Name
Abstract | ||
|---|---|---|
This paper 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 non-commutative 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 (substitution and
adjunction), and the elementary trees, i.e. the grammar. The sequent calculus is a restriction of the standard sequent calculus
for N-ILL. Trees (initial or derived) are then obtained as the closure of the calculus under two rules that mimic the grammatical
ones. We then prove the equivalence between the language generated by a TAG grammar and the closure under substitution and
adjunction of its logical representation. Besides this nice property, we relate parse trees to logical proofs, and to their
geometric representation: proofnets. We briefly present them and give examples of parse trees as proofnets. This process can be interpreted as an assembling
of blocks (proofnets corresponding to elementary trees of the grammar).
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Year | DOI | Venue |
|---|---|---|
1996 | 10.1007/BFb0052153 | LACL |
Keywords | Field | DocType |
noncommutative linear logic,tree adjoining grammars,linear logic,tree adjoining grammar,sequent calculus | Tree-adjoining grammar,Discrete mathematics,Parse tree,Natural deduction,Proof theory,Sequent calculus,Algorithm,Noncommutative logic,Linear logic,Adjunction,Mathematics | Conference |
ISBN | Citations | PageRank |
3-540-63700-1 | 3 | 0.57 |
References | Authors | |
9 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| V. Michele Abrusci | 1 | 112 | 20.96 |
| Christophe Fouqueré | 2 | 28 | 10.68 |
| Jacqueline Vauzeilles | 3 | 81 | 11.63 |