Recently M. Szabolcs [12] has shown that many substructural logics including Lambek CalculusL are complete with respect to relativized Relational Semantics. The current paper proves that it is sufficient forL to consider a relativization to the relation x dividesy in some fixed semigroupG.

We present a labelled version of Lambek Calculus without unit, and we use it to prove a completeness theorem for Lambek Calculus with respect to some relational semantics.