Deriving dynamical systems for language based on the Tolerance Principle

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.