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<Paper uid="E95-1023">
  <Title>Deterministic Consistency Checking of LP Constraints</Title>
  <Section position="2" start_page="0" end_page="165" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Within HPSG (Pollard and Sag, 1987) (Pollard and Sag, 1994) the constituent ordering principle given in (1) is intended to express the relation between the value of the PHON attribute and the DTRS attribute which contains the hierarchical structure of the derivation.</Paragraph>
    <Paragraph position="1">  However, it is not entirely clear how order_constituent is supposed to interpret various linear precedence statements such as LP1.</Paragraph>
    <Section position="1" start_page="0" end_page="165" type="sub_section">
      <SectionTitle>
1.1 Reape's approach
</SectionTitle>
      <Paragraph position="0"> The idea taken in Reape's approach (Reape, 1993) is to suggest that word-order is enforced between locally definable word order domains which are ordered sequences of constituents. Word order domains in Reape's approach are totally ordered sequences. A domain union operation as given in (3) is then employed to construct word order domains locally within a HPSG derivation step.</Paragraph>
      <Paragraph position="1">  (3) 0(,1, ,1, ,7).</Paragraph>
      <Paragraph position="2"> 0(o~,= o,~,= o oD ~ O(,,,,,,~,,,~).</Paragraph>
      <Paragraph position="3"> If A is the string &lt; a,b &gt; and B is the string &lt; c,d &gt;, their domain union C given by O(A,B,C) will produce all the sequences in which a precedes b and c precedes d i.e. the following sequences: &lt;a,b,c,d&gt; &lt;a,c,b,d&gt; &lt; a,c,d,b &gt; &lt; c,d,a,b &gt; &lt; c,d,a,b &gt; &lt; c,a,b,d &gt; However in this system to encode the property that {x, y, z} is a domain in which the ordering is arbitrary (i.e. free) then one needs the following disjunctive statements: &lt; x,y,z &gt; U &lt; x,z,y &gt; H &lt; y,x,z &gt; U &lt; y,z,x &gt; H &lt; z,x,y &gt; U &lt; z,y,x &gt;  It is simply not possible to be agnostic about the relative ordering of sequence elements within Reape's system.</Paragraph>
      <Paragraph position="4"> We identify two deficiencies in Reape's approach namely: * System is non-deterministic (generate and test paradigm) * Not possible to be agnostic about order This is so since domain union is a non-deterministic operation and secondly underspecification of ordering within elements of a domain is not permitted.</Paragraph>
      <Paragraph position="5"> In the following sections we describe a constraint language for specifying LP constraints that overcomes both these deficiencies. Additionally our constraint language provides a broad range of constraints for specifying linear precedence that go well beyond what is available within current typed feature formalisms. Our approach is in the spirit of Reape's approach but improves upon it. Furthermore, a sound, complete and terminating consistency checking procedure is described.  Our constraint solving rules axe deterministic and incremental. Hence these do not introduce costly choice-points. These constraint solving rules can be employed for building an efficient implementation. This is an important requirement for practical systems. Indeed we have successfully extended the ProFIT typed feature formalism (Erbach, 1995) with the constructs described in this paper.</Paragraph>
    </Section>
  </Section>
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