Language completeness of the Lambek calculus
Mati Reinovich Pentus · 2002
Proves that the Lambek calculus (J. Lambek, American Math. Monthly, vol. 65, no. 3, pp. 154-170, 1958), which is essentially a subsystem of noncommutative linear logic, is complete with respect to L-models, i.e. free semigroup models.>