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<Paper uid="P97-1050">
  <Title>Efficient Construction of Underspecified Semantics under Massive Ambiguity</Title>
  <Section position="3" start_page="386" end_page="387" type="intro">
    <SectionTitle>
2 The Problem
</SectionTitle>
    <Paragraph position="0"> As mentioned already, we aim at calculating from given parse forests the same compact semantic structures that have been proposed by (Schiehlen 96), i.e. structures that make explicit the common parts of different syntactic readings, so that subsequent semantic processes can use this generalised information. As he does, we assume a constraint-based grammar, e.g. a DCG (PereiraWarren 80) or HPSG (PollardSag 94) , in which syntactic constraints and constraints that determine a resulting semantic representation can be seperated and parsing can be performed using the syntactic constraints only.</Paragraph>
    <Paragraph position="1"> Second, we assume that the set of syntax trees can be compactly represented as a parse forest (cf. (Earley 70; BillotLang 89; Tomita 86)). Parse forests are rooted labeled directed acyclic graphs with AND-nodes (standing for context-free branch- null ing) and OR-nodes (standing for alternative subtrees), that call be characterised as follows (cf. Fig. 2 for an example).3  1. The terminal yield as well as the label of two AND-nodes are identical, if and only if they both are children of one OR-node.</Paragraph>
    <Paragraph position="2"> 2. Every tree reading is .a valid parse tree.</Paragraph>
    <Paragraph position="3">  Tree readings of such graphs are obtained by replacing any OR-node by one of its children. Parse forests can represent an exponential number of phrase structure alternatives in o(n 3) space, where n is the length of the sentence. The example uses the 3 OR-nodes (A, B, C) and the AND-nodes 1 through 32 to represent 5 complete parse trees, that would use 5 x 19 nodes.</Paragraph>
    <Paragraph position="4"> Third, we assume the rule-to-rule hypothesis, i.e.,  surroux~ding its children, i.e. the AND-OR-graph structure of ~ is o~.</Paragraph>
  </Section>
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