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<Paper uid="J81-3001">
  <Title>Roles, Co-Descriptors, and the Formal Representation of Quantified English Expressions</Title>
  <Section position="4" start_page="0" end_page="0" type="intro">
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3 Role-in links could be viewed logically as Skolem dependen-
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    <Paragraph position="2"> However, there is an important difference in the semantic interpretation: may-be-described-as links are interpreted as relating intensions expressed by generic nodes, whereas subset relations operate on sets of 138 American Journal of Computational Linguistics, Volume 7, Number 3, July-September 1981 William A. Martin Roles, Co-Descriptors, and the Formal Representation of Quantified English Expressions individuals. I consider the intension/extension distinction extremely important, because intensional representations appear to be more natural for certain sentenees. 5 My representation does not deal with contextual problems by assuming a set of objects called contexts (or partitions) and then somehow stipulating a context link for each node. Instead, I argue that roles allow a more natural modeling of the context phenomena. For example, Figure 2 shows how Hendrix \[10\] represents the fact that legal persons can own physical objects.</Paragraph>
    <Paragraph position="3"> Rectangles (and squares) represent partitions (contexts). An individual or set is in a partition if its representing circle is in the rectangle representing that partition. In this figure, the individual I is an implication that any individual owning X has an individual agent Y, which is a legal person; an individual object Z, which is a physical object; an individual start-time t 1, which is a time; and an individual end-time t 2, which is also a time.</Paragraph>
    <Paragraph position="4"> This same information is shown in Figure 3, using the notation presented here. Figure 3 eliminates the individuals I and X, the implication node, the context surrounding I, and the context surrounding Y, Z, t 1, and t 2. Some of these are replaced in Figure 3 with a richer variety of node types; I believe these types have better linguistic and philosophical motivations than Hendrix's abstract individuals, contexts, and implications. null</Paragraph>
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