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<Paper uid="P96-1027">
  <Title>Shieber, S. (1988). A Uniform Architecture for Parsing</Title>
  <Section position="6" start_page="201" end_page="203" type="evalu">
    <SectionTitle>
5 Indexing
</SectionTitle>
    <Paragraph position="0"> String positions provide a natural way to index the strings input to the parsing process for the simple reason that there are as many of them as there are words but, for there to be any possibility of interaction between a pair of edges, they must come together at just one index. These are the natural points of articulation in the domain of strings. They cannot fill this role in generation because they are not natural properties of the semantic expressions that are the input to the process. The corresponding natural points of articulation in  flat semantic structures are the entities that we have already been referring to as indices.</Paragraph>
    <Paragraph position="1"> In the modified version of the procedure, whenever a new inactive edge is created with label B(b ...), then for all rules of the form in (9), an active edge is also created with  label A(...)/C(c ...).</Paragraph>
    <Paragraph position="2"> (9) A(...) ~ B(b ...) C(c ...)  This represents a phrase of category A that requires a phrase of category C on the right for its completion. In these labels, b and c are (variables representing) the first, or distinguished indices associated with B and C. By analogy with parsing charts, an inactive edge labeled B(b ...) can be thought of as incident from vertex b, which means simply that it is efficiently accessible through the index b. An active edge A(...)/C(c ...) should be thought of as incident from, or accessible through, the index c. The key property of this scheme is that active and inactive edges interact by virtue of indices that they share and, by letting vertices correspond to indices, we collect together sets of edges that could interact. We illustrate the modified procedure with the sentence (10) whose semantics we will take to be (11), the grammar rules (12)-(14), and the lexical entries in (15).</Paragraph>
    <Paragraph position="4"> The procedure will be reminiscent of left-corner parsing.</Paragraph>
    <Paragraph position="5"> Arguments have been made in favor of a head-driven strategy which would, however, have been marginally more complex (e.g. in Kay (1989), Shieber, et el. (1989)) and the differences are, in any case, not germane to our current concerns. null The initial agenda, including active edges, and collecting edges by the vertices that they are incident from, is given in (16).</Paragraph>
    <Paragraph position="6"> The grammar is consulted only for the purpose of creating active edges and all interactions in the chart are between active and inactive pairs of edges incident from the same vertex.</Paragraph>
    <Paragraph position="7">  d: dog(d), def(d) s: see(s), past(s), arg 1 (s, d), arg2(s, c), cat(c), def(c) c: cat(c), def(c) s: see(s), past(s), argl (s, d), arg2(s, c), cat(c), def(c) Among the edges in (16), there are two interactions, one at vertices c and d. They cause the first and third edges in (17) to be added to the agenda. The first interacts with the active edge originally introduced by the verb &amp;quot;saw&amp;quot; producing the fourth entry in (17). The label on this edge matches the first item on the right-hand side of rule (12) and the active edge that we show in the second entry is also introduced. The final interaction is between the first and second edges in (17) which give rise to the edge in (18). This procedure confirms perfectly to the standard algorithm schema for chart parsing, especially in the version that makes predictions immediately following the recognition of the first constituent of a phrase, that is, in the version that is essentially a caching left-comer parser.</Paragraph>
    <Paragraph position="8">  The dog saw the cat s(s) dog(d), def(d), see(s), past(s),arg 1 (s, d), arg2(s, c), cat(c), def(c).</Paragraph>
  </Section>
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