Vowel Harmony, Opacity, and Finite-State OT

In this paper I propose cyclic and stratal extensions to FiniteState Optimality Theory as treatments for vowel harmony and for opaque phenomena more generally. I develop a model of grammar and an accompanying set of constraints within a software model built on the opensource PyPhon toolkit—a computational implementation of OT’s Gen and EVAL algorithms. 0 Constraint-based grammars and typology Since their introduction in the early nineteen-nineties, constraint-based grammars have been widely used in generative phonology for their ability to describe complex patterns in a way that is simple, cognitively plausible, and easily generalized across languages. In any constraint-based grammar, the great bulk of the generative labor is carried out by violable constraints. In an idealized picture, these constraints are clear and principled descriptions of phenomena that are widely dispreferred across languages, like Dep: do not epenthesize segments. The job of the language user is, for every underlying form, to find a surface form that best satisfies the constraints that matter to their language, and to do so directly, without a sequential derivation. Under the associated richness of the base hypothesis (Prince and Smolensky, 1993/2004), constraint-based grammars are expected to be able to produce an acceptable output for any input, even if (as in crosslinguistic borrowing) that input flagrantly violates basic structural principles of the target language. Because of this, it is quite common for analyses to focus on inputs for which no output satisfies all of the constraints. For example, when the grammar of a language like Japanese, which heavily restricts consonant clusters, is presented with an input containing a cluster of obstruents, it cannot produce a phonotactically well-formed output without violating some constraint against insertion (like Dep, above), deletion, or substitution. The two major constraint-based grammar frameworks—Optimality Theory (Prince and Smolensky, 1993/2004, OT) and Harmonic Grammar (Legendre et al., 1990, HG)—