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<Paper uid="C92-1035">
  <Title>CATEGORIAL SEMANTICS FOR LFG</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 Previous Work
</SectionTitle>
    <Paragraph position="0"> Most semantic analyses appeal to syntactic constraints on semantic derivations. In particular, many analyses assume that such syntactic constraints are statable in terms of phrase structure tree configurations (Montague, 1974). However, it is well-known that a variety of phrase structure configurations can express the same syntactic predicate-argunlent relations within and across languages (Kaplan and Bresnan, 1982); thus, syntactic constraints on semantic derivations are better expressed at a level at which the relevant syntactic information is expressed more uniformly. Such a level is the f-structure of LFG.</Paragraph>
    <Paragraph position="1"> Halvorsen (1983) first provided a theory of semantic interpretation for LFG in which semantic interpretation rules are related to the f-structure. His system involves an intermediate level of representation, the 'semantic structure', which is represented as a directed graph {like the f-structure). Translation rules map from f-structures to semantic structures, and these structures are then interpreted (or translated into a formula of intensional logic).</Paragraph>
    <Paragraph position="2"> The approach to be presented here also relies on f-structure configurations to provide syntactic constraints on categorial semantic derivations. However, an intermediate level of semantic representation such as Halvorsen's semantic structure is not introduced. In the categoriai semantic framework developed by Fernando Pereira (Pereira, 1990; Pereira and Pollack, 1991; Pereira, 1991), syntactic structures are directly associated with interpretations (or their types), and syntactic configurations license the combination of these interpretations in a semantic derivation. On this approach, 'logical forms' are not viewed as manipulable syntactic objects; instead, a logical formula is simply a graphical representation of a meaning that is lexically provided or that is the outcome of a semantically justified derivation. In this, the approach differs from other recent approaches to semantic interpretation in LFG (Halvorsen and Kaplan, 1988), in which the interpretation of an f-structure is represented as a directed graph, and semantic derivation proceeds principally by unification of semantic representations. As a consequence, these approaches require constraints on semantic derivations to be stated as well-formedness conditions on semantic representations, contrary to the commonly-held goal of dispensabihty of logical form.</Paragraph>
    <Paragraph position="3"> To illustrate a categorial semantic analysis within LFG, I will provide a small fragment of syntactic and semantic rules of English; the fragment contains rules for quantified noun phrases, nominal modification, and clauses headed by transitive and intransitive verbs. Many of these rules are modifications and extensions of rules originally described in Pereira (1990), though Pereira's system appeals to phrase structure configurations rather than f-structures to con-ACRES DE COLING-92. NANTES, 23-28 AOtff 1992 2 1 2 PROC. OF COLING-92, NANTES, AUG. 23-28. 1992 strain semantic derivations; in particular, the rules Pereira provides for quantifiers and relative clauses have direct counterparts in the set of rules to be described below.</Paragraph>
  </Section>
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