Deriving dynamical systems for language based on the Tolerance Principle

TL;DR

This paper derives explicit dynamical systems for language acquisition based on the Tolerance Principle, providing a mathematical framework to understand how language rules are learned and propagated over generations.

Contribution

It introduces a novel dynamical systems approach to model language acquisition using the Tolerance Principle within an acquisition-driven framework.

Findings

Framework for dynamical systems in language acquisition

Analysis of population size effects on language dynamics

Foundation for future simulations and applications

Abstract

In this research note, I derive explicit dynamical systems for language within an acquisition-driven framework (Niyogi \& Berwick, 1997; Niyogi, 2006) assuming that children/learners follow the Tolerance Principle (Yang, 2016) to determine whether a rule is productive during the process of language acquisition. I consider different theoretical parameters such as population size (finite vs. infinite) and the number of previous generations that provide learners with data. Multiple simulations of the dynamics obtained here and applications to diacrhonic language data are in preparation, so they are not included in this first note.