Harmonic Grammar with linear programming: from linear systems to linguistic typology

Harmonic Grammar is a model of linguistic constraint interaction in which wellformedness is calculated in terms of the sum of weighted constraint violations. We show how linear programming algorithms can be used to determine whether there is a weighting for a set of constraints that fits a set of linguistic data. The associated software package OT-Help provides a practical tool for studying large and complex linguistic systems in the Harmonic Grammar framework and comparing the results with those of OT. We first describe the translation from harmonic grammars to systems solvable by linear programming algorithms. We then develop a Harmonic Grammar analysis ofATRharmony in Lango that is, we argue, superior to the existing OT and rule-based treatments. We further highlight the usefulness of OT-Help, and the analytic power of Harmonic Grammar, with a set of studies of the predictions Harmonic Grammar makes for phonological typology.