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<Paper uid="W01-1510">
  <Title>Resource sharing among HPSG and LTAG communities by a method of grammar conversion from FB-LTAG to HPSG</Title>
  <Section position="5" start_page="1" end_page="1" type="metho">
    <SectionTitle>
3 Grammar conversion
</SectionTitle>
    <Paragraph position="0"> The grammar conversion from LTAG to  HPSG (Yoshinaga and Miyao, 2001) is the core portion of the RenTAL system. The conversion algorithm consists of: 1. Conversion of canonical elementary trees to HPSG lexical entries.</Paragraph>
    <Paragraph position="1"> 2. Definition of ID grammar rules to emulate substitution and adjunction.</Paragraph>
    <Paragraph position="2"> 3. Conversion of non-canonical elementary  trees to canonical ones.</Paragraph>
    <Paragraph position="3"> The left-hand side of Figure 7 shows a canonical elementary tree, which satisfies the following  Condition 2 All branchings in a tree must contain trunk nodes.</Paragraph>
    <Paragraph position="4"> Trunk nodes are nodes on a trunk, which is a path from an anchor to the root node (the thick lines in Figure 7) (Kasper et al., 1995). Condition 1 guarantees that a canonical elementary tree has only one trunk, and Condition 2 guarantees that each branching consists of a trunk node, a leaf node, and their mother (also a trunk node). The right-hand side of Figure 7 shows elementary trees violating the conditions.</Paragraph>
    <Paragraph position="5"> Canonical elementary trees can be directly converted to HPSG lexical entries by regarding each leaf node as a subcategorization element of the anchor, and by encoding them into a list. Figure 8 shows an example of the conversion. By following the trunk from the anchor &amp;quot;think&amp;quot;tothe  root node labeled S, we store each branching in a list. As shown in Figure 8, each branching is specified by a leaf node and the mother node. A feature Sym represents the non-terminal symbol of the mother node. Features Leaf, Dir, Foot? represent the leaf node; the non-terminal symbol, the direction (on which side of the trunk node the leaf node is), and the type (whether a foot node or a substitution node), respectively.</Paragraph>
    <Paragraph position="6"> Figures 9 and 10 show ID grammar rules to emulate substitution and adjunction. These grammar rules are independent of the original grammar because they don't specify any characteristics specific to the original grammar.</Paragraph>
    <Paragraph position="7"> In the substitution rule, the Sym feature of the substitution node must have the value of the Leaf feature 3 of the trunk node. The Arg feature of the substitution node must be a null list, because the substitution node must be unified only with the node corresponding to the root node of the initial tree. The substitution rule percolates the tail elements 2 of the Arg feature of a trunk node to the mother in order to continue constructing the tree.</Paragraph>
    <Paragraph position="8"> In the adjunction rule, the Sym feature of a foot node must have the same value as the Leaf feature 4 . The value of the Arg feature of the mother node is a concatenation list of both Arg features 2 and 3 of its daughters because we first construct the tree corresponding to the adjoining tree and next continue constructing the tree corresponding to the adjoined tree. The value &amp;quot;B7&amp;quot;or&amp;quot;A0&amp;quot;oftheFoot? feature explicitly determines whether the next rule application is the adjunction rule or the substitution rule.</Paragraph>
    <Paragraph position="9"> Figure 11 shows an instance of rule applications. The thick line indicates the adjoined tree (ABBD) and the dashed line indicates the adjoining  struct the branching marked with BR, where &amp;quot;think&amp;quot; takes as an argument a node whose Sym feature's value is S. By applying the adjunction rule, the Arg feature of the mother node (B) becomes a concatenation list of both Arg features of ACBD ( 8 ) and ABBD ( 5 ). Note that when the construction of ACBD is completed, the Arg feature of the trunk node (C) will be its former state (A). We can continue constructing ABBD as if nothing had happened.</Paragraph>
    <Paragraph position="10"> Multi-anchored elementary trees, which violate Condition 1, are divided into multiple canonical elementary trees. We call the cutting nodes in the divided trees cut-off nodes (Figure 12). Note that a cut-off node is marked by an identifier to preserve a co-occurrence relation among the multiple anchors. Figure 12 shows an example of the conversion of a multi-anchored elementary tree for a compound expression &amp;quot;look for&amp;quot;. We first select an anchor &amp;quot;look&amp;quot; as the syntactic head, and traverse the tree along the trunk from the root node S to the anchor &amp;quot;look&amp;quot;. We then cut off the multi- null anchored elementary tree at the node PP, and cut-off nodes PP in resulting single-anchored trees are marked by an identifier D0D3D3CZ CUD3D6.</Paragraph>
    <Paragraph position="11"> Non-canonical elementary trees violating Condition 2 have a non-anchored subtree which is a subtree of depth 1 or above with no anchor.</Paragraph>
    <Paragraph position="12"> A non-anchored subtree is converted into multi-anchored trees by substituting the deepest node (Figure 13). Substituted nodes are marked as breaking points to remember that the nodes originate from the substitution nodes. In the resulting trees, all subtrees are anchored so that we can apply the above conversion algorithms. Figure 13 shows a conversion of a non-canonical elementary tree for it-cleft. A substitution node P in the non-anchored subtree is selected, and is substituted by each initial tree. The substituted node P in resulting multi-anchored trees are marked as breaking points.</Paragraph>
    <Paragraph position="13"> The above algorithm gives the conversion of LTAG, and it can be easily extended to handle an FB-LTAG grammar by merely storing a feature structure of each node into the Sym feature and Leaf feature together with the non-terminal symbol. Feature structure unification is executed by ID grammar rules.</Paragraph>
    <Paragraph position="14"> The strong equivalence is assured because only substitution/adjunction operations performed in LTAG are performed with the obtained HPSG-style grammar. This is because each element in the Arg feature selects only feature structures corresponding to trees which can substitute/be adjoined by each leaf node of an elementary tree. By following a history of rule applications, each combination of elementary trees in LTAG derivation trees can be readily recovered. The strong equivalence holds also for conversion of non-canonical elementary trees. For trees violat- null templates in the XTAG English grammar (LTAG) and converted lexical entry templates corresponding to them (HPSG): BT: canonical elementary trees, BU: elementary trees violating only Condition 1, BV: elementary trees violating only Condition 2, BW: elementary trees violating both condi- null nodes from the substitution nodes owing to identifiers, which recover the co-occurrence relation in the original elementary trees between the divided trees. For trees violating Condition 2, we can identify substitution nodes in a combined tree because they are marked as breaking points, and we can consider the combined tree as two trees in the LTAG derivation.</Paragraph>
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