French schwa and gradient cumulativity

We model the interaction of two phonological factors that condition French schwa alternations: schwa is more likely after two consonants; and schwa is more likely in the penultimate syllable. Using new data from a judgment study, we show that both factors play a role in schwa epenthesis and deletion, confirming previous impressionistic descriptions, and that the two factors interact cumulatively: they have a stronger effect together than alone. Treating each factor as a constraint, we find that their cumulative interaction in probabilistic space is better modeled with weighted rather than ranked constraints. To accomplish this, we characterize patterns of cumulativity in terms of how cumulativity affects probability. MaxEnt and Noisy HG can model the full range of cumulativity — sublinear, linear, and superlinear — while Stochastic OT can only model sublinear cumulativity. French schwa displays superlinear cumulativity, and as a result, the pattern is unobtainable in Stochastic OT. We find that the pattern of superlinearity is too extreme even for Noisy HG, leaving MaxEnt as the model with the closest fit to the experimental data.