Double Negation in English and Ukrainian: a View from Cognitive Linguistics and a SLA Context

Irrespective of the fact that two negations in the same clause usually cancel each other out and result in an affirmative sentence, the phenomenon of double negation in English is still a disputable problem. These aspects all lead to linguistic complexity of double negation in SLA followed by a description of its relevant characteristics and contradictory aspects in English and Ukrainian. This study aims to establish a cognitive model of double negation as understatement via a mitigation operation as regards its specific contextual effects and to explore the impact of the language of instruction on the linguistic complexity of double negation to the learner of English. Within the theory of negation, this research applies the hypothesis to the assumption that English is the main language of instruction for a Ukrainian learner, and how L2 learners’ comprehension and production of double negation occur. The hypothesis is empirically tested against the English sentences with their Ukrainian equivalents and the tasks in the questionnaire written by learners of English. The results of my research suggest that when learners interpret L2 sentences with more than one negative element we identify both similar and different double negatives in a students’ first and second language that influence enhanced awareness of double negation and which is important for successful L2 comprehension and use.


L I N G U I S T I C S / K A L B O T Y R A
Irrespective of the fact that two negations in the same clause usually cancel each other out and result in an affirmative sentence, the phenomenon of double negation in English is still a disputable problem. These aspects all lead to linguistic complexity of double negation in SLA followed by a description of its relevant characteristics and contradictory aspects in English and Ukrainian. This study aims to establish a cognitive model of double negation as understatement via a mitigation operation as regards its specific contextual effects and to explore the impact of the language of instruction on the linguistic complexity of double negation to the learner of English. Within the theory of negation, this research applies the hypothesis to the assumption that English is the main language of instruction for a Ukrainian learner, and how L2 learners' comprehension and production of double negation occur. The hypothesis is empirically tested against the English sentences with their Ukrainian equivalents and the tasks in the questionnaire written by learners of English. The results of my research suggest that when learners interpret L2 sentences with more than one negative element we identify both similar and different double negatives in a students' first and second language that influence enhanced awareness of double negation and which is important for successful L2 comprehension and use.
One of the earliest and most common linguistic definitions of double negation (DN) is one by the famous Danish linguist Otto Jespersen and is described in his Negation in English and Other Languages: "It seems to be a universal rule in all languages that two negatives make an affirmative, if both are special negatives attached to the same word; this generally happens in this way that not is placed before some word of negative import or containing a negative prefix" (Jespersen, 1917, p. 63). This definition has its continuation: "All the languages seem to have a common law, that is, two negative makes a positive" (ibid., p. 33). It totally corresponds to the commonly accepted rule in linguistics where most studies claim that double negatives are incorrect because two negatives make a positive. This rule also conforms to mathematical logic. In contrast, DN in natural language is a complex phenomenon. Though based on the principle of logic, the concept of DN in English often entailed some intermediate terms concerning the issue why it was used to convey negation or affirmation, emphatic negation or emphatic affirmation, weakening negation or weakening affirmation. Consequently, they all began to refer to the causes of the semantics of DN.
In traditional grammars, DN is still one of the self-contradictory and troublesome problems in English grammar and semantics. Traditional grammars present double negatives as simply incorrect, and DN can be described as a syntactic construction in which two negative words are used in the same clause to express a single negation (What is a double negative? [online]). Thus, from a traditional linguistic point of view, DN is just another form of negation in English and using two negatives turns the sentence into a positive one.
Modern scholars Moor (1992) and Duffy (1997), who explored DN in English and other European and Asian languages, stress that the use of double negatives in speech in most cases causes misunderstanding and confusion, and the receiver faces misinterpretation about the speaker's or writer's intention. Furthermore, sometimes the use of DN involves some indirect difficulties and often makes the hearer experience cognitive discouragement, i.e., those conditions under which the receiver of a message feels resultant confusion. As these scholars claim, firstly, when double negatives are used too often, they may cause questionable use or even some cognitive disturbance. Secondly, when used often in colloquial speech, the receiver of a message should decide whether to interpret the message positively or negatively. Therefore, the present paper aims at demonstrating how cognitive linguistic theory of mental spaces is applied to the phenomenon of DN in English, and exploring the impact of the language of instruction on the linguistic complexity of DN to the Ukrainian-language learner of English. In line with this aim, this study raises the following questions: 1) What cognitive operations are employed to build a cognitive model of DN in English with certain correspondences between a negative conceptual space and a positive (alternative) space based on mental spaces theory? 2) What are the significant features of double negatives possessed by English and Ukrainian in a SLA context? 3) How do Ukrainian-speaking adults learn, interpret, and use L2 sentences with more than one negative element?
Despite the substantial amount of publications connected with the notion of DN, there are still some unexplored aspects that can provide new insights and approaches to the study of DN that demand relevant conceptions within the framework of cognitive linguistics with a special emphasis on the acquisition of double negatives in English and Ukrainian. It is useful to grasp how the notion of negation and its particular type DN have developed as a linguistic, social, and cognitive phenomenon, and thus have long attracted attention of scholars who are interested in and concentrate on this issue. Furthermore, this linguistic interest, which is not restricted to one particular language, reveals the relevance of the topic from the perspective of SLA. This kind of study has not been done so far.

Introduction
The status of DN in traditional grammars of English and standard English speech is clear cut: a double negative in one sentence is incorrect, and two negatives become a positive. This rule goes back to Robert Lowth's prescriptive grammar entitled Short Introduction to English Grammar (1762) in which the usage of DN was based on the theory that "two negatives cancel each other out and thereby make an affirmative" (Seright, 1966, p. 123). This principle goes back to the logical law of double negation within the framework of both Western (Stoic) and Eastern (Buddhist and Nyaya) logical traditions. Nevertheless, Lowth defended DN by analogy to mathematics, arguing that the sum of two negative numbers rather reinforces their emphatic function than cancels each other. There is an explanation for the presence in Lowth's grammar of the stricture against double negation at a time when double negation was no longer in current use, and the stricture on double negation first appeared in his grammar's second edition. According to the view as suggested by Tieken-Boon van Ostade (2005, p. 148), "this indicates that the rule attributed to Lowth was most likely not his own but that of one of his critical readers who considered its omission an oversight." The research of two or more negatives in one and the same clause is quite problematic for prescriptivists and sociolinguists. Prescriptive grammarians put forward a number of arguments in defence of their preferences. The use of two negatives in a statement like I can't see no animals is held to 'cancel each other out' and should 'really' mean I can see animals.
The authors of A Comprehensive Grammar of the English Language stated: "The double negative phrases require a gradable adjective or adverb as head, the negation indicating a point between the two extremes of the gradable scale" (Quirk et al., 1985, p. 791).
Even sociolinguists promote a view of non-standard language as the equal of standard language. There thus seems to be no way of escaping from the existence and influence of language norms (Mesthrie et al., 2004, p. 19). As Zhou and some other linguists claim, "the asymmetry between negation in logic and in natural language has been an important area of inquiry in both linguistics and psychology, since it provides insights into the relationship between logic and language" (Zhou et al., 2014, p. 334). In all these cases, the use of double negatives in Standard English is not common so that "double negatives, when used to express a negative idea, aren't acceptable in standard English" (Soanes, 2012). Horn's relatively recent research is concerned with the problem of multiple negation in English and other languages (Horn, 2010). Lastly, some attempts were made by the linguists regarding to the identification of the reasons for the disappearance of negative concord from the English language (e.g., Kallel, 2011).
On the other hand, DN is frequently used in non-standard language. Uneducated people continue to use double negatives in non-standard dialects and in colloquial speech. In nonstandard English, the two negators do not cancel each other; rather the second negator is used in place of a nonassertive item or a negative polarity item that can be paraphrased. For example, He didn't say nothin. → He didn't say anything (example taken from Dairong & Huiyuan, 2009, p. 80).
Accordingly, Horn (2001, p. 194) points out the pragmatic strengthening of apparent contradictory negation to the weakening effect of "logical" double negation. In addition, when two negatives occur in the same sentence, there is a subtle change in meaning between the double negative structure in and its affirmative counterpart. Although the two negatives cancel each other out, they produce a weakened affirmative. According to Horn (1978, p. 164), DN is indeed weaker than its positive equivalent, not because of the usurpation of the mental energy as Jespersen claims, but because of the fact that the cancelling out of two negatives results in the expression of the corresponding dual. This is illustrated with the example of I don't deny, which is weaker than I assert, because what it actually expresses is not "I assert", but "I suggest".

Background of the Research and Literature Review
Numerous examples can be found of such constructions as "it is not unlikely," "it is not unconceivable," "it is not impossible" or "that is not unnatural." These instances express the contrary negation resulting in complete redundancy or even pleonastic negation, which actually refers to a type of double negation. Pleonastic negation can also be called hypernegation or abusive negation, the phenomenon in which a negative marker reinforces rather than cancels the ordinary marker of sentence negation (Horn, 2001).
In English, for example, instances of pleonastic negation are infrequent, and restricted to exclamations and pseudo-interrogatives, such as All the thing you say to me! and Why don't we plant potatoes on the rooftop?, and non-factuals such as I wouldn't be surprised/wouldn't wonder if it didn't rain (Zovko Dinković & Ilc, 2017, p. 162). It follows that DN is characteristically employed to reinforce rather than qualify a description. Another term negative concord exists referring to the phenomenon of multiple negation. Thus, the terms pleonastic negation and negative concord are interchangeable to some extent.
On the ground of the tendencies mentioned, double negation as a type of negation variety is an important language phenomenon characterized by the complexity of its linguistic content followed by a description of its relevant characteristics and contradictory aspects. As for the use of double negatives within one clause in English, they are avoided in formal, nonstandard speech and writing as a matter of convention rather than logic.

Double Negation as Understatement: A Cognitive Linguistics Perspective
Based on the mental spaces theory, and specifically on the work relying on the notion of conceptual space (Fauconnier, 1994(Fauconnier, , 1997Fauconnier & Sweetser, 1996;Fauconnier & Turner, 2002), we can establish a twofold distinction between the speaker and hearer's perspectives for DN, and it becomes possible to build a common and unified model for DN with the study of understatement. From a cognitive perspective, we are going to analyze this process as a projection between two different conceptual spaces, which is mediated by a mitigation cognitive operation.
Furthermore, one should take into account the fact that the importance of the pragmatic functions of double negatives in actual language usage is subject to pragmatic constraints. Some structures with the negative meaning are generally used to point out discrepancies between a presumed expectation and the facts.
The structures with DN in which two negative operators serve to create an understatement can exist in the form of litotes. Litotes are used to denote a figure of speech and, secondly, it is a type of understatement that uses negative affixes or words with negative meaning to express the contrary. According to Trail (2004, p. 217), litotes denotes the name of a particular form of understatement in which the opposite of a value is negated. On the one hand, litotes is a way to state the affirmative without actually stating the affirmative, and on the other hand, it is quite confusing because the meaning is not what it seems. Consequently, the notion of litotes as double negation expresses the contrast between what is said and what is implicated.
In this research, we are going to examine the use of DN setting it in the frame of the mental spaces theory based on sentences from modern literary texts. We shall try to account for how both the production and understanding of double negatives are accomplished through mitigation operations resulting in litotes and the contextual effects they produce. The most frequent negative markers of DN as understatement is the negative particle not with negatively prefixed adjectives or participles (e.g. wasn't disappointed, not uneducated, not unaware, not unlike, etc.).
(1) He had not been unhappy all day (Hemingway, Big Two-Hearted River).
It is quite certain that in order to perceive understatement "as regards its mental creation and interpretation we are able to lessen certain contextual effects" (Ruiz, 2009, p. 229) and to construct a speaker-based model of understatement based on mitigation operations. The task here is to derive the speaker's intended range of contextual effects. These generalizations can be made within the framework of the mental spaces theory in terms of mappings between cognitive and linguistic domains and where "space plays a key role in mapping concepts onto physical experience" (Caracciolo, 2011, p. 178).
In example (1), the reader would assume that the logical cancelling out of two negatives not at all and unlike does not yield a positive counterpart in natural language and in a given real context. Thus, this context is related to the problem of pragmatic asymmetries produced by DN. The sentence is certainly incorrect according to the prescriptive rules of standard English. In so doing, the writer creates some contrast with what he assumes, the one between two spaces as cognitive entities: a negative space and a corresponding positive space in contrast with it. The general projection between two conceptual spaces with a mitigation operation is diagrammed in one-correspondence model (see Fig. 1 Returning to DN as understatement in the appropriate context, the meaning of it is implicated that causes "pragmatic indeterminacy" (Haugh, 2015) giving all the subtleties of meaning of two negatives together. At first sight, the sentence He had been happy all day sounds stronger than He had not been unhappy all day because of some reasons. First, from a denotative point of view they both identify the same state of mind of the character. Secondly, from a connotative point of view the first structure is stronger emotionally that manifests itself in the creation of linguistic and pragmatic asymmetry since He had not been unhappy all day does not mean that he is happy. Furthermore, it negates the assumption that He is happy all day. Consequently, from the point of view of the mental spaces theory the existence of a derivation process of additional contextual effects produced by the speaker accounts for the appearance of "the alternative space or the imagined scenario" (Sweetser, 2006, p. 315) that can be described as downgrading a concept of happiness based on the speaker's expectations and background knowledge.
Thus, the speaker is apparently scaling down the idea of happiness via a mitigation operation realized in the following meanings cheerful, in a good mood, pleased, glad, delighted, thrilled, contented, optimistic, positive (LDOCE). These positive linguistic markers inevitably build the alternative conceptual space containing the negation of a certain expression to fill in the semantic space left out after the denial. In other terms, understatement is characterized by the specific semantic structure that negates a certain utterance to express other different shades of meaning, which characterize different degrees of a given quality through a mitigation cognitive operation. It seems clear that the speaker is mitigating the full range of intended contextual effects caused by the meaning of happy into not being unhappy thus moving from a higher to a lower value of the concept represented from the point of view of the mapping process. These contextual effects are used to denote the speaker's intention to minimize them for the hearer with the help of double negatives by obviously claiming less for the quality than would ordinarily be expected.
We can represent this process via one-correspondence model in Fig. 2. Contrary to our expectations, negating the opposite of what would normally be said or implicated is not always understatement. (2) A plastic ball, in white and yellow stripes, rolled softly and with deceptive slowness from one dry tuft of dune-grass to another, not at all unlike a big bored snail, until suddenly a sharper gust of breeze caught it and tossed it bouncing high across the shore (Bates, How Vainly Men Themselves Amaze).
In example (2), DN can be interpreted in two ways. On the one hand, this sentence contains the negative expression not at all used to emphasize what you are saying with unlike denoting something completely different from a particular thing. On the other hand, this fragment consists of the expression not unlike meaning similar to something. Nevertheless, in both cases the statement means the same: the two negatives cancel each other out but they do not produce a weakened affirmative. On the contrary, the use of double negatives can reinforce the statement when the adverbial phrase not at all, which is embedded into the sentence structure, tends to be emphatic.
To sum up, a cognitive model of understatement with double negatives based on a mitigation cognitive operation manifests itself in one-correspondence between two input domains, a negative conceptual space and a positive (alternative) space. The latter, in which the opposite of a value negated (He had not been unhappy all day) is projected onto a conceptual space created by the speaker with intended contextual effects of happy in a somewhat lessened degree.
In this study, we are going to investigate the acquisition of English double negatives based on contrastive analysis. This is a contrastive investigation of negators in double negation, and more specifically the acquisition of DN in English by Ukrainian students. It is important to show common and different features of double negatives possessed by two different Indo-European languages. The goal of language comparison should be to gain a greater understanding of language, and rather, while contrastive analysis is a discipline of linguistics, its goal is to understand the nature of language (Gass & Selinker, 2008, p. 96). Furthermore, we focus on the acquisition of double negatives in English and Ukrainian as a mainly cognitive pursuit.
Within the framework of contrastive analysis, we need to discover similarities and differences between two languages according to the contrastive analysis hypothesis (CAH) known from the times when the influential Lado's book Linguistics Across Cultures was published (Lado, 1957). CAH theoretical basis lies in the fact that the native language is the driving force of second language learning in revealing the learners' potential difficulties equated to errors. As Gass and Selinker claim, "if a learner produced an error, or errors, this was a signal that the learner was having difficulty with a particular structure or sound" (Gass & Selinker, 2008, p. 99). (1) and (2), L2 learners might point out there are at least two errors in each of them from the point of view of the English grammar rules because two negatives in one sentence should cancel each other out but they do not and, as a result, these instances are incorrect. From the semantic viewpoint, two negatives in one clause turn the context into a positive but in a somewhat lessened degree, thus assuming various interpretations of their meaning.

Returning to the previous two examples
In this contrastive investigation of DN and more specifically its acquisition in English by Ukrainian students, it is important to show common and different features of double negatives in both languages. Our empirical research that relates more directly to the field of SLA aims at investigating the acquisition of English by Ukrainian learners.
From the perspective of SLA, we have made a contrastive analysis among English and Ukrainian clauses. In English, it is quite enough to use adverbs nobody, nothing, never, neither, nobody, nothing, etc. together with other lexical words to render the negation without the use of a negative particle not (не in Ukrainian), but in Ukrainian, it is not a case. Moreover, such sentences need to have canonic two negatives in the L2 structure, otherwise they will not make sense. More specifically, the double negative structures in Ukrainian often require both the adverb (never, nowhere, nobody) and the particle not. These clauses are usually translated into either double negative sentences or even affirmative sentences.
Compare the following sentences: (3) They never visit us.
In sentence (3), two negatives ніколи (never) and не (not) meaning never appear to be used together to reinforce each other. Here two negative markers are preserved in the L2 clause.
English and Ukrainian negative sentences have the following features in common: 1. They have their affirmative correspondents, which can be made negative by adding negative words.
2. In some cases, the negative words are used with other negation-related words either to intensify or soften the negation.

Method, Hypothesis, and Data Analysis
Despite these similarities, there are still differences, the most important one of which is the way of adding negative words to the affirmative sentences. In the chart below (Tables 1 and  2), we identify the main characteristics of each negative part of speech and the structural and semantic peculiarities of English and Ukrainian double negatives.
In Table 1, the bold words are the key negators not/n't and the negation-related words in English and Ukrainian, and the clause left blank signifies that two negatives make an affirmative in Ukrainian.

Table 1
Comparison between English and Ukrainian double negatives: constructions with not/n't As Tables 1 and 2 show, the negative words in English include particles, adverbs, pronouns, determiners and some set expressions (could not help + ing, could not but + infinitive, could not stop + ing). Therefore, the subject, predicate, object, adverbial modifiers or attributes can be negated in English and Ukrainian. Meanwhile, in some cases in Ukrainian, the double negation can also be expressed by adding other related words, which are placed close to the predicates and used with the particle не (not) as a scope negative marker, which add the clause a strong positive meaning. This significant difference poses a real problem for the translation of the English negative sentences into Ukrainian.
To conclude, there are at least four styles for DN in the English utterances: _ one negator not plus a lexical negator containing a negative prefix (e.g., not impossible), or they are placed close to each other in a clause, _ one negator n't plus another negator with a negative prefix (e.g., can't unprotected), or when double negatives are separated by another part of the utterance, _ some set expressions could not help + ing, could not but + infinitive, could not stop + ing, which have become affirmative utterances in Ukrainian, and finally, _ one negator is combined in the utterance consisting of an emphatic function word with a negative meaning that has focus status in the utterance it belongs to (e.g., no one could move without sweating).
In the first case, the two negators cancel out each other in meaning to acquire a softened positive meaning and it allows paraphrasing. In the second case, we have a negative concord sentence in which the two negative markers yield a single semantic negation. In the third case, not only lexical (primarily adjectives, adverbs and pronouns) but also some function words (e.g., prepositions) are used to render the negative meaning to reinforce the affirmation or get strong positive meanings of the clause. Moreover, while some English clauses have only one negator, their Ukrainian translations with two negative markers may cancel out each other to make the whole phrases emphatic (e.g., I never ceased to love her).
As the main focus of the current study is acquisition of DN in English by L2 learners, we will review DN awareness and competence of L2 students as users of double negatives. In short, DN awareness, or enhanced awareness of DN, is important for successful L2 DN comprehension and use. Enhanced DN awareness means L2 learners can: _ identify double negatives in everyday language use; _ recognize cross-cultural differences in double negatives: how the L1 Ukrainian students perceive English double negations; _ acknowledge the "self-contradictory nature" of many expressions with double negatives; _ identify cross-linguistic variation of double negatives.
The purpose of the present study is twofold. Firstly, in order to search for the similarities and differences of DN within two languages from the perspective of SLA, we intend to evaluate the comprehension and the use of DN in English that might still be difficult for L2 students. Secondly, concerning the translation of the English clauses with double negation markers into the Ukrainian language we are going to check English language learners' acquisition characteristics. All the learners in the study are a control group of 15 participants who are the students at the Vasyl Stefanyk Precarpathian National University, a state university in Ivano-Frankivsk, Ukraine. Their mother tongue as well as their first language is Ukrainian, and they are university students of English in their third and fourth year. The selected control group was composed of students from the highest English class.
We will focus on the following hypothesis in this study: the usage of double negatives is regarded as different when comparing English and Ukrainian, the languages the learners coexist with.
Being accepted and grammatically correct in Ukrainian but observed as incorrect in standard Modern English, the study of DN shows that our students may experience some confusion because of the influence of the L1 if the knowledge they have acquired of the L2 is not enough and this situation makes them aware of the distinct grammars they are dealing with.
At the same time, when acknowledging the ability to negate in the L1, the user of the native language should take into consideration at least two factors that need to be remarked: _ the presence of the external negative particles in the L2 sentence or any other negation-related words on account of the analytical character of the L2 by which DN is required; _ the ability of L2 students to differentiate between Ukrainian grammar rules where double negatives are accepted, and the rules in English grammars as well as their own proficiency in English at the same time.
Moreover, the development on linguistic complexity of DN in L2 and L1 has been considered as an indicator of L1 and L2 development. As a result of this, for this group, the normal procedure followed in a regular ESL class consists of the explanation of grammar rules followed by written exercises.
Thus, to be completely competent communicators, language learners must develop both their L2 DN awareness, or knowledge of DN and its role in language, and also L2 DN competence, or the ability to comprehend, interpret, and appropriately use double negatives in the L2. Moreover, with respect to DN, cross-cultural variation not only affects how learners interpret and use double negatives in their second language, but may also lead to misunderstanding and confusion. More specifically, DN is closely connected with both culture-specific characteristics of L1 and L2 and very often serves to create certain vague meanings, doublespeak, euphemisms, or irony that will help students to better master this fundamental category.

Results and Discussion
In order to check the acquisition characteristics of the learners, we are going to explore teaching implications of the English DN and how Ukrainian adults interpret L2 sentences with more than one negative element. How similar or different double negatives are in a students' first and second language influences the ease with which students can learn, interpret, and use L2 double negatives. In short, linguistic challenges could make double negatives more difficult for students to correctly understand and interpret in their L2.
To achieve this goal to test the knowledge and command on DN by this group of participants and their response towards this phenomenon, we tested them using a short questionnaire based on the 17 sentences with those proposed as translated versions. These clauses contain double negative markers, which were selected to give the fittest explanation for those sentence structures (see Appendix Once the questionnaire was distributed, presented, and explained, the students had 35 minutes to fill it in. These exercises were designed to evaluate the quality of their linguistic performance in the specific grammatical feature of double negation in English and their L2. The questionnaire was composed of two tasks and the students in the group were given the instructions to fulfill it as follows: Task 1 Make the following sentences correct in the questionnaire is an activity in which the students are required to make the sentence correct and explain the use of DN in each sentence proposed. We consider it important to have it compared with an equivalent in English, e.g., Я нічого йому не дав. -I didn't give him nothing/anything. With this exercise, we make the students choose among the negative contracted forms don't, didn't, can't, wouldn't, the negative particle no, the negative pronouns and adverbs, and also non-negative adverbs that are offered in the task, e.g. I will punish you if you won't pay no attention.
The contracted negative forms and a finite form of the verb appear in 8 out of 10 entries, e.g., I can't barely hear you. In sentences 5 and 8, the negative adverb never precedes the main verb, which is followed by the pronouns nobody and nowhere, e.g. I swear, I never told nobody.
Task 2 is composed of two parts. In the first part, the students are supposed to find a mistake in each of the 7 sentences with DN. Then, in the second part, they are asked to paraphrase 7 sentences and explain their meaning, e.g., He was not unaware of this. These utterances, incorrect according to standard Modern English rules but possible depending on the context are intended to check the ability of these students to differentiate between English and Ukrainian.
Once this questionnaire was fulfilled by our students, it was corrected and the results tabulated. The answers we collected were analyzed and discussed in order to obtain some conclusions that endorse, or not, our initial hypothesis. For task no. 1 in the questionnaire, in which the students were asked to make the sentences correct, we obtained 105 (70%) correct answers out of 150 possible ones. The answers are presented in Fig. 3.  Fig. 4 portrays the amount of correct responses that were proposed for the group of 15 students. At first sight, we can observe that the output of the students remains stable throughout the whole task but for some students in the class. While analyzing the sentences, we can conclude that these are the sentences no. 4 and 7 as well as 9, which seem to be problematic for our students. They are as follows: (4)  The results of this first part of the questionnaire are shown in Table 3, which shows the amount of correct answers by the group -136 (90%) out of 150 possible correct answers.
In the second part of task no. 2, seven sentences are offered to the students to No. of students spot the mistake in each of them so that the sentences become correct according to the knowledge of English grammar. At this stage of analysis, we observed the following results: (1) some difficulty in paraphrasing sentences 1, 3, 4, 5, and 6 because the transformation of the whole double negative structure into a positive one is likely to twist its meaning; and (2) the negative meaning of the adverb hardly seems ambiguous in sentence 7. Overall, in line with the results obtained, we discuss each significant finding on the performance of the students who fulfilled the questionnaire within the context of DN.
In task 1, we observe that a number of students answered correctly each of the questions except for numbers 4, 7, and 9, e.g., Q. To comment on task 2, as expected, the most frequent option students used to paraphrase was keeping the verb in its negative form and substituting the negative pronoun or adverb by the positive equivalent with the aim to avoid DN in the sentence, e.g. any, anything. It appeared to be predictable among the students because of the fact that most of them automatically transformed the coexistence of two negatives into a positive sentence. The idea that two negatives cancel out each other in English is not always valid at least of the fact that the combination of not with the adjectives uncommon, improbable, immodest and unlike results in understatement. Here while completing the questionnaire we can observe to what extent the students are influenced by their native grammar.
As for another common mistake in task 2 that concerns the use of the adverb hardly, we can conclude that the students did not pay attention to the negative meaning it might have in the context making the sentence having two negatives. On this occasion, in most cases the native language of our students turned out to be a deciding factor for the result when acquiring English as a second language.

Conclusions
This study specified and extended the theory of DN constructions containing a key negative marker (-n't or not) and a single negative constituent object in the English language. It is noteworthy that double negation, which was standard in English up to the sixteenth century, is today used as a stylistic rule in fiction to signify mitigation and as a linguistic phenomenon, which is broadly changing nowadays.
As the research shows, double negatives can either make the affirmative seem less significant or less severe than it actually is, and are represented in syntactic structures in litotes as understatement. They can intensify the content of the affirmative by giving an additional expressive force to the affirmative. A cognitive model of understatement with double negatives clearly reveals the double nature of litotes as DN based on a mitigation cognitive operation, which represent the movement from the opposite of a higher value negated to a lower value "as a 'mapping' of one semantic domain onto the other" (e.g., Bystrov, 2014, p. 2) created by the speaker. This linguistic research applied the hypothesis in the theory of negation goes back to the approach as suggested by Horn (2001, p. 194) who claimed that the form of DN can either strengthen or weaken the statement, because it varies "from the pragmatic strengthening of apparent contradictory negation to the weakening effect of 'logical' double negation." Our extension of the DN theory built on the assumption that the usage of double negatives was regarded as different when comparing English and Ukrainian, the languages the learners coexist with. Being accepted and grammatically correct in Ukrainian but observed as incorrect in standard Modern English, the study of DN showed that the selected group of students in some instances experiences some confusion because of the influence of their mother tongue. Under this hypothesis, this situation makes them aware of the distinct grammars they are dealing with.
Firstly, on the basis of the theoretical surveys concerning DN in English and Ukrainian, the findings showed some translation difficulties involved in rendering English double negatives into Ukrainian, which were realized in the differences between the two languages (e.g., Tables  1 and 2).
Secondly, from the perspective of SLA, a contrastive analysis among English and Ukrainian phrases was made. To render a single negation in English, it was quite enough to employ adverbs nobody, nothing, never. Rather, the Ukrainian structures usually require both the negative adverb or pronoun and the particle not.
Thirdly, in order to check the acquisition characteristics of L2 learners, the students' questionnaire was designed to have two tasks. The learners were supposed to make some correction of the DN sentences, select the possible explanation for such sentences and to find more or less acceptable meaning of the sentence. The quantitative method was used to show the amount of responses of the student group in the questionnaire.