The dependence of the vocabulary volume on text sample size has been studied on the material of literary texts [Grebennikov and Assel, 2019] as well as everyday spoken language [Kosareva and Martynenko, 2015]. The present research concerns the study of the morphemic type-token ratio in samples from Franz Kafka's and Thomas Mann's short stories in German. The morphemic annotation of the samples from these texts was carried out manually and was aimed at finding the asymptote of the function “morpheme token-morpheme type.” This helps to conclude whether the expansion of the list of lexemes in these authors' texts is due to the occurrence of new stems or to word formation.
Our work is based on the idea that the analysis of the morphemic structure of wordsdeservesserious attention as compounding and affixation (i.e. the concatenation of morphemes) serve as productive tools for the creation of morphologically complex words with semantically transparentstructure in many languages. Consequently, the total number of morphemes in such a language is smaller than that of lexemes. As a result, it might be easier to obtain a representative sample of morphemes from a corpus than in case of words. Of course, it should be notedthat not every lexical unit is semantically compositional at the morphemic level; this feature corresponds to the problem of syntagmatic idiomaticity. Despite this fact, knowledge about the units of the morphological system of languages with rich word formation such as German and Russian can still be considered useful. Another important aspect is that word formation is considered to play a significant role in text building. For example, Zemskaya[1992: 164] defines six ways of word formation manifestation as an activity in speech acts: derivation from a pretext word or syntagma during speech act production use of set of derivatives of the same type within a text formation of different derivatives from the same base use of words with identical derivational meaning juxtaposition of derivatives from homonymous words contrastive use of words with the same root.
These observations suggest that the study of morphemes in text can be a source of information for the description of an individual style.
This research is aimed at the modelling of the morphemic vocabulary growth (in number of morphemes) as a function of sample size on the material of German literary texts. In the next section, the research of the type-token ratio in Russian texts is briefly reviewed. In the present work, the attempt was made to adopt this basic idea to the quantitative study of texts at the morphemic level. In the third section, the data used for the present research and their annotation are discussed. Results of fitting a distribution to the datareceived are presented in the fourthsection. The last section is a summary of our conclusions and further plans. 2
In [Kosareva and Martynenko, 2015] research was done on the ORD corpus1 (“One Day of Speech” corpus) to estimate the asymptote of the function modelling the type-token dependence in spoken Russian texts. The Weibull and Haustein functions were used for approximation, the latter of which was found to fit the data better, and the asymptotic level of about 45,000 lexemes was estimated.With the same methods, approximations by the two functions on the material of short stories of Russian writers were compared in [Grebennikov and Assel, 2019] but the authors concluded that the Haustein function is not always preferable depending on the growth stabilization. It is also worth noting that a significant difference was found between the authors. The growthof thequantity of types in Chekhov’s short stories considerably slows down at a sample size of around 150,000 tokens (ca 16,000 lexemes). In case of Averchenko, however, no clear upper limit of the growth could be set.
The linguistic annotation of the data used in the present work is based on linguistic principles. [Mel’ˇcuk, 2006: 390] should be mentioned as a theoretical framework and [Fleischer and Barz, 2018] as a description of contemporary German word formation. More details will be given in the next section.
1http://www.ord-corpus.spbu.ru/SocialStudies/ORD.html
In order to perform a quantitative experiment at a subword level, it is essential to have a large amount of morphemically annotated text samples. Algorithms of automatic word segmentation into smaller meaningful units are available. For example, MorfessorFlatCat is based on hidden Markov models with hidden states “stem”, “prefix”, “suffix” and “nonmorpheme” to enable unsupervised machine learning [Gr¨onroos et al. 2014]. However, it is obvious that such an algorithm could not be applied for data annotation in our work.
Firstly, the segmentations should be maximally precise and based on linguistic principles. Secondly, even the correct identification of morphs, i.e. minimal meaningful substrings of the words is unsuitable for the planned experiment. Morphs are tokens of morphemes, each of which should be represented by a single form. For instance, the morpheme KEIT ‘-ness’ appears in forms -keit and -heit in the German words Wichtigkeit (importance) and Dunkelheit (darkness), respectively. Thirdly, the elaboration of a fine-grained system of supplementary morpheme tags is necessary in order to disambiguate homonymous morphemes. Due to these conditions, the data was annotated manually.
For the given experiment, the texts of two German authors were chosen. The short stories of Thomas Mann in a collection available in Project Gutenberg2 as well as all literary works (but not diary entries and private letters) of Franz Kafka in Project Gutenberg-DE3 were copied and saved as plain texts. The short stories only may not have contained enough tokens, so Kafka’s novels were also included into the material. Thus the document containing Kafka’s texts (ca 290,000 words) is much larger than the collection of Mann’s short stories (ca 39,000 words) but still big enough for sampling.
The texts were first annotated by TreeTagger4, which is a part-of-speech (POS) tagger that applies a Markov model and a decision tree [see Schmid 1994, 1995]. Apart from a relatively large number of POS-tags 5, lemmatization is also provided by the software. This information simplifies the process of morphemic annotation as a tuple consisting of a POS-tag and a lemma usually unambiguously determines the correct morphemic analysis.
Sampling was implemented as follows. From each of the two collections, 60 nonoverlapping text fragments of 250 tokens each were randomly selected. 3.2
The words in the obtained samples were analyzed manually; punctuation marks were ignored. As mentioned above, contextual information was not usually needed to find the right annotation, so each POS-tag–lemma tuple was processed only once. In the case when disambiguation was necessary, the given words were analyzed in context.
The annotation includes the assignment of a string that represents a morpheme and a tag which is analogous to POS-tags to each identified word segment. The latter (for simplicity, it may be referred to as a morphemic POS-tag or MPOS-tag) is a two-level tag the first component of which takes a value from the set “ST”, “PF”, “SF”; the elements of this set stand 2https://www.gutenberg.org/files/36766/36766-0.txt 3https://gutenberg.spiegel.de/autor/franz-kafka-309 4https://www.cis.uni-muenchen.de/ schmid/tools/TreeTagger/ 5Documentation for German available: https://www.cis.uni-muenchen.de/ schmid/tools/TreeTagger/ data/stts_guide.pdf for “stem”, “prefix” and “suffix”, respectively (so they correspond to three of the hidden states of model applied by MorfessorFlatCat). The second component is determined by the part of speech of the whole word form when the given morpheme is added to the stem. It takes a value from the set “NN”, “VV”, “ADJ”, “ADV”, “PP” “DET”, “PPER”, “PREL”, “PD”, “PUF”, “PAV”, “PWAV”, “KOUS”, “KOUI”, “KON”, “KOKOM”, “APPR”, “PTKVZ”, “PTKZU”, “PTKNEG”, “PTKA”, “PTKANT”, “ITJ”. These values are connected to the POS-tags assigned to the words of the samples by TreeTagger. However, it should be noted that this set is smaller than the set of all TreeTagger POS-tags,so each one of the morphemic annotation units may be associated with several original TreeTagger tags. For example, attributive and substitutive/predicative roles are not reflected at the morphemic level. A one-morpheme adjective gets the same morphemic tag (ST-ADJ) in both attributive (ADJA) and predicative positions (ADJD). Of course, an attributively used adjectival word form normally consists of at least two morphemes, the last of which is an inflectional ending. Inflectional morphemes, however, were simply ignored as their main function is marking syntactic relations within a sentence and can hardly be considered informative from the aspect of textuality or individual style. Furthermore, considering inflectional morphemes in the segmentation would make it impossible to determine the correct morphemic analysis without information about the concrete word form which is to be annotated. So-called “Fugenelemente” (meaningless segments of words on the borders of constituent morphemes) were ignored as well. Examples are given in Table 1-2.
It is worth noting that word-level POS-tags are also used in modules of word sense disambiguation systems [Wilks and Stevenson, 1997]. This means that the method of identification of morphemes by normal form and an MPOS-tag makes use of an analogy between morpheme and word level. 3.3
Although it might seem trivial to define a morpheme as the smallest segmental meaningful part of a word, in practice it can be difficult to find a theoretically supportable morphemic analysis of a particular word. For example,it needs explanation whether the following words are to be split into two morphemes or not:
All examples above were marked as single morphemes in the samples. Word a) consist of the diminutive suffix -chen and a pseudostem which cannot be considered as a sign of standard German. Following the concepts in [Mel’čuk, 2006: 384], any linguistic sign should representable as a triplet of a signified, signifier and syntactics, which condition is not met by the given pseudostem due to the lack of a signified at a synchronic level. In b) both be- and komm(en) are valid linguistic signs. However, the first is an abstract verbal prefix while the second is a verb meaning ‘come’. Obviously, the meaning of the derivative cannot be composed of these semantic elements. The possible constituents of c) are ent-, which is a verbal prefix
Meaning ‘war years’
Word form Kriegsjahren
Meaning ‘is’ ‘one, anyone’
STPUF_man
STDET_dies
STPRELS_die ST-PD_die
In case of suppletion, the lemma is
analyzed.
ST-PUF is a special tag without an
equivalent in TreeTaggertagset. It is assigned to a small set of uninflectable
words ST-DET (determiner) is a frequent tag that is assigned to articles and demonstrative pronouns without
homonyms The next examples
demonstrate the disambiguating effect of MPOS-tags (in this
case they disambiguate whole words) that implies the cancellation of an action or a state as one of its senses, and deck(en) (cover, protect, hide). Although not hiding and discovering something can be regarded as cognitively associated senses, such a weak relation did not seem to be sufficient to split the word into two parts. The compound Auge (eye) + Glas (glass) is presented in d). In fact, it is close to be semantically compositional but still the meaning of Glas is too general.
In linguistics, degrees of semantic compositionality, which can also be referred to as transparency, are sometimes distinguished. In [Ransmayr et al., 2016: 267–268] eleven degrees of transparency of German derived words with the diminutive suffix -chen were defined. The opaquest derivatives are words without a synchronically identifiable stem, like a) above, or with a non-noun stem like Frühchen (premature infant).The meanings of the most transparent derivatives are simply constructed of those of their constituent morphemes. Sometimes they can be affected by pragmatic restrictions, for example, diminutives denoting clothes such as Jäckchen (small jacket) are usually used to refer to women’s or children’s clothes. Between these extremes there are instances of weakly (e.g. metaphorically) motivated compositions such as Eichhörnchen (squirrel) and Hörnchen (croissant).
All derived words which are not maximally transparent can be considered, using the terminology in [Mel’čuk, 2006: 390], quasimorphs, which should be stored in dictionary as separate entries. However, a typical lexicographic problem often makes this principle more difficult to apply in practice: it is not always clear how to define the meaning of constituent morphemes. Taking once again the stem of c as an example, it is not self-evident without thorough corpus research whether the sense ‘protect, hide’ should be considered a simple metaphor or a word sense which needs lexicographic description.This is a usual lexicographic problem, which inevitably occurs and must be solved more or less subjectively in each case. Despite this fact, some principles of segmentation formulated in advance can serve as considerable theoretic support. In view of the aspects discussed above, they can be summarized as follows: 1. All constituents of the analyzed word should be meaningful linguistic unitsat a synchronic level. 2. A bound morpheme is to be added to the morphemic vocabulary only if it occurs in several non-synonymous words in which it has the same sense (which although might be highly general or opaque). 3. A complex unit (quasimorph) is preferable only if its meaning is not fully transparent.
Under the assumption that word meaning can be represented as a finite set of senses, which are considered to be conventionalized, this means that we expect that all senses of a morphologically complex word w can be represented as an element of the Cartesian product of the constituents senses. If some senses of w are elements of the Cartesian product, while others are not, the correspondent quasimorph should be added to vocabulary in case of the occurrence of w with a non-compositional sense.
These principles are simple, but they can help make consequent decisions. For example, it follows from 2) that such morphemes as the pseudostem of Mädchen (girl) cannot be treated as separate meaningful segments of words even if several synonymous lexemes exist in the language with the same pseudostem, e.g. Mädchen and Mädel.This idea can be generalized to any unique morpheme which occurs only as a constituent of a certain lexeme. Note that a different viewpoint is also presented in [Fleischer and Barz, 2012: 65] that is based on structural and not strictly semantic analysis.
The analysis of the noun Aufzug (the act of lifting, hoisting/elevator/act in theater) shows the consequences of principle 3). If it occurs as a noun derived straightly from the verb aufziehen (auf ‘up’ + ziehen ‘pull’), then it is correct to segment it into two constituents. However, in a sample from Thomas Mann’s texts this is not the case. It occurs in the sense ‘act in theater’ and is therefore added to the morphemic vocabulary as a whole unit.
It is obvious that the last principle suggests that knowledge about word senses is essential for morphemic analysis. It makes it necessary to rely on a lexicographic resource. DWDS6 was chosen as such a resource as it ensures quick access not only to lexicographic but also corpus data if needed. For details about DWDS see [Geyken, 2007].
However, these ideas were not extended to verbs with separable verb prefixes (and words compositionally derived from them) although they often form lexical units with semantically opaque structure. Separable prefixes can take a position very far from the verbal stem in the sentence, which makes it hard to suggest an appropriate annotation method. This remained a problem to resolve.
Since morphemes are not the only elementary linguistic signs [Mel’čuk, 2006: 295–297], it is necessary to mention how non-segmental signs were handled. In German such signs are frequently applied by means of conversion and modification. Take the nouns Schritt (step), Eintreten (the act of coming in) and the verb beenden (finish) as examples. Schritt is derived from schreiten (to step) by vowel change, Eintreten is obtained by applying conversion to the verb eintreten (come in) and in beenden the noun Ende (i.e. its allomorph end) can be observed and as be- is a verbal prefix, it must be concluded that the noun is converted to a verb (there is also another verb enden with nearly the same meaning). As our annotation is morphemic, these non-segmental signs are simply ignored. This means that the analyses of these words are ST-VV_schreit, ST-PTKVZ_ein + ST-VV_tret and PF-VV_be + STNN_ende, respectively. Of course, this is a simplification: these signs are frequent in German and the morphological process of conversion is highly productive.
Now that all major problems of the data annotation are discussed, results can be presented. 4
Having annotated the text fragments, it was necessary to find a distribution which can model the growth of morphemic vocabulary as a function of sample size. As mentioned above, the Weibull and Haustein functions were applied for similar goals [Kosareva and Martynenko, 2015; Grebennikov and Assel, 2019]. Our paper is not aimed at comparing how different functions fit the data. Only cumulative Weibull distribution was chosen for modelling, which is usually defined as follows:
Apart from the exponent, the difference is that the right side of the last equation is 6Digitales Wörterbuch der deutschen Sprache (Digital Dictionary of the German Language): https://www.dwds.de/ multiplied by Nmax which is the asymptote of the function, i.e. the theoretical maximal volume of the morphemic vocabulary.
To simplify computation, data was manipulated to enable the use of the former (more
standard) formula. Firstly, empirical values (the registered number of lexemes at a given
sample size) were divided by a hypothetical value of maximal volume. Then the equation was
linearized
Tables 3-4 show some hypothetical values of Nmax and the corresponding sum of quadratic deviations. The data necessary for calculating theoretical values of y, given the Nmax which has eventually proved best, are presented in Tables 5-6. These tables serve as illustrations and they contain only every third observed value of the morphemic type-token function (of course, the whole sets of observations were used to find distribution parameters). The curves of cumulative Weibull distributions determined by the calculated parameters and Nmax are depicted in Figure 1.
Weibull Theoretic Quadratic value value yj devia
tions 0,12 327,12 146,98 0,19 507,97 143,23 0,25 656,35 347,91 0,29 775,03 782,11 0,33 879,94 787,22 0,37 971,58 339,14 0,4 1054,26 59,95 0,43 1126,25 7,54 0,45 1195,62 0,14 0,48 1259,3 176,94 0,5 1320,37 337,4 0,52 1377,86 355,72 0,54 1431,51 210,51 0,56 1480,44 180,52 0,58 1526,8 249,71 0,59 1570,93 397,28 0,61 1611,8 7,85 0,62 1648,22 116,27 0,64 1683,86 260,59 0,65 1719,99 529,59
A logical interpretation of the results is that there are more foreign roots in Thomas Mann’s short stories than in Franz Kafka’s texts. It can be noticed that Mann uses more foreign proper names (e.g. Florentinum, Fontana). However, it seems that the type-token ratio should be considered at word level as well in order to justify this hypothesis. For example, an author whose morphemic vocabulary grows slowly but uses many different lexemes could rely on word formation to support expressivity.
In the present paper, it has been showed that quantitative aspects of derivational morphology can be regarded as a feature of individual style. A significant difference has been found between the growth of morphemic vocabulary in two German authors’ texts. In future research, larger samples need to be taken in order to compare the dependence of the number of lexeme and morpheme types on sample size. As word formation is a productive linguistic and cognitive process, this may considerably contribute to the quantitative research of style.