How (Non-)Optimal is the Lexicon?

TL;DR

This paper investigates the efficiency of natural language lexicons by modeling their structure through coding theory, revealing that morphology and graphotactics largely explain their complexity and optimality.

Contribution

It introduces a novel generative statistical model to quantify lexicon optimality and assesses the impact of linguistic constraints across diverse languages.

Findings

Morphology and graphotactics account for most of the lexicon's complexity.

The model provides upper bounds for lexicon compressibility under various constraints.

Languages tend to operate near these theoretical bounds, indicating a high level of efficiency.

Abstract

The mapping of lexical meanings to wordforms is a major feature of natural languages. While usage pressures might assign short words to frequent meanings (Zipf's law of abbreviation), the need for a productive and open-ended vocabulary, local constraints on sequences of symbols, and various other factors all shape the lexicons of the world's languages. Despite their importance in shaping lexical structure, the relative contributions of these factors have not been fully quantified. Taking a coding-theoretic view of the lexicon and making use of a novel generative statistical model, we define upper bounds for the compressibility of the lexicon under various constraints. Examining corpora from 7 typologically diverse languages, we use those upper bounds to quantify the lexicon's optimality and to explore the relative costs of major constraints on natural codes. We find that (compositional) morphology and graphotactics can sufficiently account for most of the complexity of natural codes -- as measured by code length.