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<Paper uid="P02-1007">
  <Title>OT Syntax: Decidability of Generation-based Optimizationa0</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Optimality-Theoretic (OT) grammar systems are an interesting alternative to classical formal grammars, as they construe the task of learning from data in a meaning-based way: a form is defined as grammatical if it is optimal (most harmonic) within a set of generation alternatives for an underlying logical form. The harmony of a candidate analysis depends on a language-specific ranking (a1 ) of violable constraints, thus the learning task amounts to adjusting the ranking over a given set of constraints.</Paragraph>
    <Paragraph position="1"> (1) Candidatea2a4a3 is more harmonic thana2a6a5 iff it incurs fewer violations of the highest-ranking constraint a7a9a8a11a10a13a12 in which a2a4a3 and a2a6a5 differ.</Paragraph>
    <Paragraph position="2"> The comparison-based setup of OT learning is closely related to discriminative learning approaches in probabilistic parsing (Johnson et al., 1999; Riezler et al., 2000; Riezler et al., 2002),1 however the comparison of generation alternatives - rather than parsing alternatives - adds the possibility of systematically learning the basic language-specific grammatical principles (which in probabilistic parsing are typically fixed a priori, using either a treebankderived or a manually written grammar for the given  language). The &amp;quot;base grammar&amp;quot; assumed as given can be highly unrestricted in the OT setup. Using a linguistically motivated set of constraints, learning proceeds with a bias for unmarked linguistic structures (cf. e.g., (Bresnan et al., 2001)).</Paragraph>
    <Paragraph position="3"> For computational OT syntax, an interleaving of candidate generation and constraint checking has been proposed (Kuhn, 2000). But the decidability of the optimization task in OT syntax, i.e., the identification of the optimal candidate(s) in a potentially infinite candidate set, has not been proven yet.2</Paragraph>
  </Section>
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