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<Paper uid="C02-1075">
  <Title>A Novel Disambiguation Method For Unification-Based Grammars Using Probabilistic Context-Free Approximations</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> This paper deals with the problem of how to disambiguate the readings of sentences, analyzed by a given unification-based grammar (UBG).</Paragraph>
    <Paragraph position="1"> Apparently, there are many different approaches for almost as many different unification-based grammar formalisms on the market that tackle this difficult problem. All approaches have in common that they try to model a probability distribution over the readings of the UBG, which can be used to rank the competing analyses of a given sentence; see, e.g., Briscoe and Carroll (1993), Eisele (1994), Brew (1995), Abney (1997), Goodman (1997), Bod and Kaplan (1998), Johnson et al. (1999), Riezler et al. (2000), Osborne (2000), Bouma et al. (2001), or Schmid (2002).</Paragraph>
    <Paragraph position="2"> Unfortunately, most of the proposed probability models are not mathematically clean in that the probabilities of all possible UBG readings do not sum to the value 1, a problem which is discussed intensively by Eisele (1994), Abney (1997), and Schmid (2002).</Paragraph>
    <Paragraph position="3"> In addition, many of the newer approaches use log-linear (or exponential) models. Schmid (2002) outlines a serious problem for these models: log-linear models prevent the application of dynamic programming methods for the computation of the most probable parse, if complex features are incorporated. Therefore the run-time complexity of the disambiguation algorithm is linear in the number of parses of a sentence. If the number of parses grows exponentially with the length of the sentence, these approaches are simply impractical.</Paragraph>
    <Paragraph position="4"> Our approach obviates the need for such models on the UBG side in that it shifts the responsibility to simpler CF models, indirectly obtained from the UBG. In more detail, the kernel of our novel disambiguation method for UBGs consists of the application of a context-free approximation for a given UBG (Kiefer and Krieger, 2000) and the exploitation of the standard probability model for CFGs. In contrast to earlier approaches to disambiguation for UBGs, our approach has several advantages. Firstly, probabilistic modeling/training of context-free grammars is theoretically well-understood and can be effectively done in practice, using the inside-outside algorithm (Lari and Young, 1990). Secondly, the Viterbi algorithm enables CFG parsing and disambiguation in cubic time, exploiting dynamic programming techniques to specify the maximum-probability parse of a given sentence.</Paragraph>
    <Paragraph position="5"> Thirdly, probability distributions over the CFG trees are mathematically clean, if some weak conditions for this desired behaviour are fulfilled (Booth and Thompson, 1973).</Paragraph>
    <Paragraph position="6"> In the rest of the paper, we present the context-free approximation, our novel disambiguation approach, and an experiment, showing that the approach is feasible.</Paragraph>
  </Section>
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