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<Paper uid="E89-1024">
  <Title>Expressing generalizations in unification-based grammar formalisms *</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Since Kay's seminal work (Kay 1979), the utility of unification as a general tool in computational linguistics has gained widespread recognition. One major point on which the methodology of unification grammars differs radically from that assumed by linguistic theories lies in the way they deal with generalizations that hold over the domain of description. In unification-based theories, such generalizations are typically implicit, or extremely limited in their import. The reasons for this are easy to pinpoint. First, in such theories one has to be explicit about the feature structures that the grammar manipulates, and these structures have to be described more or less directly. In PATR-II for example (Shieber et al 1983) the only means of expressing a generalization is via the notion of template, a structure which merely represents recurring information--i.e, information that *The work reported here was carried out ae part of ES-PRIT project P393 ACORD. A longer version of this paper can be found in Calder et a! (1988a).</Paragraph>
    <Paragraph position="1"> recurs in different lexical items, combination rules, lexical rules or other templates. A second reason why unification-based theories do not lend themselves easily to the expression of general statements is that there is no explicit quantification in unification formalisms. In fact, every statement in these formalisms represents a simple existential constraint, never a universal generalization.</Paragraph>
    <Paragraph position="2"> The work reported here is an attempt to introduce higher levels of organization into unification grammars. The notions we employ to do this come from sorted logics and from strong data typing in programming language theory. We will show that the typing of grammatical objects offers a way of stating structural constraints on, or equivalently universal properties of, the objects that constitute the grammar.</Paragraph>
    <Paragraph position="3"> The grammatical framework in which these ideas have been implemented is Uaificatioa Categorial Grammar (UCG) and its semantic representation language InL, both developed as part of the ESPRIT-funded project ACORD. Introductions to UCG and InL can be found in Calder et al (1988b) and Zeevat (1988). For present purposes it is sufficient to note that UCG uses a sorted logic which requires being able to express complex constraints over clusters of features. While there is no real distinction between this technique and that of data typing mentioned above, we will nevertheless continue to use the term typing only to refer to constraints on the global structure of an object and reserve the term sort to refer to constraints that hold of a variable in InL.</Paragraph>
    <Paragraph position="4"> In the following sections, we will first discuss our strategy of using global declarations to limit possible linguistic structures. We will briefly describe some of the type declarations currently implemented in UCG and discuss the unusual aspects of our type-checking algorithm. We will also infor- null mally describe the InL sort system and will show how the ability to express global constraints on the sort lattice is both perspicuous and expressively powerful. Detailed discussion of the underlying formal theory and the implementation can be found in Calder et al (1988a) and will not be attempted here.</Paragraph>
    <Paragraph position="5"> Next, we will demonstrate the usefulness of the sort system by describing ucG's adjunct resolution system, the declarative semantics of which depends crucially on our use of a logic of sorts. This treatment allows the grammar writer to write and add adjunct resolution conditions using the same notation as that used to express sort descriptions in the grammar and without having to modify any implementation code.</Paragraph>
  </Section>
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