Tree Adjoining Grammars in Noncommutative Linear Logic (Extended Abstract)

V. Michele Abrusci 1 , Christophe Fouquer'e 2 , and Jacqueline Vauzeilles 2 1 CILA, Universit'a di Bari, 70121 Bari, Italy 2 LIPN-CNRS URA 1507, Universit'e Paris-Nord, 93430 Villetaneuse Abstract. This paper 1 presents a logical formalization of Tree-Adjoining Grammar (TAG). TAG deals with lexicalized trees and two operations are available: substitution and adjunction. Adjunction is generally presented as an insertion of a tree inside another, surrounding the subtree at the adjunction node. This seems to be contradictory with standard logical ability. We prove that some logic, namely a fragment of noncommutative intuitionistic linear logic (N-ILL), can serve this purpose. Briefly speaking, linear logic is a logic considering facts as resources. NILL can then be considered either as an extension of Lambek calculus, or as a restriction of linear logic. We model the TAG formalism in four steps: trees (initial or derived) and the way they are constituted, the operations (substit..