Proof nets for the multimodal Lambek calculus

Studia Logica 71 (3):415-442 (2002)
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.
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Michael Moortgat (2009). Symmetric Categorial Grammar. Journal of Philosophical Logic 38 (6):681 - 710.
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