Word order flexibility: a typometric study (2023)

Abstract: This paper introduces a typometric measure of flexibility, which quantifies the variability of head-dependent word order on the whole set of treebanks of a language or on specific constructions. The measure is based on the notion of head-initiality and we show that it can be computed for all of languages of the Universal Dependency treebank set, that it does not require ad-hoc thresholds to categorize languages or constructions, and that it can be applied with any granularity of constructions and languages. We compare our results with Bakker’s (1998) categorical flexibility index. Typometric flexibility is shown to be a good measure for characterizing the language distribution with respect to word order for a given construction, and for estimating whether a construction predicts the global word order behavior of a language.

## introduction for half a century, research in typology centers on the discussion of word order parameters, pioneered by greenberg (1963, 1966), and elaborated by such authors as hawkins (1983), dryer (1992) and nichols (1992). bakker (1998) proposes a seminal study on word order flexibility, which we pursue here. first off, it is clear that languages differ in the flexibility of word order: greek or russian are more flexible than english or chinese. secondly, constructions differ in their flexibility across the diversity of languages: the relation between an adposition and its complement is less flexible than the relation between a verb and its direct object. to give a first idea how this can be seen on a typometric scatter plot, consider fig. 1 where each point corresponds to a language, with its x-value indicating the percentage of nominal dependents of adpositions on the right of the adposition and its y-value indicating the percentage of nominal object dependents of verbs to the right of the verb. as a first observation, note that a large majority of languages have @xmath0, leaving a rather empty space in the middle of the scatter plot. this shows that most languages have almost only prepositions or almost only postpositions; languages that mix prepositions and postpositions equally are rare. @xcite however, many more languages accept both pre-verbal and post-verbal direct objects (guzmán naranjo & becker 2018, gerdes et 1 the scatter plot view understates the fact that many languages cluster around the bottom left (0,0) and the top right (100,100) of the plot: many strictly postpositional languages also have their nominal objects on the left, and, inversely, many strictly prepositional languages also have their nominal objects to the right of their verbal governor. this is a well-established observation in typology since greenberg (1963), and is at the base of our choice of sud treebanks (see section 2 for details). how can we measure the flexibility of languages and constructions? what are the properties of flexibility across languages and constructions? we will try to give answers to these questions in section 6. most classical approaches to typology, including bakker (1998) and previous works, are categorical in the sense that languages are grouped into categories based on their order constraints, and often only one basic word order is assumed per language from which other word orders are derived by movement, dislocation, or similar operations. we propose a typometric approach (also called token-based typology by levshina 2019): with the availability of a wide range of uniformly annotated treebanks in the universal dependencies (ud) project, it has become possible to approach these questions empirically. syntactic typology outgrows the need for ad hoc categories and measures of distribution of languages across empirical observations become the center of interest (futtrell et al. 2020, levshina 2022). in gerdes et al. (2021), quantitative universals describe empty or sparsely populated spaces in unidimensional or multidimensional spaces instead of qualitative universals that are claiming rare or impossible combinations of language features based on categories. tesnière (1959) proposed a classification of languages based on the dependency direction referring to steinthal (1850) and schmidt (1926). he opposes strict word order, when head-daughter relations mostly go in one direction, to mitigated when the head is amidst its dependents going out in both directions. among languages with mitigated word order, there are languages with free order, as well as languages with mixed word order, where word order is quite strict in most constructions but inconsistent between constructions. this is what flexibility measures. in this paper we propose measures of flexibility that can be applied to dependency treebanks and discuss the distributions of these measures compared to other observations on dependency treebanks. similar measures have been first introduced by futrell (2015) under the name of word-order entropy and have been studied by levshina (2019). in this paper, we try to characterize the distribution of all languages of our sample in terms of word order direction for each construction c: we compute for each language l, the number of head-initial realization of the construction c in l, what we call the headinitiality of language l under c (section 3). we deduce from head-initiality a second measure we call flexibility and study the relation between head-initiality and flexibility for all languages in our sample, distinguishing flexible languages from mixed word order languages (section 4). the typometric measure of flexibility we introduce is compared with bakker's (1998) categorical measure of flexibility, as well as a more typometric measure à la bakker (section 5). we show that the distribution of head-initiality for every construction c can be characterized by the average head-initiality of c and the flexibility of c (section 6). in section 7, we explore the question of the predictability of word order distribution from one construction to another. ## flexibility of languages for a language l, flexibility measures the distance of a construction c from a rigid construction. in this paper, we only consider constructions involving a governor g and a dependent d by a particular relation. the construction has a wider or narrower range depending on whether the relation between g and d or the categories of g and d are more or less constrained. flexibility(l,c) = 2 min( head_initiality(l,c), ✕ 100-head_initiality(l,c) ) = twice the smallest distance of head_ initiality(l,c) to 0 or to 100 the value of flexibility(l,c) ranges from 0 to 100 and measures the distance of c from a strictly head-initial or head-final construction. a very similar measure, word order entropy, has been proposed by levshina (2019), inspired by futrell et al. (2015). @xcite she also considers the entropy for couples of dependencies, such as the relative position of subjects and objects. for a given language l, we can compute the weighted average of flexibility(l,c) for a relevant set s of constructions c, which will be discussed below. a measure very similar to flexibility(l) has been introduced by futrell et al. (2015), using conditional entropy. in information theory, the conditional entropy @xcite quantifies the amount of information needed to describe the outcome of the random variable y given that the value of the random variable x is known. the more h(y|x) is close to 1, the more y is independent from x, @xcite being equal to 0. in futrell et al. (2015), x is used to select a set s of constructions, while y describes the word order on s. in other words, entropy, like 8 precisely, entropy(l,c) = p.log 2 (p) -(1p)log 2 @xcite , with @xmath1,c). this value also ranges from 0 to 100%, with value 0 for @xmath2. the only difference with our calculation is that entropy smoothes values for p around the 50% mark. the entropy view of flexibility is very elegant, but, as mentioned by levshina (2019), futrell et al. (2015) gives "one aggregate score" for each language, rather than considering individual constructions before aggregating them. @xcite levshina (2019) also considers constructions restricted to one dependent word form. this is only possible if the corpus contains enough occurrences of the word, which commonly implies for many languages to parse raw corpora that are bigger than the manually annotated corpora of ud. @xcite on the other hand, ud does not usually distinguish prepositional dependents of the verb, which are all @xmath3, whether they are arguments or modifiers. this distinction is made only in a few treebanks, notably the native sud treebanks (with the comp and mod labels). sud uses the udep relation, for underspecified obl dependencies when the distinction in argument and modifier is not encoded. for head-initiality(l), we decide to consider the relations of type comp, mod, udep, subj, dislocated, that we call the core relations. we have included the dislocated relation, because the boundary between governed and dislocated elements is not always well defined. @xcite we have eliminated the det relation because the direction of the determiner-noun relation is controversial (see the discussion around the dp-hypothesis since hudson 1984 and abney 1987), as well as clf (for classifiers), which is used inconsistently. for flexibility(l), we could keep det and clf, because the choice of the governor of a given relation does not play any role: flexibility only measures the proportion of dependencies going in the same direction and remains the same when all dependencies are inverted. however the det and clf have only a small influence on the final result (cf. table d ) and, to be precise, we decided to use the core relations for the computation of flexibility(l) as well. other sud/ud relations are of little interest for our study as their direction is fixed in the ud annotation guidelines. this includes conj, fixed, goeswith, etc. it should also be noted that we have not considered the relations between co-dependents at all. yet, some @xcite about the relations between constructions in main and subordinate clauses, see schachter (1973). @xcite for instance, futrell et al. (2015) based on computation on ud indicates that french and italian are mostly head-final, while, based on sud, they are head-initial at 76% and 77% respectively! @xcite for instance, in a pro-drop language such as chinese, it is difficult to decide if preverbal objects are dislocated or not. see note 3. lastly, we chose to give each construction a weight equivalent to its frequency in the corpora, unlike bakker (1998), who gives the same weight to each of the 10 constructions he considers (as well as levshina (2019), who considers quantitative values for each construction but does an average with equal weight). figure 4 shows the head-initiality of sud 2.11 languages in the x-axis and the flexibility in the y-axis. for treebanks with at least 1000 core relations, we observe that ancient greek, tupinambá, emerillon(teko), turkish-german (code switching corpus) and old east slavic are the most flexible languages (with flexibilities 59.3, 56.7, 55.2, 52.9, and 51.7 respectively), while japanese, hindi, xibe, kazakh and telugu (flexibilities of around 0.5, 1.6, 2.1, 2.4, and 2.4 respectively) are the least flexible languages. languages with head-initiality equal to 0 or 100 have flexibility 0 and the closer they are to 50 the more likely they are to be flexible. but there are languages l with head_initiality(l) close to 50 and flexibility(l) close to 0, such as bambara: these are mixed order languages. languages with high flexibility(l), such as ancient greek, are free order languages. @xcite 5 comparison with bakker's flexibility bakker (1998) proposes a computation of flexibility based on the same principles but does not take into account the greater or lesser flexibility of each construction for each language. in bakker's computation, a language is either flexible or completely rigid. flexibility[bakker](c,l) = 0 if the construction c is completely rigid in l, 1 if it is flexible flexibility[bakker](l)= (equal-weighted) average over 10 constructions c of flexibility[bakker](c,l) @xcite our measures are also dependent on the corpus chosen for the calculus and its genre. the flexibility measure of ancient greek is certainly increased by the fact that the corpus contains poetry and theater. bakker gives the flexibility values for a sample of 86 european languages 47 of which are indo-european. we propose to compare bakker's values with a typometric index of the same type. some of bakker's constructions can be directly translated into sud corpus queries, others can be approximated. for example, his "adj/n" translates directly into the typometric measure noun-mod-adj. the verb-recipient relation (v/r) can only be approximated by verb-comp:obl-adp| noun (cf. table a2 in annex). the complete list of bakker's constructions and their translation into typometric measures are provided in the construction flexibility table a3 of the annex. @xcite as bakker's flexibility measure is categorical per construction, we have to arbitrarily set a threshold at 5%, considering @xcite bakker (1998: 393ff) introduces another measure which he calls consistency and which is very dependent on the set of considered constructions, which are still the 10 same constructions (see section 5): it seems to us that the consistency of a language l is well captured by our head_initiality(l), which is not dependent on the partitioning p into constructions undertaken by the linguist. moreover, bakker (1998: 401-2) notes that flexibility[bakker] and consistency[bakker] are correlated, but this is obvious as soon as there are languages whose head-initiality is close to 0 or 100. likewise, our flexibility and head-initiality are related, since flexibility(l) ≤ 2 min ✕ ( head_initiality(l), 100 -head_initiality(l) ) , which we have visualized as a triangle in figure 4 . we can compare those 3 measures across the languages that we also find in ud: 1. bakker's flexibility, 2. our recomputation of the flexibility à la bakker, as a non-weighted average over bakker's 10 constructions, with the 5% threshold as indicated above, and 3. our typometric flexibility. the scatterplot of figure 5 shows the strong correlation between the bakker-like measure of flexibility and the typometric flexibility. the bakker-like flexibility is also significantly correlated with bakker's flexibility (fig. c2 ), while there is only a weak correlation between the typometric flexibility and bakker's flexibility (fig. c1 ). see the complete results in tables b in the annex. ## flexibility of constructions having compared the overall flexibility of the languages, we can now see how the languages in a given sample s are distributed for each construction c and compare the constructions. specifically, we are interested in how the headinitiality of the languages in our sample (the 138 languages in ud 2.11) is distributed for the different constructions c. our hypothesis is that this distribution is reasonably well described by the following two values: some of bakker's constructions, such as dem/n or pro/n, involve features that are not present in all ud treebanks (@xmath4. our computation is restrained to languages with all the required features. the less flexible c is on average, the more languages are attracted to 0 and 100. the average-head-initiality indicates whether 0 or 100 attracts more to one than the other. we propose two other values that will help us to better understand this attraction towards 0 and 100. we observe that for all the most frequent c constructions, both head_initial_weights(c) > 1 and head_final_weights(c) > 1 (see table a3 in the annex where all but one of the weights for the 10 bakker constructions are greater than 1), which means that languages are attracted on both ends. to give an idea of the different distributions we encounter, the three scatter plots below show three head-initiality distributions on the treebanks: 1. num/n (noun-any-num), 19 2. aux-v (aux-comp:aux-verb), and 3. adj/n (noun-mod-adj). the first (num/n) distribution tends towards 0 and is pushed away from 100 (weights 3.6 and 0.7), while the two other distributions are attracted both by 0 and 100, with a bigger attraction to 0 for adj/n (weights 4.2 and 2.4) and to 100 for aux/v (weights 1.7 and 2.8). num/n adj/n aux/v figure 6 : head-initiality language distribution for three constructions num/n, adj/n, aux/v. again, we can compare our flexibility results with two measures: the flexibility measure proposed by bakker (1998) and a bakker-like measure that we calculate from our sample. flexibility[bakker](c)= % of languages in bakker's sample that are flexible for c. flexibility[bakker_like] s (c) = % of ls in s with flexibility(l,c)>5. bakker restricts his study to a sample s of 86 european languages, 24 of them having enough data in ud to be compared. @xcite when they are used as a quantifier (my 7 cats). in other uses, they work as a proper noun (line 7, page 7, year 2023) and receive the feature @xmath5. it is this feature, rather than the pos, that is used in all our computations. it remains that the use of nummod is not consistent across all treebanks. @xcite when looking at a particular construction c, we only consider a language l if the treebanks of l have at least 50 occurrences of c. for bakker-like measures to be calculated for l, the threshold of 20 we find that v/o is the most flexible construction, followed by v/r and adj/n. two constructions do not behave at all as in bakker's sample: aux/v appears as the most flexible construction after v/o, while rel/n appears as extremely inflexible. bakker also compares the flexibility of languages with head-initial and head-final basic order. again we can introduce typometric bakker-like measures. we consider that a language has head-initial basic order if more than 50% of core dependencies are headinitial. ## predictivity with these notions in place, it is now possible to measure which construction predicts best the overall core flexibility of a given language. for this, we measure the spearman correlation between the distribution of flexibility(l,c) for various couples of construction c (figure 8 ). we are particularly interested in the correlation with the core construction. among the 10 bakker constructions, the best predictors of the core flexibility is the v/o construction, unlike v/r. note also some notable correlations: aux/v and v/o that have a correlation of 0.59 as well as subj and comp that have a correlation of 0.53. bakker (1998: 392) however states that "the best predictors of overall flexibility are the flexibility of the recipient, genitive, numeral and relative clause. on the other hand, no prediction whatsoever can be drawn from the behavior of adpositions and articles." this is not backed up by our data with our weighted flexibility measure: the typometric genitive flexibility has a correlation of only 0.18 with must be reached for each of the 10 constructions considered. the core flexibility, numerals have a correlation of 0.01, and relatives of 0.07. table d of the annex for detailed values. nonetheless, our data agrees with a common typologist view, most notably dryer (1992), that sees v/o as a good predictor for word order constraints on other constructions. note also that the constructions with the biggest flexibility are the best predictors. this was expected because constructions with low flexibility tend to gather all languages around 0 and 100. ## conclusion we have introduced a first measure, headinitiality, which measures the variable headdependent word order on a language's treebank or on specific constructions. based on this, we develop an operational notion of flexibility that renders the intuition that the average headinitiality can be far from 0 or 100 while the languages are strict per given construction. we then show that our empirical notion of flexibility can be compared to previous definitions of flexibility of word order, notably to bakker's work. our notion of flexibility has the advantage that it can directly be computed from treebanks, that it does not require ad-hoc thresholds to categorize languages or constructions, and that it can be applied with any granularity of constructions. finally, we show which construction predicts overall word order flexibility of a language. for this, we rely on spearman's rank correlation coefficient, which allows us to calculate a correlation between two distributions. we show that over ud's language sample, the highest correlation is obtained for nominal objects (v/o construction). since the spearman correlation is a symmetric measure, we would like to continue our study by proposing an asymmetric measure that allows us to decide if one distribution can predict another. our hypothesis, to be confirmed, is that constructions with the most uniform distribution, thus being flexible and well-balanced, provide better predictions of the behavior of other constructions. the v/o construction, which many authors take as a basic construction (see in particular the study of dryer 1992) is thus an excellent candidate.