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<Paper uid="C88-1018">
  <Title>Unification Categorial Grammar: A Concise, Extendable Gragamar for Natural Language Processing</Title>
  <Section position="2" start_page="0" end_page="83" type="metho">
    <SectionTitle>
2. The Mechanisms of UCt;
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="0" end_page="83" type="sub_section">
      <SectionTitle>
2.1. Structuring Signs
</SectionTitle>
      <Paragraph position="0"> UCG signs have three basic components, corresponding to their&amp;quot; phonology, category and semantics. We will write the most unspecified sign as follows: (2) w: c: s by which we intend a sign with phonology W, categow C and semantics S. (1) and (2) give well-formedness conditions on possible instantiations for a sign's category. For the present papm', we will assume that a sign's phonology may be simply its orthography in tire case of proper names, otherwise a sign's phonology may be composite, consistiug of variables and orthographic constants sep~ated by +. The + operator is understood as denoting concatenation. 2 2 This operation might apt)ear to take us beyond tile bounds of firsto~ler unification. However in the cases we will deal with, there are equivalent signs which express concatenation by means of PROI.OG difference lists.</Paragraph>
    </Section>
    <Section position="2" start_page="83" end_page="83" type="sub_section">
      <SectionTitle>
2.2. Indexed Language
</SectionTitle>
      <Paragraph position="0"> The semantic representation language that we use to encode the semantics of a sign is called InL (for Indexed Language), and is derived from Discourse Representation Theory (cf. Kamp 1981), supplemented with a Davidsonian treatment of verb semantics (cf. Davidson 1967). The main similarity with the Discourse Representation languages lies in tile algebraic structure of InL.</Paragraph>
      <Paragraph position="1"> There are only two connectives for building complex formulas; an implication that at the same time introduces universal quantification, and a conjunction.</Paragraph>
      <Paragraph position="2"> The language InL differs in one important respect from the DRT formalism, and thus earns its name; every formula introduces a designated variable called its index. This does not mean that (sub)formulas may not introduce other variables, only that the index has a special status. The postulation of indices is crucial for the treatment of modifying expressions, but it is independently plausible on other grounds. Every sign has an associated ontological type, represented by the sort of its index. Subsumption relations hold between certain sorts; for instance, a index of sort singular will unify with an index of sort object to yield an index of sort singular. For notational purposes, we use lower case alphabetics to represent sorted variables in InL formulas.</Paragraph>
      <Paragraph position="3"> Upper case alphabetics are variables over formttlas. The index of an expression appears within square brackets in prenex position.</Paragraph>
      <Paragraph position="4">  (3) gives example translations of some expxessions.</Paragraph>
      <Paragraph position="5"> (3) \[Index\] Formula Expression Sort a. \[el WALK(e, x) walk event b. Ix\] STUDENT(x) student singular object c. \[x\] \[PARK(y),\[x\] \[IN(x,y),MAN(x)\[I man in a park singular object d. \[m\] BUTlER(m) butter mass object e. \[s\] STAY(s, x) stay state 3. UCG Binary Rules  We may write UCG rules as simple relations between signs. We require two rules, our analogs of forwards and backwards application (FA and BA respectively). Here we follow the PROLOG convention that variables srart with an upper case alphabetic.  TheSe rules state that in the case of function application, the resulting category is simply that of the functor with its active sign removed; the semantics and phonology of the result are those of the functor, thus effecting a very strict kind of Head Feature Convention. Note in particular that we view the phonological, syntactic and semantic functor as always coinciding. This has important consequences for the way we treat quantified NP's, as we discuss in the next section. Any of the features of the resulting sign may have been further instantiated in the process of unification.</Paragraph>
      <Paragraph position="6"> Importantly, (4) states that a functor may place restrictions on any of the dimensions of its argument. Likewise it will determine the role that the information expressed by its argument plays in the resulting expression. A UCG sign thus represents a complex of constraints along several dimensions.</Paragraph>
    </Section>
  </Section>
  <Section position="3" start_page="83" end_page="84" type="metho">
    <SectionTitle>
4. 1JCG Signs
</SectionTitle>
    <Paragraph position="0"> We now give some example UCG signs.</Paragraph>
    <Paragraph position="1">  4.1. Nouns and Adjectives (5) student: noun: \[x\]STUDENT(x) (6) cheerful+W: noun/(W:noun: Ix\]P):</Paragraph>
    <Paragraph position="3"> The reader is invited to work out for herself how the signs (5) and (6) will combine using the rule of forwards application.</Paragraph>
    <Section position="1" start_page="83" end_page="84" type="sub_section">
      <SectionTitle>
4.2. Determiners
</SectionTitle>
      <Paragraph position="0"> Following Montague 1973, we treat quantified NPs as type-raised terms. We can however take advantage of the polymorphic nature of UCG categories and have a single representation for NPs regardless of their syntactic context. In our analysis, the determiner introduces the type raising. This is the sign that  corresponds to a.</Paragraph>
      <Paragraph position="1"> (7) W (C/(W:C/a+Wl: np\[nom or obj\]:b):\[a\]S)/(Wl:noun:\[b\]R): \[a\]\[\[blR, S\] More verbosely, this says that a combines first with a noun which has phonology W1 and semantic index b. The semantics that results from such a combination is a conjunction, the first conjunct of which is the semantics of the noun. The second conjunct is the semantics of the resulting NP's argument. As the NP is type-raised, it has a category of the schematic form: (8) C/(C/np) That is, a type-raised NP will take as its argument some constituent which was itself to combine with a (non-type-raised) NP. When fleshed out with values for the other components of a sign, it will have the form as shown in (9). Note in particular that, as it is the verb that determines linear order, the phonology of the resulting expression depends on that of the argument to the NP. (9) shows the result of combining (7) and (5) via forward application. null (9) W C/(W:C/a+student: rip\[nora or obj\]:b):\[a\]S: \[al\[\[blSTUDENT(b), Sl  The sign corresponding to every (10) is very similar to that for a, the major difference being that every introduces DRT implication, notated here with ~.</Paragraph>
      <Paragraph position="2">  We have already seen one category of modifiers, namely adjectives, in section 4.1. We are able to make more general statements about modifiers; they all contain instances of the category</Paragraph>
      <Paragraph position="4"> Appropriate msldctions on C wilt allow us to describe, for instance, the class of VP modifiers such as adverbials and auxiliaries (Cf. Bouma 1988). The close relationship between syntax and semantic,,; allow us to give concise formulations of the distinctions between intersective, vague and intensional modifiers (Kamp 1975). In the first two cases, the semantics of the modified expression is conjoined with that of the modifying expression. In the vague case, we have to relativize the meaning of the modifying expression to that of the modified. In the third case, the semantics of the modified expression must be contained within the scope of an intensional predicate. The following examples illustrate the three cases.</Paragraph>
      <Paragraph position="5">  We have not attempted to give a fully representative list of UCG signs here. Elsewhere (Calder, Morns and Zeewtt 1986, Zeevat, Klein and Calder 1987), substantial analyses of subcategorization, prepositional and adverbial modification, negation, relative clauses and sentential .connectives have been developed. We have also extended the theory to encompass non-canonical word order, using ;t mechanism similm&amp;quot; to the GPSG SLASH (Gazdar et al. 1985), and to handle quantificational constraints on anaphora following the analysis of Johnson and Klein 1986. We have an eftie:ient implementation of the system which represents signs as PROIOG terms, using a different treatment of phonological informalion. The use of templates (Shieber et al. 1983) allows us to capture generaliztions about clases of lexical items. The compilalion of UCG structures into PROLOG temas is petformed by a general processor driven by the definitions of well-formedness of the dimensions of a sign, allowing compile-time typeocbecking of grammars (Calder, Moens and Zeevat 1986).</Paragraph>
      <Paragraph position="6"> The system u:;es a tabular shift-reduce parser.</Paragraph>
      <Paragraph position="7"> 7. Further 6evelopments of UCG The system described above is deficient in some respects. For example, requiring coincidence between the phonological, syntactic and semantic funetors may be too strict. The problem of quantifier scoping is a case in point. Zeevat 1987 suggests relaxing this requirement to allow linear ordering to become the dominant factor in determining semantic functor-argument relations. It seems likely that such a step will also be necessary for certain phonological phenomena. Current work is investigating the utility of associative and commutative unification in this respect. in extending UCG to allow u'eammnt of unbounded dependency constructions and partially fi'ee word order, heavy use is made of uttary rules (Wittenburg 1986). Current work aims to recast the notion of unary rule within the framework of paramodular unification (Siekmann 1984).</Paragraph>
    </Section>
  </Section>
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