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<Paper uid="C92-1034">
  <Title>Structure Sharing in Lexicalized Tree-Adjoining Graulmars*</Title>
  <Section position="4" start_page="0" end_page="0" type="intro">
    <SectionTitle>
3 Lexical Organization
</SectionTitle>
    <Paragraph position="0"> The lexical entries (LEs) are organized in hierarchical fashion. The value of an attribute of lexical entry in the lexicon is either obtained by inheritance or by local specification. We allow for overwriting inherited attributes by assuming that the local specification has a higher precedence. Figure 2 shows a fragment of the hierarchy for verbs. The lexicon associates lexicaJ items with a set of classes.</Paragraph>
    <Paragraph position="1"> Entries specify relationships and properties of sets of nodes in trees which will be associated with the lexical items. The framework for describing the tree that will be associated with the lexicai item is very similar to unification based tree-adjoining grammar (Vijay-Shanker, 1992) in which the trees are described with partial descriptions of their topology (Rogers and  and linear precedence. We do not discuss tile description language in which these trees are stated. Instead, we will pictorially represent these partial descriptions of trees.</Paragraph>
    <Paragraph position="2"> For the purposes of this paper, in our representation scheme, we will focus on the descriptions of associated elementary trees.</Paragraph>
    <Paragraph position="3"> Each class comprises of tile following attributes (among others): * superclasses, tile set of imnlediate ancestor classes from which the current class inherits.</Paragraph>
    <Paragraph position="4"> * nodes, the set of entities involved in the lexical entry.</Paragraph>
    <Paragraph position="5"> * description, a partial description of a tree. This description consists of partial statements of domination, immediate domination and linear precedence over the set of nodes given in the previous attribute. In tile following, we will ignore tile linear precedence relationship. The immediate domination relationship will be illustrated by a plain line and the domination relationship by a dotted line.</Paragraph>
    <Paragraph position="6"> The language of this description and its semantic is given by Rogers and Vijay-Shanker (1992). The dashed line between tree nodes does not mean they are necessarily different nodes. It is used to indicate the two nodes in question could he the same or if they are ditferent then one. of them dominates the other in the manner indicated.</Paragraph>
    <Paragraph position="7"> o constraint equations are unification equations that hold between the set of nodes. These equations specify feature structnres associated with the set of nodes. Attritmtes such as agreemeut (agr) or case (ease) are found in these equations.</Paragraph>
    <Paragraph position="8"> * completion; y = completion(x) specifies that y is the lowest node in the tree which does not require any argument of the predicative element x. This will be used, for example, in defining how the tree for wh-question is obtained.</Paragraph>
    <Paragraph position="10"> nsed in propagation of features by asl implicit assumption of head-feature convention.</Paragraph>
    <Paragraph position="11"> * argument node ; arft specifies the node for the argnment being introduced by the entry. This will be used to identify nodes that are mentioned in different classes e.g. in NP-IOBJ or used in tile syntactic rides such as for Wll-movement.</Paragraph>
    <Paragraph position="12"> * linear precedence (LP) statements which define precedence an'long nodes within the framework of ID/LP TAG proposed by Jo~hi (1987).</Paragraph>
    <Paragraph position="13"> * anchm; anchor --- xspecifies that the node x is tile aalchor node of the tree being described.</Paragraph>
    <Paragraph position="14"> For each entity in the hierarchy, attributes (such as arg) of some its aalcestors can be referred to for further specifying the description while inheriting the description of its ancestors.</Paragraph>
    <Paragraph position="15"> We can now consider an example. The following entry can be associated with the class VERB: 1 In this entry, as well ,a.q in the following entries, we do not give the full specification but specify only that part which is relevant to the discussion.</Paragraph>
    <Paragraph position="16">  up. &lt; agr &gt;= vp. &lt; ayr &gt; constraints equations: up. &lt;: cast: &gt;= nora arg : np</Paragraph>
    <Paragraph position="18"> This entry specifies partially the tree structure for every verb, indicating that (by default) each verb must have a subject. It is important to note that despite the pictorial representation used, s,np, vp, v are used to refer to node and not to their labels.</Paragraph>
    <Paragraph position="19"> The following entry is associated with the class of transitive verbs (TIL~NSITIVE): 2 1Tire tree described below could have been predicted from general principles nuch an HPSG'a rule atated on Page 149 in Pollard and Sag (1987).</Paragraph>
    <Paragraph position="20"> 2Similarly, tile tree described below could have been predicted from HPSG's rule atated on page 151 in Pollard and Sag (1987).</Paragraph>
    <Paragraph position="22"> The following entry is associated with the class of verbs taking an NP as indirect objects(IOBJ) which may be possibly found within a prepositional phrase or</Paragraph>
    <Paragraph position="24"> The following entry is associated with the class of ditransitive verbs taking a noun phrase as direct object and a prepositional phrase as an indirect object.</Paragraph>
    <Paragraph position="25"> The entry only specifies that the NP direct object must precede the NP introduced by the prepositional phrase.</Paragraph>
    <Paragraph position="27"> The following entry is associated with the class of verbs taking an NP as indirect objects (NP-IOBJ): NP-IOBJ superclaases: IOBJ nodes: vp, v, np constraints equations:...</Paragraph>
    <Paragraph position="28"> arg: np description: A</Paragraph>
    <Paragraph position="30"> The equality np= arg(IOBJ) used in the above frame forces the NP argument introduced in IOBJ (a superclass of NP-IOBJ) to be immediately dominated by the VP node, thus disallowing it being embedded in a prepositional phrase.</Paragraph>
    <Paragraph position="31"> However, the following entry is associated with the class of verbs taking a prepositional phrase (PP-IOBJ): The description of the default tree for DITRANS1 is inherited from VERB, TRANSITIVE, 10B J, PP-IOBJ. From the descriptions given in VERB and in TRANSITIVE we obtain the following structures:  Note that the VP node in VERB dominateS the verb node whereas the one introduced in TRANSITIVE immediately dominates the verb node. This results in the VP node introduced in verbs dominating (hence the dashed line) the VP node introduced in the TRANSITIVE frame. This kind of reasoning that leads to the formation of complex tree structures is given by Rogers and Vijay-Shanker (1992). Proceeding with the description of the tree structure inherited from IOBJ and PP-IOBJ we get:  which is used as default structnre for verbs that belong to DITRANS1. a In general this method for building a tree to be associated with a lexical item can be described as follows. First the nodes described in each superclass of the lex~ ical entry are collected along with the statements of relationships specified between the nodes. This may require renaming of nodes in case nodes in different classes are given the same name. For instance, when we collect the nodes specified in VERB and TRAN-S\[7'IVE, the VP nodes specified in them must be re named (say as vpl and vp~) as must the NP nodes (say, the node for the subject that is specified in VERB gets renamed as up1 and the object specified in TRANS1-TIVF gets renamed as np2). Next we must add an extra statement to explicitly equate tile anchor nodes specified. Now if we additionally inherit the descriptions from 10B,\] aud PP-IOBJ the two NP nodes introduced get renamed but identified as a result of the identification suggested in PP-IOBJ. Notice that the identification of the VP nodes in TRANSITIVI';, IOBJ, and PP-IOBJ does not get occur at this point.</Paragraph>
    <Paragraph position="32"> Such an identification gets done when we pass the tree descriptions collected to the machinery described by Rogers anti Vijay-Shanker (1992). Since the anchors specified in these three classes get identified, the three VP nodes specified (in TRANSITIVE, IOBJ, and PP-IGBJ) as the parents of these anchor nodes must also get identified. Using this type of reasoning about the structural properties of trees, the structure given above gets created. To complete the discu~qion of the inheritance of the tree descriptions, the head-daughter relations are noted in order that they can be used for feature sharing. Also the set of arg nodes are also collected and called the aTys of the lexical entry. For example, the args in the case above would be up1 (from VERB), np2 (from TRANSITIVE), npa (from IOBJ), and pp (from PP-IOB~. Later, in the syntactic rule, Wh-QUESTION, we use the a~ys of a lexieal entry to indicate tbe set of possible nodes that can be moved.</Paragraph>
    <Paragraph position="33"> In TAG the structure we derived above for DITRANS1 is represented in the form of the following tree: 3If needed, the value of the preposition can be specified by addltlona\] information at the lexical entry.</Paragraph>
    <Paragraph position="34"> np vp v np pp p np with two feature structures (toll and bottom) a.,~oelated with the VP node to indicate the collapsing of two VP nodes linked by domination. Tiffs process is also described in (Rogers and Vijay-Shanker, 1992).</Paragraph>
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