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<Paper uid="P81-1036">
  <Title>Chart Parsing and Rule Schemata in PSG</Title>
  <Section position="2" start_page="0" end_page="167" type="metho">
    <SectionTitle>
S
</SectionTitle>
    <Paragraph position="0"> The advantage of the WFST comes out if we suppose the gr~--.=r involved reeognises the structural ambiguity of this sentence. If the parsing continued in order to produce the other structure, with the PP attached at the VP level, considerable effort would be saved by the WFST. The subject NP and the PP itself would not need to be reparsed, as they are already in the graph.</Paragraph>
    <Paragraph position="1"> What the chart adds to the WFST is the idea of active edges. Where the inactive edges of the WFST (and the chart) represent complete constituents, active edges represent incomvlete constituents. Where inactive edges indicate the presence of such and such a constituent, with such and such sub-structure, extending from here to ~here, active edges indicate a stage in the search for a constituent.</Paragraph>
    <Paragraph position="2"> As such they record the category of the constituent under construction, its sub-structure as found so far, and some specification of how it may be extended and/ or completed.</Paragraph>
    <Paragraph position="3"> The fund~umental principle of chart parsing, from which all else follows, is keyed by the meeting of active with inactive edges: The Fundamental Rule ******************** Whenever an active edge A and an inactive edge I meet for the first time, if I satisfies A's conditions for extension, then build a* new edge as follows: lts left end is the left end of A Its right end is the right end of I Its category is the category of A Its contents are a function (dependent on the grammatical formalism employed) of the contents of A and the category and contents of I It is inactive or active depending on whether this extension completes A or not Note that neither A nor I is modified by the abvve process - a completely new edge is constructed, independent of either of =hem. In the case of A, this may seem surprising and wasteful of space, but in fact it is crucial to properly dealing with structural ambiguity. It guarantees that all parses will be found, independent of the order in which operations are performed. Whenever further inactive edges are added at this point the continued presence of A, together with the fundamental rule, insures that alternative extensions of A will be pursued as appropriate.</Paragraph>
    <Paragraph position="4"> A short example should make the workings of this principle clear. For the sake of simplicity, the grammar I will use in this and subsequent examples is an unadorned set of context free phrase structure rules, and the structures produced are simple constituent structure trees. Nonetheless as should be clear from what follows, the chart is equally useful for a wide range of grammutical formalisms, including phrase structure rules with features and ATNs.</Paragraph>
    <Paragraph position="5"> *In fact depending on formalism more than one new edge may be built - see below.</Paragraph>
    <Paragraph position="6">  Figures 3a-3d show the parsing of &amp;quot;the man&amp;quot; by the rule &amp;quot;::P -&gt; D N&amp;quot;. In these figures, inactive edges are light lines below the row of verteces.</Paragraph>
    <Paragraph position="7"> Active edges are heavy lines above the row. Figure 3a simply shows the two inactive edges for the string with form-class information.</Paragraph>
    <Paragraph position="8"> Figure be.</Paragraph>
    <Paragraph position="9"> Figure 3b shows the addition of an empty active edge at the left hand end. We will discuss where it comes from in the next section. Its addition to the chart invokes the fundamental rule, with this edge being A and the edge for &amp;quot;the&amp;quot; being I.</Paragraph>
    <Paragraph position="10"> Figure 3b.</Paragraph>
  </Section>
  <Section position="3" start_page="167" end_page="167" type="metho">
    <SectionTitle>
NP:D N\[\]
</SectionTitle>
    <Paragraph position="0"> O\[tho\] N\[man\] The notation here for the active edges is the category sought, in this case NP, followed by a colon, followed by a list of the categories needed for extension/ completion, in this case D followed by N, followed by a bracketed list of sub-constituents, in this case empty. Since the first symbol of the extension specification of A matches the category of I, an new edge is created by the fundamental rule, as shown in Figure 3c.</Paragraph>
    <Paragraph position="1"> Figure 3c.</Paragraph>
    <Paragraph position="2"> NP I This edge represents a partially completed NP, still needing an N to complete, with a partial structure, lts addition co the chart invokes the fundamental rule again, this time with it as A and the &amp;quot;man&amp;quot; edge as I. Once again the extension condition is meet, and a new edge is constructed. This one is inactive however, as nothing more is required to complete it.</Paragraph>
    <Paragraph position="3"> Figure 3d.</Paragraph>
  </Section>
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