 Here, \(\mathop{\mathrm{man}}'(x)?\) uses the test constructor   “\(?\)”: \(\phi ?\) is the set of all \(\langle \beta ,\beta \rangle\) such that \(\beta\) satisfies \(\phi\). The meaning of the entire program (2) therefore also is a relation between assignments. Namely, it is the set \(R\) of all pairs \(\langle \beta ,\gamma \rangle\) where \(\beta \sim_x \gamma\), and \(\gamma(x)\) walks and is a man. The meaning of (1) by contrast is the set of all \(\beta\) such that some \(\langle \beta ,\gamma \rangle \in R\). Existential quantifiers thus have ‘side effects’: the change in assignment is never undone by a quantifier over a different variable. Hence the open-endedness to the right of the existential. This explains the absence of brackets in (1). For an overview of dynamic semantics see Muskens et al. 1997.