Finding the Right Words: Implementing Optimality Theory with Simulated Annealing

Abstract

This dissertation presents an implementation of Optimality Theory (OT) that also aims at accounting for certain variations in speech. The Simulated Annealing for Optimality Theory Algorithm (SA-OT, Fig. 2.8, on page 64) combines OT with simulated annealing, a widespread heuristic optimisation technique. After a general introduction to Optimality Theory and the discussion of certain 'philosophical background questions' (especially on the role of probabilities in linguistics; Chapter 1), the SA-OT Algorithm is introduced (informally in section 2.2, mathematically in sections 3.3 and 3.4), put into a broader context (section 2.1, Chapter 4, and sections 8.2 and 8.3), and experimented with (section 2.3, Chapters 5-7). The mathematical underpinning of SA-OT is preceded by a formal analysis of OT, including the representation of violation profiles using polynomials and ordinal numbers.As section 2.1 argues, heuristic algorithms-- such as SA-OT-- may serve as adequate models of the computations performed by the human brain for at least three reasons: (1) many of these algorithms are simple, (relatively) efficient and produce some output within a predefined time span, even if (2) they may make errors, and finally (3) the algorithm can be speeded up with a price to be paid in reduced precision. A faster computation is possible, but more prone to make errors. The adequacy of such a model is corroborated if besides the grammatical forms it also reproduces the empirically observable error patterns under different conditions. Importantly, these predictions are quantitative, and the algorithm's parameters can 'fine-tune' the output frequencies of the erroneous or alternating forms. Therefore, SA-OT is claimed to be a model of linguistic performance (Table 2.1, page 43). By distinguishing between a linguistic model and its implementation, one can account for both linguistic competence and certain types of linguistically motivated performance phenomena. Thus an adequate linguistic model (a grammar, such as a well-founded OT grammar) predicts correctly which forms are judged as grammatical by the native speaker. This layer refers to the static knowledge of the language in the native speaker's brain. On top of that is built the implementation of the grammar as a model of the dynamic language production process. In particular, SA-OT requires a topology (a neighbourhood structure) on the OT candidate set. Consequently, the notion of a local optimum is introduced: a candidate that is more harmonic than all its neighbours is a local optimum, independently of whether it is the most harmonic element of the entire candidate set. Local optima are the candidates that can emerge as outputs in SA-OT. The global optimum predicts the grammatical form, whereas all other outputs should model performance errors. The second part of the dissertation experiments with SA-OT, introduces a few techniques and tricks, and analyzes the role of its parameters. For that purpose, the following phonological phenomena are modelled: metrical stress shifts in Dutch fast speech (cf. Schreuder, ROA-846), regressive and progressive voice assimilation, cliticization of the Hungarian definite article and syllabification (Prince and Smolensky's basic CV theory). Interesting side results include arguments for including loser (never winning) candidates into the candidate set and new types of ranking arguments, both based on occurrence frequencies. After a comparison to existing OT varieties and non-linguistic cognitive models, the dissertation concludes that future research should decide whether SA-OT or its competitors, the already existing stochastic OT models are more fruitful. But I believe that they may complement each other.

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