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<Paper uid="E99-1029">
  <Title>Parsing with an Extended Domain of Locality</Title>
  <Section position="3" start_page="217" end_page="218" type="metho">
    <SectionTitle>
2 Parsing Unification-Based
Grammars
</SectionTitle>
    <Paragraph position="0"> In phrase-structure rule-based parsing, each rule corresponds to a local tree. A rule is applied to a sequence of existing contiguous constituents, if they are compatible with the daughters. In the case of context-free grammar (CFG), the compatibility check is just equality of atomic symbols, and an instantiated daughter is merely the corresponding sub-constituent.</Paragraph>
    <Paragraph position="1"> However, unification-based extensions of phrase-structures grammars are used because they are able to encode local and non-local syntactic dependencies (for example, subject-verb agreement in English) with re-entrant features and feature percolation, respectively: Constituents are represented by DAGS (directed acyclic graphs), the compatibility check is unification, and it is the result of each unification that is used to instantiate the daughters. Graph unification based on the UNION-FIND algorithm has time complexity that is near-linear in the number of feature structure nodes in the inputs (Huet, 1975; Ait-Kaci, 1984); however, feature structures in wide-coverage grammars can contain hundreds of nodes (see e.g., HPSG (Pollard and Sag, 1994)), and since unification is a primitive operation the overall number of unification attempts during parsing can be very large. Unification therefore has a substantial practical cost.</Paragraph>
    <Paragraph position="2"> Efficient graph unification must also ensure that it does not destructively modify the input structures, since the same rule may be used several times within a single derivation, and also the same constituent may be used within different partial analyses with features instantiated in different ways. Copying input feature structures in their entirety before each unification would solve this problem, but the space usage renders this approach impractical. Therefore, various 'quasi-destructive' algorithms (Karttunen, 1986; Kogure, 1990; Tomabechi, 1991) and algorithms using 'skeletal' DACS with updates (Pereira, 1985; Emele, 1991) have been proposed, which attempt to minimize copying. But even with good implementations of the best of these improved algorithms, parsers designed for wide-coverage unification-based phrase-structure grammars using large HPSG-style feature graphs spend around 85-90% of their time unifying and copying feature structures (Tomabechi, 1991), and may allocate in the region of 1-2 Mbytes memory while parsing sentences of only eight words or so (Flickinger, p.c.). Although comfortably within main memory capacities of current workstations, such large amounts of short-term storage allocation overflow CPU caches, and storage management overheads become significant.</Paragraph>
    <Paragraph position="3"> In the case of unification-based LTAG the situation is even more problematic. Elementary structures are larger than productions, and the potential is that the parser will have to make copies of entire trees and associated feature structures.</Paragraph>
    <Paragraph position="4"> Furthermore, the number of trees that an LTAG  parser must consider tends to be far larger than the number of rules in a corresponding phrase-structure grammar. On the other hand, the EDOL has the potential to eliminate some or all of feature percolation, and in the remainder of this section, we explain how.</Paragraph>
    <Paragraph position="5"> An LTAG consists of a set of unanchored trees such as the one shown on the left of Figure 2.</Paragraph>
    <Paragraph position="6"> This shows a tree for transitive verbs where subject/verb agreement is captured directly with re-entrancy between the value of agr feature structures at the anchor (verb) node and the subject node. Notice the re-entrancy between the anchor node and the substitution node for the subject.</Paragraph>
    <Paragraph position="7"> However these are not the trees that the parser works with; the parser is given trees that have been anchored by the morphologically analysed words in the input sentence. For example, the tree shown on the right is the result of anchoring the tree shown on the left with the word loves. Anchoring instantiates the agr feature of the anchor node as 3sg which has the effect (due to the re-entrancy in the unanchored tree) of instantiating the agr feature at the subject node as 3sg.</Paragraph>
    <Paragraph position="8"> Anchored elementary trees are translated by the parser into a sequence of what we will refer to as parser actions. For example, once the tree shown on the right of Figure 2 has been associated with the word loves in the input, it can be recognized with a sequence of parser actions that involve finding a NP constituent on the right (corresponding to the object), possibly performing adjunctions at the VP node, and then finding another NP constituent on the left (corresponding to the subject). We say that the two NP substitution nodes and the VP node are the sites of parser actions in this tree. Problems arise, and the EDOL hypothesis is violated, when there is a dependence between different parser actions.</Paragraph>
    <Paragraph position="9"> The EDOL hypothesis states that elementary trees provide a domain of locality large enough to state co-occurrence relationship between the anchor of the tree and the nodes it imposes constraints on. If all dependencies relevant to the parser can be captured in this way then, once an elementary tree has been anchored by a particular lexical item, the settings of feature values at all of the dependent nodes will have been fixed, and no feature percolation can occur. Each unification is a purely local operation with no repercussions on the rest of the parsing process. No copying of feature structures is required, so memory usage is greatly reduced, and complex quasi-destructive algorithms with their associated computational overheads can be dispensed with.</Paragraph>
    <Paragraph position="10"> Note that, although feature percolation is eliminated when the EDOL hypothesis holds, the feature structure at a node can still change. For example, substituting a tree for a proper noun at the subject position of the tree in Figure 2 would cause the .feature structure at the node for the subject to'include pn:+. This, however, does not violate the EDOL hypothesis since this feature is not coreferenced with any other feature in the tree.</Paragraph>
  </Section>
  <Section position="4" start_page="218" end_page="221" type="metho">
    <SectionTitle>
3 Analysis of two wide-coverage
</SectionTitle>
    <Paragraph position="0"> grammars As we have seen, the EDOL of LTAGs makes it possible, at least in principle, to locally express dependencies which cannot be localized in a CFG-based formalism. In this section we consider two existing grammars: the XTAG grammar, a wide-coverage LTAG, and the LEXSYS grammar, a wide-coverage D-Tree Substitution Grammar (Rambow et al., 1995). For each grammar we investigate the extend to which they do not take full advantage of the EDOL and require percolation of features at parse time.</Paragraph>
    <Paragraph position="1"> There are a number of instances in which dependencies are not localized in the XTAG grammar, most of which involve auxiliary trees. There are  three types of auxiliary trees: predicative, modifier and coordination auxiliary trees. In predicative auxiliary trees the anchor is also the head of the tree and becomes the head of the tree resulting from the adjunction. In modifier auxiliary trees, the anchor is not the head of the tree, and the sub-tree headed by the anchor usually plays a role of adjunct in the resulting tree. Coordination auxiliary trees are similar to modifier auxiliary trees in that they are anchored by the conjunction which is not the head of the phrase. One of the conjoined nodes is a foot node, the other one a substitution node.</Paragraph>
    <Section position="1" start_page="219" end_page="219" type="sub_section">
      <SectionTitle>
3.1 Modifier Auxiliary Trees
</SectionTitle>
      <Paragraph position="0"> In modifier auxiliary trees -- an example of which is shown in Figure 32 -- the feature values at the root and foot nodes are set by the node at which the auxiliary tree is adjoined, and have to be percolated between the foot node and the root node.</Paragraph>
      <Paragraph position="1"> The LEXSYS grammar adopts a similar account of modification.</Paragraph>
      <Paragraph position="2"> From a parsing point of view, this does not result in the need for feature percolation: only the foot node of the modifier tree is the site of a parser action, and the root node is ignored by the process that interprets the tree for the parser.</Paragraph>
    </Section>
    <Section position="2" start_page="219" end_page="219" type="sub_section">
      <SectionTitle>
3.2 Coordination Auxiliary Trees
</SectionTitle>
      <Paragraph position="0"> An example of an XTAG coordination auxiliary tree is shown on the left of Figure 4. This case is different from the modification case since features of the substitution node have to be identical to features of the foot node (which wiIl match those at the adjunction site). From a parsing point of view these nodes are both the sites of actions, resulting in the need for feature percolation. For example, for the NP coordination tree shown in Figure 4, if one of the conjuncts is a wh-phrase, the other conjunct must be a wh-phrase too, as in who or what did this? but *John and who did this? The wh-feature has to be percolated between the two nodes on each side of the conjunction.</Paragraph>
      <Paragraph position="1"> In the LEXSYS grammar, a coordination tree is anchored by a head of the tree, not by the conjunction. To illustrate (see the tree on the right of Figure 4), N P-coordination trees are anchored by a noun, and features such as wh and case are ground during anchoring. As a result, there is no need for passing of these features in the coordination trees of the LEXSYS grammar.</Paragraph>
      <Paragraph position="2"> 2All examples relating to the XTAG grammar come from the XTAG report (XTAG-Group, 1995). They have been simplified to the extent that only details relevant to the discussion are included.</Paragraph>
      <Paragraph position="3"> As for agreement features, there are two cases to consider: if the conjunction is and, the number feature of the whole phrase is plural; if the conjunction is or, the number feature is the same as the last conjunct's (XTAG-Group, 1999). In both the XTAG and LEXSYS grammars, this is achieved by having separate trees for each type of conjunction. null</Paragraph>
    </Section>
    <Section position="3" start_page="219" end_page="220" type="sub_section">
      <SectionTitle>
3.3 Predicative Auxiliary Trees
</SectionTitle>
      <Paragraph position="0"> In the XTAC grammar, subject raising and auxiliary verbs anchor auxiliary trees rooted in VP, without a subject3; they can be adjoined at the VP node of any compatible verb tree. With this arrangement, subject-verb agreement must be established dynamically. The agr feature of the NP subject must match the agr feature of whichever VP ends up being highest at the end of the derivation. In Figure 5, the bought tree has been anchored in such a way that adjunction at the VP node is obligatory, since a matrix clause cannot have mode:ppart. 4 When the tree for has is adjoined at the VP node the agr features of the sub-ject will agree with those of bought. The feature structure at the root of the tree for has is unified with the upper feature structure at the VP node of the tree for bought, and the feature structure at the foot of the tree for has is unified with the lower feature structure at the VP node of the tree for bought. The foot node of the has tree is the VP node on the frontier of the tree. Note that even after the tree has been anchored, re-entrancy of features occurs in the tree.</Paragraph>
      <Paragraph position="1"> Thus, there are two sites in the tree for bought (the subject NP node and the VP node) at which parser actions will take place (substitution and adjunction, respectively) such that a dependency between the values of the features at these two nodes must be established by the parser.</Paragraph>
      <Paragraph position="2"> The situation is similar for case assignment (also shown in the Figure 5): the value of a feature ass-case (the assign case feature) on the highest VP is coreferred with the value of the feature case on the subject NP. For finite verbs, the value of the feature ass-case is determined by the mode of the verb. For infinitive verbs, case is assigned in various ways, the details of which are not relevant to the discussion here. The subject is in the nominative case if the verb is finite, and in the accusative otherwise. As with the agr feature, the value of the case feature cannot be instantiated  in the anchored elementary tree of the main verb because auxiliary verb trees can be adjoined.</Paragraph>
      <Paragraph position="3"> The same observations apply to the XTAG treatment of copula with predicative categories such as an adjective. As shown in Figure 6, these predicative AP trees have a subject but no verb; trees for raising verbs or the copula can be adjoined into them. As in the previous example, the agr features of the verb and subject cannot be instantiated in the elementary tree because the verb and its subject are not present in the same tree.</Paragraph>
      <Paragraph position="4"> From the examples we have seen, it appears that the XTAG grammar does not take full advantage of the EDOL with respect to a number of syntactic features, for example those relating to agreement and case. The LEXSYS grammar takes a rather different approach to phenomena that XTAG handles with predicative auxiliary trees.</Paragraph>
      <Paragraph position="5"> The LEXSYS grammar has been designed to localize syntactic dependencies in elementary trees.</Paragraph>
      <Paragraph position="6"> As in the XTAC grammar, unbounded dependencies between gap and filler are localized in elementary trees; but unlike the XTAG grammar, other types of syntactic dependencies, such as agreement, are also localized. All finite verbs, including auxiliary and raising verbs, anchor a tree rooted in S, and thus are in the same tree as the subject with which they agree. An example involving finite verbs is shown in Figure 7. Since verb trees cannot be substituted between the subject and the verb, the agr feature can be grounded when elementary trees are anchored, rather than during the derivation. The case feature of the subject can be specified even in the unanchored elementary tree: in trees for finite verbs the subject has nominative case; in trees for for ... to clauses it has accusative case.</Paragraph>
      <Paragraph position="7"> As can be seen from the tree on the right of Figure 7, subject raising and auxiliary verbs are rooted in S and take a VP complement. So the sentence He seems to like apples is produced by substituting a VP-rooted tree for to like into a tree for seems.</Paragraph>
      <Paragraph position="8"> Thus, for all three trees shown in Figure 7, once anchoring has taken place, all of the syntactic features being checked by the parser are grounded. Hence, the parser does not have to check for dependencies between the parser actions taking place at different sites in the tree.</Paragraph>
    </Section>
    <Section position="4" start_page="220" end_page="221" type="sub_section">
      <SectionTitle>
3.4 Semantic Dependencies
</SectionTitle>
      <Paragraph position="0"> There are many examples where the xTAG grammar, but not the LEXSYS grammar, localizes semantic dependencies: for example, dependencies  subject are localized in the same elementary tree, and selectional restrictions can be locally imposed by the adjective on the subject without the need for feature percolation. On the other hand, in the LEXSYS grammar, the dependency between upset and he in he looks upset could not be checked during parsing without the use of feature passing between the subject and AP node of the tree in the middle of Figure 7.</Paragraph>
    </Section>
    <Section position="5" start_page="221" end_page="221" type="sub_section">
      <SectionTitle>
3.5 Percolation of Features in LEXSYS
</SectionTitle>
      <Paragraph position="0"> This section considers a limited number of cases where it appears that it is not possible to set all syntactic features by anchoring an elementary tree.</Paragraph>
      <Paragraph position="1"> When two nodes other than the anchor of the tree are syntactically dependent, feature values may have to be percolated between these nodes (the anchor does not determine the value of these features). For example, in English adjectives that can have S subjects determine the verb form of the subject. Hence, in Figure 8, the verb form feature of the subject is not determined by the anchor of the tree (the verb) but by the complement of the anchor (the adjective). The verb form feature must therefore be percolated from the adjective phrase to the subject.</Paragraph>
      <Paragraph position="2"> The XTAG grammar localizes this dependency (see Figure 6). However, as we have seen, agreement features are not localized in this analysis. The problem then is that it does not seem to be possible to localize all syntactic features in this case.</Paragraph>
      <Paragraph position="3"> Feature percolation is also required in the LEXSYS grammar for prepositional phrases which contain a wh-word, because the value of the wh feature is not set by the anchor of the phrase (the preposition) but by the complement (as in these reports, the wording on the covers of which has caused so much controversy, are to be destroyed5 ). The value of the feature wh is set by the N Pcomplement, and percolated to the root of the PP.</Paragraph>
    </Section>
  </Section>
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