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<Paper uid="P88-1029">
  <Title>Conditional Descriptions in Functional Unification Grammar</Title>
  <Section position="4" start_page="236" end_page="237" type="metho">
    <SectionTitle>
3 Unification with Conditional
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="236" end_page="237" type="sub_section">
      <SectionTitle>
Descriptions
</SectionTitle>
      <Paragraph position="0"> The unification operation, which is commonly used to cornblue feature structures (i.e., non-disjunctive, non-conditional DGs), can be generalised to define an operation for combLuLug the information of two feature descriptions (i.e., formulas of FDL). In FDL, the unification of two descriptions is equivalent to their logical conjunction, as discussed in \[Kas87b\]. We  have shown in previous work \[Kas87c\] how unification can be accomplished for disjunctive descriptions without expanding to disjunctive normal form.</Paragraph>
      <Paragraph position="1"> This unification method factors descriptions into a canonical form conslstlng of definite and indefinite components. The definite component contains no dlsjunctlon, and is represented by a DG structure that satisfies all non-disjunctive parts of a description. The indefinite component of a description k a list of disjunctions. When two descriptions are unified, the first step is to unlfy their definite components. Then the indefinite components of each description are checked for compatlbility with the resulting definite component. Dlsjuncts are eliminated from the description when they are inconsistent with deflnlte information. When only one alternative of a disjunction remains, it is unified with the definite component of the description.</Paragraph>
      <Paragraph position="2"> This section details how thls unification method can be extended to handle conditional descriptions. Conditionals may be regarded as another type of indefinite information in the description of a feature structure. They are indefinite \]n the sense that they impose constraints that can be satisfied by several alternatives, depending on the values of features already present in a structure.</Paragraph>
    </Section>
    <Section position="2" start_page="237" end_page="237" type="sub_section">
      <SectionTitle>
3.1 How to Satisfy a Conditional
Description
</SectionTitle>
      <Paragraph position="0"> The constraints imposed on a feature structure by a conditional description can usually be determined most emclently by first examining the antecedent of the conditional, because it generally cont~nl a smaller amount of information than the consequent. F, xamining the antecedent k often sufficient to determine whether the consequent is to be included or discarded.</Paragraph>
      <Paragraph position="1"> Given a conditional description, C ---- ~ -+ ~, we can define the coustralnts that it imposes on a feature structure (A) as follows. When: ~ ct, then A ~ ~;6 ~ or, then C/ imposes no further constraint on A, and can therefore be elhnJnated; A ~, c~, then check whether ~ ls compatible wlth A.</Paragraph>
      <Paragraph position="2"> If compatible, then C must be retained in the description of ~.</Paragraph>
      <Paragraph position="3"> If incompatible, then ~ ~ -~a (and C/ can be elimio nated).</Paragraph>
      <Paragraph position="4"> These constraints follow directly from the interpretation (4) that we have given for conditional descriptions. These constraiuts are logically equivalent to those that would be imposed on A by the disjunction -~ V ~, as required. However, the constraints of the conditional can often be imposed more ef~ciently than those of the equivalent dJsjunctlon, because examlnlng the antecedent of the conditional carries the same cost as examining only one of the dkjuncts. When the constraints of a disjunction are imposed, both of the disjuncts must be examined in all cases.</Paragraph>
    </Section>
    <Section position="3" start_page="237" end_page="237" type="sub_section">
      <SectionTitle>
3.2 Extending the Unification
Algorithm
</SectionTitle>
      <Paragraph position="0"> The unification algorithm for dlsjunctlve feature descriptions \[Kas87c\] can be extended to handle conditionals by recognizing two types of indefinite ~uformatlon in a description: disjunctions and conditionals. The extended featuredescriptlon data structure has the components: definite: a DG structure; disjunctions: a llst of disjunctions; conditionals, a list of conditional descriptions.</Paragraph>
      <Paragraph position="1"> The part of the unification algorithm that checks the compatibility of indefinite components of a description with its definite component is defined by the function CHECK-INDEF, shown in Figure 8. Thk algorithm checks the disjunctions of a description before conditionals, but an equally correct version of thk algorithm might check conditionals before disjunctions. In our application of parsing with a systemic grammar it is generally more et~cient to check disjunctions first, but * other applications might be made more efBclent by varylng this order.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="237" end_page="238" type="metho">
    <SectionTitle>
4 Potential Refinements
</SectionTitle>
    <Paragraph position="0"> Several topics merit further investlgatlon regarding conditional descrlptions. The implementation we describe has the constraints of conditionals and dkjunctions imposed in an arbitrary order. Chang|ng the order has no effect on the final result, but it is likely that the el~clency of unification could be improved by ordering the conditionals of a grammar in a deliberate way. Another way to improve the efficiency of unification with condltiona~ would involve indexing them by the features that they contain. Then a conditional would not need to be checked against a structure until some feature value of the structure might determine the manner in which it k eat|s fled. The amount of efficiency gained by such techniques clearly depends largely on the nature of the particular grammar being used in an appllcatlon.</Paragraph>
    <Paragraph position="1"> A slightly different type of conditional might be used as a way to speed up unification with binary disjunctive descriptions. If it k known that the values of a relatively small number of features can be used to discrimlnate between two alternative descriptions, then those features can be factored into a separate condition in a description such as IF cor, ditioa THEN alt~ ELSE air2.</Paragraph>
    <Paragraph position="2"> When the condition is satisfied by a structure, then altl is selected. When the condition is incompatible with a structure, then air2 is selected. Otherwise both alternatives must remain under consideration. As it often requires a considerable amount of time to check which alternatives of a dkjunction are applicable, this technlque might offer a significant improvement in an application where large dlsjunctlve descriptions are used.</Paragraph>
    <Paragraph position="3"> Remember that we have restricted conditionals by requiring that their antecedents do not contain path equivalences.  definite component.</Paragraph>
    <Paragraph position="4"> This restriction has been acceptable in our use of conditional descriptions to model systemic grammars. It k unclear whether a treatment of conditional descriptions without thls restriction will be needed in other applications. If this restriction is lifted, then further work will be necessary to define the behavior of negation over path equivalences, and to handle such negations in a reasonably e~cient manner.</Paragraph>
  </Section>
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