Tree Adjoining Grammar, Semantic Calculi and Labelling Invariants

Recently, proposals have been made to combine Tree Adjoining Grammar (TAG) with either Glue or Flat Semantic Representation Languages. In this paper, we additionally specify the combination of TAG with λ-based semantics and compare the three approaches. We observe several invariants and suggest that semantic construction in TAG is governed by a set of general principles that can be used to facilitate the design and development of TAGs integrating a semantic dimension. 1 A brief introduction to TAG We use a unification based version of Lexicalised TAG namely, Feature-based TAG. A Feature-based TAG (FTAG, [?]) consists of a set of (auxiliary or initial) elementary trees and of two tree composition operations: substitution and adjunction. Substitution inserts a tree onto the leaf node of another tree1 while adjunction inserts an auxiliary tree into a derived tree (i.e., either an elementary tree or a tree resulting from the combination of a derived tree with an elementary tree by means either of adjunction or of substitution). In an FTAG, each tree node is associated with two feature structures called top and bottom. The top feature structure encodes information that needs to be percolated up the tree should an adjunction take place whilst the bottom feature structure encodes information that remains local to the node at which adjunction takes place. During derivation, the unifications listed in Figure 1 take place. These leaf nodes must be marked for substitution and are graphically distinguished by a downarrow.