Applicative abstract categorial grammars in full swing

Abstract

Recently introduced Applicative Abstract Categorial Grammars (AACG) extend the Abstract Categorial Grammar (ACG) formalism to make it more suitable for semantic analyses while preserving all of its benefits for syntactic analyses. The surface form of a sentence, the abstract (tecto-) form, as well as the meaning are all uniformly represented in AACG as typed terms, or trees. The meaning of a sentence is obtained by applying to the abstract form a composition of elementary, deterministic but generally partial transformations. These term tree transformations are specified precisely and can be carried out mechanically. The rigor of AACG facilitates its straightforward implementation, in Coq, Haskell, Grammatical Framework, etc. We put AACG through its paces, illustrating its expressive power and positive as well as negative predictions on the wide range of analyses: gender-marked pronouns, quantifier ambiguity, scoping islands and binding, crossover, topicalization, and inverse linking. Most of these analyses have not been attempted for ACG. AACG offers a different perspective on linguistic side-effects, demonstrating compositionality not just of meanings but of transformations.