The study of phonotactics (e.g., the ability of English speakers to distinguish possible words like blick from impossible words like *bnick) 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. Possible words are assessed by these grammars based on 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 any 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 to learn nonlocal phenomena such as stress and vowel harmony, it is necessary to augment the model with autosegmental tiers and metrical grids. Our results thus offer novel, learning-theoretic support for such representations. We apply the model to English syllable onsets, Shona vowel harmony, quantity-insensitive stress typology, and the full phonotactics of Wargamay, showing that the learned grammars capture the distributional generalizations of these languages and accurately predict the findings of a phonotactic experiment.

Abstract. This paper investigates a gradual on-line learning algorithm for Harmonic Grammar. By adapting existing convergence proofs for perceptrons, we show that for any nonvarying target language, Harmonic-Grammar learners are guaranteed to converge to an appropriate grammar, if they receive complete information about the structure of the learning data. We also prove convergence when the learner incorporates evaluation noise, as in Stochastic Optimality Theory. Computational tests of the algorithm show that it converges quickly. When learners receive incomplete information (e.g. some structure remains hidden), tests indicate that the algorithm is more likely to converge than two comparable Optimality-Theoretic learning algorithms.

Abstract Harmonic Grammar (HG) is a model of linguistic constraint interaction in which well-formedness is calculated as the sum of weighted constraint violations. We show how linear programming algorithms can be used to determine whether there is a weighting for a set of constraints that fits a set of linguistic data. The associated software package OT-Help provides a practical tool for studying large and complex linguistic systems in the HG framework and comparing the results with those of OT. We first describe the translation from Harmonic Grammars to systems solvable by linear programming algorithms. We then develop an HG analysis of ATR harmony in Lango that is, we argue, superior to the existing OT and rule-based treatments. We further highlight the usefulness of OT-Help, and the analytic power of HG, with a set of studies of the predictions HG makes for phonological typology.

Optimality Theory (OT) is a model of language that combines aspects of generative and connectionist linguistics. It is unique in the field in its use of a rank ordering on constraints, which is used to formalize optimization, the choice of the best of a set of potential linguistic forms. We show that phenomena argued to require ranking fall out equally from the form of optimization in OT’s predecessor Harmonic Grammar (HG), which uses numerical weights to encode the relative strength of constraints. We further argue that the known problems for HG can be resolved by adopting assumptions about the nature of constraints that have precedents both in OT and elsewhere in computational and generative linguistics. This leads to a formal proof that if the range of each constraint is a bounded number of violations, HG generates a finite number of languages. This is nontrivial, since the set of possible weights for each constraint is nondenumerably infinite. We also briefly review some advantages of HG. 1

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This paper presents a previously unnoticed universal property of stress patterns in the world’s languages: they are, for small neighborhoods, neighborhood-distinct. Neighborhood-distinctness is a locality condition defined in automata-theoretic terms. This universal is established by examining stress patterns contained in two typological studies, Bailey (1995) and Gordon (2002). Strikingly, many logically possible— but unattested—patterns do not have this property. Not only does neighborhood-distinctness unite the attested patterns in a non-trivial way, it also naturally provides an inductive principle allowing learners to generalise from limited data. A learning algorithm is presented which generalises by failing to distinguish same-neighborhood environments perceived in the learner’s linguistic input—hence learning neighborhood-distinct patterns—as well as almost every stress pattern in the typology. In this way, this work lends support to the idea that properties of the learner can explain certain properties of the attested typology, an idea not straightforwardly available in Optimality-theoretic and Principle and Parameter frameworks.

New methods for studying UG in phonology • The search for principles of Universal Grammar and for evidence to support them has broadened to include experimental work. • I argue for an approach that combines experimentation with the use of implemented learning models. 2. Traditional methods of studying UG • Typological study—study multiple languages, and develop a theory that � encompasses what’s “out there” � makes non-trivial predictions about what is not. • Examples: � Hayes’s (1995) parametric theory of stress systems, with an asymmetrical foot inventory � OT studies using factorial typology (Prince and Smolensky 1993, ch. 3): Kaun

Phonological constraints can, in principle, be classified according to whether they are natural (founded in principles of Universal Grammar (UG)) or unnatural (arbitrary, learned inductively from the language data). Recent work has used this distinction as the basis for arguments about the role of UG in learning. Some languages have phonological patterns that arguably reflect unnatural constraints. With experimental testing, one can assess whether such patterns are actually learned by native speakers. Becker, Ketrez, and Nevins (2007), testing speakers of Turkish, suggest that they do indeed go unlearned. They interpret this result with a strong UG position: humans are unable to learn data patterns not backed by UG principles. This article pursues the same research line, locating similarly unnatural data patterns in the vowel harmony system of Hungarian, such as the tendency (among certain stem types) for a final bilabial stop to favor front harmony. Our own test leads to the opposite conclusion to Becker et al.: Hungarians evidently do learn the unnatural patterns. To conclude we consider a bias account—that speakers are able to learn unnatural environments, but devalue them relative to natural ones. We outline a method for testing the strength of constraints as learned by speakers against the strength of the corresponding patterns in the lexicon, and show that it offers tentative support for the hypothesis that unnatural constraints are disfavored by language learners.

Acknowledgements. Portions of this work were presented at the annual meeting of the