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<Paper uid="P90-1020">
  <Title>TYPES IN FUNCTIONAL UNIFICATION GRAMMARS</Title>
  <Section position="3" start_page="0" end_page="157" type="intro">
    <SectionTitle>
1 INTRODUCTION
</SectionTitle>
    <Paragraph position="0"> Unification-based formalisms are increasingly used in linguistic theories (Shieber, 1986) and computational linguistics. In particular, one type of unification formalism, functional unification grammar (FUG) is widely used for text generation (Kay, 1979, McKeown, 1985, Appelt, 1985, Paris, 1987, McKeown &amp; Elhadad, 1990) and is beginning to be used for parsing (Kay, 1985, Kasper, 1987). FUG enjoys such popularity mainly because it allies expressiveness with a simple economical formalism. It uses very few primitives, has a clean semantics (Pereira&amp;Shieber, 1984, Kasper &amp; Rounds, 1986, E1hadad, 1990), is monotonic, and grants equal status to function and structure in the descriptions.</Paragraph>
    <Paragraph position="1"> We have implemented a functional unifier (EIhadad, 1988) covering all the features described in (Kay, 1979) and (McKeown &amp; Paris, 1987). Having used this implementation extensively, we have found all these properties very useful, but we also have met with limitations. The functional unification (FU) formalism is not well suited for the expression of simple, yet very common, taxonomic relations. The traditional way to implement such relations in FUG is verbose, inefficient and unreadable. It is also impossible to express completeness constraints on descriptions.</Paragraph>
    <Paragraph position="2"> In this paper, we present several extensions to the FU formalism that address these limitations. These extensions are based on the formal semantics presented in (Elhadad, 1990). They have been implemented and tested on several applications.</Paragraph>
    <Paragraph position="3">  We first introduce the notion of typed features. R allows the definition of a structure over the primitive symbols used in the grammar. The unifier can take advantage of this structure in a manner similar to (Ait-Kaci, 1984). We then introduce the notion of typed constituents and the FSET construct. It allows the declaration of explicit constraints on the set of admissible paths in functional descriptions. Typing the primitive elements of the formalism and the constituents allows a more concise expression of grammars and better checking of the input descriptions. It also provides more readable and better documented grammars.</Paragraph>
    <Paragraph position="4"> Most work in computational linguistics using a unification-based formalism (e.g., (Sag &amp; Pollard, 1987, Uszkoreit, 1986, Karttunen, 1986, Kay, 1979, Kaplan &amp; Bresnan, 1982)) does not make use of explicit typing. In (Ait-Kaci, 1984), Ait-Kaci introduced V-terms, which are very similar to feature structures, and introduced the use of type inheritance in unification. W-terms were intended to be general-purpose programming constructs. We base our extension for typed features on this work but we also add the notion of typed constituents and the ability to express completeness constraints. We also integrate the idea of typing with the particulars of FUGs (notion of constituent, NONE, ANY and CSET constructs) and show the relevance of typing for linguistic applications.</Paragraph>
  </Section>
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