Over the past decade, Andries Coetzee has been one of the leading voices in research on how to model variable phonological phenomena within formal models of phonological grammar. His most recent paper on this topic has just appeared in the journal Phonology.
In this paper, he shows how variable cross-word nasal place assimilation (i.e. "green boat" pronounced as either "gree[n] boat" or "gree[m] boat) is affected by both grammatical and non-grammatical factors. Most current grammatical models of phonological grammar, however, do not allow for the contribution of both grammatical and non-grammatical factors to the application of variable phenomena. Coetzee, therefore, argues that current models are inadequate, and develops a more comprehensive model that allows for the formal interaction of both grammatical and non-grammatical factors in determining observed patterns of variation. The title and abstract of the paper follows below.
The past two decades have seen the development of several constraint-based models of phonological grammar that can handle variable phenomena. Most of these models, however, are purely grammatical, and do not allow for the contribution of non-grammatical factors towards determining the frequency structure of variation. This paper reviews different approaches to phonological variation, focusing on how grammatical and non-grammatical factors co-determine patterns of variation. Based on this review, a model is developed that incorporates influences from both grammatical and non-grammatical factors. The proposed model is grammar-dominant, in the sense that grammar defines the space of possible variation while non-grammatical factors only contribute towards the frequency with which the grammar determined forms are observed. Following Coetzee & Kawahara (2013), the model is developed in a version of noisy Harmonic Grammar that allows non-grammatical factors to scale the weights of faithfulness constraints up or down.