Autosegmental Input Strictly Local Functions

Autosegmental Input Strictly Local Functions Jane Chandlee Tri-College Department of Linguistics Haverford College jchandlee@haverford.edu Adam Jardine Department of Linguistics Rutgers University adam.jardine@rutgers.edu Abstract Autosegmentalrepresentations(ARs;Goldsmith, 1976) are claimed to enable local analyses of otherwise non-local phenomena (Odden, 1994). Focusing on the domain of tone, we investigate this ability of ARs using a computationally well-defined notion of locality extended from Chandlee (2014). The result is a more nuanced understanding of the way in which ARs interact with phonological locality. 1 Introduction Autosegmental representations (ARs; Goldsmith, 1976) have long been claimed to capture non- local processes in a local way (Odden, 1994). Focusing on tone, we explore this claim from a computational perspective using a precisely defined notion of locality. Specifically, we use quantifier-free (QF) first-order (FO) logical transductions, which have been shown (Chandlee and Lindell, in prep.) in strings to correspond to the input strictly local (ISL) functions (Chandlee, 2014), a phonologically relevant notion of compu- tational locality (Chandlee and Heinz, 2018). We extend QF transductions to ARs to de- fine the autosegmental input strictly local (A-ISL) functions and give a partial abstract characteriza- tion of this class. We then examine a variety of commonly attested tone patterns that are both ISL and not ISL (i.e., local and non-local in terms of strings) to see if they are A-ISL (i.e., local over ARs). Our exploration reveals a four-way division among tone patterns: those that are local without ARs (i.e., both ISL and A-ISL), those that are local only with ARs (i.e., A-ISL but not ISL), those that are local with strings but not ARs (ISL but not A-ISL), and those that are not local at all (neither ISL nor A-ISL). The conclusion is that ARs do not automatically make non-local processes local, but that this ability is more nuanced. We also briefly explore an alternative notion of locality that extends A-ISL. The remainder of the paper is structured as follows. In §2 we review ARs, and in §3 we provide the mathematical preliminaries. In §4 we define the ISL functions. §5 extends that characterization to ARs. §6 presents analyses for a selection of tone processes, and §7 discusses the significance of these results and open questions. §8 concludes. 2 Autosegmental Representations In ARs (Clements, 1976; Goldsmith, 1976) pho- nological primitives are arranged in distinct strings or tiers, with an association relation relating units on different tiers. Examples from Arusa (Levergood, 1987; Odden, 1994) are shown in Figure 1, both as strings and as ARs. Here and throughout the paper, an acute accent [´a] indicates a high tone; unmarked vowels bear low (L) tones. In the underlying representation (UR) on the left-hand side of Figure 1, the second vowel of /ol´orika/ ‘chair’ bears a H tone, and both vowels of /s´ıd´ay/ ‘good’ bear a H tone. The AR for /s´ıd´ay/ ‘good’ shows a single H on the ‘‘autonomous’’ tonal tier that is associated to both vowels on the vowel tier. Tones associate to tone-bearing units (TBUs), which could be vowels, moras, or syllables …

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