Natural language from function dynamics

A new approach to syntax and semantics of language is presented as a form of function dynamics, which is studied both analytically and numerically. The iteration of the function dynamics leads to articulation and formation of rules, which depend on each other. A hierarchy of meta-rules as rules of rules also emerges through the iteration when the initial function is suitably embedded. Iteration of a model with dialogue between two function dynamics is shown to generate a higher level structure.