Does MaxEnt Overgenerate? Implicational Universals in Maximum Entropy Grammar

It goes without saying that a good linguistic theory should neither undergenerate (i.e., it should not miss any attested patterns) nor overgenerate (i.e., it should not predict any “unattestable” patterns). Recent literature has argued that the Maximum Entropy (ME; Goldwater & Johnson 2003) framework provides a probabilistic extension of categorical Harmonic Grammar (HG; Legendre et al. 1990; Smolensky & Legendre 2006) which is rich enough to model attested patterns of variable and gradient phonology (see for instance Hayes & Wilson 2008, Zuraw & Hayes 2017, and Smith & Pater 2017). In other words, ME is rich enough to avoid undergeneration. But does ME’s richness come at the expense of overgeneration? This is the question that we would like to start investigating in this paper. In the case of a categorical phonological theory such as HG, overgeneration can be investigated directly by exhaustively listing all the grammars predicted by the theory for certain constraint and candidate sets. That is possible because the predicted typology of grammars is usually finite. The situation is rather different for probabilistic theories such as ME. In this case, the typology consists of an infinite number of probability distributions which therefore cannot be exhaustively listed and directly inspected. A more indirect strategy is needed to glance at the boundary of the probabilistic typology and thus investigate its overgeneration. A natural indirect strategy that gets around the problem raised by an infinite typology is to enumerate, not the individual languages/grammars/distributions in the typology, but the corresponding set of implicational universals predicted by the typology. An implicational universal is an implication