Anatomy of a Linear Dynamical Model of Linguistic Generalizations

Part I of this report characterizes and assesses the Goldsmith-Larson Dynamic Linear Model (DLM) as a theory of linguistic stress systems, building on the analytic results of Parts II and III. The discussion is qualitative, eschewing formal details, and oriented to evaluating the linguistic import of the DLM. A variety of significant properties are reviewed, but it is shown that the fundamental computational assumption of the model (linearity) leads to a many nonlinguistic behaviors in the models for example, dependence on the absolute length of strings in determining the placement of stresses; and a completely gradual transition between LR→ and ←RL iterative systems. The second section shows that the DLM is a discrete approximation to a forced, more-than-lightly damped harmonic oscillator; in the Canonical Models, the damping is critical. The fundamental equation of the Critical Continuous Linear Theory of stress is stated. In the third section, formal analyis is presented in support of the new assertions in section one. Closed-form solution for the DLM’s treatment of the vector ∑ = ek is obtained in the Canonical Models and the solution space is classified. This vector is particularly significant in the economy of the model, in that it plausibly represents a string of a syllables undifferentiated as to weight, the syllabic substrate of the simplest class of stress patterns.