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<Paper uid="C96-2149">
  <Title>Learning Lineal&amp;quot; Precedence Rules</Title>
  <Section position="4" start_page="0" end_page="883" type="intro">
    <SectionTitle>
2 hnmediate Dominance/Linear
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="0" end_page="883" type="sub_section">
      <SectionTitle>
Precedence Grammars
</SectionTitle>
      <Paragraph position="0"> A standard way of expressing tile ordering of nodes in a grammar is I)y means of l,inear Precedence rules in hnme(liate l)ominance/IAnear I','ocede,,ce. (ID/LI') ,~ra.,,,,ai's. The m/U' for:mat was first introduced by (Gazdar and Pullmn, 1981) and (Gazdar el.. al., 1985) and is usually associated with GPS(\], but is also used by IIPSG (l'ollard and Sag, 1987) and, under different guises, by other formMisins a.s well.</Paragraph>
      <Paragraph position="1"> In all ll)/I,P grammar, the two types of information, constituency (or, immediate dominance) and linear order, are separated. Thus, for instance, an immediate dominance rule, say, A--~I3 C D, with no linear Precedence rules declared, stands for the mother node A expanded into its siblings occurring in any order (six Context Free Grammar rules as result of the permutations). If l;he I,\[' rule D &lt; C is added, the ID rule can be expanded in the following three CFG rules: A---~ /3 D C; d--, D I/ C; d -+ D CB. ID/LP grammars capture an important ordering generalization, missed by usual CFGs, by means of the so calle(/ &amp;quot;l'3xhaustive Partial Ordering Constraint&amp;quot;, stating that the l)artial ordering of any two sister  nodes is constant throughout the whole grammar.</Paragraph>
      <Paragraph position="2"> That is, just one of the Mlowing three situations is valid for the ordering of any two nodes A and 11: either A &lt; B (A precedes B) or d &gt; B (A follows B) or A &lt;&gt; 11 (A occurs in either position with respect to B). (The last. &lt;&gt; situation is normally state(l in ll)/LI' grammars by ~lot stating an  LP rule, but we shall use it here, as we need an explicit ~hference to it.)</Paragraph>
    </Section>
  </Section>
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