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<Paper uid="W98-0510">
  <Title>A Case Study in Implementing Dependency-Based Grammars</Title>
  <Section position="2" start_page="88" end_page="89" type="metho">
    <SectionTitle>
2 A *problematic phenomenon:
</SectionTitle>
    <Paragraph position="0"> stranded and dangling prepositions Two classes of lone prepositions which are not followed by a complement are known as dangling and stranded prepositions. There are several contexts where these prepositions are found and they are very common in standard English. We will focus primarily on pseudo-passive and relative contexts, and mention another context in our conclusion.</Paragraph>
    <Paragraph position="1"> One example of a pseudo-passive, that is a passive with a stranded preposition, is given in (1) and some relative clause examples are illustrated in (2), where the preposition is said to be dangling (Mel'~uk, 1987, p.124). The prepositions are indicated in bold in each case. (I) Pseudo-passive (stranding) He was yelled at.</Paragraph>
    <Paragraph position="2"> (2) Relatives (with dangling prepositions) a. They knew the man we talked about.</Paragraph>
    <Paragraph position="3"> b. They knew the man who he thinks we talked about.</Paragraph>
    <Paragraph position="4"> Note that these lone prepositions are not used in the same contexts as particles like out which forms a phrasal verb with take in the sentence He took the garbage out. In this latter case while there is a debate as to where the preposition should attach (to the verb take or to the NP the garbage), no NP is missing, or extraposed, contrary to the examples above.</Paragraph>
    <Paragraph position="5"> Outside the realm of dependency grammar, in phrase structure grammar, the analysis of such sentences would have the lone preposition about belonging to the verb phrase headed by  talked. In the phrase structure approach of Gazdar et al (1985, p.147), for example, there would be an empty category and SLASH notation, as indicated in (3).</Paragraph>
    <Paragraph position="6"> O) Generalized Phrase S~ucune Grammar analysis</Paragraph>
    <Paragraph position="8"> In dependency grammar, the dependence relations are the crucial ones, rather than constituency. There have been different views on what relations a lone preposition bears to the other elements in these types of constructions. We will present analyses from the conceptions of dependency grammar proposed by Mel'~uk, and by Hudson, both of whom treat such constructions.</Paragraph>
    <Section position="1" start_page="89" end_page="89" type="sub_section">
      <SectionTitle>
2.2 Mel'~uk's Analyses
</SectionTitle>
      <Paragraph position="0"> According to Mel'~uk (1987, pp.82, 124-125), a preposition must have a dependent NP, except sn the following cases. Stranded prepositions have no dependent, and dangling prepositions may or may not have the usual dependent. If the dangling preposition does have a dependent, it is not attached in the usual way, as we will illustrate.</Paragraph>
      <Paragraph position="1"> Starting with pseudo-passives, preposition stranding occurs when the dependent NP in an active construction becomes the grammatical subject in the related pseudo-passive construction. Here are two examples from Mel'~uk.</Paragraph>
      <Paragraph position="2">  (4) Peter deals with the problem.</Paragraph>
      <Paragraph position="3"> (5) The problem is dealt with by Peter.</Paragraph>
      <Paragraph position="4">  One consequence of passivization is the conversion of one of the surface syntactic relations, known as SSyntRels in Mel'~uk's terminology (see the discussion in Mel'~uk, 1987, p.31). In particular, the relation that subordinates the preposition (and its dependent NP) to the active verb in (4) is not the same as the relation between those elements in (5). The corresponding structures in (4a) and (5a) below are derived from the diagram in Mel'~uk (1987, p.124), with the passive agent omitted.</Paragraph>
      <Paragraph position="5"> In (4a) the preposition with and its dependent the problem are subordinated to the verb deals by the 2rid Completive SSyntRel. In contrast, in (Sa) the latter SSyntRel is not tolerated in a passive construction and therefore a special SSyntRel, the Colligative, is posited especially for this construction.</Paragraph>
      <Paragraph position="6">  stranded prepositions and dangling prepositions. The dangling preposition, unlike the stranded preposition, keeps the original SSyntRel that subordinates it to the verb. Consider the data for dangling prepositions in relatives. The basic sentence in (6) has no relativization, while dangling prepositions can be found in sentences involving relative clauses such as (7) and (8) (examples from</Paragraph>
      <Paragraph position="8"> (6) I talked to all the accountants.</Paragraph>
      <Paragraph position="9"> (7) All the accountants whom I talk to say receivables are piling up.</Paragraph>
      <Paragraph position="10"> (8) All the accountants I talk to say receivables are piling up.</Paragraph>
      <Paragraph position="11">  In (6) the normal Prepositional SSyntRel holds between the preposition and its complement, as illustrated in (6a) below. The dangling preposition in (7) continues to head a SSyntRel that subordinates its displaced complement whom labelled a Prepositional SSyntRel, as in (7a). Finally, in (8), since whom is deleted, there is no such relation and the preposition has no dependents, as in (8a) (structures adapted from Mel'~uk 1987, pp. 130, 366):</Paragraph>
    </Section>
    <Section position="2" start_page="89" end_page="89" type="sub_section">
      <SectionTitle>
2.3 Hudson's Analyses
</SectionTitle>
      <Paragraph position="0"> The analysis of lone prepositions in Hudson (1990) involves somewhat different relations.</Paragraph>
      <Paragraph position="1"> He points out that in his theory, Word Grammar, multiple relations between two elements are allowed, and that a word may depend on more than one head simultaneously (see the discussion in Hudson 1992, p.145).</Paragraph>
      <Paragraph position="2"> Dangling prepositions in relatives are acknowledged but not given an explicit analysis in Hudson (1990). He does, however, provide the following analysis for a pseudo-passive with a stranded preposition (adapted from Hudson 1990, p.348).</Paragraph>
      <Paragraph position="3">  Notice that the stranded preposition in (9) bears three dependency relations. It is a postdependent of the verb yelled, it has the pronoun he as its complement, and it bears a relation special to pseudo-passives with stranded prepositions labelled passive-link.</Paragraph>
    </Section>
  </Section>
  <Section position="3" start_page="89" end_page="91" type="metho">
    <SectionTitle>
3 Implementation problems
</SectionTitle>
    <Paragraph position="0"> There are a number of problems associated with the implementation of these theoretical approaches. Note that there is disagreement between linguists as to the optimal treatment. It is perhaps no coincidence that a problem which presents theoretical difficulties is also more problematic to implement.</Paragraph>
    <Paragraph position="1"> In structures like (9) above, one node, namely the node containing the word he, has three fathers: was, yelled and at. We cannot implement this structure directly since in our implementation, each node in a structure has a unique father node and only adjacent nodes may be linked by a relation. This strategy reduces considerably the number of intermediate trees to be examined while constructing a given tree. It also simplifies traversal of trees.</Paragraph>
    <Paragraph position="2"> Consider next dangling prepositions in relatives, such as the man whom we talked about, which pose a similar problem. We cannot implement Mel'~uk's analysis illustrated in (10) since the node whom has two fathers: talked and about.</Paragraph>
    <Paragraph position="3">  Our initial hypothesis for implementing such relatives was simply to attach the dangling preposition to the verb immediately to its left as in (11) while allowing other constraints to verify that the relative pronoun is correctly licensed within the structure.</Paragraph>
    <Paragraph position="5"> the talked whom we about This choice of implementation led to a number of serious efficiency problems. The main problem we will address is that too many trees were being produced and therefore too much time was being wasted.</Paragraph>
    <Paragraph position="6">  A preposition must have a complement in order to attach to the verb with its normal relation. However, a dangling preposition attaches to the verb without its complement. In the course of analyzing every sentence containing a preposition after the verb, the preposition was attached both as dangling and the tree where they are licensed. That is, attachment of a lone preposition is permitted only when there is a context that permits such a preposition, such as a passive verb or a relative clause structure. We show how our solution reduced parsing time.</Paragraph>
    <Paragraph position="7"> not as dangling, since deciding whether a 4.1 Pseudo-passives given preposition is dangling or not can be difficult locally. Even if the invalid analyses For pseudo-passives, our implementation is can eventually be discarded, their generation greatly increases parsing time. We will see in the next section how this problem disappears if the analysis is slightly modified.</Paragraph>
    <Paragraph position="8"> Let us examine some other means of avoiding misanalysis and overgeneration of trees for these sentences, and show how these means are inadequate. First, one could verify the category of the word following the preposition since a lone preposition would not be followed by a nominal complement. This kind of restriction must be used with great care, especially in English in which words often belong to several categories and inflection is not rich enough to help disambiguate between categories. Consider some concrete examples such as (12) where the preposition in is not dangling and (13) where about is a dangling preposition. In (12), this restriction does not help the parser since shops can be a verb and yet it is the complement of the preposition.</Paragraph>
    <Paragraph position="9"> Similarly, in (13), checking the category of shops is not sufficient to determine that about is a dangling preposition since shops can be either a verb or a noun.</Paragraph>
    <Paragraph position="10">  (12) He sold them in shops.</Paragraph>
    <Paragraph position="11"> (13) The man we talked about shops here.</Paragraph>
    <Paragraph position="12">  Secondly, one could propose a strategy where the preposition would attach to the verb only after the relative clause has been attached to the noun. This presupposes, however, that subtrees can be combined arbitrarily, i.e. by joining together any intermediate (non-root) nodes in the construction of the tree. This is problematic because it potentially creates trees with two roots. Moreover, this augmentation of the system is not warranted. We already have an efficient strategy that is not arbitrary which allows the combination of complete subtrees only.</Paragraph>
  </Section>
  <Section position="4" start_page="91" end_page="92" type="metho">
    <SectionTitle>
4 Solutions
</SectionTitle>
    <Paragraph position="0"> To avoid superfluous tree building, we allow lone prepositions to attach only at the point in closer to that of Mel'~uk than to that of Hudson. Recall that Hudson's analysis in (9) involved multiple fathers. We thus chose not to implement his complement relation between at and he and only a single relation between yelled and at in sentences like He was yelled at.</Paragraph>
    <Paragraph position="1"> Following Hudson we use a distinctive relation, which we label prep-strand instead of passivelink. In addition, we use a set of constraints to check that the preposition is indeed appropriate to the verb (that yell can take at). Thus our analysis is as follows, where each node has at most one father and where only one relation holds between any pair of nodes:</Paragraph>
    <Section position="1" start_page="91" end_page="92" type="sub_section">
      <SectionTitle>
4.2 Relatives
</SectionTitle>
      <Paragraph position="0"> While our solution for pseudo-passives closely follows that of Mel'~uk, the case of relatives is more complex. Recall that some of his analyses of relatives involved multiple fathers.</Paragraph>
      <Paragraph position="1"> In order to avoid this problem in relative clauses, the dangling preposition is attached in our implementation not to the governing verb, but to the noun which is the antecedent of the relative. To see the advantage of our analysis, consider sentences where the relative is not introduced by a wh-word in examples like  (15) (previously (2a)).</Paragraph>
      <Paragraph position="2"> (15) The man we talked about.</Paragraph>
      <Paragraph position="3"> (15a) our original solution ~alked the we about  (15b) implemented solution man the about we In this example, the dangling preposition is only licensed by the presence of the relative clause. Instead of (15a), we therefore prefer the analysis in (15b), where the preposition is attached to the head noun man once a relative clause has been created. Rather than implementing a relation between talked and about we verify compatibility between the verb and its prepositional complement independently. Note that an incomplete relative clause is created: we talked. Some constraints are relaxed and checked at a higher level to ensure the ultimate completeness of the overall structure.</Paragraph>
      <Paragraph position="4"> Next, consider long-distance relatives such as in (16) (previously (2a)) and the analyses in  (16a) and (16b).</Paragraph>
      <Paragraph position="5"> (16) The man who he thinks we talked about (16a) our original solution  man the thinks who he talked we about (16b) implemented solution man the thinks about who he talked we In (16), we combine the problem of dangling a preposition with that of unbounded dependency. Within our system, it is impossible to attach the relative pronoun who to the verb which subcategorizes for it in these long-distance relatives because of word order. In the same way, the dangling preposition about does not attach to talked but rather it attaches at a higher level, to man. These analyses have crucially solved the problem of tree overgeneration. The attachment of lone prepositions may be made once the licensing criteria are met (passive voice, relativization or other such contexts). Therefore only those subtrees which will likely lead to a complete and successful analysis will be built.</Paragraph>
    </Section>
    <Section position="2" start_page="92" end_page="92" type="sub_section">
      <SectionTitle>
4.3 Remaining problems
</SectionTitle>
      <Paragraph position="0"> Our analysis presupposes that the dangling preposition occurs as the last element in the relative clause. There are rare cases where another element can follow the dangling preposition, such as (17).</Paragraph>
      <Paragraph position="1"> (17) The man we talked about to Mary Since the dangling preposition about is attached to man, to avoid crossing of dependency relations, we would have to attach the phrase to Mary to the node man instead of attaching it more naturally to the verb talked. The analysis is shown in (18).</Paragraph>
      <Paragraph position="2"> (18) tough-adjective with an extra PP man /_~ ~t~&amp;quot;~ _3.</Paragraph>
      <Paragraph position="3"> the talked about Mary we to Note that there are cases where a prepositional phrase can attach to a noun following a relative. Thus the construction in (17) would have the same analysis as that in (19). (19) The man we talked about with glasses Constructions such as the one in (17) are not marked constructions. However, given their low frequency relative to the high frequency of preposition dangling in general, our constrained analysis is justified in terms of computational efficiency.</Paragraph>
    </Section>
  </Section>
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