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<Paper uid="A92-1001">
  <Title>Deriving Database Queries from Logical Forms by Abductive Definition Expansion</Title>
  <Section position="4" start_page="1" end_page="2" type="intro">
    <SectionTitle>
2 Query Translation as Definition
Expansion
</SectionTitle>
    <Paragraph position="0"> The task which the CLARE database interface carries out is essentially that of translating a logical formula in which all predicates are taken from one set of symbols (word sense predicates) into a formula in which all predicates are taken from another set (database relations) and determining the assumptions under which the two formulae are equivalent. Since database relations are generally more specific than word senses, it will often be the case that the set of assumptions is non-empty.</Paragraph>
    <Paragraph position="1"> The same mechanism is used for translating both queries and assertions into database form; moreover, the declarative knowledge used is also compiled, using a different method, so as to permit generation of English from database assertions, though further description of this is beyond the scope of the paper.</Paragraph>
    <Paragraph position="2"> The main body of the declarative knowledge used is coded in a set of equivalential meaning postulates in which word sense predicates appear on one side and database relations appear on the other. (In fact, intermediate predicates, on the way to translating from linguistic predicates to database predicates may appear on either side.) The translation process then corresponds to abductive reasoning that views the meaning postulates as conditional definitions of the linguistic predicates in terms of database (or intermediate) predicates, the conditions being either discharged or taken as assumptions for a particular derivation. We will therefore refer to th~ translation process as 'definition expansion'.</Paragraph>
    <Paragraph position="3"> If the left-hand sides of equivalences needed to be arbi.</Paragraph>
    <Paragraph position="4"> trary formulas, the whole scheme would probably be impractical. However, experimentation with CLARE ha~ lead us to believe that this is not the case; sufficient expressive power is obtained by restricting them to be nc more complex than existentially quantified conjunction, of atomic formulas. Thus we will assume that equivalen.</Paragraph>
    <Paragraph position="5"> tim meaning postulates have the general form 1 (3yl, Y2,..--P1 A P2 A P3...) *--* P' (1' In the implementation these rules are written in a nota tion illustrated by the following example, exists ( \[Event\] ,</Paragraph>
    <Paragraph position="7"> in which work_onl and projectl are linguistic predi.</Paragraph>
    <Paragraph position="8"> cates and DB_PROJECT_MEMBER is a database relation (w( will adhere to the convention of capitalizing names ol database relations).</Paragraph>
    <Paragraph position="9"> The attractive aspect of this type of equivalence stem: from the fact that it can be given a sensible interpre. tation in terms of the procedural notion of &amp;quot;definitionexpansion&amp;quot;. Neglecting for the moment the existentia quantification, the intuitive idea is that is that (1) car be read as &amp;quot;P1 can be expanded to P' if it occurs ir a Quantification over the yl on the left-hand side will offer in practice be vacuous. In this and other formulas, we assum( implicit universal quantification over free variables.</Paragraph>
    <Paragraph position="10">  an environment where /)2 ^ P3... can be inferred&amp;quot;. The &amp;quot;environment&amp;quot; is provided by the other conjuncts occurring together with P1 in the original logical form, together with other meaning postulates and the contents of the database. This provides a framework in which arbitrary domain inference can play a direct role in justifying the validity of the translation of an LF into a particular database query.</Paragraph>
  </Section>
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