11.5.1 Learning Phonological Rules

In this section we briefly summarize some early literature in learning phonological rules, generally couched either in terms of finite state models of two-level phonology

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or classic Chomsky-Halle rules.

Johnson (1984) gives one of the first computational algorithms for phonological rule induction. His algorithm works for rules of the form

(11.8) $ a \rightarrow b/C $

where $C$ is the feature matrix of the segments around $a$. Johnson's algorithm sets up a system of constraint equations which $C$ must satisfy, by considering both the positive contexts, i.e., all the contexts $C_{i}$ in which $a$ $b$ occurs on the surface, as well as all the negative contexts $C_{j}$ in which an $a$ occurs on the surface. Touretzky et al. (1990) extended Johnsons work in various ways, including dealing with epenthesis and deletion rules.

The algorithm of Gildea and Jurafsky (1996) was designed to induce transducers representing two-level rules of the type we have discussed earlier. Gildea and Jurafsky's supervised algorithm was trained on pairs of underlying and surface forms. For example, they attempted to learn the rule of English flapping, (focusing only on the phonetic context and ignoring social and other factors). The training set thus consisted of underlying/surface pairs, either with an underlying /t/ and surface flap [dx], or an underlying /t/ and surface [t], as follows:

| --- | --- | --- | --- | --- | --- |

The algorithm was based on OSTIA (Oncina et al., 1993), a general learning algorithm for the subsequent transducers defined on page ??. Gildea and Jurafsky showed that by itself, the OSTIA algorithm was too general to learn phonological transducers, even given a large corpus of underlying-form/surface-form pairs. For example, given 25,000 underlying/surface pairs like the examples above, the algorithm ended up with the huge and incorrect automaton in Fig. 11.16(a). Gildea and Jurafsky then augmented the domain-independent OSTIA system with learning biases which are specific to natural language phonology. For example they added a Faithfulness bias that underlying segments tend to be realized similarly on the surface (i.e. that all things being equal, an underlying /p/ was likely to emerge as a surface [p]). They did this by starting OSTIA with the underlying and surface strings aligned using Levenshtein distance. They also added knowledge about phonetic features (vowel versus consonant, reduced versus non-reduced vowel, etc). Together, adding these biases enabled OSTIA to learn the automaton in Fig. 11.16(b), as well as correct automatons for other phonological rules like German consonant devoicing.

This phonological learning experiment illustrates that successful learning requires two components: a model which fits some empirical data and some prior knowledge or biases about the structure of the model.

Recent work on learning has focused either on morphological learning, or on ranking of OT constraints rather than on the induction of rules and constraints, and will be discussed in the next two sections.

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Figure 11.16 Induction of a flapping rule transducer (after Gildea and Jurafsky (1996)). The transducer in (a) is the initial attempt at learning. The transducer in (b) is the correct transducer induced after a faithfulness bias.