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<Paper uid="P96-1058">
  <Title>Maximizing Top-down Constraints for Unification-based Systems</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 Notation
</SectionTitle>
    <Paragraph position="0"> We use notation from the PATR-II formalism (Shieber, 1986) and (Shieber, 1992). Directed aeyclie graphs (dags) are adopted as the representation model. The symbol -&amp;quot; is used to represent the equality relation in the unification equations, and the symbol * used in the form of pl * p2 represents the path concatenation of pl and p2.</Paragraph>
    <Paragraph position="1"> The subsumption relation is defined as &amp;quot;Dag D subsumes dag D ~ if D is more general than D'.&amp;quot; The unification of D and D ~ is notated by D tJ D ~.</Paragraph>
    <Paragraph position="2"> The extraction function D/pl extracts the subdag under path pl for a given D, and the embedding function D \ pl injects D into the enclosing dag D' such that D'/pl = D. The filtering function p is similar to (Shieber, 1992): p(D) returns a copy of D in which some features may be removed. Note that in this paper .restrictor. specifies the features to be removed by p, whereas in (Shieber, 1985, 1992) restrictor specifies the features to be retained by restriction which is equivalent to p.</Paragraph>
  </Section>
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