Learning Local Phonological Processes

This paper presents a learning algorithm for local phonological processes that exploits a restriction on the expressive power needed to compute phonological patterns that apply locally. This restriction reflects the well-recognized idea that locality plays an important role in phonology (Kenstowicz (1994); Gafos (1996), among others) and arguably in learning (Heinz, 2009). We first characterize phonological processes as functions mapping underlying to surface forms and then demonstrate how a learner with a locality bias can generalize such a function from a finite set of underlying-surface pairs. This approach to the learning problem recognizes the utility of restricting the hypothesis space of a learner. The formal grammars needed to analyze phonological patterns are less powerful than those needed for syntactic patterns (Heinz and Idsardi, 2011). It has been known since Johnson (1972), Koskenniemi (1983), and Kaplan and Kay (1994) that phonological rules of the form A⇒ B / C D, where A, B, C, and D are regular expressions, can be described with regular relations, making them more restricted than the context-free and context-sensitive patterns found in syntax (Chomsky, 1956; Schieber, 1985). The class of regular relations, however, does not appear to be learnable in the limit from positive data (Gold, 1967). In truth, however, learning the entire class of regular relations is not desirable from the phonological standpoint, since this class includes many patterns that are unattested and unexpected in natural language. Thus we propose a further restriction on the computational bound of a local phonological process, one that rules out many unexpected patterns and defines a subregular class of functions that is identifiable in the limit. The learning results presented here propose such a class, one that is delimited by a requirement of locality. There is a large and growing body of literature on learning in Optimality Theory (Tesar and Smolensky, 1993, 1998; Tesar, 1995, 1998; Boersma, 1997; Boersma and Hayes, 2001; Pater and Tessier, 2003; Hayes, 2004; Riggle, 2004, 2006; Pater, 2004; Prince and Tesar, 2004; Alderete et al., 2005; Merchant and Tesar, 2008; Magri, 2010, 2012), with relatively less attention being paid to the learning of phonological rules (Johnson, 1984; Gildea and Jurafsky, 1996; Albright and Hayes, 2002, 2003). The learner we present targets a functional mapping from an input to output form, an abstract characterization of phonological processes that is compatible with either the SPE or OT formalism. The findings then contribute to our understanding of how phonological rules can be learned, but also suggests a inductive principle that could be incorporated into a variety of learning frameworks. The organization of the paper is as follows. Section 2 introduces the computational framework we are assuming, in which phonological processes are represented as functions that map input (‘underlying’) to output (‘surface’) forms. Section 3 formalizes the notion of locality and presents a two-step algorithm that uses the locality assumption to learn a particular class of formal languages. Section 4 adapts this algorithm to the functional domain in order to learn phonological processes, and section 5 demonstrates the algorithm with the example of German final devoicing. Section 6 discusses the results of this demonstration, and section 7 concludes and identifies future directions of this research.