The above example only uses the slash Elimination of NL in the syntactic source calculus.  An important motivation for the introduction of continuations is that they make it possible to give a constructive interpretation to classical (as opposed to intuitionistic) logic; see Sørensen and Urzyczyn 2006 for discussion. It will be no surprise, then, that also the multiple-conclusion symmetric categorial grammar LG has a natural interpretation in the continuation-passing-style (Bernardi and Moortgat 2010, Moortgat 2009).  In the example we gave above, source types A are provided with a single continuation parameter. In the CPS translation for LG types, the continuization of syntactic source types is performed recursively.  Let us write V(A) for target language values of type A, K(A) for continuations, i.e., functions V(A) → R, and C(A) for computations, i.e., functions K(A) → R, where R is the response type.  For an LG syntactic source type A, the call-by-value CPS translation yields an LP value V(A) as follows.  V(p) = p for atomic types,