Extended Lambek calculi and first-order linear logic

TL;DR

This paper explores the relationship between first-order multiplicative intuitionistic linear logic (MILL1) and the Lambek calculus, demonstrating how certain fragments generate complex language classes like multiple context-free languages.

Contribution

It introduces fragments of MILL1 that extend the Lambek calculus to generate multiple context-free languages and relate to the Displacement calculus.

Findings

Fragments of MILL1 generate multiple context-free languages

Certain MILL1 fragments correspond to the Displacement calculus

Extension of Lambek calculus via MILL1

Abstract

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.