The Proper Treatment of Optimality in Computational Phonology

This paper presents a novel formalization of optimality theory. Unlike previous treatments of optimality in computational linguistics, starting with Ellison (1994), the new approach does not require any explicit marking and counting of constraint violations. It is based on the notion of "lenient composition," defined as the combination of ordinary composition and priority union. If an underlying form has outputs that can meet a given constraint, lenient composition enforces the constraint; if none of the output candidates meet the constraint, lenient composition allows all of them. For the sake of greater efficiency, we may "leniently compose" the GEN relation and all the constraints into a single finite-state transducer that maps each underlying form directly into its optimal surface realizations, and vice versa, without ever producing any failing candidates. Seen from this perspective, optimality theory is surprisingly similar to the two older strains of finite-state phonology: classical rewrite systems and two-level models. In particular, the ranking of optimality constraints corresponds to the ordering of rewrite rules.