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<Paper uid="P90-1024">
  <Title>Parsing with Combinatory Categorial Grammar in a Graph-Unification-Based</Title>
  <Section position="3" start_page="189" end_page="191" type="metho">
    <SectionTitle>
2. Compiling Zero Morphemes
</SectionTitle>
    <Paragraph position="0"> In natural language processing, simply proposing zero morphemes at each juncture in a given input string during parsing would be a nightmare of inefficiency. However, using the fact that there are only a few binary rules in Categorial Grammar and each zero morpheme can combine with only a subset of these rules because of its directionality compatibility, we can pre-compile zero morphemes into equivalent unary rules and use the latter for parsing. Our approach is an extension of the predictive combinator compilation method discussed in Wittenburg (1987). The idea is that we first unify a zero morpheme M with the left or right daugh-Let M be a zero morpheme, R be a binary rule. For each M in the grammar, do the following: For each binary rule R in the grammar if the syntax graph of M unifies with the left daughter of R then call the unified binary graph R', and make the right daughter of R' the daughter of a new unary rule R1 make the parent of R' the parent of R1 if the syntax graph of M unifies with the right daughter of R then call the unified binary graph R' make the left daughter of R' the daughter of a new unary rule R1 make the parent of R' the parent of RI.</Paragraph>
    <Paragraph position="1">  ter of each binary rule R. If they unify, we create a specialized version of this binary rule R', maintaining features of M acquired through unification. Then, we derive a unary rule out of this specialized binary rule and use it in parsing.</Paragraph>
    <Paragraph position="2"> Thus, if M is of type NB, R is forward application, and M unifies with the left daughter of R, the compiling procedure is schematized as in  Now I shall describe the algorithm for compiling zero morphemes in Figure 3. During this compiling process, the semantic interpretation of each resulting unary rule is also calculated from the interpretation of the binary rule and that of the zero morpheme. For example, if the semantics of M is M', given that the semantic interpretation of forward application is ~,fun;~arg(fun arg), we get Zarg(M' arg) for the semantic interpretation of the compiled unary rule. 8 We also have a mechanism to merge  two resulting unary rules into a new one. That is, if a unary rule R1 applies to some category A, giving A', and then a unary rule R2 applies to A', giving A&amp;quot;, we merge R1 and R2 into a new unary rule R3, which takes A as its argument and returns A&amp;quot;. For example, after compiling IMP-rule and IMP-YOU-rule from zero morphemes IMP and IMP-YOU (cf. (3)), we could merge these two rules into one rule, IMP+IMP-YOU rule. During parsing, we use the merged rule and deactivate the original two rules.</Paragraph>
    <Paragraph position="3"> 3. The Grammar with Compiled zero mor- null phemes The grammar with the resulting unary rules has the same generative capacity as the 8. See Wittenburg and Aone (1989) for the details of Lucy syntax/semantics interface.</Paragraph>
    <Paragraph position="4">  source grammar with zero morphemes in the lexicon because these unary rules are originally derived by only using the zero morphemes and binary rules in the source grammar. Thus, a derivation which uses a unary rule can always be mapped to a derivation in the original grammar, and vice versa. For example, look at the following example of CPD-RULE vs. zero mor- null pheme CPD: (5) a. dog food</Paragraph>
    <Paragraph position="6"> Now, if we assume that we use Categorial Grammar with four binary rules, namely, apply&gt;, apply&lt;, compose&gt;, and compose&lt;, as Steedman (1987) does, we can predict, among 8 possibilities (4 rules and the 2 daughters for each rule), the maximum number of unary rules that we derive from a zero morpheme according to its syntactic type. 9 If a zero morpheme is of type NB, it unifies with the left daughters of apply&gt;, apply&lt; and compose&gt; and with the right daughters of apply&gt; and corn9. Zero morphemes do not combine with wh-word type-raising rule LIFT, which is the only unary rule in our grammar besides the compiled unary rules from zero morphemes.</Paragraph>
    <Paragraph position="7"> pose&gt;. Thus, there are 5 possible unary rules for this type of zero morpheme. If a zero morpheme is of type A\B, there are also 5 possibilities. That is, it unifies with the left daughter of apply&lt; and compose&lt;, and the right daughters of apply&gt;, apply&lt; and compose&lt;. If a zero morpheme is of basic type, there are only 2 possibilities; it unifies only with the left daughter of apply&lt; and the right daughter of apply&gt;.</Paragraph>
    <Paragraph position="8"> Furthermore, in our English grammar, we have been able to constrain the number of unary rules by pre-specifying for compilation which rules to unify a given zero morpheme with. 1deg We add such compiler flags in the definition of each zero morpheme. We can do this for the morphology-level zero morphemes because they are never combined with anything other than their root morphemes by binary rules, and because we know which side of a root morpheme a given zero affix appears and what are the possible syntactic types of the root morpheme. As for zero morphemes at the syntax level, we can ignore composition rules when compiling zero morphemes which are in islands to &amp;quot;extraction&amp;quot;, since these rules are only necessary in extraction contexts. CPD, REL-MOD and IMP-YOU are such syntax-level zero morphemes. Additional facts about English have allowed us to specify only one binary rule for each syntax-level zero morpheme in our English grammar. An example of a zero morpheme definition is shown below.</Paragraph>
    <Section position="1" start_page="191" end_page="191" type="sub_section">
      <SectionTitle>
Morphemes
</SectionTitle>
      <Paragraph position="0"> In this section, we compare our approach to zero morphemes to alternative ways from the parsing point of view. Since we do not know any other comparable approach which specifically included zero morphemes in natural language processing, we compare ours to the possible approaches which are analogous to those which tried to deal with gaps. For example, in Bear and Karttunen's (1979) treatment of wh-question and relative pronoun gaps in Phrase Structure Grammar, a gap is proposed at each vertex during parsing if there is a wh-question word or a relative pronoun in the stack. We can use an analogous approach for zero morphemes, but clearly this will be extremely inefficient. It is more so because 1) there is no restriction such as that there should be only one zero morpheme within an S clause, and 2) the stack is useless because zero morphemes are independent morphemes and are not &amp;quot;bound&amp;quot; to other morphemes comparable to wh-words.</Paragraph>
      <Paragraph position="1"> Shieber (1985) proposes a more efficient approach to gaps in the PATR-II formalism, extending Earley's algorithm by using restriction to do top-down filtering. While an approach to zero morphemes similar to Shieber's gap treatment is possible, we can see one advantage of ours. That is, our approach does not depend on what kind of parsing algorithm we choose. It can be top-down as well as bottom-up.</Paragraph>
    </Section>
  </Section>
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