Modeling Transient States in Language Change

TY - CHAP

T1 - Modeling Transient States in Language Change

AU - Postma, G.J.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - language change

KW - failed changes

KW - quantitative linguistics

KW - constant-rate hypothesis

KW - diachronic syntax

M3 - Contribution to conference proceedings

BT - From Micro-change to Macro-change

A2 - Truswell, Robert

A2 - Mattieu, Eric

PB - Oxford University Press

ER -