The vocabulary of DL (Discontinuous Lambek Calculus) consists of residuated families of unary and binary type-forming operations.  A representative sample is given below.  For the binary case, in addition to the concatenation product of L and the residual slash operations, we have a discontinuous (wrapping) product ⊙, with residual infixation ↓ and extraction ↑ operations.  For the deterministic interpretation, the discontinuous type-forming operations have an indexed form ↑k, ⊙k, ↓k explicitly referring to the k-th split point of their interpretants.  The function of the unary operations is to control the creation and removal of split points.  As in the binary case, we have non-deterministic operations (bridge ∧, split ∨) and indexed forms (∧k,∨k) with a deterministic interpretation.