Learning serial constraint-based grammars

In this paper we describe a method for learning grammars in the general framework of Harmonic Serialism (see McCarthy this volume for references and an introduction). We have two main goals. The first is to address the hidden structure problem that serial derivations introduce. The second is to address the problem of learning variation, which has yet to be confronted in this framework (see also Staubs et al. 2010 and Tessier and Jesney 2014 on the learning of Harmonic Serialism). In the remainder of this section, we illustrate the grammar model, and our approach to the learning of hidden structure, with a simple example of stressepenthesis interaction. Our main contribution comes in the next section, where we introduce a method for calculating probabilities over the unbounded non-monotonic derivations that are characteristic of a stochastic serial theory. The third and last section consists of an application to data from French ‘schwa’ deletion that display variation. In Harmonic Serialism, the path from the grammar’s initial input to its final output is a series of derivational steps. In each step, a set of operations first applies to create a candidate set of outputs, from which one is chosen by a set of constraints. This output becomes the input for the next step of the derivation. The derivation terminates, or converges, when the chosen output is identical to the input of that step. From the perspective of learning, these derivations are an instance of what Tesar and Smolensky (2000) call ‘hidden structure’. Hidden structure refers to properties of the learning data that are not supplied to the learner, but must instead be inferred as part of the learning process. Our approach to learning this case of hidden structure is a generalization of Eisenstat’s (2009) method for learning phonological Underlying Representations (URs). We will explain and illustrate Eisenstat’s proposal as we discuss our toy stress-epenthesis case, since it also includes a UR learning problem.