Adjusting Mood in Mandarin Chinese: A Game Theory Approach to Double and Redundant Negation with Entropy

2.1 Previous Semantic-Pragmatic Studies of Double Negation

Jespersen (1924) explores the semantic-pragmatic nexus of double negation in English, analyzing its sentences from semantic logic and pragmatic angles. He challenges the traditional view equating double negation with affirmation, exemplified in (1). While emphasizing its attenuating effect, Jespersen fails to elaborate on the conversational implicature or provide a comprehensive account of its rhetorical functions.

1. 在我眼中, 你们不是不幸福的。 ≠ 在我眼中, 你们是幸福的。

   Zài wǒ yǎnzhōng, nǐmen bùshìbù xìngfú de. ≠ Zài wǒ yǎnzhōng, nǐmen shì xìngfú de.

   In my eyes, you are not un happy. ≠ In my eyes, you are happy.

   (From BLCU Chinese Corpus, Shu Yi 1994, How to Say Goodbye)

Grice (1975) introduced the concept of conversational implicature, wherein the speaker’s adherence to or violation of certain principles of cooperation, namely the maxim of quality, quantity, relation, and manner, leads the listener to infer non-literal meanings based on contextual clues. Grice’s theory of conversational implicature distinguishes literal meaning from implied intentions communicated in linguistic interactions. Specifically, meanings derived from adhering to a maxim are termed generalized conversational implicatures, while those arising from violating a maxim are termed particularized conversational implicatures (Bach 2006; Grice 1991; Levinson 2000). The primary distinction between the two lies in the fact that generalized implicatures are conventionalized and readily accessible to the listener, whereas particularized implicatures require the listener to engage in context-dependent inference. Grice’s cooperative principles are instrumental in understanding the pragmatic motivations behind double negation. For instance, in example (2), the double negation structure not necessarily adheres to the maxim of quality by not expressing a proposition the speaker believes to be false. However, it also violates the maxims of quantity and manner by employing a vague, indirect, and ambiguous form of double negation to convey affirmation, thus weakening the force of the utterance to convey its truth value. Through particularized conversational implicatures, listeners can further combine contextual cues with generalized meanings to interpret the specific semantic and pragmatic functions of double negation. However, while conversational implicature theory can analyze double negation, it does not offer a detailed explanation of how particularized conversational implicatures are derived, lacking a formalized interpretative approach.

1. 用典未必不足以传达思想。

   Yòngdiǎn wèibì bùzú yǐ chuándá sīxiǎng.

   The use of a dictionary is not necessarily insufficient to convey ideas.

   (From Center for Chinese Linguistics Corpus, She Lao, 1934, Lectures on Literary Theory)

Later, many scholars (e.g., Horn 1972, 1984; Lakoff 1973; Leech 1983) revised and supplemented Grice’s theory. Levinson’s conversational implicature maxims, particularly the Manner Principle, highlight differences between marked and unmarked expressions in statement forms, suggesting that marked expressions may carry distinct meanings compared to their unmarked counterparts (Huang 2017):

Speaker’s maxim:

Indicate an abnormal, non-stereotypical situation by using marked expressions that contrast with those you would use to describe the corresponding normal, stereotypical situation.

Recipient’s corollary:

What is said in an abnormal way indicates an abnormal situation, or marked messages indicate marked situations.

(Huang 2017, 57)

Subsequently, Horn (1989) develops Grice’s framework by providing a more in-depth analysis of the attenuating effect of double negation. Horn posits that, in the context of weakening the utterance’s force, listeners infer an oppositional relation from the contradictory nature of double negation. Specifically, the speaker negates one end of the oppositional relation within a negation hierarchy, thus affirming the other end, promoting the notion of deriving strong statements from weaker ones as a form of understatement. Consequently, speakers consciously utilize double negation structures to recalibrate the listener’s understanding of the speaker’s intent and conversational implicature, enabling a more accurate interpretation of the speaker’s intentions and semantic positioning of double negation expressions.

However, Horn also conceptualizes double negation as a marked form of affirmation, implying that double negation expressions complement affirmative expressions. Horn argues that listeners refrain from directly employing affirmative forms because the current context does not merit a categorical affirmation. However, this viewpoint lacks consideration of the logical semantics and presuppositions of double negation expressions with superlative affirmative functions, such as cannot but, nothing but, among others. Consequently, Horn’s viewpoint fails to capture the full complexity of conversational implicatures in such contexts.

2.2 Double and Redundant Negation in Mandarin Chinese

In modern Mandarin Chinese, two distinct forms of negative expressions have emerged as noteworthy linguistic phenomena: double negation and redundant negation. Double negation involves the use of two negative elements in a sentence, which logically equates to an affirmative statement. Redundant negation, on the other hand, includes an additional negative element that is semantically superfluous but intensifies the sentence’s overall negative sense. Despite their prevalence, the nuances these forms convey in mood and information load have been the subject of extensive research and discussion in linguistics. The term mood specifically refers to the degree of assertiveness or tentativeness conveyed by the speaker’s linguistic choices. From a pragmatic standpoint, the mood of double negation (i.e., marked form) differs from that of affirmation (i.e., unmarked form), even though they are logically equivalent. Similarly, redundant negation introduces an additional layer of emphasis on the negative meaning compared to simple negation (i.e., unmarked form).

Negative expressions encompass assertions of lacking a certain attribute and can be categorized into lexical, semantic, and pragmatic negation (Gao 2017). Lexical negation necessitates negative morphemes within words, while semantic negation implies negative meanings in grammatical forms often accompanied by negative markers. Pragmatic negation covertly conveys negative meanings in sentences, sometimes even without explicit negative words. Negation further divides into intra-word (e.g., páichú [exclude]; páichì [repel]; nán [difficult]; fá [lack]) and extra-word negation (e.g., bù [no]; méi [not]; wú [nothing]), delineating negative predicate morphemes and negative morphemes, respectively (Zhou 2023).

Double negation, prevalent in modern Mandarin Chinese, manifests in various forms – (a) universal, (b) modal, (c) euphemistic, and (d) conditional – each expressing distinct pragmatic functions (Ding 1979; Lu 1982). The universal double negation refers to the predicate’s object of assertion containing universal meaning, indicating no exceptions. It serves to intensify the assertive mood of the speaker, such as fēi…bùkě (indispensable) indicating the speaker’s assertive mood of must. This format evolved from the conditional pattern fēi X bù Y (must X not Y). But as kě (able) is often used as Y, bù (no) gradually merged with kě (able) into a negative word bùkě (not able). The modal double negation denotes ability, obligation, necessity or possibility to do something, equivalent to various mood phrases, with the mood stronger than affirmative sentences. Like the universal form, it intensifies the mood beyond affirmative sentences. Common patterns include inserting monosyllabic modal verbs like dé (able) in the bù…bù (not…not…) structure. The euphemistic double negation conveys advice, suggestions, or guesses. By emphasizing objective reasons, it adopts a more mollified, euphemistic stance compared to affirmative forms, as in wúfēi (nothing but). The conditional double negation uses two negators to express a conditional link between the negated elements. This form can be rephrased as only if… will… and frequently occurs in conditional clauses, generally intensifying the mood.

Redundant negation, a subset of double negation, involves a semantically superfluous negative component that intensifies the overall negative sense, such as bùzài (not anymore) in bìmiǎn bùzài (avoid doing). Redundant negation actually refers to mismatches between negative adverbs and negative verbs, where the verb negator is a negative morpheme (e.g., bì [avoid] and miǎn [avoid] contain negative meanings). In contrast, the adverb negator is grammatical (e.g., bù [no] in bùzài [not anymore] is a negative morpheme). Yuan (2012) also termed verbs containing implicit negative meanings (such as fángzhǐ [prevent], bìmiǎn [avoid]) as implicit negative verbs. When an implicit negative verb mismatches with an explicit negative adverb, the sentence still expresses the speaker’s negative attitude instead of an affirmative one, intensifying the negative tendency. From a semantic perspective, redundant negations seem contradictory, as they should logically express affirmation but convey negation in practice. However, pragmatically, language users employ redundant negations to intensify their negative tendency, influenced by various factors, including social constraints and communicative effects (Zhou 2023).

The use of marked forms, such as double negation and redundant negation, can be explained by the Manner Principle. This principle suggests that when marked statements convey meanings beyond those of unmarked ones, there is an inherent difference in the mood and information load conveyed by the speaker. By employing these marked forms, speakers can intensify their assertiveness, convey emphasis, or express nuances in their attitudes towards the negated elements.

2.3 The Application of Game Theory and Information Entropy in Linguistics Research

Game theory has long included the analysis of signaling games, with language being a crucial subclass of signals. Language communication is one of the important objects of analysis in the application of game-theoretic pragmatics (Allott 2006; Benz, Jäger, and van Rooij 2006a; Hintikka and Sandu 1997). Hintikka and Sandu (1997) propose the theory of language games, marking the inception of game-theoretic pragmatic studies. They point out that language games associated with a word constitute the most representative and meaningful activities revolving around that word.

In the field of linguistics, Lewis (1969) first introduced the signaling game. Signaling game theory is a mathematical model specifically designed to study how humans make decisions and update beliefs under conditions of incomplete information (Rasmusen 1989, 215). It is used to simulate the process by which signal senders convey information to achieve their goals and how receivers interpret and respond to this information. Participants in the game have multiple strategies to choose from, and the choice of strategy depends on their assessment of expected payoffs. The interactive nature of signaling games is highly similar to verbal communication, which is why it has been widely applied in research on conversational implicature (Benz 2006; Benz and Gotzner 2021; Benz and van Rooij 2007; Blutner 1998; Blutner 2000; Degen 2023; Parikh 1988; Parikh 2001), speech acts (Franke 2011; Franke 2012; Franke, Jäger, and van Rooij 2012; Jäger 2008), and the social significance of discourse (McCready 2015; Skyrms 2010; Benz and Stevens 2018; Terkourafi 2021; Wagner 2013; Yoon et al. 2020).

The introduction of game theory into pragmatic studies is warranted due to the alignment between game theory and Gricean principles. The theoretical foundations of game analysis, which establish common knowledge and beliefs, are pivotal in Grice’s discussion of speaker meaning. The strategic reasoning model employed in Grice’s account of conversational implicature is precisely the focus of clarification efforts in game-theoretic pragmatics (Benz, Jäger, and van Rooij 2006b).

Game-theoretic pragmatics views language communication as a game in which participants (communicators) select communication strategies based on their information, preferences, and expectations to achieve their desired outcomes. The success of discourse communication depends on the understanding of the discourse recipient and the overall goals of the current conversation. The choice of communicators to adhere to or violate the cooperative principle is akin to the strategic choices made by players in a game, where each player always attempts to maximize their utility. Thus, we can explain people’s pragmatic flexibility from the perspective of utility-driven behavior. If cooperation yields higher benefits for the speaker or listener, communicators will cooperate out of self-interest or altruism. Conversely, when the interests of the speaker and listener are not aligned, the speaker may choose not to cooperate, as cooperating would harm either the speaker’s or the listener’s interests. This forms the basis for applying game-theoretic pragmatics to analyze strategic language use.

Crucially, the information-theoretic concept of entropy can be integrated to quantify the uncertainty that interlocutors aim to modulate through their linguistic choices. In information theory, information is defined as a representation of uncertainty regarding changes in the states of things, with its core role being the reduction of uncertainty and provision of a basis for decision-making. Shannon (1948) adapted the concept of entropy from thermodynamics and introduced information entropy to represent the average amount of information in a source, describing the degree of uncertainty present. From an information theory standpoint, entropy serves as a gauge for the degree of randomness or unpredictability within a random variable. As the probability of an event increases, its uncertainty decreases, resulting in a reduction of the associated information entropy.

Building on the concept of information entropy, language can be viewed as a unique means of information transfer and a special form of communication in human society. To convey more information using finite linguistic resources, people often strategically introduce or eliminate uncertainty by modulating entropy levels in their language use. By calculating information entropy values for different linguistic constructions, we can quantify the degrees of uncertainty they convey. In analyzing such strategic language use, game theory provides a valuable framework for understanding decision-making and equilibrium in interactions among communicators. Game theory studies conflicts, competitions, coordination, and cooperation among actions and interactions in a game (Von Neumann and Morgenstern 1947), with the combinations of interdependent, influential decision-making behaviors and outcomes termed as games (Jiang 2008). The basic elements of a game include participants, strategies, and payoffs, which are considered the most important aspects in game-theoretic analyses.

In this study, we introduce the information entropy principle into game-theoretic frameworks by using entropy calculations to infer interlocutors’ intended modulation of uncertainty based on their linguistic choices, as observed in a discourse “game”. This uncertainty modulation is associated with the concept of mood strength, which refers to the degree of assertiveness or tentativeness conveyed by the speaker’s linguistic choices. This entropy quantification is situated within a game-theoretic perspective, viewing discourse as a cooperative game where interlocutors make strategic linguistic moves to achieve pragmatic goals based on shared knowledge and beliefs about the context. This integration provides a beneficial theoretical basis for explaining mood adjustment via quantifying the uncertainty levels conveyed through marked versus unmarked negation forms. By examining entropy as a reflection of uncertainty, we can analyze speakers’ strategic use of negation to increase or decrease the perceived uncertainties and associated mood strengths in their utterances within a cooperative game-theoretic context.

2.4 Research Gaps and Research Questions

Despite extensive research on negation, several significant gaps and limitations persist within the existing literature. Firstly, many previous studies have approached double negation primarily from a syntactic or semantic perspective, often neglecting its broader communicative functions and real-world usage contexts. This narrow focus overlooks the dynamic interaction of double negation with discourse and pragmatics, failing to capture the multifaceted nature of this phenomenon (Horn 1989; Tian, Ferguson, and Breheny 2016; Tsiakmakis and Espinal 2022). Secondly, existing studies predominantly examine double negation in English or other Indo-European languages, which restricts the generalizability and applicability of findings to diverse linguistic contexts. Neglecting non-Indo-European languages, such as Mandarin Chinese, overlooks valuable insights that could be gleaned from their distinct grammatical features and usage patterns (Déprez and Espinal 2020; Kaup and Dudschig 2020; Tian and Breheny 2016). Thirdly, a considerable portion of the literature on double negation relies heavily on reflective or theoretical analyses, often at the expense of empirical validation. This methodological limitation hinders the empirical grounding of theoretical claims, leading to speculative or unsubstantiated conclusions about the nature and function of double negation in natural language. Lastly, traditional analyses frequently oversimplify double negation, treating it as merely redundant or emphasizing its affirmative interpretation. Emerging theoretical frameworks, such as game theory and information entropy, offer promising avenues for exploring the strategic use of double negation in communication. However, these frameworks have not been extensively applied to the study of double negation, leaving a gap in understanding how speakers manipulate information load and mood through these constructions (Allott 2006; Benz, Jäger, and van Rooij et al. 2006a).

To address these gaps, this study aims to investigate the following research questions: (a) How do speakers engaged in double and redundant negation cooperate to increase or decrease the information entropy of their discourse? (b) From a pragmatic perspective, what motivates the formation of double and redundant negation constructions? Ultimately, this research endeavors to comprehensively examine the mood and information loads associated with double and redundant negation expressions, contributing to a more nuanced understanding of their roles in natural language.

3.1 Corpus

The corpus utilized in this study originated from the BCC Corpus (BLCU Chinese Corpus; Xun et al. 2016). Administered by the Beijing Language and Culture University Corpus Center (BCC), this corpus offered a comprehensive online repository primarily dedicated to the Mandarin Chinese language, supplemented by data from various other languages. The specific section of the corpus used in this study was the newspaper section, which comprised approximately 2 billion characters.

The BCC Corpus was selected for this study due to several reasons related to our research purpose. First, the BCC Corpus contained an extensive collection of contemporary Mandarin Chinese texts, making it a rich source for examining modern language usage patterns, including double and redundant negations. Second, the corpus’s newspaper section provided a representative sample of formal written Chinese, ensuring that the language structures analyzed were reflective of current, standard language practices. Third, with its vast size, including the newspaper section with approximately two billion characters, the BCC Corpus included a significant number of sentences that exhibited double and redundant negation structures, thus providing a robust dataset for statistical and entropy-based analyses. Fourth, as a well-maintained and continuously updated resource, the BCC Corpus offered high-quality data that was readily accessible, allowing for reproducibility and reliability in linguistic research.

In this study, sentences featuring double and redundant negations were systematically retrieved from the corpus. The extraction process involved using specific search expressions designed to identify these structures within the large dataset. The selected sentences were then enumerated and categorized based on their syntactic patterns. Entropy-based methods were employed to quantify the frequency and analyze the mood strength expressed by double and redundant negations. Table 1 illustrates the frequency of occurrences, search expressions utilized, and instances of various sentence patterns sourced from the BCC corpus.

3.2 Entropy Calculation

We analyzed the role of mood adjustment in game theory by means of corpus statistics and information entropy values of different sentence patterns. We used entropy as a quantifiable measure of the assertiveness-tentativeness dimension of speaker mood or attitude. Payoff matrices in the integration of information entropy to a game theory approach were used to demonstrate how pragmatic features influence gaming processes. For a probabilistic system X with n events: X ₁…X _i …X _n , with probabilities of P ₁…P _i …P _n , respectively, the information entropy H X i of an event X _i was calculated as: H X i = − log P i , representing the amount of information generated after the occurrence of a random event’s specific result. This term was also called self-information, the actual value of which was the negated logarithm of the occurrence probability. The information entropy (H _(X)) of the system, namely the average uncertainty of all events, was calculated as: H X = − ∑ i = 1 n p i ⁡ log p i , where the logarithm took 2 as base, and the unit was usually bit (namely binary 0 and 1). The negative sign was used because probabilities were less than 1. Taking the negative ensured a positive entropy. Hence, self-information only represented the uncertainty of a single symbol or event in the information source, while information entropy considered the overall statistical traits of the source, measuring the degree of ignorance, and calculating the average uncertainty of all possible outcomes. It measured uncertainty and uniformity of probability distribution of the random variable X.

The probability distribution’s uniformity determined the level of uncertainty and entropy: a more uniform distribution signified greater uncertainty and higher entropy, while a skewed distribution indicated less uncertainty and lower entropy. An increase in entropy reflected greater uncertainty, whereas a decrease in entropy implied less uncertainty and more information. Given the same amount of data, a more ordered system had a lower entropy value, while a more chaotic system had a higher value. In language, the presence of negative components in a sentence reduced uncertainty and lowered the entropy value. Affirmative sentences typically contained only one affirmative component, while double and redundant negations contained two negators. Consequently, they corresponded to the information entropy associated with affirmative words generating affirmative sentences and negative words in double and redundant negative sentences, respectively.

Python (version 3.12.4) was used to calculate the information entropy of the selected sentences, focusing on comparing differences between the information entropy of negative words in double and redundant negative sentences and affirmative words in corresponding affirmative sentences to explain relations between mood adjustment and information entropy change of the entire sentence. Therefore, we selected typical sentence examples and analyzed their entropy values. Lower entropy values corresponded to more certainty and assertiveness being conveyed, as the linguistic form reduces unpredictability. Conversely, higher entropy indicated greater uncertainty and tentativeness in the speaker’s stance.

3.3 Contextual Analysis

To complement the above quantitative analysis, contextual analysis was employed to guide the interpretation and explanation of the findings. Contextual analysis involved examining the surrounding text and situational context to understand the broader discourse in which negations were used, considering factors such as the speaker’s intentions, the communicative situation, and the interplay between different elements within the discourse (Duranti and Goodwin 1992). This method was particularly useful for identifying the pragmatic functions of linguistic structures in real-world communication.

The contextual analysis process began by identifying relevant examples of double and redundant negation from the BCC Corpus and their surrounding context. Each example underwent close reading within its full context, including preceding and following sentences. We then analyzed how the negation construction contributed to the overall discourse, considering the speaker’s intentions, situational context, interaction with other discourse elements, and specific meanings or pragmatic effects conveyed. Where applicable, the negation construction was compared with potential alternative expressions to highlight its unique pragmatic function. Based on this analysis, the pragmatic functions were analyzed. In the case of double negation using the universal form wúbù (without exception), as in the following example (3):

1. 凡来观赏者, 无不 “啧啧” 称奇。

   Fánlái guānshǎng zhě, wúbù “zézé” chēngqí.

   Anyone who comes to view it, without exception , exclaims in amazement.

   (From BLCU Chinese Corpus, Fujian Daily, 1994)

The contextual analysis revealed that the use of wúbù (without exception) emphasized the comprehensive nature of the statement. The speaker’s intention appeared to highlight the extraordinary attitude of appreciating works of art. Compared to using dōu (all), wúbù (without exception) conveyed a stronger sense of absoluteness and emphasized the speaker’s assertive mood, serving the pragmatic function of mood intensification and emphasis on completeness.

In the case of redundant negation, as exemplified by the following example (4):

1. 司机否认没有给我那100元车钱。

   Sījī fǒurèn méiyǒu gěiwǒ nà 100 yuán chēqián.

   The driver denied giving me the 100 yuan fare.

   (From Center for Chinese Linguistics Corpus, 2010)

The use of fǒurèn (deny) followed by méiyǒu (have not) formed a redundant negation in a daily statement. The situational context appeared to be a dispute over a taxi fare payment. The speaker’s intention was to report the driver’s response to an accusation of non-payment. By using the redundant negation structure, the speaker emphasized the strength of the driver’s denial. Compared to a simple negation like “Sījī méiyǒu gěiwǒ nà 100 yuán chēqián (The driver didn’t give me the 100 yuan fare)”, this structure created a more forceful refutation. The pragmatic function of this redundant negation was multifaceted. Firstly, it intensified the negative mood, underlining the driver’s insistence on having paid. Secondly, it introduced an element of reported speech, distancing the speaker from the claim and potentially implying skepticism. Lastly, it might serve to heighten the tension or drama of the situation, suggesting a more heated exchange than a simple denial would imply.

Through this analysis, we could observe how double and redundant negations convey emphasis, mood intensification, and negative attitudes. This method provided a deeper understanding of their nuances and implications in natural language, revealing how speakers use them to achieve specific communicative goals in various contexts.

4.1 Occurrences of Negations in Mandarin Chinese

In the BCC Corpus of newspapers, the proportion of double negation usage was significantly higher than that of redundant negation. As shown in Figure 1, the frequency of double negation was approximately 33 times higher than that of redundant negation. Upon further categorization of double negation sentence structures, the conditional and modal forms were more frequently utilized, followed by the universal and euphemistic forms, which were less common. Among redundant negations, the usage of jùbù (refuse) structure was the highest, occurring 6,919 times, while other instances of redundant negation were comparatively rare, averaging only 11 occurrences. The low frequency of redundant negation usage, in contrast to the high prevalence of double negation in newspaper language, suggested that redundant negation is underutilized in this context. This finding, along with the predominance of double negation, indicated a greater tendency towards expressing speaker’s affirmative moods through double negation structures.

Figure 1:

The frequency of five types of Mandarin Chinese negations in the BCC Corpus.

4.2 Double Negation

4.2.1 Mood Intensification and Overall Sentence Entropy Reduction

The contextual analysis of the universal double negation form wúbù (without exception) revealed its pragmatic function in conveying a complete and all-encompassing meaning. Examining the discourse context in which wúbù (without exception) appears, we observed that it served to include every single aspect without exception, thereby reinforcing the speaker’s affirmative attitude. In the example shown in Table 2 and Figure 2a, the situational context involved information exchange between reporters and readers. The use of the marked expression wúbù (without exception) resulted in lower information entropy (specifically 4.895) for both parties; compared to an increase of 0.1 when using dōu (all). This contextual comparison suggested that wúbù (without exception) relative to dōu (all) could reduce sentence entropy in specific discourse environments, thereby reinforcing speaker’s affirmative attitude.

Table 2:

Examples with two contexts in the universal structures of wúbù (without exception), bùnéngbù (couldn’t but) and méiyǒu…bù (without…no).

Context 1	Context 2
(1a). 尽揽澳门社团长河之大观，其背后有一条鲜明的主线贯穿始终，这就是社团的诞生及兴旺，无不伴随着社会的变革和转换，无不与祖国的荣辱兴衰紧密相连，无不依托开放与自由的社会环境。	(1b). 尽揽澳门社团长河之大观，其背后有一条鲜明的主线贯穿始终，这就是社团的诞生及兴旺，都伴随着社会的变革和转换，都与祖国的荣辱兴衰紧密相连，都依托开放与自由的社会环境。
Jìn lǎn àomén shètuán chánghé zhī dàguān, qí bèihòu yǒu yītiáo xiānmíng de zhǔxiàn guànchuān shǐzhōng, zhè jiùshì shètuán de dànshēng jí xīngwàng, wúbù bànsuí zhe shèhuì de biàngé hé zhuǎnhuàn, wúbù yǔ zǔguó de róngrǔ xīngshuāi jǐnmì xiānglián, wúbù yītuō kāifàng yǔ zìyóu de shèhuì huánjìng.	Jìn lǎn àomén shètuán chánghé zhī dàguān, qí bèihòu yǒu yītiáo xiānmíng de zhǔxiàn guànchuān shǐzhōng, zhè jiùshì shètuán de dànshēng jí xīngwàng, dōu bànsuí zhe shèhuì de biàngé hé zhuǎnhuàn, dōu yǔ zǔguó de róngrǔ xīngshuāi jǐnmì xiānglián, dōu yītuō kāifàng yǔ zìyóu de shèhuì huánjìng.
Gathering the grand spectacle of Macao’s community organizations, there is a clear thread running through it all, which is the birth and prosperity of these organizations, without exception accompanied by social changes and transitions, without exception closely linked to the rise and fall of the motherland, without exception relying on the open and free social environment.	Gathering the grand spectacle of Macao’s community organizations, there is a clear thread running through it all, which is the birth and prosperity of these organizations, all accompany social changes and transitions, all be closely linked to the rise and fall of the motherland, all rely on the open and free social environment.
(2a). 今后承办亚运会的城市，恐怕不能不与“北京模式”作一番比较，不论是场馆设施，还是精神风貌。	(2b). 今后承办亚运会的城市，恐怕必须与“北京模式”作一番比较，不论是场馆设施，还是精神风貌。
Jīnhòu chéngbàn Yàyùnhuì de chéngshì, kǒngpà bùnéngbù yǔ “Běijīng móshì” zuò yīfān bǐjiào, bùlùn shì chǎngguǎn shèshī, háishì jīngshén fēngmào.	Jīnhòu chéngbàn Yàyùnhuì de chéngshì, kǒngpà bìxū yǔ “Běijīng móshì” zuò yīfān bǐjiào, bùlùn shì chǎngguǎn shèshī, háishì jīngshén fēngmào.
Cities hosting the Asian Games in the future cannot but compare themselves to the ‘Beijing model,’ whether in terms of venue facilities or spiritual demeanor.	Cities hosting the Asian Games in the future must compare themselves to the ‘Beijing model,’ whether in terms of venue facilities or spiritual demeanor.
(3a). 共享是对共建成果的公平享有，没有共建就谈不上共享。	(3b). 共享是对共建成果的公平享有，有共建就能谈上共享。
Gòngxiǎng shì duì gòngjiàn chéngguǒ de gōngpíng xiǎngyǒu, méiyǒu gòngjiàn jiù tán bù shàng gòngxiǎng.	Gòngxiǎng shì duì gòngjiàn chéngguǒ de gōngpíng xiǎngyǒu, yǒu gòngjiàn jiù néng tánshàng gòngxiǎng.
Sharing entails the fair enjoyment of the fruits of collective construction; without collective construction, there can be no sharing.	Sharing entails the fair enjoyment of the fruits of collective construction; with collective construction, sharing becomes possible.

Figure 2:

The game matrix of wúbù (without exception), bùnéngbù (couldn’t but) and méiyǒu…bù (without…no).

Analyzing the surrounding text in Context 1, we found that the restrictive clause following wúbù (without exception) encompassed a comprehensive range. This construction emphasized an absolute correlation between the subject and object, conveying a stronger mood than dōu (all) in Context 2. The broader scope of negation conveyed through double negation, as opposed to the affirmation conveyed through unmarked positive terms, underlied this phenomenon. By reducing more uncertainty and conveying more definitive information, double negation lowers the overall entropy of the sentence, intensifying the speaker’s mood compared to its affirmative counterpart. Considering the pragmatic implications, this marked expression of double negation drew special attention from readers, prompting them to notice the emphasis on absolute affirmation within the broader communicative context.

Liu, Wenyu, and Wei (1996) noted that double negation in Mandarin Chinese often carried emotional connotations beyond simple affirmation or negation cancellation. These emotional nuances were particularly evident in modal structures of double negation sentences, such as bùnéngbù (couldn’t but). Contextual analysis of Figure 2b revealed that inserting an auxiliary verb into the bù…bù (no…no) structure transforms bùnéngbù (couldn’t but) to express affirmation while also implying compulsion or necessity. In this communicative situation, reporters tended to use bùnéngbù (couldn’t but) to slightly lower sentence entropy (by 0.027), conveying a stronger sense of compulsion that resonates more deeply with readers. Consequently, marked double negation tended to be more emphatic than an unmarked affirmative sentence. From the perspective of information entropy, the stacking of double negations in modal structures reduced the entropy of negations compared to affirmations. These negations all conveyed a sense of necessity, further reducing informational uncertainty and lowering the overall entropy of the sentence, thus amplifying the speaker’s intended mood.

In conditional structures of double negation sentences, the use of combined relationships or contracted complex sentences such as méi(yǒu)… bù… (without…no…) corresponded to affirmative expressions like yǒu… néng… (with…), indicating that subsequent events could only occur under specific conditions. The contextual analysis of Figure 2c showed that both reporters and readers used these marked expressions to highlight the conditions that needed to be met, emphasizing that collective construction was a necessary prerequisite for sharing. The conditional double negation (Context 1) reduced overall sentence entropy by 0.133, proving more appropriate for the communicative goal. Hence, the entropy of double negation words in conditional sentences was lower than that of affirmative words, leading to a decrease in the overall sentence entropy of double negation sentences and reducing the uncertainty of the information.

4.2.2 Mood Attenuation and Overall Sentence Entropy Increase

The contextual analysis of euphemistic expressions within double negation sentences revealed their role in mood attenuation and overall sentence entropy increase. When two negators were present in separate negation events, the likelihood of uncertainty rose, broadening the scope of uncertainty. This structure was often used in contexts such as persuasion, suggestion, and speculation. The following depicted the changes in information entropy reflected in euphemistic expressions within double negation sentences.

In the case of wúfēi (nothing but) in the phrase wúfēi yīmiàn zhīcí (nothing but a one-sided assertion), as illustrated in Table 3 and Figure 3a, the contextual analysis revealed its pragmatic function in conveying a sense of disdain while softening the speaker’s tone. The situational context here suggested that reporters, constrained by real-world factors, might find it inappropriate to express criticism directly. By using wúfēi (nothing but) as a marked expression, they informed the audience of the statements’ lack of credibility in a more tactful manner. The contextual comparison between Context 1 and Context 2 demonstrated that both reporters and readers in Context 1 chose to increase the information entropy value (by 0.07) to weaken their assertive attitude and express critical views more diplomatically.

Table 3:

Examples with two contexts in the conditional structures of wúfēi (nothing but) and bùshìbù…(be not).

Context 1	Context 2
(4a). 不管标题、内容，这篇报导都力图给人这样一种印象：李累的发言无非一面之辞，不可轻信！	(4b). 不管标题、内容，这篇报导都力图给人这样一种印象：李累的发言是一面之辞，不可轻信！
Bùguǎn biāotí, nèiróng, zhèpiān bàodǎo dōu lìtú gěi rén zhèyàng yīzhǒng yìnxiàng: Lǐlèi de fāyán wúfēi yīmiàn zhīcí, bùkě qīngxìn!	Bùguǎn biāotí, nèiróng, zhèpiān bàodǎo dōu lìtú gěi rén zhèyàng yīzhǒng yìnxiàng: Lǐlèi de fāyán shì yīmiàn zhīcí, bùkě qīngxìn!
Regardless of the title or content, this report endeavors to create the impression that Li Lei’s remarks are nothing but one-sided assertions and should not be taken lightly!	Regardless of the title or content, this report endeavors to create the impression that Li Lei’s remarks are one-sided assertions and should not be taken lightly!
(5a). 我们讲生态平衡，不是不讲倾向性，不是不分高低、优劣与文野，不是不分美丑，恰恰相反，我们讲生态平衡是为了给各种风格的美打开广阔的道路。	(5b). 我们讲生态平衡，是讲倾向性，是分高低、优劣与文野，是分美丑，恰恰相反，我们讲生态平衡是为了给各种风格的美打开广阔的道路。
Wǒmen jiǎng shēngtài pínghéng, bùshìbù jiǎng qīngxiàngxìng, bùshìbù fēn gāodī, yōuliè yǔ wényě, bùshìbù fēn měichǒu, qiàqià xiāngfǎn, wǒmen jiǎng shēngtài pínghéng shì wèile gěi gèzhǒng fēnggé de měi dǎkāi guǎngkuò de dàolù.	Wǒmen jiǎng shēngtài pínghéng, shì jiǎng qīngxiàngxìng, shì fēn gāodī, yōuliè yǔ wényě, shì fēn měichǒu, qiàqià xiāngfǎn, wǒmen jiǎng shēngtài pínghéng shì wèile gěi gèzhǒng fēnggé de měi dǎkāi guǎngkuò de dàolù.
When we talk about ecological balance, it’s not about disregarding inclinations, nor about ignoring distinctions of high or low, good or bad, and not about overlooking beauty or ugliness. On the contrary, we talk about ecological balance to pave the way for a wide variety of styles of beauty.	When we talk about ecological balance, we do discuss inclinations, we do differentiate between high and low, good and bad, and between beauty and ugliness. Quite the opposite, we talk about ecological balance to open up broad pathways for various styles of beauty.

Figure 3:

The game matrix of wúfēi (nothing but) and bùshìbù…(be not).

Similarly, the affirmative form of bùshìbù… (be not) was the unmarked shì or yǒu (meaning do). The analysis of bùshìbù… (be not) in Figure 3b revealed its pragmatic function in influencing the audience’s mindset. When reporters and readers chose the affirmative form in Context 2, they were merely expressing objective situations, such as differentiating between high and low, good and bad, and between beauty and ugliness. Such statements were made solely to indicate objective facts and did not involve any shared presuppositions with the audience. We observed that the use of double negation here served to adjust the audience’s preconceived notions, yielding a more tactful corrective effect. The contextual analysis showed that this structure increased the uncertainty of the information (by 0.299), requiring the audience to understand the implications of the speaker’s speculation about their psychological thoughts. From an information entropy perspective, the presence of two negators in these double negation sentences increased the probability of uncertainty, leading to an increase in the overall sentence’s information entropy value. This trend weakened the sentence’s negative form while conveying the speaker’s speculative and tentative mood.

4.3 Redundant Negation

Unlike double negation, redundant negation consistently strengthened the negative mood rather than creating affirmation through cancellation. Contextual analysis of redundant negation structures revealed their pragmatic function in emphasizing overall negative meaning. As defined by Yuan (2012), these structures involved adding an adverbial negator to the predicate object following an implicit negation verb.

Examining the discourse context of fángzhǐ bùzài (avoid doing) in Table 4 and Figure 4a, we observed that the situational context here involved discussing the dual nature of atomic energy. The reporter’s addition of bùzài (not anymore) to the object clause of fángzhǐ (avoid) emphasized their desire to prevent future misuse. Analyzing the surrounding text and applying Grice’s conversational implicature principle, we can inferred that readers would interpret bùzài (not anymore) as a redundant negation emphasizing the negative mood. Consequently, readers inferred that bùzài (not anymore) was a redundant negator, and the entire sentence still conveyed a negative meaning. From the perspective of information entropy, both reporters and readers tended to choose the mismatch method to reduce entropy (0.009), strengthening the speaker’s negative attitude.

Figure 4:

The game matrix of fángzhǐ bùzài (avoid doing) and fǒurèn méiyǒu (deny).

Similarly, the contextual analysis of fǒurèn méiyǒu (deny) in Figure 4b revealed its function in expressing a strong denial attitude. The communicative situation here involved an official government statement. The combination of fǒurèn (deny) and méiyǒu (no) formed a redundant negation, indicating a vehement denial. In Context 1, reporters and readers engaged in cooperative gaming, tending to express a strong denial attitude toward the Indian government. This context reduced the information entropy value by 0.006 and 0.0001 respectively, emphasizing the negative stance.

When redundant negation existed in negative sentences, the two negators were considered part of the same negation event, reducing the uncertainty of the overall probability system and significantly lowering the negator’s information entropy in the sentence compared to sentences with only a single negator. Redundant negation also reduced the overall sentence’s information entropy and strengthened the speaker’s negative attitude. The reasons behind redundant negation mainly included: (a) the stacking of negators, where another similar adverbial negator was added on top of the original verb negator to form a layered or nested marked language structure; (b) the strengthening of negation effects, such as using fǒurèn méiyǒu (deny) to emphasize both the denial attitude and the absence fact, achieving the effect of strengthening negation; and (c) fusion, where two components that usually did not coexist in language rules (verb negator and adverb negator) were combined into one linguistic unit, making the entire sentence still conveyed a stronger negative mood rather than an affirmative one (Ju 2010; Shen 2006). These mismatching factors resulted in a stronger expression of negation rather than affirmation, serving specific communicative goals within their discourse environments.

5.1 Overview of Findings

The present study investigated how speakers cooperate to modulate the information entropy and pragmatic motivations underlying double and redundant negation constructions in Mandarin Chinese. While both double and redundant negations affect sentence entropy, they do so in different ways: (a) Double negation can either reduce entropy (intensifying mood) or increase it (attenuating mood), depending on the specific structure and context; (b) Redundant negation generally reduces entropy, consistently strengthening the negative mood. These adjustment effects are achieved through strategic linguistic choices that increase or decrease uncertainty based on contextual factors and communicative goals. This nuanced manipulation of information entropy highlights the sophisticated ways in which Mandarin speakers manage and convey complex pragmatic meanings.

5.2 Double Negations and Sentence Entropy

Double negations, such as wúbù (without exception) and bùnéngbù (couldn’t but), demonstrate varying effects on sentence entropy. Universal double negations like wúbù (without exception), the explicit marking of the complete scope without exceptions diminishes perceived uncertainty, thereby reducing information entropy compared to the unmarked dōu (all). This meaning aligns with Levinson’s Manner Principle, wherein marked expressions convey meanings beyond unmarked forms. Reporters employ wúbù (without exception) to emphatically convey definitive, exception-free affirmation, intensifying the speaker’s mood through decreased entropy. Modal forms like bùnéngbù (couldn’t but) stack modal auxiliaries within the negation structure, further compounding negations to lower entropy and amplify the sense of compulsion or necessity. These intensifying effects demonstrate speakers’ strategic deployment of marked double negations to strengthen their communicative force, akin to Horn’s (1989) notion of deriving strong statements from weaker ones via understatement.

Conversely, euphemistic double negations such as wúfēi (nothing but) and bùshìbù (couldn’t but) increase entropy by introducing uncertainty, thereby weakening the assertive force of the speaker’s stance in line with Levinson’s Manner Principle. According to this principle, marked linguistic forms like double negations signal non-stereotypical, tentative meanings that go beyond those conveyed by their unmarked counterparts. The observed entropy increase associated with euphemistic wúfēi (nothing but) and bùshìbù (couldn’t but) patterns quantifies this pragmatic markedness effect, allowing speakers to implicate tentative critiques or gentle corrections through heightened uncertainty. This function resonates with Grice’s (1991) concept of flouting maxims to generate conversational implicatures. By employing wúfēi (nothing but), reporters can convey critiques indirectly and tactfully, relying on the audience’s pragmatic inferences facilitated by the increased entropy. Similarly, the bùshìbù (couldn’t but) structure enables reporters to gently correct presumed audience mindsets, increasing entropy to facilitate audience identification with the intended perspective. Such weakening effects align with Horn’s view of double negation attenuating utterance force while still operating within the negation-affirmation continuum.

These findings are consistent with previous research and demonstrate the complementary nature of Gricean implicature, signaling game theory, and information entropy in understanding negation constructions. Gricean implicature provides the foundation for understanding how speakers convey meanings beyond literal semantic content. Signaling game theory offers a framework for analyzing how speakers strategically choose linguistic forms to signal their intentions and beliefs. Information entropy quantifies the uncertainty in these linguistic choices, allowing us to measure the pragmatic effects of different negation patterns.

For instance, the use of universal double negations like wúbù (without exception) can be seen as a cooperative move in the Gricean sense, where the speaker provides more information than is strictly necessary to ensure clear communication. From a signaling game perspective, this choice signals the speaker’s high degree of certainty. The reduction in entropy quantifies this certainty, providing a measurable indicator of the pragmatic effect. Conversely, euphemistic double negations like wúfēi (nothing but) exemplify how speakers can flout Grice’s maxims to generate implicatures. In signaling game terms, this creates a more complex signal that requires additional processing from the receiver. The increase in entropy quantifies this added complexity, reflecting the indirect nature of the communication.

5.3 Redundant Negations and Sentence Entropy

Redundant negations, characterized by the co-occurrence of verbal and adverbial negators, reduce overall sentence entropy by compounding negations within a single negation event. This stacking effect strengthens the speaker’s negative mood, as observed in forms like jùbù (refuse) and fǒurèn méiyǒu (deny). In these cases, speakers cooperate to underscore negation by fusing typically incompatible components, creating marked structures that emphatically convey intended meanings. These findings corroborate previous claims by Yuan (2012) and Zhou (2023) regarding redundant negations intensifying the speaker’s negative mood despite seeming contradictory from a logical perspective.

The interaction between verbal and adverbial negators in redundant negations demonstrates a deliberate linguistic strategy to enhance the negative connotation and reduce entropy. This phenomenon aligns with the findings of Yuan (2012), who observed that Mandarin speakers use redundant negations to create stronger emphatic statements. Zhou (2023)’s research further supports this by showing that such constructions, while logically complex, are pragmatically effective in conveying strong negative stances. Our study builds on these observations by providing a quantitative analysis of how entropy is manipulated in redundant negations, thereby offering a more precise understanding of their pragmatic impact.

These findings are consistent with previous research indicating that double negations serve multiple communicative functions. For instance, research by Horn (1989) and Levinson (2000) highlights the role of marked forms in conveying nuanced meanings that are not captured by unmarked forms. Our study extends these insights by providing quantitative evidence of how entropy levels are manipulated through double negations to achieve specific pragmatic outcomes. This empirical grounding supports the theoretical claims about the communicative efficacy of marked linguistic forms.

The implications of these findings extend beyond theoretical linguistics. They have a significant impact on signaling game theory and pragmatic markedness, offering valuable insights into how speakers strategically use linguistic structures to convey complex meanings. In the context of signaling game theory, our results demonstrate how speakers use double negations as signals to convey information about their mood, certainty, and intentions. The strategic manipulation of entropy through these negation patterns can be seen as a form of costly signaling, where the cognitive effort required to process complex negations is a marker of the speaker’s commitment to the conveyed message.

5.4 Refining Frameworks and Widening the Cross-Linguistic Lens

This study refines and integrates theoretical frameworks encompassing Gricean implicature, signaling game theory, and information theory through an entropy-based approach to Mandarin Chinese negation patterns. Specifically, the findings provide quantitative grounding for Grice’s cooperative principle and implicature mechanisms by analyzing how speakers strategically adjust entropy/uncertainty levels through marked negation choices beyond literal semantic content. Levinson’s claims about marked forms conveying non-stereotypical meanings are extended by linking euphemistic double negations to quantifiable entropy increases instantiating pragmatic markedness effects. Signaling game theory offers a framework for analyzing the strategic choices speakers make in selecting linguistic forms to convey their intentions and beliefs. Information entropy quantifies the uncertainty in these linguistic choices, allowing us to measure the pragmatic effects of different negation patterns. The integration of these frameworks allows for a more comprehensive analysis of negation constructions. Gricean implicature explains why certain forms are chosen over others, signaling game theory provides a model for the strategic nature of these choices, and information entropy offers a quantitative measure of their pragmatic effects. This interdisciplinary approach provides a richer understanding of how speakers navigate the complex landscape of cooperative discourse.

The strategic adjustment of entropy through marked double negations reflects speakers’ nuanced pragmatic considerations within cooperative discourse. Intensifying forms assert strong, unequivocal stances, while weakening forms allow for indirect, face-saving communication. These findings extend previous accounts by empirically grounding the relationships between double negation, mood strength, and information exchange within the cooperative principle framework proposed by Grice (1991), while also providing quantitative support for Levinson’s predictions about the pragmatic markedness of non-stereotypical linguistic forms like euphemistic double negations.

The quantification of uncertainty through entropy measures provides a novel approach to understanding how interlocutors navigate cooperative discourse, making contextually-optimal linguistic choices for assertion, indirectness, and emphasis. This approach has potential applications in various fields. In natural language processing, the entropy-based analysis of negation patterns can inform the development of more sophisticated algorithms capable of detecting nuanced meanings in text, improving sentiment analysis, machine translation, and dialogue systems. In cross-cultural communication, understanding how different languages use negation to modulate information entropy can facilitate more effective interactions in diplomatic, business, and educational contexts. Additionally, these findings can contribute to the development of more accurate computational models of pragmatic reasoning, which could be used to simulate human-like language understanding and generation in artificial intelligence systems.

Looking ahead, future research could explore these phenomena in other languages, providing a more comprehensive understanding of how different linguistic systems achieve similar pragmatic goals. Additionally, investigating cognitive and social factors in negation use could shed light on the mental processes and sociocultural influences underlying these linguistic choices. Such research could involve neuroimaging studies, psycholinguistic experiments, or sociolinguistic analyses to examine the cognitive load, processing strategies, and social variables associated with different negation constructions. These future directions promise to yield valuable insights that can further inform both theoretical linguistics and practical applications in an increasingly interconnected world.