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<Paper uid="J03-1001">
  <Title>c(c) 2003 Association for Computational Linguistics Optimization Models of Sound Systems Using Genetic Algorithms</Title>
  <Section position="4" start_page="31" end_page="31" type="concl">
    <SectionTitle>
5. Conclusions and Discussion
</SectionTitle>
    <Paragraph position="0"> In this article, we apply optimization models using GAs to study the configuration of vowels and tone systems. The approach we use is similar to that in previous explanatory models that have been used to study vowel systems. Certain criteria, which are assumed to be the principles governing the structure of sound systems, are used to predict optimal systems. In most of the previous studies (Liljencrants and Lindblom 1972; Crothers 1978; Lindblom 1986), only one criterion has been considered.</Paragraph>
    <Paragraph position="1"> When two criteria have been considered, the two objectives are combined into a single weighted function (Bo&amp;quot;e, Schwartz, and Vall 'ee 1994). In our study of vowel systems, the simple GA model we use also adopts a weighted function to combine two criteria, perceptual contrast and focalization. In our study of tone systems, however, we apply a MOGA model that uses a Pareto ranking method to consider two criteria, perceptual contrast and markedness complexity, simultaneously, without combining them into a scalar function. A priori knowledge of the weights of the two criteria are not necessary.</Paragraph>
    <Paragraph position="2"> Another advantage of an MOGA is that we can obtain a set of Pareto-optimal results, instead of only one. An MOGA model generates more optimal predictions than a single-objective model, and therefore it is more likely to predict more systems that are close to the systems actually observed. Although the consistency between the predicted systems and the observed systems in the current study is not as significant as that obtained for vowel systems, further investigation along this line is promising.</Paragraph>
    <Paragraph position="3"> Following the deductive approach pursued in this study, we can design various criteria to predict optimal systems. The deductive approach provides convenience and freedom in the manipulation of different parameters in the models, such as the param- null Ke, Ogura, and Wang Optimization Models of Sound Systems Using GA eters l and a in Schwartz et al. (1997a), to test different hypothesized mechanisms. It is necessary, however, to seek explanations for such parameters in terms of physiological or cognitive constraints.</Paragraph>
    <Paragraph position="4"> Studies taking the deductive approach must not be pursued independent of the inductive approach. For example, in the study of tone systems, few comprehensive tone databases are available. The resources on which our investigation of tone systems relies, including the experiment in Gandour (1983) and the database in Cheng (1973), are based mostly on the observation of tone languages found in Asian. The incorporation of data from other types of tone languages in Africa and America is expected to help in refining our explanatory hypothesis about the configuration of the systems.</Paragraph>
    <Paragraph position="5"> Lastly, we would like to point out that although in this study we apply optimization to predict vowel and tone systems, we do not imply that there exist any explicit and/or global optimization processes in the formation of such systems. We have no grounds to believe that speakers are aware of what sounds will provide maximal perceptual contrast or require the least production effort and therefore deliberately choose those sounds. Optimization must be an emergent property from the interactions of language users (de Boer 2000, 2001). Each individual speaker has certain physiological and cognitive constraints which limit the sounds it is possible for him to make and assign preference to certain of those sounds over others. These constraints, however, provide only a range of possible sounds. It is the interactions among individuals that determine precisely which systems among those that are possible will emerge. This is why different configurations of sound systems, even suboptimal ones in the sense of some hypothesized criteria, can be observed in real systems. Research including modeling from this perspective is promising and may lead to more realistic predictions of sound systems.</Paragraph>
  </Section>
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