We use the standard notion of coordination which is shown in Figure 22.10 which maps two constituents of like type, but with different interpretations, into a constituent of the same type.
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 22.10 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), and gives us the derivation tree and derived structure for the constituent in (438) shown in Figure 22.11.
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 , the conjoin operation would create the auxiliary structure shown in Figure 22.12. 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.
More information about predicative coordination can be found in ([#!anoopjoshi96!#]), including an extension to handle gapping constructions.