On the Logical Complexity of Autosegmental Representations

Abstract

Autosegmental mapping from disjoint strings of tones and tone-bearing units, a commonly used mechanism in phonological analyses of tone patterns, is shown to not be definable in monadic second-order logic. This is abnormally complex in comparison to other phonological mappings, which have been shown to be monadic second-order definable. In contrast, generation of autosegmental structures from strings is demonstrated to be first-order definable.

Tone Association and Output Locality in Non-Linear Structures

“…Here, 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 also solves a problem noted in Jardine (2017b), which demonstrates that autosegmental mapping from tones to TBUs is beyond established computational characterizations for phonology. Finally, it also provides the first computational definition of output-based locality in functions for non-linear structures.…”

Autosegmental Input Strictly Local Functions

“…The computational properties of ARs have been studied before (Kay, 1987;Wiebe, 1992;Bird and Ellison, 1994;Kornai, 1995;Jardine, 2017). However, tone maps, such as the one exemplified in Figure 1, have not yet been studied under a computational notion of locality.…”