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<Paper uid="C00-2099">
  <Title>A Statistical Theory of Dependency Syntax</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> The theory of dependency grammar culminated in the seminal book by Lncien TesniSre, (Tesnihre, 1959), to which also today's leading scholars pay homage, see, e.g., (Mel'enk, 1987). Unfortunately, Tesnibre's book is only available in French, with a partial translation into German, and subsequent descriptions of his work reported in English, (Hays, 196/1), (Gaifinan, 1965), (Robinson, 1970), ,etc., stray increasingly t'urther fi:om the original, see (Engel, 1996) or (,15~rvinen, 1998) for an account of this. The first step when assigning a dependency description to an input string is to segment the input string into nuclei. A nucleus can he a word, a part of a word, or a sequence of words and subwords, and these need not appear eontiguonsly in the input string. The best way to visualize this is perhaps the following: the string is tokenized into a sequence of tokens and each lmcleus consists of a subsequence of these tokens. Alternative readings may imply different ways of dividing the token sequence into nuclei, and segmenting the input string into nuclei is therefore in general a nondeterministic process.</Paragraph>
    <Paragraph position="1"> The next step is to relate the nuclei to each other through dependency links, which are directed and typed. If there is a dependency link froln one nucleus to another, the former is called a dependent of the latter, and the latter a regent of the former.</Paragraph>
    <Paragraph position="2"> Theories of dependency syntax typically require that each nucleus, save a single root nucleus, is assigned a unique regent, and that there is no chain of dependency links that constitutes a cycle. This means that the dependency links establish a tree structure,  where each node is labeled by a nucleus. Thus, the label assigned to a node is a dependent of the label assigned to its parent node, and conversely, the label assigned to a node is the regent of the labels assigned to its child nodes. Figure 1 shows two dependency trees tbr the sentence John ate beans.</Paragraph>
    <Paragraph position="3"> In Tesni~re's dependency syntax, only the dependency strncture, not the order of the dependents, is represented by a dependency tree. This means that dependency trees are unordered, a.nd thus that the two trees of Figure 1 are equivalent. This also mea.ns that specitying the sm'face-string realization of a dependency description becomes a separate issue.</Paragraph>
    <Paragraph position="4"> We will model dependency desc,:iptions as two separate stochastic processes: one top-down process generating the tree structure T and one bottom-up process generating the surt3.ce string(s) S given the tree structure: 1)(7, s) = \]'(7). p(s 1 7) This can be viewed as a variant of Shannon's noisy channel model, consisting of a language model of tree structures and a signal model converting trees to surface strings. In Section 2 we describe the top-down process generating tree structures and in Section 3 we propose a series of increasingly more sophisticated bottom-up proccsses generating surl~ce strings, which resnlt in grammars with increasingly greater expressive power. Section el describes how the proposed stochastic model of dependency syntax was realized as a probabilistic chart parser.</Paragraph>
  </Section>
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