This book investigates the possible linguistic applications of proof nets, redundancy free representations of proofs, which were introduced by Girard for linear logic.
We will adapt the notion of proof net to allow the formulation of a proof net calculus which is sound and complete for the multimodal Lambek calculus.
Finally, we will investigate the computational and complexity theoretic consequences of this calculus and give an introduction to a practical grammar development tool based on proof nets.