Proof-Theoretic Aspects of the Lambek-Grishin Calculus
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 . 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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