A Mutual Information-based Approach to Quantifying Logography in J apanese and S umerian (2023)

Abstract: Writing systems have traditionally been classified by whether they prioritize encoding phonological information (phonographic) versus morphological or semantic information (logographic). Recent work has broached the question of how membership in these categories can be quantified. We aim to contribute to this line of research by treating a definition of logography which directly incorporates morphological identity. Our methods compare mutual information between graphic forms and phonological forms and between graphic forms and morphological identity. We report on preliminary results here for two case studies, written Sumerian and written Japanese. The results suggest that our methods present a promising means of classifying the degree to which a writing system is logographic or phonographic.

## introduction writing systems vary regarding how much they encode phonological versus morphological (or semantic) information: systems which prioritize conveying phonological information are conventionally labeled as phonographic, and systems which prioritize morphological/lexical information are labeled as logographic @xcite . while this taxonomic split is convenient as a broad-strokes shorthand for classifying different writing systems, more precise categories, as well as more precise definitions for existing categories, remain a point of ongoing research, and debate, among scholars of writing systems. defining what it means to be logographic has been a particular point of inconsistency in the literature on writing systems; see section 2 of @xcite for a review. while cases where a single character maps to an entire word would generally be considered logographic and cases where a single character always maps to a particular seg-ment would be considered phonographic, the numerous in-between cases present points of possible contention. for example, the fact that english spells many homophones differently (e.g., where, wear, ware), while spelling distinct allomorphs of a given morpheme the same way (e.g., the root in heal and health), has motivated treating written english as somewhat logographic. @xcite @xcite . relative to any particular category definitions is the question of how one might quantify the degree to which a writing system belongs to that taxonomic category. while not always framed as a matter of typology, a few methods have been used to quantify the consistency of character string-sound string mappings (orthographic transparency/depth). these include using binary consistent/inconsistent distinctions (e.g., @xcite ), entropy-based measures (e.g. @xcite ; @xcite ; @xcite ; @xcite ), and machine learning @xcite . with regards to consistency of mapping, results differ depending on whether one considers the perspective of the reader or the writer: it's possible to have ambiguity of reading but not spelling (e.g., english bass), or vice versa (e.g. english /ô > ait/). @xcite and @xcite more directly focused on the question of quantifying taxonomic category membership (rather than orthographic transparency). we aim to build on the work in this vein by proposing a simple metric of logography which incorporates graphic forms, phonological forms, and morphological identity. ## logography via morpheme identity one can view graphic forms and spoken forms as two points of a triangle, with the third point being semantics or lexical identity foot_0 . since sproat and gutkin (2021) focus on their distinct homophones interpretation of logography, the role of morphology (and semantics) do not play a role in their experiments. we aim to add morpheme identity to the mix, which helps to complete the missing side of the triangle. given that traditional definitions of logography have placed emphasis on the role of morphology or semantics in how words are read and written, a complete account of how to quantify logography would benefit from including the graphic form-morphology leg of the triangle. intuitively, if a system is more logographic, then graphic forms and morphological identity will provide more information about each other; if a system is more phonographic, then graphic forms and phonological forms will provide more information about each other. we propose that the degree to which a writing system is logographic l can be quantified by comparing the mutual information between graphic forms g and morphemes m with the mutual information between graphic forms g and phonological forms p: one advantage that mutual information has in this context is its symmetry, with the consequence that it's agnostic as to whether the writing system is being analyzed from the reader's perspective or the writer's perspective. measures such as sproat and gutkin's s and l metrics can only be done from one of the two reader/writer perspectives at a time (sproat and gutkin's experiments only took the writer's perspective); while there's nothing stopping one from getting those measures from both perspectives separately, this would give two separate measures rather than the single unified measure that mutual information offers. ## data -sumerian and japanese as an initial testing ground, we focus on the writing systems of two unrelated languages: modern japanese and ur iii sumerian. these writing systems are considered to be highly logographic, with morphemes often being spelled with a single character. sumerian and japanese happen to both be agglutinating in their morphology, with additional similarities including postnominal case marking, root+affix verbal morphology, and extensive use of compounding @xcite ; given the role that morphology plays in our analysis, it is convenient to start by considering two languages which, by chance, have similar morphological profiles and similar writing systems. in addition, this choice of writing systems also allowed us to have one writing system (japanese) which was considered by sproat and gutkin, and one writing system (sumerian) which hasn't yet been explored in this vein. to our knowledge, this work constitutes the first attempt at quantifying how logographic or phonographic written sumerian is. these systems were also chosen in part because of data availability and author background. to avoid any diachronic variation within sumerian, all of the sumerian data were from documents composed during the ur iii period (c. 2112-2004 bc), drawn from 71,712 ur iii administrative documents within oracc, the open richly annotated cuneiform corpus @xcite . this corpus was chosen for its robust size and lexical and morphological annotation. during cleaning, we removed tokens which contained damaged written forms, had uncertain readings/translations, or were proper nouns. morphologically complex tokens, including compounds and inflected forms, were further processed into morpheme-length (rather than word-length) tokens via both automated and manual parsing by the first author. this resulted in a total of 1,875,351 morpheme-sized tokens. japanese data were drawn from bccwj, the balanced contemporary corpus of written japanese @xcite . bccwj tokenizes by lemma, with each token annotated with graphic form and phonological form information. morphologically complex tokens were further processed into morpheme-length tokens by the first author. the analyses reported here include the 5,000 most frequent lemmas, with a total of 62,929,634 morpheme tokens. ## results and discussion results are given in the results are most salient for japanese. the sumerian results, while still in-line with expectations, are weaker in magnitude; whether or not this is a consequence of the smaller dataset or of an actual difference in how logographic written sumerian was remains a point of future consideration. additional points of comparison will be needed to get a more complete picture of whether the magnitude of the results (rather than just the valence) correlates with how logographic a system is. with respect to the phonographized monochar sumerian, the fact that i(g; m ) = i(g; p ) makes sense given how phonographized sumerian was crafted, and given that, for reasons stated earlier, each sumerian morpheme only has one possible pronunciation form. it is interesting to note that the scores for phonographized sumerian are close to zero rather than strongly negative, i.e. written forms were about as informative about morpheme identity as they were about phonological form. this system could thus be viewed as more logographic than our phonographized japanese, despite both systems being exemplar minimally logographic system in the distinct homophones sense. the ability to capture such a distinction marks another potential advantage of incorporating morpheme identity when quantifying logography. ## conclusion the preliminary studies reported here offer a simple but promising means of measuring how logographic a writing system is. the inclusion of all three of phonological forms, graphic forms, and morphological identity paints a more complete picture of what it means for a writing system to be logographic. ongoing work is focused on expanding these methods to a wider range of writing systems, as well as incorporating semantics.