Cumulative markedness effects and (non-)linearity in phonotactics

This study uses an Artificial Grammar Learning experiment to test for a synchronic relationship between the severity of an individual phonotactic violation and the linearity of its cumulative interaction with other violations, prompted by previous experimental findings (Albright 2012, Breiss (submitted)). We find that as individual phonotactic patterns are made more exceptionful, their interaction moves from linear to super-linear, and argue that this provides evidence for a non-linear relationship between Harmony and probability. We evaluate five contemporary phonological frameworks using this data, and find that those which incorporate such a non-linear relationship -- Maximum Entropy HG and Noisy HG -- are able to capture the super-linear patterns observed significantly better than other frameworks. Further, we demonstrate that a MaxEnt model provided the same training data as experimental participants exhibits similar emergent super-linear cumulativity, and explore the weighting conditions under which MaxEnt models yield sub-linear, linear, and super-linear cumulativity.