Syntactic units and their length distributions: A case study in C zech (2025)

Abstract: This study investigates the length distributions of syntactic units in Czech across multiple hierarchical levels: sentences, independent clauses, clauses, phrases, subphrases, and chunks. Using a diverse dataset – including Universal Dependency treebanks, presidential speeches, the Czech Bible, and random sample from corpora of modern Czech – the analysis examines whether lengths of these syntactic units follow consistent distributional patterns. Length is defined as the number of immediate subunits, and the distributions were modeled using the hyper-Poisson distribution. The results demonstrate that the hyper-Poisson model fits well distributions of length of all abovementioned syntactic units, pointing to a common principle underlying the organization of syntactic structure in Czech.

## introduction the relationship between linguistic units has long been an important topic in quantitative linguistics, particularly through the study of the menzerath-altmann law (mal henceforward, @xcite . the law expresses the relationship between the length of a construct and the length of its constituents (parts of the construct); specifically, the longer the construct, the shorter the constituent on average. while the mal has been extensively validated using words and syllables, its applicability at the syntactic level remains a subject of ongoing investigation @xcite @xcite @xcite . recent study @xcite has explored the mal across several units in the language unit hierarchy (sentences -independent clausesclauses -phrases -subphrases -chunks -words -syllables). these investigations suggest that the mal holds across all these levels, indicating a consistent pattern also with respect to syntactic constructions. it is the first paper that considers several neighbouring language units simultaneously; all previous papers on this topic limited themselves to partial results, mostly only to one triad of units (such as, e.g., @xcite focus solely on clause length in phrases and phrase length in words). building upon this foundation, the present paper aims to analyze distributions of lengths of syntactic units mentioned in the previous paragraph. length of a unit is measured in the number of its direct lower neighbours in the language unit hierarchy. specifically, we will examine length of sentences (measured in the number of independent clauses the sentence contains), of independent clauses (in clauses), of clauses (in phrases), of phrases (ecubphrases), of subphrases (in chunks), of chunks (in words), and of words (in syllables). the goal is to determine whether length distributions of abovementioned syntactic units display similar patterns that might provide insight into the structure and organization of language units. ## language material the language material for this study is sourced from multiple treebanks and corpora, each offering a distinct representation of the czech language across various genres and time periods. a significant portion is drawn from the universal dependencies 2.13 @xcite . specifically, we utilize six czech dependency treebanks: in addition to the ud treebanks mentioned above, we analyze 89 annual speeches delivered by twelve czechoslovak and czech presidents. these speeches are the object of research in @xcite . our study also incorporates the czech ecumenical translation of the bible (cet), a contemporary czech translation undertaken between 1961 and 1979. this translation renders biblical texts into modern czech while preserving traditional diction and style. we use the 2001 revision of the cet translation. finally, we utilize sentences from the syn2020 corpus @xcite , a comprehensive and balanced collection of contemporary written czech developed by the czech national corpus. predominantly encompassing texts from 2015 to 2019, the corpus contains 100 million words and is structured into three equally sized segments: fiction, non-fiction, and newspapers/magazines. for this study, a random sample of 50,000 sentences from each segment was used. the individual parts were merged and treated as a whole, thus encompassing various genres. the language material used is quite heterogeneous. @xcite formulated the relation between word length (in syllables) and the mean syllable length (in phonemes) as valid for the vocabulary. similarly, we suppose that the menzerath-altmann law in general is valid for the inventory of units rather than for particular texts or text genres. of course no dictionary or corpus contains the whole vocabulary, and it is even less realistic to speak 1 these sentences form a part of the parallel universal dependencies (pud) treebanks created for the conll 2017 shared task on multilingual parsing from raw text to universal dependencies ( http://universaldependencies.org/conll17/ ). about the complete inventory of sentences, clauses, etc., but some measure of heterogeneity reduces the risk of genre-specific syntactic units. ## methodology and operationalization in this section, we present language units we analyze, following the approach from @xcite . those parts of our corpus that do not come from ud treebanks (i.e., the presidential speeches, the bible translation, and the sentences from the syn2020 corpus; see section 2) were processed using udpipe 2.0 @xcite , a trainable pipeline that, among other functions, performs dependency parsing. subsequently, all the annotated texts were converted to the surface syntactic universal dependencies (sud) annotation scheme @xcite using grew software @xcite . the reason is that the sud annotation reflects more closely dependency syntax based on purely syntactic (rather than semantic or functional) criteria. sud provides a representation closer to surface-syntactic frameworks such as meaning-text theory @xcite , word grammar @xcite , and the prague dependency treebank @xcite . we took sentences as they are determined by the annotation tool. only sentences satisfying the following three criteria were included in the analysis: (i) they contain a predicate (a finite verb or an auxiliary) as the sentence root; (ii) they do not contain abbreviations, digits, foreign words, words with unknown syntactic functions, special characters, and words assigned the flat foot_0 or orphan foot_1 syntactic function; (iii) they do not contain a chain of more than two coordinated words, with exception of predicates of independent clauses (discussed below). sentence length is expressed as the number of independent clauses the sentence contains. the first independent clause comprises the root of the sentence and all words that are directly or indirectly syntactically linked with it if the links are not coordinations with another predicate. if there is another predicate coordinated with the sentence root, it becomes the root of another independent clause within the sentence. the immediate constituent of an independent clause is a clause, which consists of the predicate and all its direct or indirect dependents, excluding other predicates. to illustrate these units foot_2 , figure 1 presents the dependency tree of the sentence (1) divided into individual independent clauses (on the left) and clauses (on the right). the immediate unit of the clause is a phrase. a phrase is commonly understood as a multi-word constituent where one word, known as the head or root, holds prominence over the others @xcite . for our purposes, the initial phrase of a clause includes the predicate and its leftmost dependent, along with all its own dependents. this approach emphasizes the linear progression of the sentence. subsequent dependents of the predicate are treated as heads of their own phrases, each encompassing the head and all words dependent on it, directly or indirectly, if applicable. a subphrase is a newly defined unit introduced by @xcite . it is defined as the longest sequence of dependent words in which each word (except the head) has at most one dependent. figure 2 provides a detailed view of the first clause in sentence (1). the left side of the figure illustrates the individual phrases. the first phrase includes the predicate and its leftmost dependent, while the second phrase consists of the remaining dependent -functioning as the head of the phrase -along with all of its own dependents. this results in the following division of the first clause: the right side of the figure shows the individual subphrases. the first subphrase of the first phrase consists of the predicate nemůžeme on its own, because its dependent u has more than one dependent and cannot be included. the second subphrase is formed by u and all its dependents, since each of them has at most one dependent. hence, the subphrases of the first phrase are [nemůžeme], [ani u uvědomované motivace]. the second phrase makes up a single subphrase, as every word in it has at most one dependent. a subphrase then consists of chunks defined according to the following criteria: (i) all words within the chunk share the same immediate parent (head); (ii) the chunk comprises only one level of dependency; (iii) the words are contiguous in the subphrase; (iv) no dependent word in the chunk has dependents outside of it. 5 figure 3 presents the first phrase of the first clause of the sentence (1), divided into subphrases (on the left side) and individual chunks (on the right side). the first subphrase contains a single chunk, as it consists of only one word -nemůžeme. the second subphrase is divided into two chunks, [ani u] and [uvědomované motivace], since only these combinations satisfy all the criteria outlined above. ## results the hyper-poisson distribution (wimmer and altmann, 1999, pp. 281-282) is defined as x) , @xmath0, 1, . . . (1) with @xmath1; @xcite . however, distribution (1) is defined on the set of all non-negative integers, while our data attain values from a finite set (no length exceeds the value of 13), and, moreover, it attains also the value of 0, while the lowest value of length in our data is 1. therefore, we use a modification of distribution (1), namely, its righttruncated version shifted to the right by 1, with as a model for length distributions of the units from section 3. the value of the parameter n is determined as the highest observed length value in the data. for the normalization constant c it holds we express the goodness-of-fit of the model in terms of the determination coefficient r 2 , with r 2 ≥ 0.9 indicating a satisfactory fit (see @xcite . we created a simple script in statistical software environment r 7 to fit this dataset. estimated values of the parameters and the resulting determination coefficients are presented in tables 2 and 3 , and visualized in figure 4 . one can see that the hyper-poisson distribution fits all the data sufficiently well (all values of the determination coefficient are at least 0.9927). we remind the reader that the hyper-poisson distribution is one of standard mathematical models for length of linguistic units. the poisson distribution and its modifications and generalizations (including the hyper-poisson distribution) and its applications to word length modelling can be found e.g. in @xcite and @xcite . thus, one can say that length of syntactic units (as they are defined in section 3) behaves in the same way as word length. in addition, the hyper-poisson distribution is a special case of a very general model of the linguistic theory from @xcite . therefore, although some of the new units used are waiting for their linguistic interpretation, they at least display a behaviour analogous to the units that are well established. while the parameters of the hyper-poisson distribution do not vary systematically between levels, there is a strong hint that their ratios b/a depend on the empirical repeat rate rr defined as @xmath2, with r k being the relative frequency of length k, see @xcite and @xcite . the repeat rate is a measure of diversity (or, from the opposite point of view, of uniformity) of the observed distribution. it can attain values from 1/n to 1. in the context of this paper, the value of 1/n corresponds to the same frequency of all lengths from 1 to n, whereas the value of 1 characterizes the deterministic distribution, i.e., all item have the same length. the values of the ratios b/a and the repeat rates rr for particular levels can be found in ## conclusion analysis of the lengths of sentences, independent clauses, clauses, phrases, subphrases, chunks, and words revealed that these syntactic units exhibit length distribution patterns comparable to those found in more traditional linguistic units (especially in words). in each case, the length distribution can be modelled by the hyper-poisson distribution, which has often been used as a mathematical model for (especially, but not only) word length. moreover, based on @xcite , these units consistently conform to the menzerath-altmann law across all structural levels, from sentences to syllables. thus, they fit into the framework of interconnected linguistic units in which units and their properties are not isolated, but, rather, they influence each other @xcite .