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Proof Nets for the Multimodal Lambek Calculus

Richard Moot and Quintijn Puite
Studia Logica: An International Journal for Symbolic Logic
Vol. 71, No. 3, The Lambek Calculus in Logic and Linguistics (Aug., 2002), pp. 415-442
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016443
Page Count: 28
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Proof Nets for the Multimodal Lambek Calculus
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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 L as an instance of our general correctness criterion.

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