Split-scope negation in German

This paper investigates split-scope readings of German negative determiners ("kein(-e)") in syntactic constructions like (1), where the negative quantifier seems to divide into a negative operator and an indefinite, the modal operator taking scope inbetween the two:
(1) Peter muss keine Tomaten kaufen.
There seem to be two distinct conditions that influence the occurrence of such split-scope readings: (i) the semantic properties of the head noun modified by "kein", and (ii) the semantic class of the verb, in particular the distinction between stage-level vs. individual-level predicates.

We will offer an HPSG account of split-scope readings that is based on the semantic properties mentioned above and on the argument-composition analysis of the verbal complex.