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<Paper uid="J89-3003">
  <Title>NON-SINGULAR CONCEPTS IN NATURAL LANGUAGE DISCOURSE</Title>
  <Section position="9" start_page="183" end_page="183" type="concl">
    <SectionTitle>
8 CONCLUSION
</SectionTitle>
    <Paragraph position="0"> We presented an approach to representing various kinds of non-singular concepts in natural language discourse. 13 The major observation of our theory is that 184 Computationan Linguistics, Volume 15, Number 3, September 1989 Tomek Strzalkowski and Nick Cercone reality, as perceived by an intelligent individual, can be regarded as a partially ordered structure of levels such that each level contains only those objects that are considered relatively singular. Observe that there are virtually no restrictions imposed upon the notion of relative singularity, so that the distribution of objects between levels of the world model may differ among different individuals. Non-singular objects, called superobjects, are placed at a number of higher levels, which are related to the current level with various coordinates. Conversely, a singular object may be decomposed along a coordinate, and new objects, so obtained, will be placed at some lower level. This same coordinate can be used then to obtain instances of other objects at this lower level, so that the relative singularity of objects within each level is maintained. This theory also contributes to a better understanding of discourse internal cohesion by introducing the notion of remote reference in text.</Paragraph>
    <Paragraph position="1"> We believe that our approach promotes computational tractability of some more difficult properties of natural language discourse. Among these, the notion of intension as formalized by Montague (1974a-d) has long been considered difficult for a practical realization, and a more tractable alternative has been sought ever since.</Paragraph>
    <Paragraph position="2"> Our theory of names and descriptions takes us a step in this direction, although an implementation or a formal complexity evaluation have yet to be attempted. Observe that with the concept of superobject and coordinate, we no longer have to identify general terms like &amp;quot;temperature,&amp;quot; &amp;quot;president,&amp;quot; or &amp;quot;water&amp;quot; with intensions, that is, functions over possible worlds. Superobjects are not some mysterious, extra-world entities, but they acquire a concrete status which makes them as comprehensible as ordinary objects. In a simplified account, our notion of coordinate can be loosely related to the possible world theory's concept of index. The coordinate is, however, far more selective than the index. In a particular discourse situation, we can pick up that aspect of intensionality of some concept that is, at present, relevant to our understanding of the discourse. Our freedom in selecting that or another coordinate is all important. Note also that structures of coordinates may vary considerably. For example, a pure time coordinate may consist of time points as well as consists of time periods, and time periods are of much greater significance in practice (examine &amp;quot;the president&amp;quot; example). Coordinates connote more than indices. They can be used to define a non-singular status of an object which is otherwise purely extensional (the examples of &amp;quot;water&amp;quot; from the last section). In this sense, the concept of non-singularity has a local, and often subjective, character.</Paragraph>
  </Section>
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