Learning Vowel Harmony

It is possible to construct an unsupervised learning system for vowel harmony, which makes accessible general-isations. Furthermore, such a learning system can be constructed with little built-in knowledge, and, consequently, be applicable to data from a wide range of domains. This paper presents a learning system which fulllls these criteria, and examines the results of applying an implementation of it to data from a number of natural languages. A language exhibits vowel harmony if it imposes contextual constraints between adjacent vowels in the same word. A number of languages exhibit vowel harmony: Finnish, Hungarian, Turkish, various Mongolian languages, a number of African languages such as Yoruba and Okpe, and, it has been claimed, the Australian language, Warlpiri. Some languages show similar type of adjacency constraints on proximal consonants, or between some aspects of consonants and vowels. Guaran for instance shows nasal harmony between voiced consonants and vowels. This type of harmony is, however, rarer, and, consequently, more diicult to nd data for. For this reason, this paper only examines cases of vowel harmony. The constraints which vowel harmony imposes on the vowel sequence of a word increase the redundancy of naive representations. Take, for example, the case of Turkish. Turkish has eight vowels in its phoneme inventory, but given its left or right neighbour, there may be only four or fewer values which a vowel may take. A representation of sequences of vowels which ignores this contextual information will necessarily be redundant: a representation which uses the contextual dependencies will be much shorter. This diierence in representation sizes can be used to learn vowel harmonies. Diierent harmony generalisa-tions will vary in their level of restrictiveness as well as in how well they t the data. A generalisation which is very restrictive and ts the data well will lead to a very concise representation. A worse t or a less restrictive generalisation will lead to more verbose representations. This paper presents a measure on representations. Using this measure, we can determine which generalisation excludes the most redundancy, and deem it the correct generalisation of the data. The paper is organised into 11 sections. Section(s) 1 introduces the basic notion of vowel harmony, together with the more exotic harmonic behaviours: transparency and opacity. 2 shows how the constraints imposed by harmony systems can be described using two-state automata. 3 discusses the restrictions which an automaton imposes on a string, and how these …