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<Paper uid="C88-2151">
  <Title>Using Constraints in a Constructive Version of GPSG</Title>
  <Section position="7" start_page="742" end_page="742" type="concl">
    <SectionTitle>
4 Conclusion
</SectionTitle>
    <Paragraph position="0"> With this method of constraint computation, evaluation and propagation,&amp;quot; a new definition of the admissibility of trees is necessary.</Paragraph>
    <Paragraph position="1"> Definition: admissibility of trees A tree is adndssible iff all of its local trees are admissible and the evaluations 'eval fcr' and 'eval lp' of constraints of theroot category are defined and both are the empty set {}. A local tree t is admissible iff it is a projection of a lexical rule or iff it - is a projection of an ID rule with the FCR constraint (C~, APP(0)) on the mother C/~ and - satisfies all of the FlPs and - is LP-consistent with the LP constraints LPc(i,j) on all daughters C\[ and ~ which ,are propagated to the mother where 1 _&lt; i &lt; j &lt; n and - the evaluation 'eval_fcr(FCRc(i))' of every daughter C\[ isdefined where 1 ~ i &lt; n and their results are propagated to the mother and - the evaluation 'eval_lp(LPc(i))' of every daughter C i is defined where 1 ~ i ~ n and their results are propagated to the mother. The consequence for the root category R of an entire tree of one input string of a natural language will be the fact that all features fi of R, where ~spec(R(fi)), and where fl is needed for the evaluation of the constraints of the tree, have to be instantiated according to their domain D(fi) because such a tree represents a class of ambiguous solutions. After that the constraints on every tree of this class are evaluated and only the trees where FCRc(0 ) and LPc(0 ) are defined and their evaluation is { } are admissible.</Paragraph>
  </Section>
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