On Reduction Systems Equivalent to the Non-associative Lambek Calculus with the Empty String

摘要

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 (NL_0) 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.