Non-linear Second order Abstract Categorial Grammars and deletion

Sylvain Salvati (1, 2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 PoSET - Models for a Structured Programming of Space and Time

We prove that non-linear second order Abstract Categorial Grammars (2ACGs) are equivalent to non-deleting 2ACGs. We prove this result first by using the intersection types discipline. Then we explain how coherence spaces can yield the same result. This result shows that restricting the Montagovian approach to natural language semantics to use only ΛI-terms has no impact in terms of the definable syn-tax/semantics relations. Moreover from the ACG perspective this result is a generalization of a result by Yoshinaka: it shows that deletion add no expressive power to second order ACGs.

Mots clés: lambda-calculus; abstract categorial grammars; linear logic

Domaines: Théorie et langage formel [cs.FL]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

Sylvain Salvati. Non-linear Second order Abstract Categorial Grammars and deletion. NLCS 2015: Natural Language and Computer Science, Makoto Kanazawa, 2015, Kyoto, Japan. ⟨hal-01251127⟩