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<Paper uid="J90-1002">
  <Title>AN INTERPRETATION OF NEGATION IN FEATURE STRUCTURE DESCRIPTIONS</Title>
  <Section position="8" start_page="0" end_page="0" type="concl">
    <SectionTitle>
6. CONCLUSIONS
</SectionTitle>
    <Paragraph position="0"> A logical formalism with a complete set of logical operators has come to be accepted as a means of describing feature structures. While the intended semantics of most of these operators is well understood, the negation and implication operators have raised some problems, leading to a variety of approaches in their interpretation.</Paragraph>
    <Paragraph position="1"> In Dawar and Vijay-Shanker 1989 and the present work, we introduced the framework of three-valued logic as a means of defining the semantics of a feature structure description language with negation. This framework permits us to say that a formula such as ~1:4~ does not have a truth value defined in a feature structure that does not have a feature l. This enables us to define an interpretation that, unlike the classical approach to negation, is monotonic, as a log\]\[c describing partial structures should be.</Paragraph>
    <Paragraph position="2"> We presented one particular interpretation of FDL within this three-valued framework and compared it with other apl:,roaches to defining the semantics of negation. We showed that several different such approaches could be cast in the three-valued framework. In particular, we showed that the special case of the Moshier-Rounds intuitionistic approach, in which forcing is always considered with respect to K* could be captured in our framework.</Paragraph>
    <Paragraph position="3"> One motivation cited by Moshier and Rounds for considering forcing sets other than K* was so that formulae of the form -~I:NIL could be considered satisfiable. The same reason led us to examine an augmented notion of feature structure models for FDL that yields an interpretation that is conceptually simple, motivated by the preservation of monotonicity, and is computationally no harder than the original Rounds-Kasper logic. We also showed that our interpretation meets the conditions set out by Pereira (1987) for a satisfactory interpretation of negation.</Paragraph>
  </Section>
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