On reduction systems equivalent to the non-associative Lambek calculus with the empty string
The article concludes a series of results on cut-rule axiomatizability of the Lambek calculus. It is proved that the non-associative product-free Lambek calculus with the empty string (NL0) is not finitely axiomatizable if the only rule of inference admitted is Lambek's cut rule. The proof makes use of the (infinitely) cut-rule axiomatized calculus NC designed by the author exactly for that purpose.
lambek calculus axiomatizability cut rule