interaction of negation and aspect in French (de swart and Molendijk 1999), scope ambiguities with negative quantifiers in g ermanic (de swart 2000), and negative concord in r omance (de swart and sag 2002). a lthough I felt my proposals were contributing to a better understanding of the phenomena under consideration, they did not lead to an explanatory theory of cross-linguistic variation in the area of negation. Meanwhile, the discussion of semantic universals and cross-linguistic variation in meaning assumed more imp- tance in the literature (cf. von Fintel and Matthewson 2008), which made it all the more urgent to develop such a theory. o ther proposals came along in the literature, exploiting syntactic and lexical notions of variation, and making claims about u- versal grammar and typological generalizations.