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<Paper uid="P01-1024">
  <Title>Topological Dependency Trees: A Constraint-Based Account of Linear Precedence</Title>
  <Section position="3" start_page="0" end_page="0" type="metho">
    <SectionTitle>
2 Discontinuous Constructions
</SectionTitle>
    <Paragraph position="0"> In free word order languages, discontinuous constructions occur frequently. German, for example, is subject to scrambling and partial extraposition.</Paragraph>
    <Paragraph position="1"> In typical phrase structure based analyses, such phenomena lead to e.g. discontinuous VPs:  (dass) einen Mann Maria zu lieben versucht Since this is classically disallowed, discontinuous constituents must often be handled indirectly through grammar extensions such as traces.</Paragraph>
    <Paragraph position="2"> Reape (1994) proposed the theory of word order domains which became quite popular in the HPSG community and inspired others such as M&amp;quot;uller (1999) and Kathol (2000). Reape distinguished two orthogonal tree structures: (a) the unordered syntax tree, (b) the totally ordered tree of word order domains. The latter is obtained from the syntax tree by flattening using the operation of domain union to produce arbitrary interleavings. The boolean feature [[ ] of each node controls whether it must be flattened out or not. Infinitives in canonical position are assigned [[+]:  As a consequence, Reape's theory correctly predicts scrambling (2,3) and full extraposition (4), but cannot handle the partial extraposition in (5):  (2) (dass) Maria einen Mann zu lieben versucht (3) (dass) einen Mann Maria zu lieben versucht (4) (dass) Maria versucht, einen Mann zu lieben (5) (dass) Maria einen Mann versucht, zu lieben</Paragraph>
  </Section>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3 Topological Dependency Trees
</SectionTitle>
    <Paragraph position="0"> Our approach is based on dependency grammar.</Paragraph>
    <Paragraph position="1"> We also propose to distinguish two structures: (a) a tree of syntactic dependencies, (b) a tree of topological dependencies. The syntax tree (ID tree) is unordered and non-projective (i.e. it admits crossing edges). For display purposes, we pick an arbitrary linear arrangement:  Its edge labels are called (external) fields and are totally ordered: df mf vc. This induces a linear precedence among the daughters of a node in the LP tree. This precedence is partial because daughters with the same label may be freely permuted. null In order to obtain a linearization of a LP tree, it is also necessary to position each node with respect to its daughters. For this reason, each node is also assigned an internal field (d, n, or v) shown above on the vertical pseudo-edges. The set of internal and external fields is totally ordered: d df n mf vc v Like Reape, our LP tree is a flattened version of the ID tree (Reape, 1994; Uszkoreit, 1987), but the flattening doesn't happen by 'unioning up'; rather, we allow each individual daughter to climb up to find an appropriate landing place. This idea is reminiscent of GB, but, as we shall see, proceeds rather differently.</Paragraph>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 Formal Framework
</SectionTitle>
    <Paragraph position="0"> The framework underlying both ID and LP trees is the configuration of labeled trees under valency (and other) constraints. Consider a finite set L of edge labels, a finite set V of nodes, and E V V L a finite set of directed labeled edges, such that (V; E) forms a tree. We write w !' w0 for an edge labeled ' from w to w0. We define the '-daughters '(w) of w 2 V as follows: '(w) = fw0 2 V j w !' w0 2 Eg We write bL for the set of valency specifications b' defined by the following abstract syntax: b' ::= ' j '? j ' (' 2 L) A valency is a subset of bL. The tree (V; E) satisfies the valency assignment valency : V ! 2bL if for all w 2 V and all ' 2 L:</Paragraph>
    <Paragraph position="2"/>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
4.1 ID Trees
</SectionTitle>
      <Paragraph position="0"> An ID tree (V; EID; lex; cat; valencyID) consists of a tree (V; EID) with EID V V R, where the set R of edge labels (Figure 1) represents syntactic roles such as subject or vinf (bare infinitive argument). lex : V ! Lexicon assigns a lexical entry to each node. An illustrative Lexicon is displayed in Figure 1 where the 2 features cats and valencyID of concern to ID trees are grouped under table heading &amp;quot;Syntax&amp;quot;. Finally, cat and valencyID assign a category and an bR valency to each node w 2 V and must satisfy:</Paragraph>
      <Paragraph position="2"> (V; EID) must satisfy the valencyID assignment as described earlier. For example the lexical entry for versucht specifies (Figure 1): valencyID(versucht) = fsubject; zuvinfg Furthermore, (V; EID) must also satisfy the edge constraints stipulated by the grammar (see Figure 1). For example, for an edge w !det w0 to be licensed, w0 must be assigned category det and both w and w0 must be assigned the same agreement.1</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
4.2 LP Trees
</SectionTitle>
      <Paragraph position="0"> An LP tree (V; ELP; lex; valencyLP; fieldext; fieldint) consists of a tree (V; ELP) with ELP V V Fext, where the set Fext of edge labels represents topological fields (Bech, 1955): df the determiner field, mf the 'Mittelfeld', vc 1Issues of agreement will not be further considered in this paper.</Paragraph>
      <Paragraph position="1"> the verbal complement field, xf the extraposition field. Features of lexical entries relevant to LP trees are grouped under table heading &amp;quot;Topology&amp;quot; in Figure 1. valencyLP assigns a dFext valency to each node and is subject to the lexicalized constraint:</Paragraph>
      <Paragraph position="3"> (V; ELP) must satisfy the valencyLP assignment as described earlier. For example, the lexical entry for zu lieben2 specifies: valencyLP(zu lieben2) = fmf ; xf?g which permits 0 or more mf edges and at most one xf edge; we say that it offers fields mf and xf. Unlike the ID tree, the LP tree must be projective. The grammar stipulates a total order on Fext, thus inducing a partial linear precedence on each node's daughters. This order is partial because all daughters in the same field may be freely permuted: our account of scrambling rests on free permutations within the mf field. In order to obtain a linearization of the LP tree, it is necessary to specify the position of a node with respect to its daughters. For this reason each node is assigned an internal field in Fint. The set Fext [Fint is totally ordered: d df n mf vc v xf In what (external) field a node may land and what internal field it may be assigned is determined by assignments fieldext : V ! Fext and fieldint : V ! Fint which are subject to the lexicalized constraints: fieldext(w) 2 lex(w):fieldext fieldint(w) 2 lex(w):fieldint For example, zu lieben1 may only land in field vc (canonical position), and zu lieben2 only in xf (extraposed position). The LP tree must satisfy: w !' w0 2 ELP ) ' = fieldext(w0) Thus, whether an edge w !' w0 is licensed depends both on valencyLP(w) and on fieldext(w0). In other words: w must offer field ' and w0 must accept it.</Paragraph>
      <Paragraph position="4"> For an edge w !' w0 in the ID tree, we say that w is the head of w0. For a similar edge in the LP</Paragraph>
      <Paragraph position="6"> wird fvfing fsubject; vinfg fvg fvcg fmf ; vc?; xf?g haben fvinfg fvpastg fvg fxfg fmf ; vc?; xf?g hat fvinfg fsubject; vpastg fvg fvcg fmf ; vc?; xf?g zu lieben1 fzuvinfg fobject?g fvg fvcg fg zu lieben2 fzuvinfg fobject?g fvg fxfg fmf ; xf?g versucht fvfing fsubject; zuvinfg fvg fvcg fmf ; vc?; xf?g  tree, we say that w is the host of w0 or that w0 lands on w. The shape of the LP tree is a flattened version of the ID tree which is obtained by allowing nodes to climb up subject to the following principles: Principle 1 a node must land on a transitive head2 Principle 2 it may not climb through a barrier We will not elaborate the notion of barrier which is beyond the scope of this article, but, for example, a noun will prevent a determiner from climbing through it, and finite verbs are typically general barriers.</Paragraph>
      <Paragraph position="7"> 2This is Br&amp;quot;ocker's terminology and means a node in the transitive closure of the head relation.</Paragraph>
      <Paragraph position="8"> Principle 3 a node must land on, or climb higher than, its head Subject to these principles, a node w0 may climb up to any host w which offers a field licensed by fieldext(w0).</Paragraph>
      <Paragraph position="9"> Definition. An ID/ LP analysis is a tuple (V; EID; ELP; lex; cat; valencyID; valencyLP; fieldext; fieldint) such that (V; EID; lex; cat; valencyID) is an ID tree and (V; ELP; lex; valencyLP; fieldext; fieldint) is an LP tree and all principles are satisfied. null Our approach has points of similarity with (Br&amp;quot;oker, 1999) but eschews modal logic in favor of a simpler and arguably more perspicuous constraint-based formulation. It is also related to the lifting rules of (Kahane et al., 1998), but where they choose to stipulate rules that license liftings, we opt instead for placing constraints on otherwise unrestricted climbing.</Paragraph>
    </Section>
  </Section>
  <Section position="6" start_page="0" end_page="0" type="metho">
    <SectionTitle>
5 German Verbal Phenomena
</SectionTitle>
    <Paragraph position="0"> We now illustrate our theory by applying it to the treatment of word order phenomena in the verbal complex of German verb final sentences. We assume the grammar and lexicon shown in Figure 1.</Paragraph>
    <Paragraph position="1"> These are intended purely for didactic purposes and we extend for them no claim of linguistic adequacy. null</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
5.1 VP Extraposition
</SectionTitle>
      <Paragraph position="0"> Control verbs like versuchen or versprechen al- null low their zu-infinitival complement to be optionally extraposed. This phenomenon is also known as optional coherence.</Paragraph>
      <Paragraph position="1"> (6) (dass) Maria einen Mann zu lieben versucht (7) (dass) Maria versucht, einen Mann zu lieben Both examples share the following ID tree: (dass) Maria einen Mann zu lieben versucht</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
5.2 Partial VP Extraposition
</SectionTitle>
      <Paragraph position="0"> In example (8), the zu-infinitive zu lieben is extraposed to the right of its governing verb versucht, but its nominal complement einen Mann remains in the Mittelfeld: (8) (dass) Maria einen Mann versucht, zu lieben In our account, Mann is restricted to land in an mf field which both extraposed zu lieben2 and finite verb versucht offer. In example (8) the nominal complement simply climbed up to the finite verb:</Paragraph>
    </Section>
    <Section position="3" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
5.3 Obligatory Head-final Placement
</SectionTitle>
      <Paragraph position="0"> Verb clusters are typically head-final in German: non-finite verbs precede their verbal heads.</Paragraph>
      <Paragraph position="1">  where mf vc v, and subject and object, both in field mf, remain mutually unordered. Thus we correctly license (9) and reject (10).</Paragraph>
    </Section>
    <Section position="4" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
5.4 Optional Auxiliary Flip
</SectionTitle>
      <Paragraph position="0"> In an auxiliary flip construction (Hinrichs and Nakazawa, 1994), the verbal complement of an auxiliary verb, such as haben or werden, follows rather than precedes its head. Only a certain class of bare infinitive verbs can land in extraposed position. As we illustrated above, main verbs do not belong to this class; however, modals such as k&amp;quot;onnen do, and may land in either canonical (11) or in extraposed (12) position. This behavior is called 'optional auxiliary flip'.</Paragraph>
      <Paragraph position="1">  Our grammar fragment describes optional auxiliary flip constructions in two steps: wird offers both vc and xf fields: valencyID(wird) = fmf ; vc?; xf?g k&amp;quot;onnen has two lexical entries, one canonical and one extraposed:</Paragraph>
      <Paragraph position="3"> guity concerning the topological placement of Mann: lieben in canonical position does not offer field mf; therefore Mann must climb to the finite verb.</Paragraph>
      <Paragraph position="4"> Thus we correctly account for examples (11) and (12) with the following LP trees:  The astute reader will have noticed that other LP trees are licensed for the earlier ID tree: they are considered in the section below.</Paragraph>
    </Section>
    <Section position="5" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
5.5 V-Projection Raising
</SectionTitle>
      <Paragraph position="0"> This phenomenon related to auxiliary flip describes the case where non-verbal material is interspersed in the verb cluster:  (13) (dass) Maria wird einen Mann lieben k&amp;quot;onnen (14)*(dass) Maria lieben einen Mann k&amp;quot;onnen wird (15)*(dass) Maria lieben k&amp;quot;onnen einen Mann wird  The ID tree remains as before. The NP einen Mann must land in a mf field. lieben is in canonical position and thus does not offer mf, but both extraposed k&amp;quot;onnen2 and finite verb wird do. Whereas in (12), the NP climbed up to wird, in  (13) it climbs only up to k&amp;quot;onnen.</Paragraph>
      <Paragraph position="1"> (dass) Maria wird einen Mann lieben k&amp;quot;onnen  vc of wird, therefore lieben must be in the vc of k&amp;quot;onnen, and einen Mann must be in the mf of wird. Therefore, einen Mann must precede both lieben and k&amp;quot;onnen. Similarly for (15).</Paragraph>
    </Section>
    <Section position="6" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
5.6 Intermediate Placement
</SectionTitle>
      <Paragraph position="0"> The Zwischenstellung construction describes cases where the auxiliary has been flipped but its verbal argument remains in the Mittelfeld. These are the remaining linearizations predicted by our theory for the running example started above: (16) (dass) Maria einen Mann lieben wird k&amp;quot;onnen (17) (dass) einen Mann Maria lieben wird k&amp;quot;onnen where lieben has climbed up to the finite verb.</Paragraph>
    </Section>
    <Section position="7" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
5.7 Obligatory Auxiliary Flip
</SectionTitle>
      <Paragraph position="0"> Substitute infinitives (Ersatzinfinitiv) are further examples of extraposed verbal forms. A substitute infinitive exhibits bare infinitival inflection, yet acts as a complement of the perfectizer haben, which syntactically requires a past participle. Only modals, AcI-verbs such as sehen and lassen, and the verb helfen can appear in substitute infinitival inflection.</Paragraph>
      <Paragraph position="1"> A substitute infinitive cannot land in canonical position; it must be extraposed: an auxiliary flip involving a substitute infinitive is called an 'obligatory auxiliary flip'.</Paragraph>
      <Paragraph position="2">  In (18) einen Mann climbs up to hat, while in (19) it only climbs up to k&amp;quot;onnen.</Paragraph>
    </Section>
    <Section position="8" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
5.8 Double Auxiliary Flip
</SectionTitle>
      <Paragraph position="0"> Double auxiliary flip constructions occur when an auxiliary is an argument of another auxiliary.</Paragraph>
      <Paragraph position="1"> Each extraposed verb form offers both vc and mf: thus there are more opportunities for verbal and nominal arguments to climb to.</Paragraph>
      <Paragraph position="2">  Obligatory coherence may be enforced with the following constraint principle: if w is an obligatory coherence verb and w0 is its verbal argument, then w0 must land in w's vc field. Like barriers, the expression of this principle in our grammatical formalism falls outside the scope of the present article and remains the subject of active research.4</Paragraph>
    </Section>
  </Section>
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