Inner association links between elements of a binomial sequence

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Inner association links between elements of a binomial sequence

I. Rizhok

I. Dilay

The paper provides the analysis of the connection existing between constituent components of a binomial expression. The need to study this connection is predetermined by the lack of a clear distinction between binomials and other types of formulaic language, collocations in particular. Internal association strength has proven to be the unique feature that makes them different and is necessitated by an obligatory presence of a coordination conjunction which functions as a mediator and prevailingly takes the central position within the entire expression. A new modified log-r formula was generated to compensate for the incapacities of other types of measurement and include the coordination conjunction in the study. The results yielded on the basis of the IWEB corpus have proven to accurately reflect the bond existing between the elements of a binomial taking into consideration both the frequency of separate words and the one of the whole expression and their tendency to co-occur in the same context.

Key words: binomials, collocations, Mutual Information, log-likelihood value, log-r formula, the IWEB corpus.

З метою виправити похибки попередніх статистичних вимірів і залучити сурядний сполучник у дослідження була запропонована формула \og-r, котра була модифікована від формули спрямованої на визначення внутрішнього зв'язку між частинами біграмів, запропонованої японськими вченими.

Дослідження складалося з декількох етапів, а саме: пошук закономірностей та тенденцій серед груп біномів та колокацій у сучасній англійській мові за допомогою електронного лінгвістичного корпусу; аналіз попередньо використаних статистичних вимірів у відношенні до біномів; застосування спеціально розробленої \og-r формули, щоб пояснити внутрішній асоціативний зв'язок, який існує між елементами біномної конструкції; повторне використання корпусу з метою підтвердити точність і ефективність результатів, отриманих в результаті застосування \og-r формули.

Ключові слова: біноми, колокації, показник взаємної інформації МІ, функція правдоподібності, формула \og-r, корпус ШЕВ.

Binomials, generally defined as coordinated pairs of linguistic units that share some semantic relations between their constituents, are one of the most heterogeneous, and therefore, convoluted phenomena that exist in the English language. Regardless of the fact that the frequency of their usage in daily communication is exceedingly high, binomials remain, in the majority of cases, overlooked by most English language users. This is the core explanation of why the concept of binomial expressions, though being the focus of a large amount of studies, is still full of «grey areas» which perplex the minds of linguists even nowadays.

In spite of a great deal of research dedicated to the concept of binomial pairs, the main emphasis in this paper is laid upon those aspects of the linguistic notion of binomials that have not been mentioned or thoroughly dealt with until now. The points that have already been generally agreed on and do not need any further studying could be roughly narrowed down to the definition of the notion of binomials, the related terminology, classification and the study of diachronic changes of binomials. In contrast, one preliminary issue that is still worth attention includes the establishment of the bond existing between different components of a binomial pair.

The theoretical foundation of binomials as it is today could be based on pioneering works composed in accordance with numerous aspects of binomial constructions. To begin with, such scholars as Hans Sauer, Birgit Schwan, Joanna Kopaczyk, William E. Cooper and John R. Ross concentrated a lot of their attention on the issue of the diachronic study of binomials. H. Sauer and other linguists (Sauer, Kopaczyk, 2017; Sauer, Schwan, 2017) elaborated the clear definition putting a stress on only partial semantic connection between the components. Its apparent benefit is that it permits excluding all the phrases or word clusters to be considered as binomials solely owing to their irreversibility or high frequency of occurrence. Understanding of this fact triggered the appearance of properly thought-out classification of this linguistic notion. Medvedieva and Daineko (Medvedieva, Daineko, 1994) composed an English-Ukrainian dictionary of binomials. Other pioneers in this domain such as William E. Cooper and John R. Ross, refreshed the existing views on binomials in their paper World Order. There, the two functionalists named binomials as «freezes» and explained them in a following way: «While the ordering of frozen conjuncts cannot be reversed in many instances, a number of other cases exist in which the ordering of conjoined elements is fixed only when the elements occur in idiomatic constructions» (Cooper, Ross, 1975, p. 63). As opposed to other scholars, Cooper and Ross had a goal to separate linguistic environments in which binomials frequently occur and formulate certain rules that could regulate their existence there. Even though they considered previously suggested phonological and semantic constrains determining the linear order of the majority of binomial pairs, they were also the first to attract the attention to a psychological element that conditions their usage and functioning.

Yakov Malkiel, Sandra Mollin and Marita Gustafsson, in their turn, tackled the problem of binomials' degree of reversibility. Y. Malkiel is considered in modern linguistics as the founder of the term itself, which he first mentioned in his paper titled Studies in Irreversible Binomials, published as early as in 1959. At that time, it was mistakenly believed that only irreversible coordinated pairs of words can belong to the class of binomials. The linguist defined the concept as «the sequence of two words pertaining to the same form- class, placed on an identical level of syntactic hierarchy, and ordinary connected by some kind of lexical link» (Malkiel, 1959, p. 120). As it can be observed, this interpretation did not allow any transcendence from the syntactic patterns and, consequently, other groups of words with a more freely established word order were not recognized as a binomial sequence. The issue of binomials' degree of reversibility was highlighted, though, by S. Mollin, who wanted to distribute all the binomials on the cline of collocative strength with regard to the frequency of their usage in one of her experiments, with strongly collocated binomials being at one end and hapax legomena being at the other. Although later the author acknowledged an error and agreed that «the term collocation cannot be used to refer to the entirety of examples of binomials, even though this has the potential to apply to many binomials of differing degrees of reversibility, not requiring fixedness» (Mollin, 2014, p. 17), it triggered the thought of another type of binomials, a reversible one, to be precise. M. Gustafsson outlined that «a «binomial» is a sequence of two words which share specific syntactic and semantic relations with one another. The members of a binomial are usually syntactically coordinate words belonging to the same part of form-class [,..].Their semantic relation is one of synonymy, opposition, complementation, etc» (Gustafsson, 1976, p. 625). The linguist emphasized that binomials are not `tied down' to idiomaticity. Her work is considered as a turning point between old and new interpretations of this linguistic phenomenon. binomial formulaic language

The organisation of ordering constraints was promoted by Arne Lonmann and Vincent Renner. Lohmann (Lohmann, 2014) succeeded in singling out two essential points adjacent to coordinated pairs. The former is that corpus analysis involving statistic models showed better samples of fixed binomials while the latter is that there a difference should be made between binomials with conjunctions and/ or and other conjunctions as their behaviour may vary accordingly. Furthermore, he as many other scholars addressed ordering in terms of syntax and pragmatics, rhythm, syllable weight, vowel length, complexity, etc. Among the principles, the most crucial one is the so-called Me-First principle that Cooper and Ross originally came up with. Vincent Renner comments that «the left position in a binomial is generally to be reserved for the element in empathy with a virtual prototypical speaker's vision of the world» (Renner, 2014, p. 141). Finally, the role of mental lexicon on the formation of coordinated pairs, including binomials, as well as conceptual studies was guided by Jean Aitchison, Kathy Conklin, Gareth Carrol and many others. Aitchison (Aitchison, 1987), for instance, revolutionized the conventional understanding of binomials claiming that it is most likely that the smallest meaningful units existing in the mental lexicon do not necessarily have to be the exact equivalents of words or even morphemes in the language but may present an in-between category.

Consequently, all of the abovementioned linguists have made a viable contribution into the current interpretation of binomials.

The aim of the current paper is to study the relationship that lies between constituent members of a binomial construction. The principal tasks are directed to accomplish the stated aim and singled out as follows:

- to establish the role a coordinating conjunction plays in the functioning of a binomial sequence;

- to compare the efficiency of various statistical methods to accurately measure the degree of association within a binomial;

- to design the most adequate statistical means specifically for binomial expressions;

- to test its effectiveness in comparison to other statistical types of measurement.

Therefore, in this paper, it is going to be analysed how profoundly the elements of binomials are associated with one another and whether their unique features may suffice to give them a right to be separated from the other lexical bundles they are typically confused with, i.e. collocations.

It has already been mentioned by many linguists who had dealt with this matter before, e.g. Mollin, Carrol & Conklin, that the two lexical clusters do possess their own characteristics that enable them to be distinct. Mollin, for instance, managed to draw a prolific study on the issue of binomials' collocability by simultaneously making use of the most sophisticated statistical methods available at the time, namely Mutual Information (MI) and log-likelihood. The goal was to discover if binomials could be submerged into the broad concept of collocations owing to their salient tendency to co-occur in various contexts. The results of the analysis have proved that there are both strongly and weakly collocated pairs among the binomials that had been tested at random. Interestingly, the expressions with low collocability form the majority of the cases and, vice versa, words that have an exceedingly high frequency when tested individually may not always be as commonly used in the frame of coordinated pairs. The fact demonstrates that it would be fallible to state that they belong to the class of collocations proper and equalise the status of both linguistic phenomena. Therefore, the observation motivated Mollin to claim that «... binomials do fall along the cline of collocative strength, showing that most binomials may be considered strong collocations, but others less so» (Mollin, 2014, p. 20).

It is crucial to outline that binomials even structurally differ from collocations. There is the obligatory coordination of two or more constituents by means of a conjunction that separates them. It would be totally unfair to ignore its presence in the course of the analysis of the entire group. Moreover, it must have a substantial impact of the inner association power, which with the help of MI or log-likelihood methods only excludes the third element that definitely makes the final results biased.

This paper bases its analysis on the IWEB corpus (The IWEB corpus, n.d.), for, unlike any other contemporary corpus, it consists of the largest number of words, i.e. 14 billion, and has an input of around 20 million web pages. Its content, for this reason, is relevant to the study of binomials in the modern language system. A manual analysis of concordance lines yielded on IWEB binomial search has shown that irrespective of the size of the span that was set in regard with the node word, which is always placed in the central position, the vast majority of cases where both constituents co-occur contain a coordinated conjunction in the middle that determines their relation to each other, and is, in fact, the nucleus of a sequence. The other words that distance the key elements solely make the binomial extended or add to its structure, transform a binomial into a multinomial, but do not trigger any essential alternation in the core meaning. An excellent example is the binomial pair safety and health. Although it occurs in the original form quite frequently, there are more examples of this phrase that is altered with additional words, as in safety and security of health; the safety and quality of heath care; quality, safety and better health outcomes; safety, security, health, and a positive culture; food safety, nutrition, heath care, and economic development. On the contrary, collocations do not generally contain any coordinate conjunctions in their inner structure. The study of concordance lines of the collocation, analysed in Carrol & Conklin's work, i.e. fatal mistake (Carrol, Conklin, 2019, p. 21), illustrated that there is a limited occurrence of the conjunction in between the two constituents, such as a correctable mistake and a fatal error, a mistake and its potentially fatal outcome, but in most of the cases they are used without it, for example, a mistake can be fatal, a mistake here is fatal to virtue. This observation proves the point made earlier, that a conjunction governs a binomial and makes it different from collocations or any other formulaic units. Subsequently, it ought to be taken into account while researching the whole group of binomials.

Mollin later acknowledged that the two association measures used in her study had considerable drawbacks and made a complete investigation of the notion of `a binomial' inaccurate. MI prioritises infrequent samples whereas log-likelihood works in the opposite way. The latter, however, does not filter findings from unnecessary for the study grammatical collocations, for instance of... the constructions.

Thus, this field of study is in an urgent need of a medium between the MI and log- likelihood score. It is exactly where log-r formula, specially designed for binomials and their structural uniqueness, comes in handy.

When conducting a research that is focus on the measure of degree of inner association, scholars opt to use the MI score, despite its incapability to address all the problems and eliminate ambiguities. A new method, suggested by Japanese scholars Itsuko Fujimure and Shigenobu Aoki (Fujimura, Aoki, 2015), was elaborated to compensate for the absence of a unified technique that would enable establishing the strength of association as accurately as it is only possible. The developers have claimed that the constant investigation of associative bond between elements of different forms of formulaic language shows that MI is not sufficient to explain all the blurry areas in the sphere. As a result, they propose Log-r formula, which is defined by them as «a common logarithm of the correlation coefficient r that expresses the attribute correlation of two variables (word x and word y)» (Renner, 2014) that consists in the following:

The scores derived from this approximation formula can either equal 0 or be less in number. Subsequently, log-r is 0 only if 100 % in frequency of the first word (x) co-occurs with 100 % of the second one (y). The perfect case in point is the expression lingua franca, which possesses such a tight link between the two components that is perceived more as one word rather than a phrase. However, such expressions are extremely scarce in any corpus. Additionally, the lower the log-r score is, the less intense internal association becomes.

The MI approximation formula differs significantly, even though the central ideas remain the same. It goes as follows:

log-r = log₁₀-^ 1)

In this paper, the correlation estimate is created on the basis of the Poisson's regression model since it gives an access to distributions on a large amount of information even with the words that are, if taken separately, low in frequency.

MI = log2 ^(2)

^a2 fxfy^{y J}

In contrast to MI calculation formula, log-r has f x f y square rooted in the denominator which allows having general ratio between fx, fy and fxy balanced even when the size of the corpus changes or raw frequency yields have to be compared with the normalised ones. In the case of MI, expressions with high frequency of co-occurrence between x and y would obtain much smaller values than they should have in theory.

The log-r method was tested by Fujimure and Aoki on collocations and the linguists assured that it can be as effective on any other bi-gram. However, no matter how much binomials are associated with collocations, it would not be fair to fit them to the same formula. The principal reason for this is that fact that the formula is suitable for only for a construction containing two elements, while a binomial consists of at least three. As it was mentioned above, a coordinated conjunction plays a function of the core of the entire sequence and cannot be neglected. Thus, a new modified formula is suggested in this paper, created to account for the associative power existing between all the constituents of the binomial set. It is demonstrated below:

^log -- r = log₁₀-j===(3)

Here, the first key element in the sequence (word x) and the second (word y) go alongside with their coordinated conjunction (word z). In the denominator, the square root is calculated on the basis of frequency of co-occurrence of the words x and z, the first binary set, and the words z and y, the second binary set. As the formula clearly shows, the correlation of each element of a sequence is tested separately due to the fact that word z, a conjunction, predetermines the likelihood of the surrounding constituents being used so closely to each other in multiple contexts. As a conclusion, unlike previous pieces of research, where a lot of importance was attached to the latter, this paper pays more attention to the former.

In order to draw a comparison between MI score and Log-r formula generated for binomials, there was compiled a list of 30 random binomial pairs extracted from aforementioned high-frequency list based on the IWEB corpus. The sequences were, subsequently analysed by the frequency of co-occurring elements, logarithms of these frequencies, and, ultimately, log-r and MI data. The logarithms were used in order to quantitatively compare the last two methods with the rank of binomials in the corpus without involving big and confusing numbers in the diagrams that visualise them. The order of binomials on the list was arranged according to their general frequency from top to bottom. Having calculated all the data and compared it accordingly, some noticeable results have been yielded.

Firstly, log-r formula has identified a number of expressions the value of which equals 0. As it was mentioned earlier, it indicates that the sum of members in the sequence possesses such a strong inner association that it functions rather as a single word and demonstrates an exceedingly high binomial non-compositionality. The list consists of six expressions, namely whether or not, terms and conditions, colleges and universities, username and password, born and raised, current and future. Some of them do not possess high frequency, yet an extremely common statistic measure used in corpus linguistics governed by Zip's law, does not reflect the reality of the relationship between elements and, therefore, should not be abundantly relied on. Nevertheless, MI method accorded high scores only in relation to two phrases, i.e. colleges and universities, username and password. Other expressions were either slightly undervalued, e.g. terms and conditions, born and raised, or greatly undervalued, e.g. whether or not, current and future.

Secondly, the extreme value which comprises MI coefficient 10 or higher appeared to be exaggerated for such sequences as pros and cons, strengths and weaknesses, vitamins and minerals. Their log-r values are relatively lower which proves the fact that the real connection is not as strong as it was shown.

Last but not the least, other binomial constructions the associative strength of which was miscalculated by MI are as follows: life and death, safety and security copy and paste, tips and tricks, with the score being overrated, oil and gas, come and go, wait and see, with the score underrated, correspondingly.

Graph 1. MI and Log (f xzy)

Graph 2. Log-r and log (f xzy)

All of these inconsistencies can be better grasped with the aid of two-dimensional diagrams, see graphs 1 and 2 below.

Having analysed both of them, it becomes apparent that they are positioned differently in relation to the log (f xzy). In the case of the first visual representation that reflects log-r scores, the line of log (f xzy) is fairly close to the 0 axis, where phrases with a higher degree of association are also the ones that are more frequently used. In the case of the second representation that reflects MI scores, this line is distanced from the highest and lowest scores, which means that MI method is not able to adequately correlate high-frequency phrases with the most coherent ones. Therefore, only the first graph seems natural and displays the behaviour of binomials as it happens in the actual language use.

Conclusions

The association link existing between the elements of a binomial expression has proven to be determined by an obligatory coordinator. This feature makes it distinct from other types of formulaic language units. The modified log-r formula suggested in the paper was designed to address the issue and compensate for the lack of an adequate statistical method directed at the measurement of the link existing between constituent components of binomials. The formula has proved to be efficient in comparison to other statistical means such as MI score or log-likelihood value, since the latter dealt exclusively with bi-grams. Future pieces of research could be aimed at retesting the log-r formula on the basis of other linguistic corpora that have a different sphere of application that the corpus that was used in the paper, i.e. IWEB, to trace other distinct patterns or regularities and account for their usage.

Бібліографічний список

1. Медведєва, Л. М. та Дайнеко, В. В., 1994. Англо-український словник парних словосполучень. Київ: Видавництво «Українська енциклопедія імені М. П. Бажана».

2. Aitchison, J., 1987. Words in the Mind: An Introduction to the Mental Lexicon. Oxford: Basil Blackwell.

3. Carrol, G. and Conklin, K., 2019. Is All Formulaic Language Created Equal ? Unpacking the Processing Advantage for Different Types of Formulaic Sequences. Language and Speech, 63 (1), pp. 95-122. https://doi.org/10.1177/0023830918823230 Cooper, W. E. and Ross, J. R., 1975. World Order. In: R. E. Grossman, L. James San and T. J. Vance, eds, Papers from the Parasession on Functionalism. Chicago: Chicago Linguistic Society, pp. 63-111.

4. Fujimura, I. and Aoki, S., 2015. A New Score to Characterise Collocations: Log-r in Comparison to Mutual Information. In: G. C. Pastor, ed. EUROPHRAS 2015 - Computerised and Corpus-based Approaches to Phraseology: Monolingual and Multilingual Perspectives, Malaga, Spain, 29 June-1 July 2015, [online] pp. 271-282. Available at: <http://www.lexytrad.es/assets/Europhras2015%20-%20Book%20of%20full%20papers.pdf> [Accessed 25 March 2021].

5. Gustafsson, M., 1976. The Frequency and Frozenness of Some English Binomials. NeuphilologischeMitteilungen. 77 (4), pp. 623-637.

6. Lohmann, A., 2014. English Coordinate Constructions: A Processing Perspective on Constituent Order. Cambridge: Cambridge University Press.

7. Malkiel, Y., 1959. Studies in Irreversible Binomials. Lingua, 8, pp. 113-160.

8. Mollin, S., 2014. The Ir(reversibility) of English Binomials: Corpus, Constraints, Development. Amsterdam ; Philadelphia: John Benjamins Publishing Company. https:// doi.org/10.1075/scl.64

9. Renner, V., 2014. A Study of Element Ordering in English Coordinate Lexical Items. English Studies, 95 (4), pp. 441-458. DOI: 10.1080/0013838X.2014.908039 Sauer, H. and Kopaczyk, J., 2017. Defining and Exploring Binomials. In: Kopaczyk, J. and Sauer, H. eds. Binomials in the History of English. Fixed and Flexible. Cambridge: Cambridge University Press, pp. 1-24. DOI: https://doi.org/10.1017/9781316339770.001

10. Sauer, H. and Schwan, B., 2017. Heaven and Earth, Good and Bad, Answered and Said: A Survey of English Binomials and Multinomials. Studia Linguistica Universitatis Iagellonicae Cracoviensis, 134 (1), pp. 83-96. DOI: 10.4467/20834624SL.17.007.6922 The IWEB corpus, n.d. [online] Available at: <https://www.english-corpora.org/iweb/> [Accessed 25 March 2021].

References

1. Aitchison, J., 1987. Words in the Mind: An Introduction to the Mental Lexicon. Oxford: Basil Blackwell.

2. Carrol, G. and Conklin, K., 2019. Is All Formulaic Language Created Equal ? Unpacking the Processing Advantage for Different Types of Formulaic Sequences. Language and Speech, 63 (1), pp. 95-122. https://doi.org/10.1177/0023830918823230

3. Cooper, W. E. and Ross, J. R., 1975. World Order. In: R. E. Grossman, L. James San and T. J. Vance, eds, Papers from the Parasession on Functionalism. Chicago: Chicago Linguistic Society, pp. 63-111.

4. Fujimura, I. and Aoki, S., 2015. A New Score to Characterise Collocations: Log-r in Comparison to Mutual Information. In: G. C. Pastor, ed. EUROPHRAS 2015 - Computerised and Corpus-based Approaches to Phraseology: Monolingual and Multilingual Perspectives, Malaga, Spain, 29 June-1 July 2015, [online] pp. 271-282. Available at: <http://www.lexytrad.es/assets/Europhras2015%20-%20Book%20of%20full%20papers.pdf> [Accessed 25 March 2021].

5. Gustafsson, M., 1976. The Frequency and Frozenness of Some English Binomials. Neuphilologische Mitteilungen. 77 (4), pp. 623-637.

6. Lohmann, A., 2014. English Coordinate Constructions: A Processing Perspective on Constituent Order. Cambridge: Cambridge University Press.

7. Malkiel, Y., 1959. Studies in Irreversible Binomials. Lingua, 8, pp. 113-160.

8. Medvedieva, L. M. and Daineko, V. V., 1994. Anhlo-ukrainskyi slovnyk parnykh slovospoluchen [English-Ukrainian Dictionary of Binomial Expressions], Kyiv: Vydavnytstvo «Ukrainska entsyklopedia imeni M. P. Bazhana».

9. Mollin, S., 2014. The Ir(reversibility) of English Binomials: Corpus, Constraints, Development. Amsterdam ; Philadelphia: John Benjamins Publishing Company. https://doi .org/10.1075/scl.64

10. Renner, V., 2014. A Study of Element Ordering in English Coordinate Lexical Items. English Studies, 95 (4), pp. 441-458. DOI: 10.1080/0013838X.2014.908039 Sauer, H. and Kopaczyk, J., 2017. Defining and Exploring Binomials. In: Kopaczyk, J. and Sauer, H. eds. Binomials in the History of English. Fixed and Flexible. Cambridge: Cambridge University Press, pp. 1-24. DOI: https://doi.org/10.1017/9781316339770.001

11. Sauer, H. and Schwan, B., 2017. Heaven and Earth, Good and Bad, Answered and Said: A Survey of English Binomials and Multinomials. Studia Linguistica Universitatis Iagellonicae Cracoviensis, 134 (1), pp. 83-96. DOI: 10.4467/20834624SL.17.007.6922 The IWEB corpus, n.d. [online] Available at: <https://www.english-corpora.org/iweb/> [Accessed 25 March 2021].

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