Tone Association and Output Locality in Non-Linear Structures

Nate Koser,Adam Jardine,Chris Oakden

doi:10.3765/amp.v7i0.4476

Abstract

This paper offers a computational characterization of tone-to-TBU association processes using a restricted least-fixed point logic. Crucially, least fixed point logics allow recursive definitions which capture output-oriented processes. The added requirement that these definitions are quantifier-free ensures that they are inherently local, a restriction that is well-motivated for phonological processes in general. The typology developed here distinguishes between possible and impossible tone mappings, capturing a wider range of attested tone mappings (left-to-right, right-to-left, edge-in, quality-sensitive) than previous rule-based or optimization approaches, while also explaining why certain unattested mapping patterns (for example center-out association) are impossible. This thus represents a strong first approximation of a definition for output-based local functions over non-linear structures

Highlights

In this paper, we pursue a computational theory that distinguishes between possible and impossible autosegmental tone mapping patterns (Leben, 1973; Williams, 1976; Goldsmith, 1976), in which unassociated tones are mapped to tone-bearing units (TBUs)
We show that tone mapping patterns are describable by a restricted least fixed point logic, which gives a typological characterization of the nature of tone association that is unavailable to derivation-based frameworks but can capture patterns that cannot be captured by the alignment constraints used in optimization-based frameworks (Prince & Smolensky, 1993)
It solves a problem noted in Jardine (2017b), which demonstrates that autosegmental mapping from tones to TBUs is beyond established computational characterizations for phonology

Summary

Introduction

We pursue a computational theory that distinguishes between possible and impossible autosegmental tone mapping patterns (Leben, 1973; Williams, 1976; Goldsmith, 1976), in which unassociated tones are mapped to tone-bearing units (TBUs). We show that tone mapping patterns are describable by a restricted least fixed point logic, which gives a typological characterization of the nature of tone association that is unavailable to derivation-based frameworks (as noted by Zoll 2003) but can capture patterns that cannot be captured by the alignment constraints used in optimization-based frameworks (Prince & Smolensky, 1993). It solves a problem noted in Jardine (2017b), which demonstrates that autosegmental mapping from tones to TBUs is beyond established computational characterizations for phonology. It provides the first computational definition of output-based locality in functions for non-linear structures

Logical Maps

Analyses

Discussion

Conclusion