The Colexification of Xià in Modern Chinese

Xià ‘down’ is a hot topic in the study of directional verbs in modern Chinese. Previous studies mainly focus on its syntactic property, syntax-semantics, and diachronic evolution. Few studies explore the lexical-semantic meanings of xià ‘down’, let alone taking a cross-dialectal or cross-linguistic perspective. This paper discusses the lexical semantics of xià ‘down’ in modern Chinese and builds the colexificational network for xià ‘down’ based on its 21 different meanings. Through analyzing the colexifications for xià ‘down’ in Mandarin Chinese and different languages, it is found that the common colexification between the two networks. This paper also discusses the mechanisms for colexification of xià ‘down’, i.e., similarity and metaphorical rules. The similarity mechanism calls for the Goldilocks principle: meanings are more likely to attach to the same word when they are related to an optimal degree. The metaphorical rules of xià ‘down’ map onto the space domain, time domain, state domain, and quantity domain, following the cline of “SPACE > TIME > STATE> QUANTITY”.


Introduction
Directional verb is one of the hot topics in the study of modern Chinese.Many scholars have made profound research synchronically and diachronically.Xià 'down', as a pivotal directional verb in Chinese, its basic meaning is "moving to a lower position" (Liu, 1998).Xià 'down' is sensitive to semantic changes like many other directional verbs.Previous studies mainly focus on syntactic property, syntax-semantics, and diachronic evolution of xià 'down' in Mandarin Chinese.Few studies explore the lexical-semantic meanings of xià 'down', let alone taking a cross-dialectal or cross-linguistic perspective.The rise of typology and the Database of Cross-linguistic Colexifications3 (CLICS3) have provided a new perspective for the in-depth study of its lexical-semantics.Using the data from CLICS3 and cross-dialectal evidence, this paper attempts to build a modern Chinese-specific colexificational network, and then discusses mechanisms for colexification of xià 'down' in different languages throughout the world are much stronger.François (2008) initiatively adopts the notion of colexification in cross-linguistic lexical studies and defines colexification as that a given language is said to colexify two functionally distinct senses iff it can associate them with the same lexical form.
The following part discusses the lexical semantics of Xià 'down' in Modern Chinese.The data is mainly collected from the Modern Chinese Dictionary (7th ed.), and Chinese Dialectal Dictionaries.Firstly, 13 senses of Xià 'down' have been identified in Mandarin Chinese.Then, as more dialects are explored, another 8 meanings of Xià 'down' are added to the semantic list.Finally, 21 senses of lái 'come' are identified as follows (Mao, 2020;Guo, 2021): (i) Go down (descent): This is the basic meaning of Xià 'down' which indicates the direction that is opposite to Shàng 'up', meaning "moving to a lower place or position".This meaning can be found in Mandarin Chinese and all dialects.Examples are as follows: (ii) Behind (follow): The meaning of "behind (follow)" in the phrase of xià gè yuè (下个月) 'behind the month', xià nián (下年) 'behind this year' can be found in Mandarin Chinese and all Chinese dialects.Examples are as follows: 3)下 半 年 我 要出一趟 远 门。(Mandarin Chinese) down half year me go CL remote door I will go to a remote place behind (following) the first half year.(v) End: The meaning of "end" refers to "the finish of task".(xv) Few: The meaning of "few" is often found in Mandarin Chinese, Urumqi dialect, and Yinchuan dialect.For example:

This meeting NEG down CL people
There has no fewer than five people in this meeting.(xvii) Blow or under a place: The meaning of "blow or under a place" is often found in the phrase of dǐ xià (底下) 'under the ground' in Chongming dialect, Dongguan dialect, Meixian dialect, Nanning dialect, Chengdu dialect and Fuzhou dialect.For example:

CL desk down have CL book
There is a book under the desk.(xx) Small: The meaning of "small" is often found in the phrase of xià xì (下细) 'be careful' in Chengdu dialect and Guiyang dialect.For example: doing thing down thin Be careful when doing things.
Based on the above investigation, the lexical meanings of xià 'down' in Mandarin Chinese and 15 dialects of nine Chinese dialectal families can be represented as follows:

The Colexificational Network of Xià 'Down'
To clarify the semantic classifications of xià 'down' in Modern Chinese, this paper resorts to the Database of Cross-linguistic Colexifications3 (CLICS3) which covers more than 3100 language varieties of the world, showing the concepts that share the same lexical form with the target concept.CLICS3 has been proved to be scientific in psychological and cognitive researches (Jackson et al., 2019).
When DOWN is selected as the target concept, the result can be presented as follows： The edges be esents how fre oncepts, the g al form they sh r xià 'down' e. Whereas, th ificity.For exa ct, Guiyang di nchuan dialect ect.However, s language-spe cations (e.g.g istic data, so ding to Table 1 ts can be estab gure 2. The col nes that connec h of the edges derived from t o" (Guo, 2021)

Colexification Mechanisms of Xià 'Down'
This session discusses mechanisms for semantic colexification of xià 'down'.The colexification of xià 'down' is not evolved arbitrarily, but is guided by similarity and metaphorical rules.

Colexificational Similarity of Xià 'Down'
Similarity plays a significant role in human's cognition, and is also important for shaping colexification patterns.
A series of experiments (Karjus et al., 2021;Floyed et al., 2021) has been conducted and provided a multitude of evidence for the important role of similarity in colexification.Whereas, it does not show the trend that more similar senses are more prone to be colexified.Brochhagen and Boleda (2022) propose that colexification follows a Goldilocks principle that balance the two pressure: meanings are more likely to attach to the same word when they are related to an optimal degree, that is, neither too much, nor too little.And they found a large quantity of evidence suggesting that languages evolve to strike a balance between competing functional and cognitive pressure, or in other words, a balance between simplicity and informativeness.
The colexification of xià 'down' in Mandarin Chinese also observes the Goldilocks principle.As Figure 2 expresses, the colexificational network is built on the bases of the principle, or in other words, it expresses the Goldilocks zone or colexificational zone.And the shadowing region expresses the sharing colexificational zone between Mandarin Chinese and different languages throughout the world.Xià 'down' has the basic meaning of moving to a lower position, and its colexified meanings are related to this basic one.Distributional similarity and associativity are two measures that can be used to test the similarity in the process of colexification (Brochhagen & Boleda, 2022).Distributional similarity measures how similar the contexts of use of different linguistic expressions are, quantifying their contextual overlap based on a large amount of data, especially the text corpora (Harris, 1954;Landauer & Dumais, 1997).For example, in Mandarin Chinese and most Chinese dialects, the meaning of "follow" as in "follow this month", has the similar contexts of the use to xià 'down' as in "xià yì gè yuè (下一个月)", which manifests a strong distributional similarity between the two meanings.Mao (2020) collects 13,687 items of xià 'down' in the "xià 'down'+ Noun" construction, providing solid evidence for the strong distribution similarity of the meanings of xià 'down' in modern Chinese.On the other side, the associativity is derived from large-scale association norms from daily uses (Deyne et al., 2018).For example, in Mandarin Chinese and most Chinese dialects, the meaning of "end" as in "class ends" or "schooling day ends" shares a similar association norm with the use of xià 'down' as in "xià kè (下课)" or "xià xué (下学)", expressing the two meanings have a strong associativity.Mao (2020) adopts the method of constructional analysis to test the association strength of xià 'down' in the construction of "xià 'down'+ Noun" and "Verb + xià 'down'", and Guo (2021) also used the similar method to calculate the association strengthen and analyze the meanings of xià 'down' in Chinese and English from the perspective of crossing languages, both expressing strong evidence for a strong associativity of the meanings of xià 'down' in modern Chinese.
While the strong distributional similarity and associativity do not indicate that xià 'down' can colexify the meanings as long as the meanings are related or similar.For example, the meaning of "go" as in "go to restaurant to have dinner" can only be found in a few dialects like the Chengdu dialect and Danyang dialect as in "xià guǎn zi (下馆子)".Besides, lái 'come' has the meaning of "give birth" in Mandarin Chinese (Wang, 2021), which is similar to xià 'down' expressing the meaning of "give birth".Only the meanings of "go" and "give birth" can be found in both lái 'come' and xià 'down', providing the evidence that the optimal degree of similarity can best predicate the tendency to colexification.
To sum up, similarity holds an indispensable role in the process of colexfication, while it does not mean that stronger similarities among senses indicate higher tendency to be colexified by the same linguistic form.Instead, it follows the Goldilocks principle that meanings colexify if they are neither too unrelated, nor too related, that is, just to an optimal degree.Besides, communicative needs also need to take into consideration in the process of colexification, or in other words, they should be highlighted in the analyses of colexification (Karjus et al., 2021;Floyed et al., 2021).Communicative need varies in different language communities relying on such factors as environment and culture, which is corresponded to the view that lexicon meaning is language-specific in which different environments and cultures have specific cognitive lexicon zone sharing some similarities and differences across the communities (Croft, 2001(Croft, , 2021)).

Metaphorical Rules of Xià 'Down'
When one concept is constructed by another, they share the same cognitive typology (Lakoff & Johnson, 2003).
To put it simply, the structural metaphor is at work when the source meaning and the extended meaning belong to two different cognitive domains, but the cognitive typology is similar in the two domains.
Previous studies have shown that many abstract linguistic concepts derived from space concepts are generally considered as the most fundamental concepts in human language (Heine et al., 1991;Anderson, 1971).Xià 'down' has the basic meanings of "go down", "at a lower place" and "blow or under a place" (Guo, 2021), and as a directional verb, it is typically a space concept.The meanings of xià 'down' are found to map onto four domains, i.e., the space domain, the time domain, the state domain, and quantity domain.

Space Domain
The metaphoric mappings in the space domain account for the commonest way for semantics of xià 'down'.This can be illustrated as follows: The first cline of semantic extension is "from none to existence" or "from higher to a lower place":down > fall, down > give birth, down > unload, down > play, down > cook, down > invest, down > accompany, down > use, down > go into, down > come, down > directional meaning As mentioned before, the image schema of xià 'down' represents that something or somebody moves toward a lower position.When something or someone is moving to a lower position, the thing being observed would be "closer, visible, and perceptible".When the meanings of xià 'down' map onto the space domain, it involves physical or virtual movement in the space.For example, the meaning of "fall" in xià yǔ le (下雨了) 'it is raining' refers to that "rain" moves to the ground so that xià 'down' can refer to the "the rain is falling"."Rain" here is metaphorically conceptualized as a moving entity.When it moves to the lower place, the ground, it becomes visible or perceptible so that the speaker can realize that something fell.
Besides, Mao (2020) points out that xià 'down' can indicate an increase of prominence.This is in accordance with Shen (1999), who proposes that something big is more salient than something small, and something visible is more prominent than something invisible.The meaning of "give birth" in xià zhū zǎi (下猪崽) 'give birth to the piglets' refers to that the "piglets" move from the inside of the sow's body toward the outside and thus the piglets become visible.Therefore, we use xià 'down' to express the meaning of "be born".
The meaning of "unload" is extended from the meaning of xià 'down' in the space domain and refers to "remove something or take something down".Since "being closer and lower" is more salient than "being farther and higher", xià 'down' can be used to express "unload"."To unload something" can be construed as "to remove from a higher position to a lower position" so that the result becomes salient.For example, in the phrase of xià huò (下货) 'unload goods', the ground is conceptualized as "the destination" when the goods have reached the ground.And the sense of "use" can also be conceptualized as taking down the tools to use as in the instance of xià jiā huo(下家伙)'use tools'.Lakoff and Johnson (2003) points out that "no metaphor can ever be comprehended or even adequately represented independently of its experiential basis".The experiential basis here is that when the entity moves to the handy position, it becomes closer to the speaker so that the speaker can use it.
In the same vein, the sense of "go into" can be construed to move from a higher position into a lower position that can be regarded as a container.When someone or something moves into the container and becomes part of it, xià 'down' derives the meaning of "go into".In xià kuàng (下矿) 'go into the mine', "the mine" is regarded as a container.The concept of "going into" focuses on the path of how someone travels.
The meaning of "play" is derived from the meaning of xià 'down' in the space domain in which the chess piece is moving from the higher position toward a lower one, focusing on the path of playing.And the meaning of "cook" is also from the process of cooking in which food moves toward the lower place, the cooker, emphasizing the path of cooking.
The meaning of "invest" is extended from the process of investing in which putting a part of money down to the gambling desk as in the instance of xià zhù (下注) 'invest money'.And the meaning of "accompany" is derived from the space domain in which the dish is used to accompany the rice moving toward the stomach, as in the example of xià fàn cài (下饭菜) 'accompany the rice'.
The meaning of "come" is extended from the meaning of xià 'down' in the space domain and refers to "something or someone comes from a far place to a closer one".In xià guǎn zi (下馆子) 'go to the restaurant', "the restaurant" is regarded as a destination.The concept of "go" focuses on the goal of the place where someone arrives.
When xià 'down' serves as a directional complement to indicate the direction of moving, it derives the "directional meaning".For example, in fàng xià shū bāo (放下书包) 'put down bags', "the bag moves towards the ground" implies "the transfer of the bag".The concept of "directional meaning" emphasizes the path from a higher place to a lower place.

Time Domain
The metaphoric mapping in the time domain can be illustrated by the following cline: The second cline of semantic extensions "moving time": down > follow, down > end The process of moving from a higher position to a lower position takes time, and thus the image schema of xià 'down' can map onto the time domain.The meaning of "follow" as in xià yí gè yuè (下一个月) 'the following month' can be understood through the orientation metaphor that "DOWN IS FUTURE", which is different from the English-speaking culture, that is, "UP IS FUTURE" (Qi, 2014).And Nisbett (2003) points out that Chinese people think that people's ability to control the environment is limited, so they tend to think that time is moving and they cannot influence the direction or speed of how time moves.As the basic meaning of xià 'down' refers to "move to a lower place", when it maps onto the time domain, it adopts the Moving Time instead of the Ego Moving metaphor, that is, the observer or ego is stationary and time moves from the high to the low.According to the figure and ground relation, the moving time is a figure and the stable Ego is the ground or reference point, which serves as the deictic center of the temporary frame, labeled as "Ego's Now" (Sweetser & Gaby, 2017).
According to THE PAST IS UP metaphor from the Chinese culture, there is a tendency to regard the time up the "Ego's Now" as "past", while the time down the "Ego's Now" as "future" in accordance with the metaphor "DOWN IS FUTURE".When "Ego's Now" is taken as the reference point and time moves from the higher side to the lower one, as seen in the expression "xià yì nián (下一年) 'the following year'", it acquires the meaning of "follow".When time moves from the higher side to the lower end, xià 'down' derives the meaning of "end", focusing on the endpoint of the motion, as demonstrated in xià kè (下课) 'the class ends'.Therefore, when "Ego's Now" serves as the reference point, time can move from two directions on the vertical level, but "time" is conceptualized as a "moving object" moving from the higher past to the lower future in Chinese.

State Domain
The metaphoric mappings in the state domain can be illustrated by the following cline: The third cline of semantics "moving towards a state": down > give, down > concede, directional meaning > resultative meaning The meaning of "give judgement" as in xià dìng lùn (下定论) 'give final judgment' refers to that the "conclusion" moves from the air to action.In this situation, where the question hanging in the air is set as the reference point.
When the reference point moves to the conclusion, they are conceptualized as "come to conclusion".Therefore, xià 'down' derives the meaning of "give judgment".The sense of "concede" can be similarly conceptualized as moving from the state of "balancing" to the state of "conceding" as in the instance of jiāng chí bú xià (僵持不下) 'without conceding'.Hu (2012) argues that when the image schema of xià 'down' maps from the space domain onto the state domain as in dǎ xià (打下) 'conquer', it can be understood as "to move toward the peaceful state".The destination in the physical space can be mapped onto the final state in the state domain.Liu (1998) points out that there is an obvious derivative relationship between the resultative meaning and directional meaning.The directional meaning of xià 'down' is "to move toward a lower place or a referential point", while the resultative meaning of xià 'down' is "to step into a state".Directional meaning focuses on the change of position after movement while resultative meaning focuses on the change of state.For example: Xià 'down' in instance zuò xià (坐下) 'sit down' serves as directional meaning expressing the motion of the body from a higher place to a lower place.While xià 'down' in instance dǎ xià (打下) 'conquer' focuses on the results of the action, that is the conquering of the lands, serving as resultative meaning.

Quantity Domain
The metaphoric mappings in the quantity domain can be illustrated by the following cline: The fourth cline of semantic extensions "lower than a quantity": down > few, down > small The meaning of "few" as in bú xià yú wǔ rén (不下于五人) 'no fewer than 5 people' refers to that the quantity moves to a lower one.In this case, where the quantity is set as the reference point.When the fact moves under the reference point, they are conceptualized as "fewer than the quantity".Therefore, xià 'down' derives the meaning of "few".The sense of "small" can be similarly conceptualized as moving from the quantity of "sketch" to the quantity of "detail" as in the instance of xià xì diǎn (下细点) 'be more careful'.
Xià 'down' observes the metaphorical rules, expanding its meaning through mapping its image schema onto the space domain, time domain, state domain, and quantity domain.In general, the semantic meanings of xià 'down' are in line with the metaphoric hierarchy proposed by Heine et al. (1991): person > object > activity > space > time > quality.Wu (2003) explains that the essence of this hierarchy is in accordance with the concept of "embodiment" that people understand things from the most familiar empirical category to the empirical category that is away from people's vision.So the meanings of xià 'down' follow the metaphorical rules of "SPACE > TIME > STATE > QUANTITY".

Conclusion
Few studies explore the lexical-semantic meanings of xià 'down' in modern Chinese, let alone taking a cross-dialectal or cross-linguistic perspective.This paper has identified 21 meanings of xià 'down' in Mandarin and Chinese dialects by the data from the Modern Chinese Dictionary (7th ed.), and Chinese Dialectal Dictionaries, and then the colexificational network of xià 'down' in Mandarin Chinese is built based on the 21 meanings.Using the apparatus of CLICS3, the colexificational network of xià 'down' is built across languages throughout the world, then the common area of colexification of xià 'down' can be found after the comparison between the two networks.This paper then explores the colexificational mechanisms for the semantic meanings of xià 'down', that is, similarity and metaphorical rules.The similarity mechanism calls for the Goldilocks principle: meanings are more likely to attach to the same word when they are related to an optimal degree, that is, neither too much, nor too little.The metaphorical rules of xià 'down' map onto the space domain, time domain, state domain, and quantity domain, following the cline of "SPACE > TIME > STATE> QUANTITY".This paper elaborates on the colexificational mechanisms of xià 'down', that is, similarity and metaphoric rules that will shed light on studies of other directional verbs.
Dialect) you run PERF house up do what quick down Why did you come onto the roof?Go down quickly.
4)下 二 回故有 机会无？(Fuzhou Dialect) down CL level have opportunity Whether do I have opportunity behind (following) this time?(iii) At a lower place: The meaning of "at a lower place" in the phrase of xià bā (下巴) 'jaw', xià bàn shēn (下半 身) 'the lower part of the body' can be found in every Chinese dialect.And its extended meaning in the phrase of xià děng (下等) 'lower level', and xià zuò (下作) 'low down' also can be found in every Chinese dialect.Examples are as follows: 5)他下巴 很 长，看起来 很 搞笑。(Mandarin Chinese) he jaw very long look very hilarious He is hilarious because of his long jaw.6)佢 食野咁 下作嘅! (Guangzhou Dialect) you eat food low You are too low down while eating.(iv) Fall: The meaning of "fall" can be found in Mandarin Chinese, Urumqi dialect, Yinchuan dialect, Harbin dialect, Nanning dialect, Nanchang dialect, Changsha dialect, Taiyuan dialect, Guiyang dialect, Danyang dialect Chongming dialect and Chengdu dialect.For example: 7)天 黑 了， 开始下 大雨了。(Mandarin Chinese) Heaven dark PERF begin down big rain It begins raining after the darkness coming.8)一 下 露水，菜就 活泛了。(Yinchuan dialect) one fall dew vegetables live PERF Once the drew falls, vegetables revive.
， 扛起 了整 个 家庭 的 重任。(Mandarin Chinese) CL man down mine dig coal shoulder PERF CL family DE responsibility This man go into the mine to feed his whole family.24) 下 种 底 时节 误 不得!! (Urumqi dialect) down seeds DE season delay NEG DE Do not miss the season when making seeds go into the soil.(xiii) Directional meaning: The directional meaning of xià 'down' is found when xià 'down' serves as a directional verb, or directional complement to refer to "moving to a lower position".This use is found in Mandarin Chinese and many Chinese dialects.For example: Resultative meaning: The resultative meaning of xià 'down' refers to the change of state.It can be found in Mandarin Chinese, Urumqi dialect, and Yinchuan dialect.For example: 27) 打 下 基础。(Mandarin Chinese) Beat down foundation Lay the foundation.28) 东 西 搁下了。(Yinchuan dialect) things down PERF Things have been laid down.
30) 这些 座位坐 不 下。(Urumqi dialect) these seats sit NEG down There are fewer seats than what we needs.(xvi) Concede: The meaning of "concede" is loose colexification for xià 'down' in Mandarin Chinese and Urumqi dialect, because it only consists in the compounds of xià 'down' such as xiāng chí bú xià (相持不下) 'without conceding'.For example: 31) 他们 相 持 不 下。(Mandarin Chinese) they each other NEG down They are not willing to concede each other.
the top of the mountain, and potato under the ground.(xviii) Go: The meaning of "go" is often found in the phrase of xià tián (下田) 'go to land' or xià guǎn zi (下馆 子) 'go to restaurant' in Urumqi dialect, Yinchuan dialect, Harbin dialect, Taiyuan dialect, Guiyang dialect, Danyang dialect and Chengdu dialect.For example: 34) 他 病 了 一个 月， 现在才能 下 地 干活。(Taiyuan dialect ) He sick PERF CL month now down land do work He can come to land to farm after being sick for a month.35) 今天 我们下 馆子。(Chengdu dialect) today we down restaurant We come to restaurant to have dinner today.(xix) Cook: The meaning of "cook" is often found in the phrase of xià miàn (下面) 'cook noodle' in Urumqi dialect, Guangzhou dialect, Changsha dialect, Dongguan dialect, Danyang dialect and Chongming dialect.For example: 36) 下 饺子。(Urumqi dialect ) down dumpling Cook the dumplings. Fig of xià 'down' in word languages according to Figure1.The colexifications for DOWN across languages provide cross-linguistic evidence for colexifications for xià 'down' in modern Chinese which in turn supplement the former.
fight down CL mountainConquering the land.

Table 1 .
The lexical-semantic functions of xià 'down' in Mandarin Chinese and 15 dialects