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<Paper uid="P00-1009">
  <Title>An Improved Parser for Data-Oriented Lexical-Functional Analysis</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 Summary of LFG-DOP
</SectionTitle>
    <Paragraph position="0"> In accordance with Bod (1998), a particular DOP model is described by * a definition of a well-formed representation for utterance analyses, * a set of decomposition operations that divide a given utterance analysis into a set of fragments, * a set of composition operations by which such fragments may be recombined to derive an analysis of a new utterance, and * a definition of a probability model that indicates how the probability of a new utterance analysis is computed.</Paragraph>
    <Paragraph position="1"> In defining a DOP model for LFG representations, Bod &amp; Kaplan (1998) give the following settings for DOP's four parameters.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
2.1 Representations
</SectionTitle>
      <Paragraph position="0"> The representations used by LFG-DOP are directly taken from LFG: they consist of a cstructure, an f-structure and a mapping ph between them. The following figure shows an example representation for Kim eats. (We leave out some features to keep the example simple.)  Bod &amp; Kaplan also introduce the notion of accessibility which they later use for defining the decomposition operations of LFG-DOP: An f-structure unit f is ph-accessible from a node n iff either n is ph-linked to f (that is, f = ph(n) ) or f is contained within ph(n) (that is, there is a chain of attributes that leads from ph(n) to f). According to the LFG representation theory, c-structures and f-structures must satisfy certain formal well-formedness conditions. A cstructure/f-structure pair is a valid LFG representation only if it satisfies the Nonbranching Dominance, Uniqueness, Coherence and Completeness conditions (Kaplan &amp; Bresnan 1982).</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
2.2 Decomposition operations and Fragments
</SectionTitle>
      <Paragraph position="0"> The fragments for LFG-DOP consist of connected subtrees whose nodes are in phcorrespondence with the correponding sub-units of f-structures. To give a precise definition of LFG-DOP fragments, it is convenient to recall the decomposition operations employed by the orginal DOP model which is also known as the &amp;quot;Tree-DOP&amp;quot; model (Bod 1993, 1998):  (1) Root: the Root operation selects any node of a tree to be the root of the new subtree and erases all nodes except the selected node and the nodes it dominates.</Paragraph>
      <Paragraph position="1"> (2) Frontier: the Frontier operation then  chooses a set (possibly empty) of nodes in the new subtree different from its root and erases all subtrees dominated by the chosen nodes.</Paragraph>
      <Paragraph position="2"> Bod &amp; Kaplan extend Tree-DOP's Root and Frontier operations so that they also apply to the nodes of the c-structure in LFG, while respecting the principles of c/f-structure correspondence. When a node is selected by the Root operation, all nodes outside of that node's subtree are erased, just as in Tree-DOP. Further, for LFG-DOP, all ph links leaving the erased nodes are removed and all f-structure units that are not ph-accessible from the remaining nodes are erased. For example, if Root selects the NP in figure 1, then the f-structure corresponding to the S node is erased, giving figure 2 as a possible fragment:  In addition the Root operation deletes from the remaining f-structure all semantic forms that are local to f-structures that correspond to erased c-structure nodes, and it thereby also maintains the fundamental two-way connection between words and meanings. Thus, if Root selects the VP node so that the NP is erased, the subject semantic form &amp;quot;Kim&amp;quot; is also deleted:</Paragraph>
    </Section>
  </Section>
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