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<Paper uid="W97-0116">
  <Title>Acquiring German Prepositional Subcategorization Frames from Corpora</Title>
  <Section position="3" start_page="153" end_page="160" type="intro">
    <SectionTitle>
2 Method
</SectionTitle>
    <Paragraph position="0"> The automatic extraction of German prepositional SFs is based on the observation that certain constructs involving so-called pronominal adverbs are high-accuracy cues for prepositional subcategorization. Pronominal adverbs are compounds in German consisting of the adverbs da(r)- and wo(r)- and certain prepositions. For instance in (4c), the pronominal adverb daran ('about it') is used as a pro-form for the personal pronoun es ('it') as the  object of the preposition an ('about'). (Note that the usage of the pronoun (4b) is ungrammatical.) In (4d), the pronominal adverb daran occurs in a correlative construct with a subordinate daft ('that') clause immediately following it.</Paragraph>
    <Paragraph position="1"> (4) a. Mary denkt an Johns Ankuft.</Paragraph>
    <Paragraph position="2"> Mary thlnk~ on John's arrival 'Mary thinks about John's arrival .'  d. Mary denkt damn, da6 John bald aukommt.</Paragraph>
    <Paragraph position="3"> Mary thinks on it that John soon arrives 'Mary thinks about the fact that John will arrive soon.' Unlike prepositional phrases, pronominal adverb correlative constructs provide reliable cues for prepositional subcategorization. For instance the occurrence of the pronominal adverb damn in the correlative construct in (4d) can be used to infer that the verb denken ('to think') subcategorizes for a PP headed by the preposition an (~about').</Paragraph>
    <Paragraph position="4"> In the next section, a learning procedure is described which makes use of pronomln~.1 adverb correlative constructs to infer prepositional subcategorization. It consists of four components: SF detection, mapping, disambiguation, and ranldng.</Paragraph>
    <Section position="1" start_page="155" end_page="155" type="sub_section">
      <SectionTitle>
2.1 SF Detection
</SectionTitle>
      <Paragraph position="0"> This component makes use of shallow parsing tte,,hn~ques to detect possible prepositional SF ~ructures; a standard CFG parser is used with a hand-written grammar d~qn~ng pairs of main and subordinate clauses in correlative constructs such as (4d). Main clauses covered by the grammar include copular constructs as well as active and passive verb-second and verb-final constructs. Subordinate clauses considered include those headed by daft ('that'), indirect interrogative clauses, and infinitival clauses.</Paragraph>
      <Paragraph position="1"> The internal structure of the clause pair consists of phrase-like constituents; these include nominative (NC)~ prepositional (PC), adjectival (AC), verbal (VC), and clausal constituents. Their deiq-ltion is non-standard; for instance, all prepositional phrases, whether complement or not, are left unattached. As an example, the shallow parse structure for the sentence fragment in (5) is shown in (5') below.</Paragraph>
      <Paragraph position="2"> (5) Er lobte die Reaktion der 5ffentlichen Meinung in RuBland he praised the reaction the public opinion in Russia als Beweis dafiir, daB...</Paragraph>
      <Paragraph position="3"> as proof for it that 'He praised the reaction of the public opinion in Russia as proof of the fact that ...'</Paragraph>
    </Section>
    <Section position="2" start_page="155" end_page="158" type="sub_section">
      <SectionTitle>
2.2 SF Mapping
</SectionTitle>
      <Paragraph position="0"> The SF Mapping component maps a shallow parse structure of a main clause in a pronominal adverb correlative construct to a set of putative subcategorization frames reflecting structural as wen as morphological ambiguities in the original sentence. Alternative SFs usually stem from an ambiguity in the attachment of the pronominal adverb PP. The mapping is defined as follows.</Paragraph>
      <Paragraph position="1"> (In the following, p denotes the preposition within the pronomlnal adverb</Paragraph>
      <Paragraph position="3"> in a correlative construct main clause, VC the main verbal constituent in the clause; v in VC\[v\] denotes the head Iemm~ of the verbal constituent, analogously for NC\[n\].) VC\[v\]/NC\[n\]. An active verb-second or verb-final clause with one NC is m~tpped to {PP\[p\] V\[v\]} if the NC precedes the finite verb/auxi~ary in the clause, otherwise to {PP\[p\] V\[v\], PP\[p\] N\[n\]}.</Paragraph>
      <Paragraph position="4"> For instance, sentence (6) is a verb-second clause with an adverbial in the first position in the clause and one NC following the verb. In this construct, the PP headed by the pronominal adverb may potentially be attached to the verb phrase or to the nominal phrase immediately preceding it. According to this rule, this sentence is mapped to {PP\[an\] V\[arbeiten\], PP\[anl N\[Student\]}.</Paragraph>
      <Paragraph position="5"> (6) Jetzt arbeitet der Student daran, ...</Paragraph>
      <Paragraph position="6"> Now works the student on it 'The student is now working on ... ' VC\[v\]/NCl\[nl\]/NC2\[n2\]. An active verb-second or verb-final clause with two nominal constituents NC1 and NC~ such that NC,2 follows NC1 in the clause is mapped to {PP\[p\] NPA V\[v\], PP\[p\] N\[n2\]}, if the head of NC2 is a noun, and to {PP\[p\] NPA V\[v\]} otherwise.</Paragraph>
      <Paragraph position="7"> Sentences (Ta,b) are examples to which this rule applies. In (Ta) the verb erinnern ('to remind') subcategorizes for an accusative NP and a PP headed by the preposition an ('on'), while in (To), the verb nehmen ('to take') is a support verb and Racksicht ('consideration') a noun which subcategorizes for a PP headed by the preposition auf. Since their shallow structure is ambiguous, they are each mapped to a SF set reflecting both attar hment alternatives; (Ta) is mapped to the set {PP\[an\] NPA V\[erirmern\], PP\[an\] N\[Freund\]}, and (Tb) to the set {PP\[auf\] NPA V\[nehmen\], PP\[auf\] N\[R~eksicht\]}.</Paragraph>
      <Paragraph position="8"> (7) a. Mary erinnert ihren Freund daran, daB...</Paragraph>
      <Paragraph position="9"> Mary reminds her friend on it that 'Mary reminds her friend of the fact that ... ' b. Mary nimmt keine Rficksicht darauf, daft...</Paragraph>
      <Paragraph position="10"> Mary takes no consideration on it that 'Mary shows no consideration for the fact that ... ' Copula/NCl\[nl\]/NC2\[n2\]. A copula clause with two nominal constituents NCt\[nl\] and NC2\[n2\] such that NC2 follows NC1 and n2 is a noun is mapped to {PP\[p\] N\[n2\]}. For instance (8) is mapped with this rule to {PP\[auf\] \[nin is\]}.  (8) Weft dies ein Hinweis darauf ist, da6...</Paragraph>
      <Paragraph position="11"> because this an indication on in is that 'Because this is an indication (of the fact) that ...' Copula/NC\[n\]/AC\[a\]. A copula clause with one nominal and one adjectival constituent is mapped to {PP\[p\] N\[n\], PP\[p\] A\[a\],}. For instance, with this rule the clause in (9) is mapped to {PP\[auf\] A\[stolz\], PP\[auf\] N\[Student\]} (9) Stolz ist der Student darauf, da6...</Paragraph>
      <Paragraph position="12"> proud is the student on it that 'The student is proud of the fact that ...' PCs. Any clause in wt~ch a PC immediately precedes the prronomlna\] adverb is mapped as in the appropriate rule with the additional element 'PP\[p\] N\[n\]' in the set, where n is the head of the NC within the prepositional constituent. For instance, (10) is mapped to {PP\[an\] V\[arbeiten\], PP\[an\] N\[Woche\]} with the VC/NC and PC rules.</Paragraph>
      <Paragraph position="13"> (10) Mary arbeitet seit zwei Wochen daran, ...</Paragraph>
      <Paragraph position="14"> Mary works since two weeks on it 'Mary has been working for two weeks on ...' Morphology. Any clause in wldch a possible locus of attachment is morphologicaUy ambiguous is mapped with the appropriate rule applied to all morphology alternatives. For instance, (11) is mapped with the VC/NC and Morphology rules to {PP\[an\] V\[denken\], PP\[an\] V\[gedenken\]}, since g~acht is the past participle of both the verbs nken ('to think') and g~enken ('to consider').</Paragraph>
      <Paragraph position="15"> (11) Er hat daran gedacht, dat3 ...</Paragraph>
      <Paragraph position="16"> he has on it thought/considered that 'He thought of...' Passive/VC\[v\]/NC\[n\]. This rule is applied to 'werden ('to be') passive verb-second or verb-final clause with one NC. In case n is not the pronoun es ('it'), the clause is mapped to (PP\[p\] NPA V\[v\]} ifNC precedes the verb, and to {PP\[p\] NPA V\[v\], PP\[p\] N\[n\]} otherwise. In case n is the pronoun ~, the clause is mapped to {PP\[p\] NPA V\[v\], PP\[p\] V\[v\]}. For instance,  (12) is mapped to {PP\[an\] NPA V\[erinnern\]}.</Paragraph>
      <Paragraph position="17"> (12) Mary wird daran erinnert, da6...</Paragraph>
      <Paragraph position="18"> Mary is on it reminded that 'Mary is reminded (of the fact) that ...'</Paragraph>
      <Paragraph position="20"/>
    </Section>
    <Section position="3" start_page="158" end_page="159" type="sub_section">
      <SectionTitle>
2.3 SF Dis~rnbiguation
</SectionTitle>
      <Paragraph position="0"> The dis~rnhiguation component uses the expectation-maTirni~tion (EM) algorithm to assign probabilities to each frame in an SF alternative, given all SF sets obtained for a given corpus. The EM algorithm (Dempster, Laird, and Rubin, 1977) is a general iterative method to obtain maximum likelihood estimators in incomplete data situations. See (Vardi and Lee, 1993) for a general description of the algorithms as well as numerous examples of its application. The EM algorithm has been used to induce valence information in (Carrol and Rooth, 1997).</Paragraph>
      <Paragraph position="1"> In the current setting, the algorithm is employed to rank the frames in a given SF set by using the relative evidence obtained for each frame in the set. The algorithm is shown below.</Paragraph>
      <Paragraph position="2"> Algorithm. Let F be a set of frames. Further, let ~q be a finite set of nonempty subsets of ~(F), and let F0 = I.J X. XE8 Initialization step: for each frame z in F0:</Paragraph>
      <Paragraph position="4"> Where ge is a ftmetion from S to the natural n-tubers mapping a set X to the number of times it was produced by the SF mapping for a given corpus C. Fm-ther, I, Pk, and Pk are run.ions defined as follows:</Paragraph>
      <Paragraph position="6"> Definition. A frame z is best in the set X at the iteration k if z E X and p~(z) is an absolute maximum in U Pk(~)- ~EX  In the algorithm above, 8 denotes the set of SF sets produced by the SF mapping for a given corpus C. In the initialization step, co assigns an initial &amp;quot;weight&amp;quot; to each frame, depending on its relative frequency of occurrence, and on whether the structures in which it occurred are ambiguous. The weight ck(x) of a frame x is used to estimate its probability pk(x). In each iteration of the algoritBrn, the weight of a frame C/ is calculated by considering the totality of alternatives in which ~c occurs (i.e., the sets for which z E X and IX\[ &gt; 1), and its probability within each alternative.</Paragraph>
      <Paragraph position="7"> The best frames in a set are the most probable frames given the evidence provided by the data. In the experiment described in section 3~ the 6n~:l number of iterations was set empirically.</Paragraph>
    </Section>
    <Section position="4" start_page="159" end_page="160" type="sub_section">
      <SectionTitle>
2.4 SF l~klng
</SectionTitle>
      <Paragraph position="0"> This component ranks the SFs obtained by the previous component of the system. Let PSc be the set of head lemmata (verbs, nouns and adjectives) in the subcategorization cues (i.e., best frames in the SF sets) for a given corpus C. Let .~&amp;quot; be the set {NPA V\[-\], NPD V\[-\], V\[-\], PP\[an\] V\[.\], PP\[an\] NPA V\[-\], ...} of SF structures. (Roughly, an SF structure is an SF without its head lernm~) The analysis of SF cues is performed by creating a contingency table cont~inlng the following counts for each lemma L E PSc and prepositional structure S E yr: k(L S) (k(L S)) is the count of lemm~ L with (without) structure S, and k(L S) (k(L S)) is the count of all \]~mm~ta in PSc except L with (without) structure S.</Paragraph>
      <Paragraph position="1"> If a lemma L occurs independently of a structure S, then one would expect that the distribution of L given that S is present and that of L given that S is not present have the same underlying parameter. The log likelihood statistic is used to test this hypothesis. This statistic is given by -2 log A = 2(log L(p1, kl, hi) /log L(p2, k2, n2)-log L(p, kl, R1)--log L(p, k2, n2)), where log LCo, k, n) = k logp + (n - k)log(1 -- p), and Pl = ~, P2 = ~, P = ,~',~; (For a detailed description of the statistic used, see (Dunning, 1993)).</Paragraph>
      <Paragraph position="2"> In the formulae above, kl is k(L S), nl is the total number of occurrences  of S, k2 is/c(L S), and n2 the total number of occurrences of structures other than S. A large value of -2 log A for a lemma L and structure S m~n~ that  the outcome is such that the hypothesis that the two distributions have the same underlying parameter is ,mllicely, and that a lemm~ L is highly associated with a structure S in a given corpus. This value is used to rank the subcategorization cues produced by the previous components of the system.</Paragraph>
    </Section>
  </Section>
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