Learning Phonological Mappings by Learning Strictly Local Functions

Abstract

<p>In this paper we identify strict locality as a defining computational property of the input-output mapping that underlies local phonological processes. We provide an automata-theoretic characterization for the class of Strictly Local functions, which are based on the well-studied Strictly Local formal languages (McNaughton & Papert 1971; Rogers & Pullum 2011; Rogers et al. 2013), and show how they can model a range of phonological processes. We then present a learning algorithm, the SLFLA, which uses the defining property of strict locality as an inductive principle to learn these mappings from finite data. The algorithm is a modification of an algorithm developed by Oncina et al. (1993) (called OSTIA) for learning the class of subsequential functions, of which the SL functions are a proper subset. We provide a proof that the SLFLA learns the class of SL functions and discuss these results alongside previous studies on using OSTIA to learn phonological mappings (Gildea and Jurafsky 1996).</p>

Computationally, tone is different

“…The third contribution is to offer an account of the unbounded circumambient asymmetry in terms of such classes of maps. Previous work has found segmental processes to be at most weakly deterministic (Chandlee et al 2012, Heinz & Lai 2013, Chandlee 2014, Payne 2014). The unbounded circumambient asymmetry can thus be captured in terms of a complexity bound on segmental phonology: segmental phonology is restricted to weakly deterministic maps, but tonal phonology is not.…”

“…The discussion in the previous section suggests how local processes are subsequential. For a thorough survey of the subsequentiality of local processes, including epenthesis, deletion, metathesis, substitution and partial reduplication, see Chandlee (2014). Work on long-distance segmental processes such as vowel harmony (Gainor et al 2012, Heinz & Lai 2013) and dissimilation (Payne 2014) has also found them to be largely left- or right-subsequential.…”

Inductive learning of locality relations in segmental phonology

“…Admittedly, there is not yet a deep understanding of the formal and learnability properties of subregular functions that can model string-to-string mappings. However, recent work has defined a number of relevant classes and identified some of their formal properties (e.g., Chandlee, 2014;Chandlee, Eyraud, & Heinz, 2015;Mohri, 1997), including a number of promising results regarding learnability (Chandlee, Eyraud, & Heinz, 2014;Chandlee & Jardine, 2014). Of particular relevance is the finding that subsequential functions (Mohri, 1997) characterize many attested patterns of longdistance consonant dissimilation (Payne, 2014) and consonant harmony (Luo, 2017), while excluding a number of complex pathologies.…”

Input Strictly Local opaque maps

“…Specifically, we study the typology of opaque generalisations provided by Baković (2007) in the light of Chandlee's (2014) theory of local, subregular functions. We show that the variety of opaque generalisations discussed by Baković, and an additional case from Kavitskaya & Staroverov (2010), have the property of being Input Strictly Local (ISL), the definition of which is given in §2.…”

“…ISL functions have been characterised in terms of automata theory, formal language theory (Chandlee 2014, Chandlee et al 2014) and first order logic (Chandlee & Lindell to appear). Here we provide a finite-state transducer (FST) characterisation.…”