### Abstract

Models of language change may include, apart from an initial state and a terminal state, an intermediate transient state T. Building further on they Failed Change Model (Postma 2010) that ties the dynamics of the transient state T to the dynamics of the overall change A → B, we present an generalized algebraic model that includes both the failed change 0 → T → 0 and the successful change A → B. As a preparatory step, we generalize the algebraic function (logist) of two-state change A → B to a differential equation (DE) which represents the law that rules the change. This DE has a bundle of time shifted logistic curves as its solution. This is derives Kroch's Constant Rate Hypothesis. By modifying this DE, it is possible to describe the dynamics of the entire A → T→ B process, i.e. we have a model that includes both the successful and the failed change. The algebraic link between failed change and successful change (the former is the first derivative of the latter) turns out to be an approximation.

Original language | English |
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Title of host publication | From Micro-change to Macro-change |

Subtitle of host publication | Proceedings of DIGS 15 |

Editors | Robert Truswell, Eric Mattieu |

Publisher | Oxford University Press |

Publication status | Accepted/In press - 2015 |

### Keywords

- language change
- failed changes
- quantitative linguistics
- constant-rate hypothesis
- diachronic syntax

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## Cite this

Postma, G. J. (Accepted/In press). Modeling Transient States in Language Change. In R. Truswell, & E. Mattieu (Eds.),

*From Micro-change to Macro-change: Proceedings of DIGS 15*Oxford University Press.