Zipf’s laws of meaning in Catalan

Abstract

In his pioneering research, G. K. Zipf formulated a couple of statistical laws on the relationship between the frequency of a word with its number of meanings: the law of meaning distribution, relating the frequency of a word and its frequency rank, and the meaning-frequency law, relating the frequency of a word with its number of meanings. Although these laws were formulated more than half a century ago, they have been only investigated in a few languages. Here we present the first study of these laws in Catalan. We verify these laws in Catalan via the relationship among their exponents and that of the rank-frequency law. We present a new protocol for the analysis of these Zipfian laws that can be extended to other languages. We report the first evidence of two marked regimes for these laws in written language and speech, paralleling the two regimes in Zipf’s rank-frequency law in large multi-author corpora discovered in early 2000s. Finally, the implications of these two regimes will be discussed.

Exploring Semanticity for Content and Function Word Distinction in Catalan

“…However, after Zipf's groundbreaking research, one of the most noteworthy findings regarding the rank-frequency law in sizable textual corpora with multiple authors is that the power law proposed by Zipf (Equation ( 6)) must, for the most part, be expanded into a double-power law Montemurro 2001;Williams et al 2015), something related to the small-world structure of the linguistic network (Ferrer-i-Cancho and Solé 2001). In fact, in the case of Catalan, the target language of the present study, the existence of these two Zipfian regimes for Equations ( 4) and ( 6) has already been documented in previous studies for multi-author corpora (Català et al 2021). The structure of the linguistic network means that, in the first regime of low ranks, there is an abundance of function words.…”

“…where γ ≈ 1/2 (Català et al 2021). To unify the terminology, we refer to the number of meanings of a word (µ) as the sum of the total number of senses that appear in the dictionary, i.e., what has also been called semantic ambiguity (Hoffman et al 2013).…”

“…Thus, word frequency f , frequency rank r, and its number of meanings µ, a quantity that dictionaries approximately capture, are related in such a way that the exponents of these equations satisfy that δ = γ/α (Català et al 2021;Ferrer-i-Cancho and Vitevitch 2018).…”

“…The definitions of semanticity and the protocols developed in this paper can be extrapolated to any language for which we have the appropriate data to study. We have used Catalan because of the availability of access to the official normative dictionary and corpora and also because it is a language for which the relationship between the frequency of words and their meaning has already been statistically analyzed in a robust way (Català et al 2021), along with other patterns or linguistic laws (Hernández-Fernández et al 2019, 2022.…”

Explaining ambiguity in scientific language

“…Zipf presented empirical evidence for the first law but derived the second one from theoretical considerations; for a recent analysis, see Ferrer-i Cancho et al (2020). Using newly available databases such as WordNet, linguists have started to study the second law as an empirical subject and found substantial initial support in multiple languages (Piantadosi et al, 2012;Català et al, 2021). For example, Piantadosi et al "argue that ambiguity can be understood by the trade-off between two communicative pressures which are inherent to any communicative system: clarity and ease.…”