi-le__qiaokeli

in.addition__eat-PERV__cookie__drink-PERV__tea__Xiaomei__HAI__ eat-PERV__chocolate

Xiaomei ate cookies and drank tea. She even ate chocolate.

The above example means that Xiaomei is less likely to eat chocolate (i.e., the focused denotation) than to eat cookies and drink tea (i.e., the alternatives). That is, there is a scale of likelihood and the focused denotation is located in the lower part of the scale than the alternatives. I proposed that hai only contributes the additive sense to the sentence. That is, hai asserts that Xiaomei did the focused action (i.e., eating chocolate) and the alternatives actions (i.e, eating cookies, drinking tea), as in 36.

(36) The function of hai in 35

a. the focused denotation: {eating chocolate}

b. the alternatives: {eating cookies, drinking tea}

Based on 36, the context induces the scale and ordering. Xiaomei is on a diet, as the context mentions, so the information about the calorie content of food is very important. Thus, the scale of the amount of calories is induced in this context, as presented in 37.

As the scale shows, eating chocolate causes Xiaomei to absorb more calories than its alternatives (i.e., drinking black tea, eating cookies), so it is the least likely thing that Xiaomei, who is on a diet, would do; this results in the scalar meaning. To sum up, hai only denotes an addition meaning. The apparent scalar meaning results from the high degree of the focused property in the contextually induced scale and it is unlikely for the subject to have this property.

3.3.2 The temporal sense

As discussed in Section 1.1.2, hai in the temporal use attaches to AspP headed by the imperfective aspect, such as 在 zai 'PROG'. See Example 38.

(38) (李四剛剛在洗碗,) 他現在還在洗。

(lisi__ ganggang__zai__xi__wan,)__ta__xianzai__hai__zai__xi

Lisi__just.now__PROG__wash__bowl__he__now__HAI__PROG__wash

Lisi was doing dishes just now, and he is still doing now.

The imperfective aspect regulates the relation between the situation time (e.g., the time when Lisi is washing dishes) and the topic time (e.g., 現在 xianzai 'now'): the latter must be included in the former (Klein 1994). In other words, the state is required to hold through the topic time. Notice that the topic time is encoded as a variable (henceforth, t_Top) in the aspect marker and its reference is left unspecified until TP, where the topic time is merged. For example, in 38, AspP denotes that the state of doing the dishes holds through t_Top, and its value is assigned as now when xianzai is merged in the TP later, yielding the meaning that this state holds through now. That is, Lisi is doing the dishes now.

Adjoining to AspP headed by zai, the temporal hai has AspP as the focus domain and t_Top as the focus associate, as sketched in 39. As in 40a, the focused denotation is that the activity denoted by the predicate (i.e., doing the dishes) holds through the focus associate t_Top. By replacing t_Top with other salient topic times t_Top’ in the context, the alternatives of the focused denotation are states which hold through t_Top’, as in 40b. Notice that t_Top and t_Top’ are variables. T_Top is bound by the temporal adverbial xianzai when it is merged in TP, and t_Top’ is bound by the salient topic time in the context, like 剛剛 ganggang 'just now'.

(39) [_CP … [_IP…[_AspP hai _temporal …[ _{AspP (=FD) …} [ _Asp ⁰ t _Top ] _F …]]]]]

(40) The function of hai in 38

a. the focused denotation: {doing dishes at t _Top }

b. the alternatives: {doing dishes at t _Top ’, …}

Hai asserts that the state of doing the dishes holds through the topic time in focus (i.e., now) and presupposes that this state also holds though the alternative topic time (i.e., just now). This meaning suggests that hai still contributes the additive sense to a sentence. That is, hai asserts that the state in question holds through t_Top and t_Top’.

However, the previous analyses, like Liu (2000), suggest that the temporal hai denotes a sense of persistence. That is, the state in question should persist from t_Top’ to t_Top. By contrast, in my analysis, this persistence sense is not part of the semantics of hai. Instead, it is just a conversational implicature. If t_Top and t_Top’ at which the state holds are not temporally distant from each other, it is easy to imply that the state persist from t_Top’ to t_Top. See 41 for an illustration.

Being a conversational implicature, the persistence sense can be cancelled, as predicted. See the dialogue in 42.

(42) Context: Zhangsan went to sleep at 3:00 yesterday afternoon, and he was still sleeping at 9:00 last night. At 10:00 this morning, Lisi, Zhangsan’s brother, found that it seemed that Zhangsan had not woken up. He asked his mom:

李四: 張三還在睡嗎?

Lisi: zhangsan__hai__zai__shui__ma

Zhangsan__HAI__PROG__sleep__Q

Is Zhangsan still sleeping?

媽媽: 是啊, 他還在睡, 不過中間有醒來過。

Mom: shi-a,__ta__hai__zai__shui,__buguo__zhongjian__you__xinglai-quo

yes-SFP__he__HAI__PROG__sleep__but__between__have__wake.up-EXP

Yes, he is still sleeping. But he woke up a few hours ago.

In the context of 42, Lisi knew that Zhangsan was sleeping from 3:00 p.m. to 9:00 p.m. yesterday, and he wondered whether Zhangsan is still sleeping now (i.e., 10:00 a.m. today). Mom replied his question by the answer, which contains hai. It means that Zhangsan is sleeping at 10:00 a.m., in addition to other salient topic times (e.g., 3:00 p.m. and 9:00 p.m. yesterday). Besides, this sentence also implies that he was sleeping from 3:00 p.m. yesterday to 10:00 a.m. today. However, this implicature is not true. Thus, Mom cancelled the implicature by the second conjunct that indicates that Zhangsan woke up between 9:00 p.m. yesterday and 10:00 a.m. today. The cancellability suggests that the persistence sense is a conversational implicature triggered by the temporal scale, which is induced by the focus associate t_Top and other salient topic time t_Top’ in the context. What hai contributes to a sentence is the additive meaning.

3.3.3 The marginal sense

When hai immediately precedes gradable predicates, a sentence containing it may convey a sense of marginality. For example, 43 indicates that Zhangsan’s room is considered marginally clean.

(43) 張三的房間[_DegP 還 [ _{DegP (=FD)} [ _Deg ⁰ pos ] _F [_AP 乾淨]]]。

zhangsan-de__fangjian__hai__ganjing

Zhangsan-DE__room__HAI__clean

Zhangsan’s room is still clean.

Before discussing the marginal sense, I digress to explain how to judge whether an object has a gradable property in the semantics. For example, to judge whether a cup of coffee is expensive, one should see if the degrees of the property (i.e., being expensive) of the cup of coffee are higher than those of the standard of comparison in the context. If so, the cup of coffee is judged to have the property of being expensive. This intuition is formalized by the semantics of the positive morpheme (pos) (Kennedy 2007; also see Liu 2010a).

With this in mind, let us return to 43. Syntactically, hai adjoins to DegP, so the focus domain is DegP. I propose that the focus associate of hai is the standard encoded in pos (henceforth, the standard_Foc), which is in the focus domain. Imagine that there is no garbage but some stuff is piled up in Zhangsan’s room. To let the speaker judge that Zhangsan’s room is clean, the degrees of the cleanness of the standard_Foc should be lower than the cleanness of Zhangsan’s room. For example, the standard_Foc may refer to rooms with no garbage but with much stuff piled up. Hence, the focused denotation of DegP indicates that the rooms that are cleaner than rooms with no garbage but with much stuff piled up are considered clean, as in 44a. By replacing the standard_Foc with other standard salient in the context (e.g., rooms without garbage and with few stuff piled up) (henceforth, standard_Alt), the alternatives are obtained, namely, the alternative judgments of the property cleanness, as in 44b. The gradable property of being clean induces a scale of cleanness, in which Zhangsan’s room, the standard_Foc and the standard_Alt are ordered according to the degrees of the cleanness of them. Please see 45.

(44) The function of hai in 43

a. the focused denotation: {rooms cleaner than rooms with no garbage but with stuff piled up are clean}

b. the alternatives: {rooms cleaner than rooms without garbage and with few stuff piled up are clean, …}

The standard_Foc are less clean than the standard_Alt. Therefore, Zhangsan’s room is considered marginally clean because this room is only higher than the standard_Foc, which has lower degrees of cleanness.

Attentive readers may wonder why the standard_Foc has lower degrees of properties than the standard_Alt, but not vice versa. I suggest that this restriction has to do with the nature of the additive meaning. Being an additive particle, hai requires the focused denotation to provide different information from its alternatives. As in 46, if the standard_Foc is less clean than the standard_Alt, the domain of being clean is widened from rooms that are at least as clean as rooms without garbage and with only few stuff piled up (i.e., the standard_Alt) to the set of rooms that are at least as clean as rooms without garbage but with much stuff piled up (i.e., the standard_Foc). This extension makes more rooms to be counted as being clean, which satisfies the requirement of the additive meaning. By contrast, if the standard_Foc is cleaner than the standard_Alt, the focused denotation would not extend the domain of being clean, and hence, it would provide no more information from the alternatives. See 46b. That is the reason why the standard_Foc can never have higher degrees than the standard_Alt.

Hai asserts that there is a standard (i.e., standard_Foc) of the property denoted by the gradable predicate, in addition to other standards (i.e., the standard_Alt). The standard_Foc must have lower values than the standard_Alt because the nature of the additive meaning requires that the focused denotation should provide more information. Accordingly, since being judged by the standard of comparison with lower degrees, the subject is considered to have the property in a marginal way.

3.3.4 The comparative sense

It is observed that the comparative hai triggers the positive presupposition, which requires that the subject and the standard both have a positive sense of the property denoted by the predicate (Michaelis 1993; Liu 2000). For example, with the occurrence of hai, 47 presupposes that Zhangsan and Lisi are tall. This is supported by the infelicity of 47, where the comparative hai is followed by a clause that negates the positive presupposition. By contrast, if hai does not appear (Liu 2011: 34), no positive presupposition is induced and it is felicitous to have the same follow-up sentence.

(47) 雖然張三比李四[_DegP (#還) [ _DegP(=FD) [ _Deg0 geng ] _F 高]], 但他們兩個都不高。

suiran__zhangsan__bi__lisi__(#hai)__geng __gao,__dan__ta-men__liang-ge__dou__bu__gao

although__Zhangsan__than__Lisi__HAI__geng__tall__but__they__

two-CL__all__not__tall

Although Zhangsan is still taller than Lisi, but both of them are not tall.

Thus, the contrast above seems to suggest that hai is a presupposition inducer. But a careful examination indicates that it is just an illusion. In 48, when the comparatives contain a differential phrase like 三公分 san-gongfen 'three centimeter', this effect disappears¹⁸. Speakers who observe the contrast in 47 find that it is felicitous to conjoin the comparative with a follow-up sentence that negates the so-called positive presupposition.

(48) 雖然張三比李四[_DegP 還[ _DegP(=FD) geng 高 [三公分] _F ], 但他們兩個都不高。

suiran__zhangsan__bi__lisi__hai__gao__san-gongfen,__dan__ta-men__

liang-ge__dou__bu__gao

although__Zhangsan__than__lisi__HAI__tall__three-centimeter__but__they__two-CL__both__not__tall

Although Zhangsan is still three centimeters taller than Lisi, but both of them are not tall.

The cancellability of the positive effect in 48 suggests that the infelicity in 47 is more like an implicature than a presupposition. Besides, whether hai induces this positive implicature depends on what is the focus associate in the focus domain, DegP.

On the one hand, the focus associate in 47 is the comparative morpheme geng, which denotes a superiority relation. Thus, as 49a shows, the focused denotation is the property taller. The alternatives are obtained by making a substitution of this relation by other salient in the context, like equality or inferiority. Consider 49.

(49) The function of hai in 47

a. the focused denotation: {taller}

b. the alternatives: {as tall as, less tall}

Based on 49, hai asserts that the superiority relation of tallness holds for the subject (i.e., Zhangsan) and standard of the comparison (i.e., Lisi). If Lisi is not tall, it is normal that Zhangsan is taller than him. Therefore, emphasizing the superiority relation, which is not prominent enough, violates the maxim of manner (Grice 1989), and results in the infelicity effect in 47.

On the other hand, the focus associate in 48 is the differential san gongfen. Replacing this in the focus domain with other differentials that are salient in the context yields the alternative set, as in 50.

(50) The function of hai in 48

a. the focused denotation: {taller by three centimeters}

b. the alternatives: {taller by two centimeters, taller by four centimeters, …}

Different from 47, 48 conveys enough information because the focus associate in the sentence is differentials rather than the relation of superiority. Therefore, the standard does not need to have a positive sense. Hence, the positive implicature is not derived in 48.

Before ending this section, it is worthwhile to discuss sentences in which hai precedes the bi phrase. One reviewer suggests that these sentences also have the positive effect, as in 51.

(51) 張三很高, 李四還比張三高。

zhangsan__hen__gao,__lisi__hai__bi__zhangsan__gao.

Zhangsan__very__tall__Lisi__HAI__than__Zhangsan__tall

Zhangsan is very tall, and Lisi is even taller than him.

The standard of comparison has a positive sense of tallness, but this is because the degree is already set to be at least as tall as the general standard in the context. It has nothing to do with hai.

Besides, there are some examples where the standard following hai does not have a positive sense. Take 52 for example. In the context, Lisi is only 155 cm tall and would be considered to be short. However, in the third clause in 52, Lisi can be used as the standard of comparison.

(52) Context: Zhangsan is 150 cm tall, Lisi is 155 cm tall, and Wangwu is 160 cm tall.

張三150公分高, 李四比他高, 王五[_DegP 還 [ _DegP(=FD) 比李四高] _F ]。

zhangsan__yibaiwushi__gongfen__gao,__lisi__bi__ta__gao,__wangwu__hai__bi__lisi__gao

Zhangsan__150__centimeter__tall__Lisi__than__he__tall__Wangwu__HAI__ than__Lisi__tall

Zhangsan is 150 cm tall. Lisi is taller than him. Wangwu is even taller than Lisi.

Preceding the bi phrase, the focus domain is DegP containing the standard of comparison, as in 52. I propose that the focus associate is the degrees more than the degrees of the tallness of Lisi (i.e., the degrees of tallness of Wangwu). To obtain the alternatives, the focused degrees are replaced by other degrees salient in the context, such as the degrees to which Lisi is tall (i.e., 155 cm tall), as in 53. The gradable predicate induces a scale of tallness and ranks the focused degrees and the alternatives, as in 54.

(53) The function of hai in 52

a. the focused denotation: {taller than 155 cm}

b. alternatives: {155cm tall, 150cm tall, …}

Then, hai asserts that focused degrees of tallness are true of the subject, in addition to the alternative degrees. Because the focused denotation must provide more information than the alternatives, the focused degrees should be higher than alternative degrees. By doing so, the degrees which are true of the subject can be expanded from those that are not higher than 155 cm to those higher than 155 cm, as in 54. Therefore, similar to the other uses of hai, hai in 52 only contributes the additive meaning to a sentence, and the scales and ordering are instead provided by other components, such as gradable predicates.

As for the lack of the positive implicature, since the focus associate in 53 is degrees instead of superiority relation (cf. 49), the participants in the conversation do not need to assume that the standard has the positive sense to make sentences informative¹⁹.

3.3.5 The focus domain

So far, I have discussed how the various meaning of hai is derived by the interaction of the core meaning and the different focus associates. In this section, I point out that the focused denotation (i.e., the denotation of the focus domain) also helps to restrict the meaning of hai.

Hai in each meaning has a semantic selection of the semantic types of the focused denotation and the alternatives: the marginal hai requires the focused denotation and alternative to refer to judgments with different standards; the comparative hai requires them to refer to different comparative relations; the temporal hai requires them to refer to states holding through different topic times; the additive hai requests them to refer to different events, propositions, or possibilities.

For example, when hai adjoins to MP^Epi and has MP^Epi as the focus domain, the correspondent focused denotation and alternatives refer to different possibilities, as in 55. As mentioned above, the additive hai selects this semantic type, so hai adjoining to MP^Epi, has the additive reading.

(55) a. 張三在浴室洗臉, 他還或許在洗澡。 [additive]

zhangsan__zai__yushi__xilian,__ta__hai__huoxu__zai__xizao

Zhangsan_PROG__bathroom__wash.fash__now__he__HAI__maybe__ PROG__take.bath

Intended: Zhangsan is washing his face in the bathroom, and it is also possible he is taking a bath.

b. 除了可以自己吃飯, 張三還或許可以走路。 [additive]

chule__keyi__ziji__chifan,__zhangsan__hai__huoxu__keyi__zoulu

in.addition__able__self__eat__Zhangsan__HAI__maybe__able.to__walk

In addition to being able to eat on his own, it is also possible that Zhangsan is barely able to walk.

Interestingly, in 55 hai in this position cannot have other interpretations, such as the temporal and marginal meaning, as shown in 56.

(56) a. ??張三剛剛在洗澡, 現在他還或許在洗。 [temporal]

??zhangsan__ganggang__zai__xizao,__xianzai__ta__hai__huoxu__zai__xi

Zhangsan__just.now__PROG__take.bath__now__he__HAI__maybe__ PROG__take.bath

Intended: Zhangsan was taking bath just now. Perhaps, he is still taking a bath now.

b. #張三還或許可以走路。 [marginal]

#zhangsan__hai__huoxu__keyi__zoulu

Zhangsan__HAI__maybe__able.to__walk

Intended: Perhaps, Zhangsan is barely able to walk.

In the above sentences, hai adjoins to MP^Epi and have MP^Epi as the focus domain. Since any element in the focus domain can be the focus associate, hai can have the same focus associate as the focus associates of the temporal hai and the marginal hai. Consider 57a and 58a. However, hais in 56 cannot have these two meanings²⁰.

(57) Temporal sense

a. …xianzai_i ta_j hai [ _MP ^Epi _(=FP) huoxu [_TP t_i t_j…[_AspP…[ _Asp ⁰ zai-t _Top ] _F xi]]]

b. the focused denotation: {probably he is taking a shower right now}

c. alternatives: {probably he was taking a shower just now,… }

(58) Marginal sense

a. Zhangsan_i hai [ _MP ^Epi _(=FP) huoxu [_TP t_i…[_DegP [ _Deg ⁰ pos ] _F [_MP ^Dyn keyi zoulu]]]]

b. the focused denotation: {probably Zhangsan is counted as able to walk based on the judgment that people can walk if able to move by their own leg}

c. alternatives: {probably Zhangsan is counted as able to walk based on the judgment that people can walk if able to walk smoothly, …}

The awkwardness of the temporal and marginal meaning of hai in 56 is caused by the incompatible semantic types of the focused denotation and alternatives. As in 57b,c and 58b,c, the focused denotation and alternatives refer to possibilities in 56. However, the temporal hai selects those denoting states, and the marginal hai chooses those denoting judgments of a gradable property. This is the reason why 56 cannot have these two interpretations.

This section shows that the semantic type of the denotation of the focus domain plays an important role in deriving the reading of hai. More interestingly, these semantic types are mapped into distinctive projections in syntax, so the syntactic positions of hai determine the semantic types of the denotation of the focus domain, which results in a transparent mapping between syntactic positions and semantic interpretations: when adjoining to DegP, hai has DegP as the focus domain, which may denote judgments with different standards or different comparatives relations. By combining them with the additive meaning of hai, the marginal meaning and the comparative meaning are derived, respectively. Besides, the temporal meaning is derived if hai adjoins to AspP: the focus domain is AspP, which can denote states holding at different topic times. Moreover, the additive reading is derived when hai is attached to AspP, IP, and MP^Epi. Thus, the focus domain can be AspP, IP, and MP^Epi, which have the denotation of events, propositions, and possibilities, respectively. These semantic types are compatible with the additive meaning.

4 An alternative analysis: hai as a scalar particle

To the best of my knowledge, not much research has been done to examine and explain the various interpretations of hai in the theoretical linguistics literature. In this section, I review one of the previous analyses. Liu (2000) adopts the scalar model proposed by Fillmore et al. (1988) to account for the semantics of hai (also see Kay 1990). Different from Krifka (1999), who takes the focused denotation and alternatives to be ordered along the scale of likeliness, the scale model ranks them in terms of informativeness. Along this line, Liu proposes that hai is a scalar particle with the meaning of persistence (also see Michaelis 1993), ranking two propositions. One refers to the proposition uttered with hai, which is called the text proposition (tp). The other one, known as the context proposition (cp), is the proposition already presented in the context. As a scalar particle, hai specifically requires tp to be ranked higher than cp in the scale model. The more informative proposition entails, the less informative one, so tp should entail cp.

With this core meaning, Liu further composes it with different dimensions of the scale model to derive various meanings. For example, the semantic dimension of the temporal hai is persistence through time. As shown in 59, the tp is 現在在看電視 xianzai zai kan dianshi 'watching TV now', and the covert cp is watching TV just now. Due to the persistence property, the former implies the latter and hence is more informative. Thus, hai can be used in this sentence.

(59) 老王現在還在看電視。 [temporal]

laowang__xianzai__hai__zai__kan__dianshi

Laowang__now__HAI__PROG__watch__TV

Laowang is still watching TV now.

As for the additive hai, the semantic dimension is the number of events related to the topic. For instance, the topic of 60 (Liu 2000: 30) refers to the things Laowang has done. The tp is the entire sentence, and the cp consists of all conjuncts in 60 except for the last one. Then, the tp entails that four things were done and the cp entails that three things were done. Thus, the former entails the latter, hence satisfying the requirement of hai.

(60) 老王買了車, 洗了衣服, 寫了一封信, 還做了一個蛋糕。 [additive]

laowang__mai-le__cai,__xi-le__yifu,__xie-le__yi-feng__xin,__hai__zuo-le__ yi-ge__dangao

Laowang__buy-PERV__groceries__wash- PERV__clothes__write- PERV__ one-CL__letter__HAI__make- PERV__one-CL__cake

Laowang bought groceries, did the laundry, wrote a letter and also made a cake.

Besides, Liu mentions that the comparative hai can be explained along the same line. In 61, the sentence itself provides the tp and the standard 我的 wode 'mine' offers information for the cp, as in 62a,b respectively. Then, it is assumed that the tp entails the cp, which obeys the requirement of hai.

(61) 老王的房間比我的還乾淨。 [comparative]

laowang-de__fangjian__bi__wode__hai__ganjing

Laowang-DE__room__than__mine__HAI__clean

Laowang’s room is even cleaner than mine.

(62) a. Laowang’s room is y degree clean, where y > x. (text proposition)

b. My room is x degree clean. (context proposition)

In sum, Liu tries to decompose these readings into a core meaning and distinct dimensions. This approach is very inspiring but analyzing hai as a scalar particle in the scalar model still needs more elaborations. One of the concerns is that it is hard to tell what hai contributes to a sentence. Although Liu proposes that hai requires the tp to be more informative than the cp, it is still unclear what is the meaning that hai contributes to a sentence. Take 60 as an example: the cp involves three conjuncts about what Laowang has done, and the tp involves four conjuncts; hence, tp entails cp, as hai requires. In fact, this increase of informativeness may just follow from the rationale of pragmatics instead of hai: The more propositions the speaker uttered for a topic, the more information he provided. Thus, an utterance that contains four conjuncts about what Laowang has done is more informative than an utterance that contains three conjuncts.

Besides, the entailment of tp and cp is hard to test when degrees are involved. For example, to me, it is weird to claim that the tp of comparative hai entails the cp.

Moreover, since the informativeness of a proposition is evaluated in the pragmatics, this proposal does not respect the structure of a sentence. That is, the syntactic position of hai is considered irrelevant to its interpretation according to his proposal. As a result, Liu’s analysis predicts that hai can have as many readings as the context allows. For example, the comparative hai in 61 should also have the temporal reading and additive reading in appropriate contexts. Unfortunately, the prediction is not borne out, as evidenced by the examples in 63 and 64.

(63) Context: Laowang’s room was cleaner than mine yesterday.

#老王的房間現在比我的還乾淨。 [temporal]

#laowang-de__fangjian__xianzai__bi__wode__hai__ganjing

Laowang-DE__room__now__than__mine__HAI__clean

Laowang’s room is still cleaner than mine now.

(64) Context: Laowang’s room is cleaner than mine.

#老王的房間比我的還乾淨。 [additive]

#laowang-de__fangjian__bi__wode__hai__ganjing

Laowang-DE__room__than__mine__HAI__clean

Laowang’s room is also cleaner than mine.

The context in 63 suggests that the dimension is persistence through time, so the tp is Laowang’s room is cleaner than mine now and the cp is Laowang’s room is cleaner than mine yesterday (cf. 59). The former implies the latter, and therefore obeys the requirement of hai. Under this circumstance, it is predicted that hai can have the temporal sense, which is, however, contrary to the fact. Besides, based on the context in 64, the dimension is the number of the properties of Laowang’s room, such as the space and the cleanness (cf. 60). The tp is Laowang’s room is bigger than mine and is also cleaner than mine, entailing two properties, and the cp is Laowang’s room is bigger than mine, only entailing one; hence, tp entails cp. Therefore, hai in 64 could have the additive reading, but the prediction is not borne out.

By contrast, the analysis that I argue for in this paper avoids these problems. First, hai is treated as an additive particle (König 1991), so the semantic contribution of hai is clear: Hai asserts that the focused denotation can participate in the following semantic computation of the sentence, in addition to alternatives (cf. Section 2.1.2). Second, this analysis restricts the interpretations of hai by the syntactic position of hai (cf. Section 2.1.3): the meaning of hai is determined by the semantic types of the denotation of the focus domain, which is the sister of hai, and the focus associate, which must be in the scope of hai (Büring and Hartmann 2001; Sudhoff 2010). For example, in 63 and 64, hai can only have the comparative meaning because hai adjoins to DegP, in which hai only scopes over the comparative morpheme. To have the temporal meaning and the additive meaning, hai should occur in a position high enough to scope over AspP. Accordingly, my analysis can exclude these unwanted readings.

Before ending this section, let us look at some more examples, in which hai seems to occur in the same place, and yet several interpretations are possible. Consider 65–66.

(65) Context: Laowang’s room was cleaner than mine yesterday.

老王的房間現在還(是)比我的乾淨。 [temporal]

laowang-de__fangjian__xianzai__hai__(shi)__bi__wode__ganjing

Laowang-DE__room__now__HAI__be__than__mine__clean

Laowang’s room is still cleaner than mine now.

(66) (老王的房間比我的大,) 老王的房間還比我的乾淨。 [additive]

(laowang-de__fangjian__bi__wode__da,)__laowang-de__

fangjian__hai__bi__wo-de__ganjing

Laowang-DE__room__HAI__than__mine__big__Laowang-DE__room__than__ mine__clean

Laowang’s room is bigger than mine and is also cleaner than mine.

From the surface word order, hai in 65 and 66 seems to appear in the same position. However, they, in fact, occur in different positions and have different focus domains and focus associates. Thus, different meanings can be derived. First, hai in 65 adjoins to AspP, so AspP is the focus domain and the focus associate is the topic time encoded in Asp⁰. Thus, the focused denotation is the state of cleaner than mine holding in the focus associate t_Top. Replacing t_Top with other salient topic times t_Top’ in the context results in states holding through the alternative t_Top’. Then, hai asserts that the state holds through t_Top and t_Top’, which will be valued as xianzai and 昨天 zuotian 'yesterday' later, hence the temporal sense. Second, the additive hai in 66 is also attached to AspP, having AspP as the focus domain and DegP as the focus associate. By making a substitution of the focus associate (i.e., cleaner than mine), the alternatives are obtained (i.e., bigger than mine). Based on this, hai asserts that the subject 老王的房間 laowang-de fangjian 'Laowang’s room' has the focused property (cleaner than mine), in addition to the alternative properties (i.e., bigger than mine), yielding the additive sense.

The discussion of 63–66 suggests that it is necessary to consider the syntactic position in order to derive the meanings of hai. This is because the syntactic position of hai determines what the focus domain is and what elements can be the focus associate. In other words, these components cooperate to derive the meaning of hai. By doing so, this proposal not only accounts for the correct readings of hai (c.f., 65–66) but also avoids the problem of overgeneration (c.f. 63–64).

5 Conclusion

In this paper, I examine the distribution of the particle hai with the additive meaning, temporal meaning, comparative meaning, and marginal meaning in Mandarin Chinese. Through the word order between hai on the one hand and adverbials, aspects and modals, on the other hand, it is observed that there is a transparent mapping of the syntactic positions and the semantic interpretations of hai: the additive hai adjoins to AspP, IP, or MP^Epi; the temporal hai is attached to AspP; the marginal hai and the comparative hai are DegP adjuncts. I suggest that hai only has one core sense, the additive meaning (König 1991), and the various meanings are derived from the composition of the core sense and the denotation of the focus domain, as well as its alternatives induced by the focus associate, along the line of alternative semantics (Rooth 1985, 1992). The focus domain is the sister of hai and the focus associate should in the scope of hai. Therefore, the syntactic position of hai plays an important role in determining the meaning of hai. Different from the previous studies, this paper argues that to derive the meaning of hai, one should also take the syntactic position of hai into consideration. This idea also echoes the cartographic framework, which assumes a transparent mapping between syntax and semantics (Rizzi 1997; Cinque 1999; Cinque and Rizzi 2010).