 Stalnaker’s interpretation of the scheme in  (15)  is pragmatic: when we encounter a series of clauses in discourse, we interpret these clauses in light of a context that is already informed by the interpretation of previous clauses. This idea of incremental interpretation is simple yet powerful and it makes perfect sense for complex discourses with conjunctive interpretations (for instance, coordinations with and and simple sequences of declarative sentences). Since the conjuncts in a conjunction have assertoric force, they can be used to update the context in order to create a new local context. The problem is though that presuppositions do not just disappear in conjunctive environments. Just like  (14),  (16) also lacks the requirement that it should be common knowledge that John is late. But here the first disjunct does not have assertoric force (see, for instance, Schlenker 2009 for discussion). It is not obvious what kind of pragmatic rule could account for the lack of a presupposition in  (16).