Article

Studia Logica

, Volume 71, Issue 3, pp 415-442

First online:

Proof Nets for the Multimodal Lambek Calculus

  • Richard MootAffiliated withUtrecht Institute of Linguistics OTS, Utrecht University
  • , Quintijn PuiteAffiliated withDepartment of Mathematics, Utrecht University

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Abstract

We present a novel way of using proof nets for the multimodal Lambek calculus, which provides a general treatment of both the unary and binary connectives. We also introduce a correctness criterion which is valid for a large class of structural rules and prove basic soundness, completeness and cut elimination results. Finally, we will present a correctness criterion for the original Lambek calculus Las an instance of our general correctness criterion.

Cut Elimination Lambek Calculus Linear Logic Multimodal Lambek Calculus Proof Nets Proof Theory