Predicative Coordination

This section describes the method for predicative coordination (including VP coordination of various kinds) used in XTAG. The description is derived from work described in ([#!anoopjoshi96!#]). It is important to say that this implementation of predicative coordination is not part of the XTAG release at the moment due massive parsing ambiguities. This is partly because of the current implementation and also the inherent ambiguities due to VP coordination that cause a combinatorial explosion for the parser. We are trying to remedy both of these limitations using a probability model for coordination attachments which will be included as part of a later XTAG release. This extended domain of locality in a lexicalized Tree Adjoining Grammar causes problems when we consider the coordination of such predicates. Consider ((385)) for instance, the NP the beans that I bought from Alice in the Right-Node Raising (RNR) construction has to be shared by the two elementary trees (which are anchored by cooked and ate respectively).

(384)0(384

(385)

(((Harry cooked) and (Mary ate)) the beans that I bought from Alice) 

We use the standard notion of coordination which is shown in Figure 21.10 which maps two constituents of like type, but with different interpretations, into a constituent of the same type.

  

Figure 21.10: Coordination schema

We add a new operation to the LTAG formalism (in addition to substitution and adjunction) called conjoin (later we discuss an alternative which replaces this operation by the traditional operations of substitution and adjunction). While substitution and adjunction take two trees to give a derived tree, conjoin takes three trees and composes them to give a derived tree. One of the trees is always the tree obtained by specializing the schema in Figure 21.10 for a particular category. The tree obtained will be a lexicalized tree, with the lexical anchor as the conjunction: and, but, etc. The conjoin operation then creates a contraction between nodes in the contraction sets of the trees being coordinated. The term contraction is taken from the graph-theoretic notion of edge contraction. In a graph, when an edge joining two vertices is contracted, the nodes are merged and the new vertex retains edges to the union of the neighbors of the merged vertices. The conjoin operation supplies a new edge between each corresponding node in the contraction set and then contracts that edge. For example, applying conjoin to the trees Conj(and), $\alpha(eats)$ and $\alpha(drinks)$ gives us the derivation tree and derived structure for the constituent in (386) shown in Figure 21.11.

(385)0(385

(386)

$\ldots$ eats cookies and drinks beer 

  

Figure: An example of the conjoin operation. $\{1\}$ denotes a shared dependency.

Another way of viewing the conjoin operation is as the construction of an auxiliary structure from an elementary tree. For example, from the elementary tree $\alpha(drinks)$, the conjoin operation would create the auxiliary structure $\beta(drinks)$ shown in Figure 21.12. The adjunction operation would now be responsible for creating contractions between nodes in the contraction sets of the two trees supplied to it. Such an approach is attractive for two reasons. First, it uses only the traditional operations of substitution and adjunction. Secondly, it treats conj X as a kind of ``modifier'' on the left conjunct X. This approach reduces some of the parsing ambiguities introduced by the predicative coordination trees and forms the basis of the XTAG implementation.

  

Figure 21.12: Coordination as adjunction.

More information about predicative coordination can be found in ([#!anoopjoshi96!#]), including an extension to handle gapping constructions.