Linear Logic based Semantics for LTAG -- and what it teaches us about LFG and LTAG --
We review existing appoaches to semantics construction in LTAG (Lexicalised Tree Adjoining Grammar) based on the notion of derivation (tree)s. We argue that derivation structures in LTAG are not appropriate to guide semantic composition, due to a non-isomorphism, in LTAG, between the syntactic operation of adjunction on the one hand, and the semantic operations of complementation and modification, on the other.
Linear Logic based "glue semantics", as developed within the LFG framework (cf. Dalrymple (1999)), allows for flexible coupling of syntactic and semantic structure. We investigate application of glue semantics to LTAG syntax, using as underlying structure the derived tree, which is more appropriate for principle-based semantics construction. We show how Linear Logic semantics construction helps to bridge the non-isomorphism between syntactic and semantic operations in LTAG. The glue approach captures non-tree local dependencies in control and modification structures, and extends to the treatment of scope ambiguity with quantified NPs and VP adverbials. Finally, glue semantics applies successfully to the adjunction-based analysis of long-distance dependencies in LTAG, which differs significantly from the f-structure based analysis in LFG.
On a more general perspective, the exercise is instructive in that it elucidates the role that f-structure plays in LFG syntax and semantics, and helps clarify the similarities and differences between the two frameworks.