Since its inception in the 1980s, Dynamic semantics has provided an extremely influential theory of anaphora. While largely successful, it's been known for some time that dynamic semantics has a major wrinkle - negation is treated as a destructive operation. This makes a number of erroneous empirical predictions, for example, in the domain of doubly negated and disjunctive sentences.
In this talk, I'll argue that the destructive theory of negation also hamstrings Chierchia's (2020) recent attempt to explain crossover phenomena on the basis of dynamic semantics. Taking this as an initial motivation, I'll develop a dynamic fragment where negation is only selectively destructive; it leaves determinate discourse referents completely unscathed. As well as improving on Chierchia's account of crossover, this will also address the problem of negation in dynamic semantics more generally.
If time permits, I'll show how to modify the fragment to incorporate Veltman's (1996) test semantics for epistemic modals, addressing related problems for anaphoric theories of modal subordination.