An Information-Theoretic Characterization of Morphological Fusion (2021)

Abstract: Linguistic typology generally divides synthetic languages into groups based on their morphological fusion. However, this measure has long been thought to be best considered a matter of degree. We present an information-theoretic measure, called informational fusion, to quantify the degree of fusion of a given set of morphological features in a surface form, which naturally provides such a graded scale. Informational fusion is able to encapsulate not only concatenative, but also nonconcatenative morphological systems (e.g. Arabic), abstracting away from any notions of morpheme segmentation. We then show, on a sample of twenty-one languages, that our measure recapitulates the usual linguistic classifications for concatenative systems, and provides new measures for nonconcatenative ones. We also evaluate the long-standing hypotheses that more frequent forms are more fusional, and that paradigm size anticorrelates with degree of fusion. We do not find evidence for the idea that languages have characteristic levels of fusion; rather, the degree of fusion varies across part-of-speech within languages.

## introduction traditional morphological typology divides synthetic languages into two distinct groups, agglutinative and fusional @xcite . agglutinative languages have morphemes which can be separated into identifiable parts corresponding to single features. for example, the hungarian form embereknek can be separated into a root and two suffixes, each of which expresses a single morphological feature: ember-ek-nek (person-pl-dat). on the other hand, fusional languages express multiple features in a single morpheme, such as latin servīs (servant-dat.pl), where the suffix -īs indicates the dative and plural simultaneously and *equal contribution by mh and rf. linguistic typologists have long recognized that this distinction is more of a spectrum than a categorical distinction, with @xcite defining an 'index of agglutination' metric to determine the degree to which a language is agglutinative across its morphological paradigms. interestingly, the notion appears to be graded even within a language. for example, the latin adjectival feminine genitive plural suffix is -ārum, where the thematic vowel ā corresponds weakly to the feminine. here, we provide an information-theoretic characterization of the degree of fusion of any given form in a language, naturally providing a graded measure. our core intuition is that a form which expresses a given set of features can be classified as fusional if it cannot be predicted given the forms for other sets of morphological features (i.e. the "rest of the paradigm"). for example, the latin ending -īs in our measure of fusion abstracts away from issues of morpheme segmentation. 'agglutination' and 'fusion' traditionally refer to the extent to which individual features correspond to individual concatenated morphemes: for example, the hungarian example is considered agglutinative because the suffix -nek for the feature dative is concatenated to the morpheme -ek for the feature plural. in contrast, our measure of fusion indicates the extent to which a form may be explained as a result of individual morphological processes corresponding to features, including nonconcatenative processes such as infixation, vowel alternations, reduplication, etc. effectively, we measure the extent to which a form cannot be predicted or explained in terms of any strict subset of its morphological features. because our measure abstracts away from the form of the morphological processes involved, we name it informational fusion. previous work has argued that the idea of 'fusion' conflates (at least) three distinct ideas: phonological fusion (the extent to which morphemes are phonologically merged or interleaved with the root), flexivity (the degree of allomorphy with the root), and exponence or cumulativity (the number of distinct features expressed by an unanalyzable morpheme) @xcite . informational fusion aligns most closely with the idea of exponence, measuring the extent to which multiple features are expressed by an unanalyzable morphological process. in the remainder of the paper, we formally state our fusion measure and describe its implementation and estimation from data (section 2), and then evaluate our measure's ability to capture linguistic intuitions and use it to test linguistic hypotheses (section 3). section 4 concludes. ## results and discussion here we study whether our fusion measure recapitulates the familiar classifications for selected languages, and study whether it covaries systematically with paradigm size and form frequency, testing linguistic hypotheses. ## conclusion we introduced an information-theoretic measure of the fusion of a form within a morphological paradigm, called informational fusion. we have shown that informational fusion recapitulates linguists' intuitions and allows for quantitative tests of linguistic hypotheses, including a tradeoff between fusion and frequency. our work joins a growing body of recent research that aims to operationalize basic linguistic concepts in terms of information theory @xcite @xcite @xcite . informational fusion is the extent to which a form cannot be predicted based on any strict subset of its morphological features. as such, it aligns closely with the linguistic notion of the exponence of a form. it can be adapted to provide fusion measures for specific morphemes and features by carefully choosing which features are held out during the training of the predictive model.