French Schwa And Gradient Cumulativity

We explore the interaction of two phonological factors that condition schwa-zero alternations in French: schwa is more likely after two consonants than a singleton; and schwa is more likely between stressed syllables than elsewhere. Using new data from a judgment study, we show that both factors play a role in schwa epenthesis and deletion, and that the two factors interact cumulatively: they have a stronger effect together than individually. Treating each factor as a constraint, we find that their cumulative interaction is better modeled with weighted than with ranked constraints. We provide a characterization of patterns of cumulativity in probability space in terms of the effect of constraint on its own versus its effect in a cumulative interaction with another constraint. Stochastic OT can model cumulative interactions, but only sublinear ones, where the effect of a constraint is weaker in the cumulative context than on its own. Weighted constraint models, MaxEnt and Noisy HG, can model the full range of cumulativity - sublinear, linear, and superlinear. In examining the ability of these models to fit our experimental data, we find that Stochastic OT is hampered by the fact that the data displays superlinear cumulativity. Noisy HG and MaxEnt fare better on this dataset, with MaxEnt yielding the best fit.