 The result of updating a context \(c\) with a disjunction \((\phi \vee \psi)\) consists in the union of (i) the result of updating \(c\) with \(\phi\) and (ii) the result of updating with \(\psi\) the context \(c \setminus c [\phi]\) obtained by subtracting from \(c\) all worlds which verify \(\phi\). By defining the presupposition of a sentence as what has to be true (or supported) in a context \(c\) in order for an update with the sentence to be defined in \(c\), the dynamic account of disjunction captures the pattern in  (9)–(11).  Simplifying, suppose \(c\) does not support the information that there is a king of France, then  (9)  and  (11)  will be undefined in \(c\), because \(c [\phi]\) and/or \((c \setminus c [\phi])[\psi]\) will be undefined. But  (10)  will be defined. This is because the second disjunct in  (10),  which presupposes that there is a king of France, is interpreted here with respect to the local context \((c \setminus c [\phi])\) which is the context obtained by subtracting from \(c\) all worlds which verify the first disjunct, i.e., all worlds in which there is no king of France. Such local context will support the information that there is a king of France. So the whole disjunction does not presuppose anything. The ordering between disjuncts however matters in a dynamic account and so the analysis predicts a difference in presupposition between  (10)  and the following variant where the presupposition trigger occurs in the first disjunct rather than the second: