The evolution of grammatical systems of syntactic and semantic composition is modeled here with a novel application of reinforcement learning theory. To test the functionalist thesis that speakers' expressive purposes shape their language, we include within the model a probability distribution over different messages that could be expressed in a given context. The proposed learning and production algorithm then breaks down language learning into a sequence of simple steps, such that each step benefits from the message probabilities. The results are presented in the form of numerical simulations of language histories and analytic proofs. The potential for applying these mathematical models to the study of natural language is illustrated with two case studies from the history of English.
Wechsler et al. (Mon,) studied this question.