The discontinuous Lambek calculi that have been developed by Morrill and co-workers (see Morrill et al. 2007, 2009) and Chapter 6 of the forthcoming monograph (Morrill 2010) extend the associative Lambek calculus L. We saw that L is the logic of strings composed by concatenation.  The discontinuous calculi enrich the ontology with a notion of split strings: expressions consisting of detached parts, as in the idiom ‘take — to task’. To build the phrase ‘take someone to task’, one wraps the discontinuous expression around its object. In this particular example, there is a single point of discontinuity, but one can also think of cases with more than one split point. This naturally leads to two notions of discontinuous composition: a deterministic view, where wrapping targets a particular split point, and a non-deterministic view where the targeted split point is arbitrary. In the case of expressions with a single split point, these two notions coincide.