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<Paper uid="P86-1038">
  <Title>A LOGICAL SEMANTICS FOR FEATURE STRUCTURES</Title>
  <Section position="3" start_page="0" end_page="257" type="intro">
    <SectionTitle>
2 Disjunction and
Non-Local Values
</SectionTitle>
    <Paragraph position="0"> Karttunen \[5\] has shown that disjunction and negation are desirable extensions to PATR-II which are motivated by a wide range of linguistic  phenomena. He discusses specifying attributes by disjunctive values, as shown in Figure 1. A ~alue disjuactioa specifies alternative values of a single attribute. These alternative values may be either atomic or complex. Disjunction of a more general kind is an essential element of FUG. Geaera/ disjunction is used to specify alternative groups of multiple attributes, as shown in Figure 2.</Paragraph>
    <Paragraph position="1"> Karttunen describes a method by which the basic unification procedure can be extended to handle negative and disjunctive values, and explains some of the complications that result from introducing value disjunction. When two values, A and B, are to be unified, and A is a disjunction, we cannot actually unify B with both alternatives of A, because one of the alternatives may become incompatible with B through later unifications.</Paragraph>
    <Paragraph position="2"> Instead we need to remember .a constraint that at least one of the alternatives of A must remain compatible with B.</Paragraph>
    <Paragraph position="3"> An additional complication arises when one of the alternatives of a disjunction contains a value which is specified by a non-local path, a situation which occurs frequently in Functional Unification Grammar. In Figure 2 the obj attribute in the description of the adjunct attribute is given the value &lt; actor &gt;, which means that the obj attribute is to be unified with the value found at the end of the path labeled by &lt; actor &gt; in the outermost enclosing structure. This unification with a non-local value can be performed only when the alternative which Contains it is the only alternative remaining in the disjunction. Otherwise, the case = objective attribute might be added to the value of &lt; actor &gt; prematurely, when the alternative containing adjunct is not used. Thus, the constraints on alternatives of a disjunction must also apply to any non-local values contained within those alternatives. These complications, and the resulting proliferation of constraints, provide a practical motivation for the logical treatment given in this paper. We suggest a solution to the problem of representing non-local path values in Section 5.4.</Paragraph>
  </Section>
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