An ongoing debate in phonology concerns the treatment of cumulative constraint interactions, or ‘gang effects’, and by extension the question of which phonological frameworks are suitable models of the grammar. This paper uses a series of artificial grammar learning experiments to examine the inferences that learners draw about cumulative constraint violations in phonotactics in the absence of a confounding natural-language lexicon. I find that learners consistently infer linear counting and ganging cumulativity across a range of phonotactic violations.

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There has been a dramatic rise of interest in sound symbolism, systematic associations between sounds and meanings. Despite this, one aspect that is still markedly under-explored is its cumulative nature, i.e., when there are two or more sounds with the same symbolic meaning, whether these effects add up or not. These questions are important to address, since they bear on the general question of how speakers take into account multiple sources of evidence when they make linguistic decisions. Inspired by an accumulating body of research on cumulativity in other linguistic patterns, two experiments on sound symbolism using Pokémon names were conducted with native speakers of English. The experiments tested two types of cumulativity: counting cumulativity, which holds if the effects of multiple instances of the same factor add up, and ganging-up cumulativity, which holds when the effects of different factors add up. The experiments addressed whether these patterns of cumulativity hold in sound symbolism, and, more importantly, if so, how. We found that (1) three factors can show ganging-up cumulativity, (2) counting cumulativity and ganging-up cumulativity can coexist in a single system, (3) ganging-up cumulativity patterns can plausibly be considered to be linear, and (4) counting cumulativity effects can be sub-linear.

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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.