# Proof-Theoretic Aspects of the Lambek-Grishin Calculus

Conference paper

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## Abstract

We compare the Lambek-Grishin Calculus (**LG**) as defined by Moortgat [9, 10] with the non-associative classical Lambek calculus (**CNL**) introduced by de Groote and Lamarche [4]. We provide a translation of **LG** into **CNL**, which allows **CNL** to be seen as a non-conservative extension of **LG**. We then introduce a bimodal version of **CNL** that we call 2-**CNL**. This allows us to define a faithful translation of **LG** into 2-**CNL**. Finally, we show how to accomodate Grishin’s interaction principles by using an appropriate notion of polarity. From this, we derive a new one-sided sequent calculus for **LG**.

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