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<Paper uid="C90-3033">
  <Title>When Something Is Missing: Ellipsis, Coordination and the Chart</Title>
  <Section position="3" start_page="184" end_page="184" type="intro">
    <SectionTitle>
3. Coordination
</SectionTitle>
    <Paragraph position="0"> If the pm'ser uses a top-down strategy (as is usual in ATN and logic grammars), it must hypothesize a structure for the second conjunct without any knowledge of its actual structure. Since this may be any structure that parallels that of a constituent that ends immediately before the conjunction, the parser must build and check all these possibilities to find the right ones; all this leads to a combinatorial explosion of possfbilities.</Paragraph>
    <Paragraph position="1"> A chart-based approach allows a natural factorization in constituent construction, thereby limiting the exponential explosion of possible analyses, a negative characteristic of SYSCONJ and other systems. Moreover, a bottom-up strategy provides further inlormation to guide the parser in the analysis of successive coordination constituents.</Paragraph>
    <Paragraph position="2"> In the following, only coordination of constituents belonging to the same syntactic category and adjacent is considered.</Paragraph>
    <Paragraph position="3"> Three changes to the normal chart mechanism are necessary to treat coordination (plus the introduction of metarules for the coordination of constituents containing gaps, see SS 3.1) and concern:  1) the configuration of an inactive edge Ix followed by an inactive edge Iand (conjunction type), that causes the insertion of new active edges; 2) features that must be associated with coordinated exlges; 3) for a system that incorporates a mechanism  based on unification (see, for example, \[Shieber, 1986\]), the way in which the mechanism is activated when an active edge incorporates an inactive ont.</Paragraph>
    <Paragraph position="4"> The first change (shown in Figure 3) causes the insertion of an active edge AX (of the same category as Ix and nmrked as destined to recognize a coordinated  structure) that covers the two inactive edges i x and IAnd, and of a cycling edge A'X of the same category as Ix (if not there already). The cycling extge A'x is meant to recognize the coordinated constituent.</Paragraph>
    <Paragraph position="5"> As for tile features associated with the edge, in case of coordination it may occur that a noun phrase has some features (in particular gender and number) different from those of the coordinated elements: for example, the noun phrase il ragazzo e la ragazza (the boy and the girl) has the features &amp;quot;Gender Masculine, Ntnnber Plural&amp;quot;, in part different from those of the noun phrases that compose it. This modification is necessary for running control of agreement (as, tor example, between subject and verb). Finally, it is necessary to modify the unification mechanism so as to permit manipulation of sets of elements (as it occurs in coordination): such modifications allow correct management of the features of sets (as illustrated in the preceding paragraph) and must keep track of the semantic representation with which to label the sets.</Paragraph>
    <Paragraph position="6"> An example of coordination of complete constituents is now considered, to illustrate what happens inside the chart: Giotto e Orcagna dipinsero un alfresco a Padova? \[Did Giotto andOrcagna paint a fresco in Padova .6\] Here coordination concerns the two noun phrases Giotto and Oreagna; obviously, the verb is conjugated in the third person plural because it agrees with the two coordinated noun phrases that must therefore have the features &amp;quot;Gender Masculine, Num~r Plural&amp;quot; (confirming the necessity of the change previously presented on the features of tile sets formed because of coordination).</Paragraph>
    <Section position="1" start_page="184" end_page="184" type="sub_section">
      <SectionTitle>
3.1. Coordination of constituents with
</SectionTitle>
      <Paragraph position="0"> gaps Our approach to the problem of constituents containing gaps consists of introducing metarules associated with some configurations of the rules. The memrules allow an active edge to be inactivated under conditions for which this normally is not permitted (for example, when the head of a constituent has not yet been found). These metarules must be applicable only to active edges contiguous with a conjunction type inactive edge (thereby limiting the growth of inactive edges introduced by metarules). Introduction of metarules carries out only a part of the work necessary to treat coordination of constituents containing gaps ; the remaining part must be carried out during unification of the edges that have recognized the two conjuncts. At this point it is necessary to fill the gaps, using intormation brought 4 187 by the complete constituent. Several proposals have been made for carrying out this role (among them \[Sag et al., 1984\] and \[Kaplan, 1987\]). For example, priority union (proposed in \[Kaplan, 1987\] as a means of assigning correct interpretations to constructions containing gaps in the framework of Lexical-Functional Grammar) which, in Kaplan's original formulation, is an operator that transforms a pair of f-structures into a new f-structure, so that the values of one of the two f-structures (that with priority) are conserved and the other f-structure furnishes default values, if any. The suitability of this method for confronting the phenomenon needs further study, as do many aspects of metarules.</Paragraph>
      <Paragraph position="1"> The following sentence will be used as an example: Giotto dipinse un affresco e Orcagna un polittico? \[Did Giotto paint a fresco and Orcagna a polyptych .9\] The parser works normally until an active S edge (that covers the sentence fragment Oreagna un poZittico) is inserted into the chart to the immediate right of the conjunction. Such an edge may be made inactive by a metarule that establishes that a type S (coordinated) constituent may be accepted even without its head. The parser then continues working regularly until unification of the edges that recognize the conjunction is attempted and an effort is made to fill the gap present in the second conjunct using the head of the first conjunct.</Paragraph>
      <Paragraph position="2"> In applying metarules it is possible to use heuristics that put restrictions on the ordering of the constituents contained in the second conjunct. For example, it is more likely that the correct interpretation is that in which the last constituent present (linearly) in the input part of the sentence recognized by the right conjunct corresponds to the constituent that is found furthest to the right in the first conjunct. Another possibility is that of imposing that the order of the constituents inside the two conjuncts must be parallel; but, in this case, the sentence Giotto dipinse un alfresco e un polittico Orcagna? tilt. Did Giotto portray a fresco and a polyptych Orcagna ?\] would not be correctly interpretable. Certainly, sentences such as this last are to be considered correct, even if unusual in spoken language. On the other hand, these restrictions serve to limit the proliferation of interpretations that afflicts languages such as Italian that have relatively free ordering of the elements inside single constituents,</Paragraph>
    </Section>
  </Section>
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