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<Paper uid="P94-1023">
  <Title>ON DETERMINING THE CONSISTENCY OF PARTIAL DESCRIPTIONS OF TREES</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
INTRODUCTION
</SectionTitle>
    <Paragraph position="0"> In Marcus, Hindle &amp; Fleck (1983), the authors proposed an approach to syntactic tree structures which took the primary structural relation to be remote dominance rather than immediate dominance. Recently, researchers have shown a revived interest in variants of Marcus et al.'s D-Theory, most likely due to the availability of approaches and techniques developed in the study of feature structures and their underlying logics. For example, both Rogers &amp; Vijay-Shanker (1992) and Cornell (1992) present formal treatments of many notions which Marcus et al. (1983) treated only informally and incompletely. Furthermore, work on the psycholinguistic implications of this approach has continued apace (Weinberg 1988; Gorrell 1991; Marcus &amp; Hindle 1990), making all the more necessary sustained foundational work in the theory of description-based tree-building applications (parsers, generators, etc.) This paper addresses one particular problem that arises in this approach to tree building. As with feature-structures, the essential operation here is the combination of two collections of partial information about the syntactic structure of an expression. It may happen that the two 1 Many thanks to Dick Oehrle, Ed Stabler, Drew Moshier and Mark 3ohnson for comments, discussion and encouragement. Theirs the gratitude, mine the fault.</Paragraph>
    <Paragraph position="1"> collections to be combined contain contradictory information. For example one might contain the assertion that &amp;quot;node 7 dominates node 12&amp;quot; while the other claims that &amp;quot;node 12 precedes node 7&amp;quot;. No tree structure can satisfy both these constraints. The operation of description combination is thus not simple set union, but, like unification, involves taking a least upper bound in a semi-lattice where lub's are not everywhere defined.</Paragraph>
    <Paragraph position="2"> Both Rogers &amp; Vijay-Shanker (1992) and Cornell (1992) propose to solve the D-Theoretic consistency problem by using essentially Tableau-based approaches. This can lead to combinatorial explosion in the face of disjunctions inherent in the theory of trees. But as it happens, proof techniques designed to handle general disjunctions are more powerful than we need; the disjunctions that arise from the theory of trees are of a restricted kind which can be handled by strictly polynomial means. We will see that we can efficiently handle richer notions of description than those in the &amp;quot;classical&amp;quot; D-Theory of Marcus, et al. (1983).</Paragraph>
  </Section>
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