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<Paper uid="P99-1013">
  <Title>Compositional Semantics for Linguistic Formalisms</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
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    <Paragraph position="0"> Developing large scale grammars for natural languages is a complicated task, and the problems grammar engineers face when designing broad-coverage grammars are reminiscent of those tackled by software engineering (Erbach and Uszkoreit, 1990). Viewing contemporary linguistic formalisms as very high level declarative programming languages, a grammar for a natural language can be viewed as a program.</Paragraph>
    <Paragraph position="1"> It is therefore possible to adapt methods and techniques of software engineering to the domain of natural language formalisms. We believe that any advances in grammar engineering must be preceded by a more theoretical work, concentrating on the semantics of grammars.</Paragraph>
    <Paragraph position="2"> This view reflects the situation in logic programming, where developments in alternative definitions for predicate logic semantics led to implementations of various program composition operators (Bugliesi et al., 1994).</Paragraph>
    <Paragraph position="3"> This paper suggests a denotational semantics tbr unification-based linguistic formalisms and shows that it is compositional and fully*I am grateful to Nissim Francez for commenting on an em'lier version of this paper. This work was supported by an IRCS Fellowship and NSF grant SBR 8920230.</Paragraph>
    <Paragraph position="4"> abstract. This facilitates a clear, mathematically sound way for defining grammar modularity. While most of the results we report on are probably not surprising, we believe that it is important to derive them directly for linguistic formalisms for two reasons. First, practitioners of linguistic formMisms usually do not view them as instances of a general logic programming framework, but rather as first-class programming environments which deserve independent study. Second, there are some crucial differences between contemporary linguistic formalisms and, say, Prolog: the basic elements -- typed feature-structures -- are more general than first-order terms, the notion of unification is different, and computations amount to parsing, rather than SLD-resolution. The fact that we can derive similar results in this new domain is encouraging, and should not be considered trivial.</Paragraph>
    <Paragraph position="5"> Analogously to logic programming languages, the denotation of grammars can be defined using various techniques. We review alternative approaches, operational and denotational, to the semantics of linguistic formalisms in section 2 and show that they are &amp;quot;too crude&amp;quot; to support grammar composition. Section 3 presents an alternative semantics, shown to be compositional (with respect to grammar union, a simple syntactic combination operation on grammars). However, this definition is &amp;quot;too fine&amp;quot;: in section 4 we present an adequate, compositional and fully-abstract semantics for linguistic formalisms. For lack of space, some proofs are omitted; an extended version is available as a technical report (Wintner, 1999).</Paragraph>
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