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<Paper uid="E93-1013">
  <Title>LFG Semantics via Constraints</Title>
  <Section position="6" start_page="103" end_page="103" type="concl">
    <SectionTitle>
6 Conclusion
</SectionTitle>
    <Paragraph position="0"> Our approach results in a somewhat different view of semantic composition, compared to h-calculus based approaches. First of all, notice that both in ~calculus based approaches and in our approach, there is not only a semantic level of meanings of utterances and phrases, but also a glue level or composition level responsible for assembling semantic level meanings of constituents to get a meaning for an entire utterance.</Paragraph>
    <Paragraph position="1"> In h-calculus based approaches, the semantic level is higher order intensional logic. The composition level is the rules, often not stated in any formal system, that say what pattern of applications to do to assemble the constituent meanings. The composition level relies on function application in the semantic level to assemble meanings. This forces some conflation of the levels, because it is using a semantic level operation, application, to carry out a composition level task. It requires functions at the semantic level whose primary purpose is to allow the composition level to combine meanings via application. For example, in order for the composition level to work right, the semantic level meaning of a transitive verb must be a function of two arguments, rather than a relation. This rather artificial requirement ~s a symptom of some of the work of the composition level being done at the semantic level.</Paragraph>
    <Paragraph position="2"> Our approach, on the other hand, better segregates the two levels of meaning, because the composition level uses its own mechanism (substitution) to assemble semantic level meanings, rather than relying on semantic level operations. Thus, the linear logic operations of the composition level don't appear at the semantic level and the classical operations of the semantic level don't appear at the composition level. 7 Our system also expresses the composition level rules in a formal system, first order linear logic. The composition rules are expressed by relations in the lexical entries and the mapping rules. There is no separate process of deciding how the meanings of lexical entries will be combined; the relations they establish, together with some background facts, just imply the high level meaning. All the necessary connections between phrases are made at the composition level when lexical entries are instantiated, through the shared variables of the sigma projections. From then on, logical inference at the composition level assembles the semantic level meaning.</Paragraph>
    <Paragraph position="3"> These examples illustrate the capability of our framework to handle the combination of predicates with their arguments, modification, and arityaffecting operations. The use of linear logic provides a simple treatment of the requirements of completeness and consistency and of complex predicates. Further, our deduction framework enables us to use linear logic to state such operations in a formally well-defined and tractable manner.</Paragraph>
    <Paragraph position="4"> In future work, we plan to explore more fully the semantics of modification, and to pursue the addition of a type system to the logic to treat quantifiers analogously to Pereira \[1990; 1991\].</Paragraph>
  </Section>
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