The meaning distributions on different levels of granularity

The meaning distributions of certain linguistic forms generally follow a Zipfian distribution. However, since the meanings can be observed and classified on different levels of granularity, it is thus interesting to ask whether their distributions on different levels can be fitted by the same model and whether the parameters are the same. In this study, we investigate three quasi-prepositions in Shanghainese, a dialect of Wu Chinese, and test whether the meaning distributions on two levels of granularity can be fitted by the same model and whether the parameters are close. The results first show that the three models proposed by modern quantitative linguists can both achieve a good fit for all cases, while both the exponential (EXP) model and the right-truncated negative binomial (RTBN) models behave better than the modified right-truncated Zipf-Alekseev distribution (MRTZA), in terms of the consistency of the goodness of fit, parameter change, rationality, and simplicity. Second, the parameters of the distributions on the two levels and the curves are not exactly the same or even close to each other. This has supported a weak view of the concept of ‘scaling’ in complex sciences. Finally, differences are found to lie between the distributions on the two levels. The fine-grained meaning distributions are more right-skewed and more non-linear. This is attributed to the openness of the categories of systems. The finer semantic differentiation behaves like systems with open set of categories, while the coarse-grained meaning distribution resembles those having a close set of few categories.