Classical non-associative Lambek calculus (Q1850952)

The aim of the paper is to present CNL, a classical version of the nonassociative Lambek calculus NL. CNL is presented as a sequent calculus, along with its associated theory of proof-nets. This theory includes a correctness criterion, which is defined on the cut-free proof-structure. It is proved that CNL is decidable in polynomial time. It is also shown that CNL can be treated as a conservative extension of NL.