One More Perspective on Semantic Relations in TAG

It has often been noted that the derivation trees of “standard” TAG grammars for natural languages (Group, 1998) resemble semantic dependency trees (Mel’ĉuk, 1988). More interesting, from a formal perspective, are the ways in which the derivation trees and the dependency trees diverge for certain problematic constructions. The desire to fix these cases has led to a variety of proposals for modifying or extending the TAG formalism ranging from Tree-Local Multi-component TAGs (TL-MCTAG) and Set-Local Multi-component TAGs (SL-MCTAG), through reconceptualization of the adjoining operation (Schabes and Shieber, 1994), through D-Tree Grammars (DTG) (Rambow, Vijay-Shanker and Weir, 1995) and Graph-driven Adjunction Grammar (GAG) (Candito and Kahane, 1998b), through reformalization of elementary trees in terms of C-Command rather than domination (Frank, Kulick and Vijay-Shanker, 2000), through the use of Meta-Grammars (Dras, 1999; Dras, Chiang and Schuler, To Appear), and through interpreting the semantic relations in a predicate-argument structure derived, but distinct, from the derivation trees (Joshi and Vijay-Shanker, 1999; Schuler, 1999). In this note, we look at some of these problematic constructions from yet another formal perspective—a mild extension of TAGs with well-constrained generative capacity which allows semantic dependency to be expressed as a relation orthogonal (in a quite literal sense) to constituency and linear precedence. We should be clear at the outset, our focus is nearly exclusively formal—we explore ways of expressing these relationships in the extended formalism without pursuing their potential linguistic repercussions. Neither is our account exhaustive. There are problematic constructions that have not yet yielded to this approach. Our goal is to introduce the techniques involved, to explore their limits and, possibly, open up discussion of their linguistic consequences. We will look five at examples from the literature: