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<Paper uid="J90-1002">
  <Title>AN INTERPRETATION OF NEGATION IN FEATURE STRUCTURE DESCRIPTIONS</Title>
  <Section position="9" start_page="0" end_page="0" type="ackno">
    <SectionTitle>
NOTES
</SectionTitle>
    <Paragraph position="0"> In the original Rounds-Kasper formulation, the output function is not required to be total. This is because every terminal node in the transition graph is considered to be a final state. However, since the notion of finality of a state is not crucial to the formalism, we have chosen this equivalent alternative for presentation.</Paragraph>
    <Paragraph position="1">  2. Strictly speaking, we should be taking the least upper bound in the ordering on equivalence classes of automata under isomorphism.</Paragraph>
    <Paragraph position="2"> 3. See Section 3.3.3.</Paragraph>
    <Paragraph position="3"> 4. A similar notion was used by Kasper (1988a), who introduces the notion of compatibility. We shall compare this approach with ours in greater detail in Section 3.3.3.</Paragraph>
    <Paragraph position="4"> 5. In this paper we will not consider cyclic feature structures. 6. And therefore it satisfies the formula ---~.</Paragraph>
    <Paragraph position="5"> 7. Equality here is strong equality (i.e. if I(~, (Aft) is undefined then so is I(l:~, A)).</Paragraph>
    <Paragraph position="6"> 8. Two automata are not unifiable if and only if they do not have a least upper bound.</Paragraph>
    <Paragraph position="7"> 9. Langholm (1989) has defined a similar notion of negatively extended  feature structures. We will take up a comparison of his approach with ours later in this section.</Paragraph>
    <Paragraph position="8"> 10. Up to isomorphism.</Paragraph>
    <Paragraph position="9"> 11. We are implicitly assuming that the sets of atoms and labels are both infinite. If this is not the case, the definition of closure of a set of labeled signed formulae and this construction can be suitably modified. null</Paragraph>
  </Section>
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