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<Paper uid="J92-4004">
  <Title>Using Descriptions of Trees in a Tree Adjoining Grammar</Title>
  <Section position="4" start_page="493" end_page="495" type="intro">
    <SectionTitle>
3.10A Constraint
</SectionTitle>
    <Paragraph position="0"> In the definition of TAG, given in Section 1.2, it was stated that if a node has an OA constraint, then adjoining is mandatory at that node. In terms of quasi-nodes this means that the corresponding pair of quasi-nodes must be separated. Therefore, the use of an OA constraint at a node may be interpreted as stating that the related pair  of quasi-nodes are indeed distinct, i.e., there must be some feature that distinguishes them. Hence the linguistic basis for making the claim that the node has an OA constraiht must be stated in such a way that the feature structures on the two quasi-nodes are incompatible. As an example, consider c~8 given in Figure 10. The feature structure of the quasi-root of c~8 has a value of + for the tense attribute to specify that any tree rooted at this quasi-node must satisfy the constraint that it describes a tensed sentence. On the other hand, the feature structure of the paired bottom quasi-node has a value of - for the tense attribute since it only reflects the descendants. Since these two feature structures are incompatible, this pair of quasi-nodes has an &amp;quot;OA constraint&amp;quot; (since it is not possible to stop the derivation process and identify the top with the bottom quasi-node). However, % that results from the adjoining of/37 does not have any pair of quasi-nodes with an &amp;quot;OA constraint.&amp;quot;</Paragraph>
    <Section position="1" start_page="494" end_page="495" type="sub_section">
      <SectionTitle>
3.2 SA Constraints
</SectionTitle>
      <Paragraph position="0"> Recall that an SA constraint of a node lists a subset of auxiliary trees that can be adjoined at this node. The definition of adjunction used here is stated in terms of a pair of substitutions (and thus adjunction involves two unifications). In terms of quasi-trees, we allow the &amp;quot;SA&amp;quot; constraints to be determined as a consequence of the unifications required by identifications of quasi-nodes. If an auxiliary quasi-tree cannot be adjoined at a pair of quasi-nodes, then it must be the case that there is an incompatibility among the relevant pairs of feature structures that we unify when we attempt adjunction.</Paragraph>
      <Paragraph position="1"> When we attempt adjunction the feature structure of the top quasi-node (in the pair</Paragraph>
      <Paragraph position="3"> &amp;quot;SA&amp;quot; constraints.</Paragraph>
      <Paragraph position="4"> where adjunction is attempted) and the feature structure of the quasi-root (of the auxiliary quasi-tree) are unified, as are the feature structure associated with the bottom quasi-node (in the pair where adjunction is attempted) and the feature structure of the quasi-foot (of the quasi-tree being adjoined). If at least one of these unifications fails then adjunction is not possible.</Paragraph>
      <Paragraph position="5"> Consider f18 given in Figure 11. This quasi-tree cannot be adjoined at the pair (s\], s2) in c~8 (Figure 10) but can be adjoined at the pair (sl, s2) of ag. On the other hand, we saw that f17 can be adjoined at the pair (sl, s2) of a8. Thus we can say that the pair (sl, s2) of a8 has an &amp;quot;SA constraint&amp;quot; that includes/37 but not f18.</Paragraph>
    </Section>
    <Section position="2" start_page="495" end_page="495" type="sub_section">
      <SectionTitle>
3.3 NA Constraints
</SectionTitle>
      <Paragraph position="0"> Recall that a node with an NA constraint cannot be the target of an adjunction. Traditionally, this is specified by stating that the set of auxiliary trees that can be adjoined at such a node is the empty set. For this reason, it is often stated that NA constraints are special form of SA constraints.</Paragraph>
      <Paragraph position="1"> There are two possible ways of interpreting &amp;quot;NA constraints&amp;quot; in the quasi-tree framework. Firstly, a pair of quasi-nodes with an &amp;quot;NA constraint&amp;quot; may be interpreted as a stipulation that insists that no quasi-tree can be adjoined at this pair; a statement made regardless of the nature of the auxiliary quasi-trees in the grammar. This may for instance be made if we wish to allow only certain derivation sequences. One could argue that the reason for insisting that foot nodes of complement 3 auxiliary trees have NA constraints, as is the case in most TAG accounts, is to avoid certain derivation sequences (Kroch and Joshi 1985).</Paragraph>
      <Paragraph position="2"> On the other hand, we may also interpret the association of &amp;quot;NA constraint&amp;quot; with a pair of quasi-nodes as a statement that none of the auxiliary quasi-trees in the grammar matches the requirements of the type of auxiliary quasi-trees that can be</Paragraph>
    </Section>
  </Section>
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