A type-theoretical approach to categorical interaction and complex system adaptation: an empirical study based on register classification

Type theories provide a formal foundation for logic, mathematics, and computing. They have also been applied to the study of language in formal syntax and semantics, such as categorial grammar and Montague semantics. In this paper, we adopt insights from the type-theoretical definition of grammatical categories to model different registers in Mandarin Chinese. Through the modeling study of the classification of registers, we provide empirical evidence for a type-theoretical definition of grammatical categories. Type-theoretical categories are defined as function applications of basic types, unlike set-theoretical categories, which are all defined in terms of membership of different sets. Thus, a type-theoretical approach predicts that dynamic relations such as ratios between category/type pairs will more effectively represent different linguistic systems than distributions of categories. We model the frequency ratios of pairs of categories, similar to unit-constituency ratios, to classify registers. The ratios of all possible pairs among the four major grammatical categories in three different registers are calculated and visualized with boxplots. Linear regression is then applied to investigate how these ratios vary in different registers. Lastly, texts from all registers are clustered according to these ratios. Visualization in the 2-dimensional planes shows that the three registers are successfully classified. In addition, two sub-corpora, the News Co-Broadcasting and Science texts, are separated, even though both belong to the written formal register. Further analyses show that only ratios between categorical pairs with functional application relations are valid predictors. We conclude that a type-theoretical approach captures the categorial dynamics represented by typed functions and is well-equipped to model the nature of languages as complex self-adaptive systems.