Extended Lambek calculi and first-order linear logic

Richard Moot (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

First-order multiplicative intuitionistic linear logic (MILL1) can be seen as an extension of the Lambek calculus. In addition to the fragment of MILL1 which corresponds to the Lambek calculus (of Moot & Piazza 2001), I will show fragments of MILL1 which generate the multiple context-free languages and which correspond to the Displacement calculus of Morrilll e.a.

Mots clés: first-order linear logic; Lambek calculus; Displacement calculus; Multiple Context-Free Grammars; proof nets

Domaines: Informatique et langage [cs.CL]

Richard Moot. Extended Lambek calculi and first-order linear logic. Claudia Casadio, Bob Coecke, Michael Moortgat and Philip Scott. Categories and Types in Logic, Language and Physics: Essays Dedicated to Jim Lambek on the Occasion of His 90th Birthday, 8222, Springer, pp.297-330, 2014, Lecture Notes in Computer Science, 978-3-642-54788-1. ⟨hal-00826416⟩