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<Paper uid="C92-4174">
  <Title>DIRECT PARSING WITH METARUI~ES</Title>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
2 Metarules in GPSG
</SectionTitle>
    <Paragraph position="0"> Metamles are one of file most criticized devices of the GPSG lonnalisnl. GPSG is a grmnmar fomvalism that states most ol ils generalizations on the level of local trees. Melarules were introduced to capture generalizations on tile mt of 1D rules. An ID rule states tile d()ulinance relation bctweA~n tile mother category and a umltiset of (laughter categories in a local tree with()ut fixing the linear precedence relation of tile (laughters. ID rules have the following torrent:</Paragraph>
    <Paragraph position="2"> Melarutes define a relation on ID rules. They have the lollowing tk~rlnat: 'input ll) rule scheme' ~ 'output ID rule scheme' and can be read as: If tile ~t of \[D rules contains an ID rule which is nlatched by 'input ID rule scheme', then it also contains an Ill rule that matches 'output ID nile seheule', where the feature SlW.cifications of the input ID rnle are tanled over to file output ID rule if not specilied otherwise by the melarule, For example the metamle VP\[-PAS\] --~ W, NP\[acc\] ~ VP\[+PAS\] --) W, (PPIby\]) states the connection between active and passive, where W is a vltriablc ranging over a (possibly empty) nmltiset of categories. The major point of criticism against mcumdes is tlmt they increase the generative power of GPSG ill an undesirable way when they are recursively applicable, because this may lead to arl infinite set of ID rules. The resulting grammar need not be context free. Ill order to remedy the situation, suggestions of varying radicality were made.</Paragraph>
    <Paragraph position="3"> The pruposal of \[Thompson 82\] and \[Gazdar et al. 85\], which tries to maintain metarules, was simply to apply a nleulrule ill most once in the generation of an ID rule. This stipulation is somewhat strange, because it allows for recursive metarules and just prevents them from being applied recnrsively.</Paragraph>
    <Paragraph position="4"> \[Kilbury 861 suggested to eliminate nletarules by using category co~K;cnrrence restrictions.</Paragraph>
    <Paragraph position="5"> The most radical prolxlsal was to dispense with metarules. Bnt our aim was to stay within the ti'amework of GPSG, and it would be a loss to dispense with melarules, beeanse GPSG formulates for example valency of verbs and other constituents on the level of ID rules aud nm'tarules are the means to capture generalisations on diat level.</Paragraph>
    <Paragraph position="6"> For this rca.son we formalize the properties of metarules that terulhiate recursive application and state ACTES I)E COLING-92, NANTI.:S, 23 28 AOL'I 1992 l 1 l 1 I)ROC. Of U.OLING-92. NANTES, Au(i. 23-28, 1992 them as a condition that a set of metarules narst fulfil. Metarules can then be applied freely.</Paragraph>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3 Application time
</SectionTitle>
    <Paragraph position="0"> There are two possibilities for the time to apply the metarules. The first is to compile the basic set of ID rules (compile-time application) in a preprocessing step. Thompson calls it all-at-once approach. The other possibility is to apply the metarules during the parsing process (run-time application or direct application), which Thompsoo calls as-needed approach.</Paragraph>
    <Paragraph position="1"> Thompson argued for the compile-time application because the direct application of metarules has the following disadvantages (see \['/homlrson 82\]: p.5):  (1) If a metarule can be applied to an ID rule during the parsing process, the metarule has to be applied again when the ~me ID rule is involved in the same or a subsequent parse.</Paragraph>
    <Paragraph position="2"> (2) To store the structures generated by ID rules which are the result of the application of a metarnle is just another instanoe of the compile-time application.</Paragraph>
    <Paragraph position="3"> (3) Derivations of ID rtdes of length greater than one,  i.e. ID rules which are the results of applying more than one metarule to one basic ID rule, will rapidly expand the .search slmme.</Paragraph>
    <Paragraph position="4"> In order to look a little bit closer to Thompson's arguments and to stay on his line, we presuppose that a kind of top-down parsing method is used and there are n basic ID rules and m ID rules, generated by the . application of the metarules.</Paragraph>
    <Paragraph position="5"> Wheu looking to argument (1), we see that it is an argument lor the ran-time approach. If the metarules are applied at compile-time a huge set of ID rules is compiled from the basic set. For exanlple if we would apply the metarules of our MT system (see section 5) to our basic set of 80 ID rules at compile-time, wc wonld get about 240 ID rules in the object grammar. Let us assume that some category C has to be expanded m~d there are i ID rules in our grammar with mother category C. In the compile-time approach the parser would have to check (n+m)/n*i ID rules on average, whereas in the run-time approach i ID rules and (n+m)/u metandes ((n+m)/n+i rules) have to be checked for application to these ID rules. In the normal case that are less than in the compile-time approach. Argument (2) is indeed an argument for the run-time approach. Let as again consider the above example and each of the i ID rules has d daughters on average. If the category C is expanded according to all ID rules, in the worst case (n+m)/n*d*i (partial) structures have to he stored ou average in the compile-time approach. These structures are very similar, because in general the metarules modify the ID rules slightly. The run-time approach can make use of this fact and stores only approximately d*i (partial) structures and additionally (n+m)/n*i structures after the application of the metarules. That makes ((n+m)/n+d)*i sn-netures to be stored in the run-time approach. The common parts of die ID rules generated by metarules need not to be stored, that are (n+m)/n*(d-1)*i-d*i partial structures less. For example if n = 80, m = 160, d = 3 and i = 10 then Otis would mean that on average 30 partial structures less have to he stored for the corresponding constituent.</Paragraph>
    <Paragraph position="6"> Conceruing argument (3), \[Barton et al. 87\]: p.226 showed that the computation of the Finite Closure (FC) of a GPSG G with x ID rules and y metarules can increase the number of the ID rules worse than exponentially, namely from x to more than X 2y, i.e.</Paragraph>
    <Paragraph position="7"> there is no difference between the compile-time and run-time approach.</Paragraph>
    <Paragraph position="8"> In order to sum up fltis discussion, we can say that there is no difference in complexity between the complile-time and file run-time approach with respect to the arguments in \['lltompson 821. The direct approach is even preferable to the eomplile time approach when looking at the arguments (1) and (2), which are indeed arguments for direct application of metarules.</Paragraph>
    <Paragraph position="9"> There is another argument for direct application of metarules. The FC in \['lltompson 82\] states that every metarule can apply at most once in the derivation of any given object grammar rule from one basic rule. An example for the recursive application of a metarule has been proposed in \[Uszkoreit 87\]: p.145 in his German grammar. It makes the adverbial phrase (AdvP) a sister node of the verb and its arguments: V2\[-AUX\] --~ V, W ~ V2\[-AUX\] --~ V, W, AdvP This metarule is to solve the problem that adverbial phrases can be interspersed freely among the arguments of the verb and the number of AdvPs in a verb phrase is not limited (but it is finite) and the metarule has to be applied recursively. This fact would rule out the definition of this metarule with respect to the definition of the FC wltich has been adopted also in \[Gazdar et al. 85\] to avoid the production of an infinite number of ID rules. Uszkoreit tried to circumvent the l~rublem in redefining the above metarule such that it fits the requirements of the FC. It employs the Kleene star operator:.</Paragraph>
    <Paragraph position="10"> V2\[-AUX\] -+ V, W :=~ V2\[-AUX\] --~ V, W, AdvP* This change of the memrule is not uecessary if the metarules are applied directly during the parsing process and the above melarule without the Kleene star can be applied freely, because the termination is determined by tile finiteness of the input string.</Paragraph>
  </Section>
  <Section position="6" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 Termination
</SectionTitle>
    <Paragraph position="0"> No matter whether the metarules are applied directly or at compile-time, we have to cam for the termination.</Paragraph>
    <Paragraph position="1"> We think that the restriction on the application of metarules imposed by the Finite Closure (FC) is too strong. That may have crucial consequences for some metarnles. Look for example at the Complement Omission Metarule from the English grammar in \[G~dar et al. 85\], which is \[+N, BAR 1\] --~ N deg, W :=2, \[+N, BAR 1\] --~ N deg. This metarule deletes optional complements of nouns. For example the noun gift may have two optional prepositional phrases as complements, i.e. N I ~ N o , (PP\[of\]), (PP\[to\]). The prepositions of add to are fixed but either of the PPs or both may be left out: the gift, the gift of John, the gift to Paul, the gift of John to Paul. The above metarule only allows for the gift and the gift of John to Paul, because it deletes all complements of the noun. The correct me &amp;quot;tarule would be: \[+N, BAR 1\] --~ N deg, X, W :::*, \[+N, BAR 1\] --~ N d, W \[(;~dar et al. 85\] have not been able to define this metarule, because it has to be applied recarsively add the FC does not allow recursive application. For this reason we decided to define another constraint which is not so restrictive.</Paragraph>
    <Paragraph position="2"> As it Ires turned out, most of the metarules which have been defined within the fragment of English in \[Gazdar et al. 85\] or of German (see the .section below for a more detailed diseussion) are or can be defined in a ACRES DE COI.1NG-92, NANIES, 23-28 AO~r 1992 1 l 1 2 PRO(:. OF COLING-92, NANTES, AUG. 23-28, 1992 way that guarantees rite termination of the recursive application of metarules. In order to prove the termination, some research results within the field of term-rewriting can be applied (see \[Dershowitz 82 and 85\] for general results and \[Weisweber 89\], \[Weiswebet/ llanen~hild 901 and \[Weisweber 92\] for an application to mappiugs within machiue translation).</Paragraph>
    <Paragraph position="3"> ID rules can be viewed as tenns and metarales can be viewed as term-rewrite rules, because they derive one ID rule from another. A set of term-rewrite rules terufinates if an ordering '&gt;' on the terms of the left-hand and right-hand sides (lhs and rhs, respectively) of the rewrite rules can be defined. This may be a quantitative ordering, e.g. a category occuring on the lhs of a metarule is deleted on its rhs, or a qualitative ordering, e.g. art operator precedeuce. We think that a mixture of both types of orderings is needed to prove the termination of sets of metarules. If a qualitative and a quantitative ordering are merged, the resulting ordering guarantees termination (see \[Dershowi~ 82 and 85\]). The operator precedence that is nsed in our MT system is in fact a precedence ordering on feature values occurring at rite categories of the lhs and rhs of the metarules.</Paragraph>
    <Paragraph position="4"> Termination condition for metarule application For every metarule lhs ::&gt; rhs, Ihs &gt; rhs. lhs &gt; rhs (it a daughter category occnrriug on the lhs is deleted on the rhs and/or (it) an operator precedence &gt;or. on feature values occurring at the categories of the lhs and rhs can lye defined, which is not contradictory for the whole set of metarules and (iii) every variable for (multisets of) categories occurring on the rhs occtws on the lhs.</Paragraph>
    <Paragraph position="5"> Melarnles have to fulfil the conditions (it and (iii) or (it) attd (iii). The condition (it is a quantitative ordering and the termination of melarules which fulfil (it is obvious, because everytime such a meuu'alc is applied one category is deleted aud the number of daughter categories in an ID rule is finite.</Paragraph>
    <Paragraph position="6"> The condition (it) is a qualitative orderiug. The termination of metarules which fulfil (it) is not as obvious as in (it. It means that a feature value of a category h,'ts to be changed and there must not be another melarule, which reverses the change of this feature value. It allows\[br not haviug to delete categories, addiug categories or adding values to a list, which may be a feature value, on the rhs of a metarule, if a feature value is changed on another category. This is the reason why we decided to impose cotttrol on the definition of metarules and not to move away frum such devices ,as recent research iu coutputational linguistics does. If a metarulc fulfils condition (it) it cannot be applied for a second time iu a derivation of an ID rule, because once a feature value has been cluanged it will never be reversed and the metarule will not be applicable again, qhis part of the termination condition simulates the tenninatiou condition of the FC.</Paragraph>
    <Paragraph position="7"> ~lhe condition (iii) prohibits the introdnetion or doubling of variables for (mnltisets of) categories on the rhs.</Paragraph>
    <Paragraph position="8"> Thus the termination of a certain set of metarules can be guaranteed, iff for all metarules either the metarule deletes a category occuring on its Ihs and/or a non-contradicting precedence on operators (feature values of the categories occurring iu the metarule) can be defined and all variables occurring on the rhs occur on the lhs.</Paragraph>
    <Paragraph position="9"> qt~e application of the termination condition is demonstrated with the melarules for Germm~ in the next .section.</Paragraph>
  </Section>
  <Section position="7" start_page="0" end_page="0" type="metho">
    <SectionTitle>
5 Metarules for German
</SectionTitle>
    <Paragraph position="0"> Our GPSG syutax of German is based on the grammar developed in \[Uszkoreit 87\]. We assume a fiat structure for the verb and its complements including the subject. Subeategorization of verbs is staled in ID rules of the following form:</Paragraph>
    <Paragraph position="2"> fixed value for the subeategorization feature in the 1D rule with n arguments, but for every subeategorization there is a seperate rule. The subject of main verbs is included in the rhs of the rule. Unlike Uszkoreit's approach we do not add the subject to the complements of a verb phrase via metarule application but reduce a sentential category to a verb phrase and delete the subject. The following Subject Deletion Metarule fulfils the termination cottditions (i) and (iii), because it deletes the category DP\[nom\].t</Paragraph>
    <Paragraph position="4"> Additionally, the operator precedence 'BAR 3' &gt;oP 'BAt/2' has to be defined, because the feature BAR at the mother category is changed on the rhs. This additional definition is needed in order to get a noncontradicting set of operator preeexlence definitions out of the whole set of mctarules in the grammar.</Paragraph>
    <Paragraph position="5"> &amp;quot;lhe Slash &amp;quot;fermination Metarule is responsible for ending (or from the bottom-up view, for the introduction of) a long distance relationship that is handled in GPSG via the category-valued feature SLASIt. Unlike \[Gazdar et al. 85\] we do artt have a trace. Traces cause problents in fiat structures without fixed word order, becau~ there are multiple analyses that are only different with respect to the position of the trace.</Paragraph>
    <Paragraph position="7"> Here the tenninatiotL conditions (it and (iii) are al~ fulfilled, because a category of the rhs of the ID rule is deleted. The operator precedence definitions are 'SLASH ~,2 &gt;o~, 'SLASH X 2' and 'SLASH ~' &gt;oP 'SLASH V 9', respectively.</Paragraph>
    <Paragraph position="8"> &amp;quot;lt~e Extraposition Metarule handles complement sentences and infinitive constructions that we treat as dislocated when they appear in the fianl position of a sentence. Another category-vahted feature, SLASHI, is The category DP is a determiner phrase according to the X-Bar-Schema in the Government and Binding Theory.</Paragraph>
    <Paragraph position="9"> 'F ~' means that the feature F has the value '~' (see \[Busemann/ Hauenschikl 88\] and \[Busemaan/ Hauenschild 89\]). This is equivalent to file notation -\[F\] of \[Gazdar et at. 85\] mad means that the value for F is always undefined, i.e. the corresponding category does not take a value for F. &amp;quot;lqm value '7' is sw~ially treated by the unification and the feature instaariation principles.</Paragraph>
    <Paragraph position="10"> AcrEs DE COLING-92, NA1Vn:.s, 23-28 not',~r 1992 1 1 1 3 PROC. OF COL1NG 92, NANTES. Anti. 23-28, 1992 introduced for them. The feature specification -COH(erent) marks categories that can be extraposed.</Paragraph>
    <Paragraph position="11"> This metarule fulfils the termination conditions (i) and (iii) and 'SLASH1 ~' &gt;op 'SLASH1 X\[-COH\]' has to be defined.</Paragraph>
    <Paragraph position="13"> The metarule for passive is an example in which the termination conditions (ii) and (iii) are necessary, because no category is deleted and an optional prepositio~ml phrase is introduced that replaces the accusative determiner phrase:</Paragraph>
    <Paragraph position="15"> Here the change of the feature specification of PAS at the mother category can be used for terminating melarule application and we have to define '-PAS' &gt;or, '+PAS '3 and &amp;quot;DP\[acc\] &gt;oP PP\[vonl &amp;quot;.4 The Auxiliary Metarule is similar to the Passive Metarule in that feature values of some categories are changed and the termination conditions (ii) and (iii) are fulfilled. Here it is the BAR level of the mother and V3-daughter that are lowered in analogy to to the Subject Deletion Metarule. The operator precedence to be defined is 'BAR 3' &gt;oe 'BAR 2', which already has been defined in connection with that metarule.</Paragraph>
    <Paragraph position="16"> A uxUiary Metarule: V3\[+AUX\] --4. V 0, V 3 ~ VPI+AUX\] --4 V deg, VP AS we have seen, the Subject Deletion, the Slash Termination and the Extraposition Metarule fulfil the criterion of deleting a category on the rhs of the 1D rule; the Passive and the Auxiliary Metarule change feature values at the categories. For all metarules a non-contradictory set of operator precedences can be defined and the application of the whole set of metanfies will terminate in every case.</Paragraph>
    <Paragraph position="17"> Even the AdvP-metarule in section 3 proposed by \[Uszkoreit 87\] can be treated when the me 'tarules are applied directly, because we can give a proof for its termination, which is guaranteed by the finite length of the input string in connection with direct application. This is another argument for the direct application of metarales.</Paragraph>
    <Paragraph position="18">  because of its shortcomings (see \[Urnbach 87\]), but developed a semantic level of our own that captures file functor argument structures (FAS, see \[Busemann/Hau- enschild 891 and \[Hanan~hild/Umbach 88\]) of sentences and is derived from the syntactic strucnlre via term- rewrite rules. Here an explicit assignment of semantic roles to complements of verbs takes place that is dependent on the subcategorization of the verb and its voice.</Paragraph>
    <Paragraph position="19"> 4 In this case we have to define a procedence for all feature values which are changed. detailed description of file parser without direct application of metandes), the metarules are defined according to the following scheme: Co ~ Co, W, Cd ~ C6 ~ C~, W, (C~) Co, Cc and Cd arc categories and W is a variable for a (possibly empty) multiset of categories. The categories C6 and C~ correspond to Co and Co, respectively, in terms of {Gazdar et at. 85\]. The category C~ can be viewed as a condition category for the application of the metarule. Cd is the category which is to be deleted or modified. This is indicated by the brackets arround C~, If Cd is to be deleted, C,~ is left out on the rhs of the metarule. If C d is to be modified, C d is replaced by C,~. The feature values of the categories are cospecified on the lhs and rhs of a metarule, if not specified otherwise.</Paragraph>
    <Paragraph position="20"> This causes the values to be carried over to the rhs. If the metarule should only be applied to lexical ID rules as proposed in \[Gazdar eta!. 85\], the category Cc has to be Ihe lexical head with respect to Co.</Paragraph>
    <Paragraph position="21"> The proof for the termination of .sets of such metarules is simple. At first we look at the case in which C~ is deleted, then the termination condition (i) holds.</Paragraph>
    <Paragraph position="22"> The second case is that the category CA is replaced by the category C,~ and the number of categories is not reduced. Now the termination condition (ii) has to be applied and at least one feature value of the categories {Co, C~},~ Um W has to be changed, which must not be reversed by another metarule.</Paragraph>
    <Paragraph position="23"> The termination condition (iii) holds in every case, because the variable W occurs on both sides of the metarule.</Paragraph>
    <Paragraph position="24"> In order to apply the metarules directly during the parsing process, all the categories of an ID rule, which are matched by the multiset {C~},,, t.-)m W, have to be collected by the parser. This is done for example by the Completer of the modified Earley algorithut (see \[Earley 70\], \[Shieber 84\], \[Kilbury 84\] and \[IMirre/ Momma 85\]). Suppose the Completer tries to complete with the inactive edge (C~, i, j, T'{},~), which is spanning li'om node i to node j of the chart, where ~' is a multiset of daughter categories which have already been analysed and the remainder, i.e. the tnultiset of daughter categories still to be analysed, is empty and C,~ is the mother category of the ID rule, which is licensing this edge. M is the ~t of metarules.</Paragraph>
    <Paragraph position="25"> If (Co, h, j, (x.\[~) is an inactive edge and ~ Cc, W,C,~ :=:, C;~ ~ C~, W) ~ Mand \[Cd}~ and fee (~ t..Jm 1~ then the Completer introduces a new inactive edge (C;~, h, j, (Z'{}m) and computes its closure. The category C~ in O~ t..3~ ~ is replaced by C~.</Paragraph>
    <Paragraph position="26"> If (Co, h, i, C/z-13 ) is an inactive edge and</Paragraph>
    <Paragraph position="28"> C~ is consistent to the categories in ~/{C,l}m with respect to linear precedence then the Completer introduces a new edge (C6, h, j. 0C/ u,,, (C~}~-~/{C,j}m) and the category C~ in O~ t.J~ 13 is replaced by C~. If the remainder \[~/{Cd},, = { }m then the closure of this edge has to be computed.</Paragraph>
    <Paragraph position="29"> The advantage of direct parsing with melarules is an increase of efficiency, because all the inactive edges which are licensed by ID rules indroduced by metarules need not to be stored seperately and the number of inactive edges generated by the Earley parer is reduced considerably.</Paragraph>
  </Section>
  <Section position="8" start_page="0" end_page="0" type="metho">
    <SectionTitle>
ACRES DI~ COL1NG-92, NAN'IX.S, 23-28 Ao(rr 1992 1 1 1 4 I'ROC. Ol: COLING-92, NANTES, AUG. 23-28, 1992
</SectionTitle>
    <Paragraph position="0"> Another interesting approach to direct parsing with metamles, in which the metarules are treated as special kinds of context-free roles, is presented in \[Kay 83\].</Paragraph>
  </Section>
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