Deriving dynamical systems for language based on the Tolerance Principle
This work addresses language acquisition modeling for theoretical linguistics, but it is incremental as it builds on existing frameworks without new empirical validation.
The paper derives explicit dynamical systems for language acquisition by assuming learners follow the Tolerance Principle to determine rule productivity, but does not present results or numbers as simulations and applications are still in preparation.
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.