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<Paper uid="E95-1006">
  <Title>A Specification Language for Lexical Functional Grammars</Title>
  <Section position="2" start_page="0" end_page="39" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Unlike most linguistic theories, LFG (see Kaplan and Bresnan (1982)) treats grammatical relations as first class citizens. Accordingly, it casts its linguistic analyses in terms of a composite ontology: two independent domains -- a domain of constituency information (c-structure), and a domain of grammatical function information (f-structure) -linked together in a mutually constraining manner. As has been amply demonstrated over the last fifteen years, this view permits perspicuous analyses of a wide variety of linguistic data.</Paragraph>
    <Paragraph position="1"> However standard formalisations of LFG do not capture its strikingly simple underlying intuitions.</Paragraph>
    <Paragraph position="2"> Instead, they make a detour via the LFG construction algorithm, which explains how equational constraints linking subtrees and feature str.uctures are to be resolved. The main point of the present paper is to show that such detours are unnecessary. We define a specification language PS in which (most of) the interactions between cand f-structure typical of LFG grammars can be stated directly.</Paragraph>
    <Paragraph position="3"> The key idea underlying our approach is to think about LFG model theoretically. That is, our first task will be to give a precise -- and transparent -- mathematical picture of the LFG ontology. As has already been noted, the basic entities underlying the LFG analyses are composite structures consisting of a finite tree, a finite feature structure, and a function that links the two.</Paragraph>
    <Paragraph position="4"> Such structures can straightforwardly be thought of as models, in the usual sense of first order model theory (see Hodges (1993)). Viewing the LFG ontology in such terms does no violence to intuition: indeed, as we shall see, a more direct mathematical embodiment of the LFG universe can hardly be imagined.</Paragraph>
    <Paragraph position="5"> Once the ontological issues have been settled we turn to our ultimate goal: providing a specification language for LFG grammars. Actually, with the ontological issues settled it is a relatively simple task to devise suitable specification languages: we simply consider how LFG linguists talk about such structures when they write grammars. That is, we ask ourselves what kind of constraints the linguist wishes to impose, and then devise a language in which they can be stated.</Paragraph>
    <Paragraph position="6"> Thus we shall proceed as follows. After a brief introduction to LFG, 1 we isolate a class of models which obviously mirrors the composite nature of the LFG ontology, and then turn to the task of devising a language for talking about them. We opt for a particularly simple specification language: a propositional language enriched with operators for talking about c- and f-structures, together with a path equality construct for enforcing synchronisation between the two domains. We illustrate its use by showing how to capture the effect of schemata annotated rules, and the LFG uniqueness, completeness and coherence principles.</Paragraph>
    <Paragraph position="7"> Before proceeding, a word of motivation is in order. Firstly, we believe that there are practical reasons for interest in grammatical specification languages: formal specification seems important (perhaps essential) if robust large scale grammars are to be defined and maintained. Moreover, the essentially model theoretic slant on specification we propose here seems particularly well suited to this aim. Models do not in any sense &amp;quot;code&amp;quot; the LFG ontology: they take it pretty much at face value. In our view this is crucial. Formal approaches 1This paper is based upon the originM formulation of LFG, that of Kaplan and Bresnan (1982), and will not discuss such later innovations as functional uncertainty.</Paragraph>
    <Paragraph position="8">  to grammatical theorising should reflect linguistic intuitions as directly as possible, otherwise they run the risk of being an obstacle, not an aid, to grammar development.</Paragraph>
    <Paragraph position="9"> The approach also raises theoretical issues. The model theoretic approach to specification languages forces one to think about linguistic ontologies in a systematic way, and to locate them in a well understood mathematical space. This has at least two advantages. Firstly, it offers the prospect of meaningful comparison of linguistic frameworks.</Paragraph>
    <Paragraph position="10"> Secondly, it can highlight anomalous aspects of a given system. For example, as we shall later see, there seems to be no reasonable way to deal with LFG's --c definitions using the simple models of the present paper. There is a plausible model theoretic strategy strategy for extending our account to cover =c; but the nature of the required extension clearly shows that =c is of a quite different character to the bulk of LFG. We discuss the matter in the paper's concluding section.</Paragraph>
  </Section>
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