Traduction des Grammaires Catégorielles de Lambek dans les Grammaires Catégorielles Abstraites
This work addresses the unification of computational models for natural language processing, specifically for syntax-heavy languages like English, but it is incremental as it builds on existing grammars without introducing a new paradigm.
The paper tackles the problem of expressing Lambek Grammars (LG) within Abstract Categorial Grammars (ACG) by transforming LG's type rewriting system into that of Context-Free Grammars, preserving derivations and allowing iterative control over infinite generative processes. It demonstrates that every LG can be efficiently expressed in ACG, though the algorithm was not fully implemented.
Lambek Grammars (LG) are a computational modelling of natural language, based on non-commutative compositional types. It has been widely studied, especially for languages where the syntax plays a major role (like English). The goal of this internship report is to demonstrate that every Lambek Grammar can be, not entirely but efficiently, expressed in Abstract Categorial Grammars (ACG). The latter is a novel modelling based on higher-order signature homomorphisms (using $λ$-calculus), aiming at uniting the currently used models. The main idea is to transform the type rewriting system of LGs into that of Context-Free Grammars (CFG) by erasing introduction and elimination rules and generating enough axioms so that the cut rule suffices. This iterative approach preserves the derivations and enables us to stop the possible infinite generative process at any step. Although the underlying algorithm was not fully implemented, this proof provides another argument in favour of the relevance of ACGs in Natural Language Processing.