The study of phonotactics is a central topic in phonology. We propose a theory of phonotactic grammars and a learning algorithm that constructs such grammars from positive evidence. Our grammars consist of constraints that are assigned numerical weights according to the principle of maximum entropy. The grammars assess possible words on the basis of the weighted sum of their constraint violations. The learning algorithm yields grammars that can capture both categorical and gradient phonotactic patterns. The algorithm is not provided with constraints in advance, but uses its own resources to form constraints and weight them. A baseline model, in which Universal Grammar is reduced to a feature set and an SPE-style constraint format, suffices to learn many phonotactic phenomena. In order for the model to learn nonlocal phenomena such as stress and vowel harmony, it must be augmented with autosegmental tiers and metrical grids. Our results thus offer novel, learning-theoretic support for such representations. We apply the model in a variety of learning simulations, showing that the learned grammars capture the distributional generalizations of these languages and accurately predict the findings of a phonotactic experiment.

The Gradual Learning Algorithm (Boersma 1997) is a constraint-ranking algorithm for learning optimality-theoretic grammars. The purpose of this article is to assess the capabilities of the Gradual Learning Algorithm, particularly in comparison with the Constraint Demotion initiated the learnability research program for Optimality Theory. We argue that the Gradual Learning Algorithm has a number of special advantages: it can learn free variation, deal effectively with noisy learning data, and account for gradient well-formedness judgments. The case studies we examine involve Ilokano reduplication and metathesis, Finnish genitive plurals, and the distribution of English light and dark /l/.

Are morphological patterns learned in the form of rules? Some models deny this, attributing all morphology to analogical mechanisms. The dual mechanism model (Pinker, S., & Prince, A. (1998). On language and connectionism: analysis of a parallel distributed processing model of language acquisition. Cognition, 28, 73-193) posits that speakers do internalize rules, but that these rules are few and cover only regular processes; the remaining patterns are attributed to analogy. This article advocates a third approach, which uses multiple stochastic rules and no analogy. We propose a model that employs inductive learning to discover multiple rules, and assigns them confidence scores based on their performance in the lexicon. Our model is supported over the two alternatives by new "wug test" data on English past tenses, which show that participant ratings of novel pasts depend on the phonological shape of the stem, both for irregulars and, surprisingly, also for regulars. The latter observation cannot be explained under the dual mechanism approach, which derives all regulars with a single rule. To evaluate the alternative hypothesis that all morphology is analogical, we implemented a purely analogical model, which evaluates novel pasts based solely on their similarity to existing verbs. Tested against experimental data, this analogical model also failed in key respects: it could not locate patterns that require abstract structural characterizations, and it favored implausible responses based on single, highly similar exemplars. We conclude that speakers extend morphological patterns based on abstract structural properties, of a kind appropriately described with rules.

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In Hungarian, stems ending in a back vowel plus one or more neutral vowels show unusual behaviour: for such stems, the otherwise general process of vowel harmony is lexically idiosyncratic. Particular stems can take front suffixes, take back suffixes or vacillate. Yet at a statistical level, the patterning among these stems is lawful: in the aggregate, they obey principles that relate the propensity to take back or front harmony to the height of the rightmost vowel and to the number of neutral vowels. We argue that this patterned statistical variation in the Hungarian lexicon is internalised by native speakers. Our evidence is that they replicate the pattern when they are asked to apply harmony to novel stems in a ‘wug’ test (Berko 1958). Our test results match quantitative data about the Hungarian lexicon, gathered with an automated Web search. We model the speakers' knowledge and intuitions with a grammar based on the dual listing/generation model of Zuraw (2000), then show how the constraint rankings of this grammar can be learned by algorithm.