Argument lowering is valid in NL, hence also in L, LP. Function composition depends on associativity; it is invalid in NL, valid in L(P). Function composition has been used to build up partial semantic representations, running in parallel with the incremental (left-to-right) processing of a string. Argument raising, finally, is valid only in LP, i.e., this form of meaning assembly cannot be obtained as the image of a derivation in any of the syntactic calculi (N)L. But, as we will see below, this transition plays an important role in the analysis of natural language scope ambiguities.