 It is easy to see that a dynamic semantics with presuppositions does not validate LEM, because, if \(\phi\) contains a presupposition trigger, \((\phi \vee \neg \phi)\) will be undefined in any context in which the presuppositions of \(\phi\) are not satisfied. For the fragment without presuppositions, however, LEM is validated, but there is a non-trivial sense in which bivalence is still rejected: truth and falsity in dynamic semantics are defined relative to a context, for example, \(\phi\) is true (or supported) in \(c\) iff \(c[\phi]=c\); and \(\phi\) is false in \(c\) iff \(c[\phi]=\emptyset\). But then \(p\) might be neither true nor false in a context \(c\) (e.g., if \(c\) contains both \(p\) worlds and non-\(p\) worlds), while, for all \( c\), it holds that \((p \vee \neg p)\) is true in \(c\).