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<Paper uid="P80-1013">
  <Title>CAPTURING LINGUISTIC GENERALIZATIONS WITH METARULES IN AN ANNOTATED PHRASE-STRUCTURE GRAMMAR</Title>
  <Section position="6" start_page="44" end_page="47" type="concl">
    <SectionTitle>
6. Matching
</SectionTitle>
    <Paragraph position="0"> An important part of the derivation process is the definition of a match between a metarule matching form and a grammar rule. The matching problem is complicated by the presence of RSET and ASET predications in the grammar rules. Thus, it is helpful to define a match in terms of the phrase markers that will be admitted by the grammar rule and the MF. We will say that an MF matches a grammar rule just in case it admits at least those phrase markers admitted by the grammar rule. This definition of a match is sufficient to allow the formulation of matching algorithms for grammar rules complicated by annotations.</Paragraph>
    <Paragraph position="1"> We divide the matching process into two parts: matching phrase-structures, and matching feature sets. Both parts must succeed in order for the match to succeed.</Paragraph>
    <Section position="1" start_page="45" end_page="45" type="sub_section">
      <SectionTitle>
6.1. Matching Phrase-structures
</SectionTitle>
      <Paragraph position="0"> For phrase-structures, the definition of i match can be replaced by a direct comparison of the phrase-structures of the MF and grammar rule. Variables in the MF phrase-structure are used to indicate Idofllt care a parts of the grammar rule phrase-structure, while constants must match exactly. SIn|le lower case letters are used for variables that must match single categories of the grammar rule. A typical MF might be:  grammar rule. Double letter variables are used to match a number of consecutive Catllorils (including none) fR the rule. We have:</Paragraph>
      <Paragraph position="2"> Note that double letter variables are bound to an ordered list of elements fTom ~he matched rule. Because of this characteristic, a~ MF with more thin one double letter variable may match t rule in several different ways:</Paragraph>
      <Paragraph position="4"> All of these are considered to be valid, independent matches.</Paragraph>
      <Paragraph position="5"> Double and single letter variables may be intermixed freely in an MF.</Paragraph>
      <Paragraph position="6"> While double letter variables match multiple categories In l phrase structure rule, string variables match parts of a category. String variables occur in both double and single letter varieties; as expected, the former match any number of consecutive characters, while the litter match sln|le characters. String variables are assumed when an MF category contains i mixture of upper and lower case characters, e.g.:  etc.</Paragraph>
      <Paragraph position="7"> String variables are most useful for matching category names that may use the ~ convention.</Paragraph>
    </Section>
    <Section position="2" start_page="45" end_page="45" type="sub_section">
      <SectionTitle>
6.2. Feature Matching
</SectionTitle>
      <Paragraph position="0"> So far variables have matched only the phrase-structure part of grammar rules, and not the feature annotations. For feature matching, we must return to the original definition of matching based on the admissibility of phrase markers. The RSET of a grammar rule is a closed formula involvlng the feature sees of the phrase marker constructed by the rule; let P stand for this formula. If P is true for a given phrase marker, then that phrase marker is accepted by the rule; if not, It ts rejected. Similarly, the RSET of a matching form is an open formula on the feature sets of the phrase marker; let R(xl,x2...Xn) stand for this formula, where the x I are the variables of the RSET. For the MF;s restrictions to match those of the grammar rule, we must be able to prove the formula:</Paragraph>
      <Paragraph position="2"> That Is. whenever P admits a phrase marker, there exists some blndin |for R0s free variables that also admits the phrase marker.</Paragraph>
      <Paragraph position="3"> Now the importance of restricting the form of P and R can be seen. Proving that the above implication holds for general P and R can be a hard problem, requiring, for example, a resolution theorem prover. By restricting P and R to simple conjunctions of equalities, inequalities, and set membership predicates, the match between P and R can be performed by a simple and efficient algorithm.</Paragraph>
    </Section>
    <Section position="3" start_page="45" end_page="47" type="sub_section">
      <SectionTitle>
6.3. Instanttation
</SectionTitle>
      <Paragraph position="0"> When a matarule matches a grammar rule, the CSET of the metaruia Is evaluated to see if the metaruie can indeed be applied. For example, the MF: VP-&gt; &amp;quot;BE&amp;quot; xP CSET: x ~t 'V will match any rule for which x is not bound to V. When an MF matches a rule, and the CSET is satisfied, the Instantlatlon form of the metarule is used to produce i new rule. TN~ variables of the IF are instantiated with their values from the match, producing I new rule. In addition, restriction and assignment features that do not conflict with the IF's features are carried over from the rule that matched. This latter is a very handy property of the instanttation, since that is usually what the metarule writer desires. Consider metarule that derives the subject-aux inverted form of a main clause with a finite verb phrase: grammar rule: S -&gt; NP AUX VP RSET: (NBR NP) = (NBR AUX);</Paragraph>
      <Paragraph position="2"> if features were not carried over during an instan.iation, the result of matching and Instantlating the metarule would be: SAI -&gt; AUX NP VP This does not preserve number agreement, nor does it restrict the VP to being finite. Of course, the metarule could be rewritten to have the correct restrictions in the IF, but this would sharply curb the utility of the metarules, and lead to the proliferation of metaruies with slightly different RSETs.</Paragraph>
      <Paragraph position="3">  7. An Example: Dative Movement and Passive We are now ready to give a short example of two met,rules for dative movement and passive transformations. The predicate/argument structure will be described by the feature PA, whose value is a list: (V NP 1 Np 2 ...) where V is the predicating verb, and the NPs are its arguments. The order of the arguments is significant, since:  (&amp;quot;gave&amp;quot; &amp;quot;John&amp;quot; &amp;quot;a book&amp;quot; &amp;quot;Mary&amp;quot;) &lt;=&gt; gift of a book by John to Mary 'gave&amp;quot; &amp;quot;John' &amp;quot;Mary m &amp;quot;a book') &lt;=&gt; ?? gift of Mary to a hook by John  In dative movement, the prepositional NP becomes a noun phrase next to the verb:  1. John gave a book to Mary =&gt; 2. John gave Mary a book  The first object NP of (2) fills the same argument role as the prepositional NP of (1). Thus the dative movement met,rule can be formulated as follows:  DATMOVE accepts VPs with a trailing prepositional argument, and moves the NP from that argument to just after the verb. The verb must be marked as accepting dative arguments, hence the DATIVE feature restriction in the RSET of the instantlation form. Also, since there is no longer a prepositional argument, the PREP feature of the VP doesn't have to match it. As for the predicate/argument structure, the NP#D constituent takes the place of the prepositional NP in the PA feature.</Paragraph>
      <Paragraph position="4"> DATMOVE can be applied to the dltransltlve VP rule to yield the dltransitive dative construction. The variable bindings are:  There are other grammar rules that dative movement will apply  to, for example, verbs with separable particles: Make up a story for me =&gt; Make me up a story. This is the reason the double-letter variable &amp;quot;uu' was used in DATMOVE. As long as the final constituent of a VP rule is a PP, DATMOVE can apply to yield a dative construction. 7.2. Passive In the passive transformation, the NP immediately following the verb is moved to subject position; the original subject moves to an age.rive BY-phrase:  (1) John gave a book to Mary =&gt; (2) A book was given to Mary by John.</Paragraph>
      <Paragraph position="5">  PASSIVE deletes the NP immediately following the verb, and adds a BY-prepositional phrase at the end. PPL is a past participle suffix for the verb. In the predicate/argum=nt structure, the BY-phrase NP substitutes for the original subject, while the new subject is used in place of the original  object NP. Applying PASSIVE to the ditransittve rule yields: AP -&gt; V PPL PP PP#A RSET: (TRANS V) = 'DIs (PREP V) = (PREP PP); ASET: (PA VP) := '((V VP) (NP PP#A) (SUBJ VP) (NP PP));  e.g.. &amp;quot;A book was given to Mary by John&amp;quot; will be analyzed by this rule to have a PA feature of (&amp;quot;givea mJohn~ na book&amp;quot; &amp;quot;Mary&amp;quot;), which is the same predicate/argument structure as the corresponding active sentence.</Paragraph>
      <Paragraph position="6"> PASSIVE can also apply to the rule generated by DATMOVE to yield the passive form of VpIs with dative objects:  A system has been designed and implemented to test the validity of this approach. It consists of a matcher/instantiator for met,rules, along with an iteration loop that applies all the met.rules on each cycle until no more new rules are generated. Met.rules fur verb subcategorization and finite and non-finite clause structures have been written and input to the system. We were especially concerned: - To check the perspicuity of metarules for describing significant fragments of English using the above representation for grammar rules.</Paragraph>
      <Paragraph position="7"> - To check that a reasonably small number of new grammar rules were generated by the metarules for these fragments.</Paragraph>
      <Paragraph position="8"> Both of these considerations are critical for the performance of natural language processing systems. Preliminary tests indicate that the system satisfies both these concerns; indeed, the metarules worked so well that they exposed gaps in a phrase-structure grammar that was painstakingly developed over a five year period and was thought to be reasonably complete for a large subset of English 19\]. The number of derived rules generated was encouragingly small:</Paragraph>
    </Section>
  </Section>
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