 In light of such criticisms, there has been a recent resurgence of static approaches to presupposition projection, such as the pragmatic approaches of Schlenker (2008, 2009), Chemla (2008, Other Internet Resources) and the semantic (trivalent) approaches of George (2008) and Fox (2008). As Rothschild points out though, there is a route to making a semantics along the lines of  (17)  explanatory. To do so, one has to show that permissible dynamic interpretations of connectives share certain properties. As Rothschild (2011) shows, an explanatory and empirically adequate dynamic treatment of presupposition is possible if we assume that context change potentials adhere to certain principles of definedness. Let us assume that \(C[S]\) (for a simple clause \(S\)) is only defined if and only if any presupposition of \(S\) is true in all the worlds in \(C\). The rules in  (17)  determine the definedness conditions for complex statements. For instance, according to  (17)  [not S] is only undefined in \(C\) if \(S\) is undefined in \(C\). Rothschild’s insight is that we can constrain dynamic interpretation by constraining the resulting definedness conditions.