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<Paper uid="P94-1035">
  <Title>An Attributive Logic of Set Descriptions Set Operations</Title>
  <Section position="12" start_page="260" end_page="261" type="concl">
    <SectionTitle>
8 Summary and Conclusions
</SectionTitle>
    <Paragraph position="0"> In this paper we have provided an extended feature logic (excluding disjunctions and negations) with a range of constraints involving set descriptions. These constraints are set descriptions, fixed cardinality &amp;quot;set descriptions, set-membership constraints, restricted universal role quantifications, set union, set intersection, subset and disjointness. We have given a model theoretic semantics to our extended logic which shows that a simple and elegant formalisation of set descriptions is possible if we add relational attributes to our logic as opposed to just functional attributes available in feature logic.</Paragraph>
    <Paragraph position="1"> For realistic implementation of the logic described in this paper, further investigation is needed to develop concrete algorithms that are reasonably efficient in the average case. The consistency checking procedure described in this paper abstracts away from algorithmic considerations and clearly modest improvements to the basic algorithm suggested in this paper are feasible.</Paragraph>
    <Paragraph position="2"> However, a report on such improvements is beyond the scope of this paper.</Paragraph>
    <Paragraph position="3"> For applications within constraint based grammar formalisms such as HPSG, minimally a type system \[Carpenter, 1992\] and/or a Horn-like extension \[HShfeld and Smolka, 1988\] will be necessary.</Paragraph>
    <Paragraph position="4"> We believe that the logic described in this paper provides both a better picture of the formal aspects of  current constraint based grammar formalisms which employ set descriptions and at the same time gives a basis for building knowledge representation tools in order to support grammar development within these formalisms.</Paragraph>
  </Section>
class="xml-element"></Paper>