Taking Primitive Optimality Theory Beyond the Finite State

TL;DR

This paper extends Primitive Optimality Theory by integrating higher-level grammars like Multiple Context-Free Grammars to represent candidate sets, enabling modeling of phenomena such as reduplication and phrasal stress beyond finite state limitations.

Contribution

It introduces a novel mechanism combining weighted finite state constraints with higher-level grammars for candidate sets in OTP, expanding its applicability.

Findings

Successfully models reduplication using multiple context-free grammars

Develops an extended Earley Algorithm for applying constraints

Demonstrates increased expressive power over finite state approaches

Abstract

Primitive Optimality Theory (OTP) (Eisner, 1997a; Albro, 1998), a computational model of Optimality Theory (Prince and Smolensky, 1993), employs a finite state machine to represent the set of active candidates at each stage of an Optimality Theoretic derivation, as well as weighted finite state machines to represent the constraints themselves. For some purposes, however, it would be convenient if the set of candidates were limited by some set of criteria capable of being described only in a higher-level grammar formalism, such as a Context Free Grammar, a Context Sensitive Grammar, or a Multiple Context Free Grammar (Seki et al., 1991). Examples include reduplication and phrasal stress models. Here we introduce a mechanism for OTP-like Optimality Theory in which the constraints remain weighted finite state machines, but sets of candidates are represented by higher-level grammars. In particular, we use multiple context-free grammars to model reduplication in the manner of Correspondence Theory (McCarthy and Prince, 1995), and develop an extended version of the Earley Algorithm (Earley, 1970) to apply the constraints to a reduplicating candidate set.