The Conjoinability Relation in Discontinuous Lambek Calculus

In 2013 Sorokin proved that the criterion of type conjoinability in 1-discontinuous Lambek calculus is the equality of interpretations in the free abelian group generated by primitive types. We extend the method to obtain the analogous result in full discontinuous Lambek calculus. It holds that the criterion is exactly the same as in 1-discontinuous Lambek calculus.