Modeling phonological interactions using recursive schemes

This dissertation pursues a computational theory of phonological process interactions whereby individual processes are formalized as input-output mappings (i.e. functions), and interactions are the combinations of those functions using a set of two operators: one previously defined in the literature and another defined in this dissertation. Building on hypotheses regarding the computational complexity of phonological processes in isolation (Heinz and Lai, 2013), the primary novel contribution of this dissertation is to extend these insights to interactions within larger phonological grammars, but in a systematic way. Specifically, it shows that the subsequential class of functions, sufficient to describe a great majority of phonological generalizations in isolation, also provides a well-motivated upper bound on the complexity of phonological interactions. Analyses developed in this work offer a straightforward solution to a number of outstanding cases of interactions in the Chinese tone sandhi literature. Crucially, this includes sandhi paradigms for which traditional generative phonological theories (rule-based SPE (Chomsky and Halle, 1968) and Optimality Theory (Prince and Smolensky, 2004)) fail to account. Thus this novel approach permits an explicit, restrictive theory of phonological interactions whose predictions more closely align with attested data. The formal apparatus for defining functions and operators used in this work is boolean monadic recursive schemes (BMRS; Bhaskar et al., 2020; Chandlee and Jardine, 2020). BMRS are a logical formalism rooted in theoretical computer science, and have been recently applied to computational analyses of phonology. Thus another important contribution of this dissertation is that it represents the first major work using BMRS to explore a specific type of linguistic phenomenon. In addition to demonstrating its application to specific tone sandhi paradigms, this study identifies advantages to BMRS in modeling interactions more generally, especially in comparison to other computational formalisms. The dissertation also leverages the phenomenon-independent nature of this logical formalism by applying BMRS to questions of phonological representation. Specifically, it is shown how operations over BMRS contribute to recent computational work using model theory and logic to explore notational equivalence across representational theories (Strother-Garcia and Heinz, 2015; Danis and Jardine, 2019; Oakden, 2020).Ph.D.Includes bibliographical reference