Modelling transient states in language change

Abstract

Abstract Models of language change may include, apart from the initial and terminal state, an intermediate state T. Building further on Postma (2010), who observed that the dynamics of the transient state T (’failed change’) is algebraically related to the overall change A → B (the former is the first derivative of the latter), we present a generalized algebraic model that includes both the failed change A → B and the successful change A → B. We first generalize the two-state logistic function of A → B to a differential equation (DE) that represents the underlying processes. This DE has a bundle of time shifted logistic curves as its solution. This derives Kroch’s Constant Rate Effect. By modifying this DE, we describe the dynamics of the entire A → T → B process, i.e. we develop a model that includes both the successful and the failed change. The algebraic link between failed change and successful change turns out to be an approximation.

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