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<Paper uid="P90-1024">
  <Title>Parsing with Combinatory Categorial Grammar in a Graph-Unification-Based</Title>
  <Section position="2" start_page="0" end_page="189" type="intro">
    <SectionTitle>
ABSTRACT
</SectionTitle>
    <Paragraph position="0"> In this paper, we report on our use of zero morphemes in Unification-Based Combinatory Categorial Grammar. After illustrating the benefits of this approach with several examples, we describe the algorithm for compiling zero morphemes into unary rules, which allows us to use zero morphemes more efficiently in natural language processing. 1 Then, we discuss the question of equivalence of a grammar with these unary rules to the original grammar.</Paragraph>
    <Paragraph position="1"> Lastly, we compare our approach to zero morphemes with possible alternatives.</Paragraph>
    <Paragraph position="2"> 1. Zero Morphemes in Categorial Grammar In English and in other natural languages, it is attractive to posit the existence of morphemes that are invisible on the surface but have their own syntactic and semantic definitions. In our analyses, they are just like any other overt morphemes except for having null strings (i.e. &amp;quot; &amp;quot;), and we call them zero morphemes. Most in Categorial Grammar and related forms of unification-based grammars, on the other hand, take the rule-based approach. That is, they assume that there are unary rules that change features or categories of their arguments (cf. Dowty 1977, Hoeksema 1985, Wittenburg 1986, Wood 1987). Below, we will discuss the advantages of our zero morpheme approach over the rule-based approach.</Paragraph>
    <Paragraph position="3"> Zero morphemes should be distinguished from so-called &amp;quot;gaps&amp;quot; in wh-questions and relative clauses in that zero morphemes are not traces or &amp;quot;place holders&amp;quot; of any other overt  least two types of zero morphemes: zero morphemes at the morphology level and those at the syntax level.</Paragraph>
    <Paragraph position="4"> A zero morpheme at the morphology level applies to a free morpheme and forms an inflected word. Such examples are present tense zero morpheme (PRES) as in 'I like+PRES dogs&amp;quot; and a singular zero morpheme (SG) as in &amp;quot;a dog+SG&amp;quot;. These two are the counterparts of a third person singular present tense morpheme C+s&amp;quot; as in &amp;quot;John like+s dogs&amp;quot; and a plural morpheme C+s&amp;quot; as in 'two dog+s'~, respectively. null  Notice that, unlike the rule-based approach, the declarative and compositional nature of the zero morpheme approach makes the semantic analysis easier, since each zero morpheme has its semantic definition in the lexicon and therefore can contribute its semantics to the whole interpretation just as an overt morpheme does. Also, the monotonicity of our 'feature adding&amp;quot; approach, as opposed to &amp;quot;default feature&amp;quot; approach (e.g., Gazdar 1987), is attractive in compositional semantics because it does not have to retract or override a semantic translation contributed by a word with a default feature. For example, &amp;quot;dog&amp;quot; in both &amp;quot;dog+SG&amp;quot; and &amp;quot;dog+s&amp;quot; contributes the same translation, and the suffixes &amp;quot;+SG&amp;quot; and &amp;quot;+s&amp;quot; just add the semantics of number to their respective head nouns. In addition, this approach helps reduce redundancy in the lexicon. For instance, we do not have to define for each base verb in the lexicon their present-tense counterparts.</Paragraph>
    <Paragraph position="5"> a man REL-MOD the daughter of whom</Paragraph>
    <Paragraph position="7"> Some zero morphemes at the syntax level are those which may apply to a constituent larger than a single word and change the categories or features of the constituent. They are like ordinary derivational or inflectional morphemes except that their application is not confined within a word boundary. In English, one example is the noun compounding zero morpheme (CPD), which derives a noun modifier from a noun. In Categorial Grammar, its syntactic type is (N/N)\N. 2 For instance, a noun compound &amp;quot;dog food&amp;quot; might have the following derivation.</Paragraph>
    <Paragraph position="8"> (2) dog CPD food</Paragraph>
    <Paragraph position="10"> In knowledge-based or object-oriented semantics (cf. Hirst 1987); which our LUCY system uses, the treatment of compound nouns is straightforward when we employ a zero morpheme CPD. 3 In LUCY, CPD has a list of translations in the semantic lexicon, each of which is a slot relation (a two-place predicate as its syntactic type) in the knowledge base. For example, for &amp;quot;dog food&amp;quot; CPD may be translated into (food-typically-eaten x y), where x must be an instance of class Animal and y that of Food.</Paragraph>
    <Paragraph position="11"> Thus, a translation of CPD is equivalent to a  2. CPD is leftward-looking to parallel the definition of a hyphen as in &amp;quot;four-wheeler&amp;quot;. 3. Some compound nouns are considered as &amp;quot;idiomatic&amp;quot; single lexical entries, and they do not have a CPD morpheme. (e.g. &amp;quot;elephant garlic&amp;quot;)  value bound to the &amp;quot;implicit relation&amp;quot; called nn that Hobbs and Martin (1987) introduce to resolve compound nouns in TACITUS. In our case, having CPD as a lexical item, we do not have to introduce such an implicit relation at the semantics level.</Paragraph>
    <Paragraph position="12"> An analogous zero morpheme provides a natural analysis for relative clauses, deriving a noun modifier from S. This zero morpheme, which we call REL-MOD, plays an important role in an analysis of pied-piping, which seems difficult for other approaches such as Steedman (1987, 1988). (See Pollard (1988) for his criticism of Steedman's approach.) Steedman assumes that relative pronouns are type-raised already in the lexicon and have noun-modifier type (N\N)/(S/(SINP). In Figure 1, we show a derivation of a pied-piping relative clause &amp;quot;a man the daughter of whom John liked &amp;quot; using REL-MOD.4 s Other zero morphemes at the syntax level are used to deal with optional words. We define a zero morpheme for an invisible morpheme that is a counterpart of the overt one. An example is an accusative relative pronoun as in &amp;quot;a student (who) I met yesterday&amp;quot;. Another example of this kind is '~ou&amp;quot; in imperative 4. We assume that accusative wh-words are of basic NP type in the lexicon. A unary rule LIFT, which is similar to type-raising rule, lifts any NP of basic type with \[rel:+\] feature to a higher type NP, characteristic of fronted phrases. This feature is passed up by way of unification.</Paragraph>
    <Paragraph position="13"> 5. We actually use predictive versions of combinators in our runtime system (Wittenburg  sentences. Having a zero morpheme for the unrealized '~'ou&amp;quot; makes parsing and the interpretation of imperative sentences  Analogous to the treatment of optional words, VP-ellipsis as in &amp;quot;Mary likes a dog, and Bill does too&amp;quot; is handled syntactically by defining a syntax-level zero morpheme for an elided verb phrase (called VP-ELLIPSIS). During the discourse process in LUCY, the antecedent of  Now to summarize the advantages for having zero morphemes, first, zero morphemes like PRES and SG reduce redundancy in the lexicon. Second, zero morphemes seem to be a natural way to express words that do not appear 6. Each sentence must have one of the three  mood features -- declarative, interrogative, and imperative mood. They are added by zero morphemes DECL, QUES, and IMP, respectively.</Paragraph>
    <Paragraph position="14"> 7. See Kameyama and Barnett (1989). 190 on the surface but have their overt counterparts (e.g., null accusative relative pronouns, vp-ellipsis). Third, since each zero morpheme has its own syntax and semantic interpretation in much the same way as overt morphemes, and since the semantic interpretations of binary rules that combine a zero morpheme with its argument (or functor) are kept as simple as they are in Categorial Grammar, semantic interpretations of sentences with zero morphemes are compositional and straightforward. Typically in the rule-based approach, the semantic operations of unary rules are more complicated: they might perform such operations as introducing or retracting some semantic primitives that do not exist in the semantic lexicon. But with our zero morpheme approach, we can avoid such complication. Lastly, using zero morpheme REL-MOD makes the analysis of pied-piping and preposition fronting of relative clauses in Categorial Grammar possible.</Paragraph>
    <Paragraph position="15"> In the following section, we propose an approach that keeps all these advantages of zero morphemes while maintaining the efficiency of the rule approach in terms of parsing.</Paragraph>
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