 Several proposals (e.g. Beaver 2001, Singh 2007, 2009; Schlenker 2011) try to motivate this kind of strengthening mechanism to explain when exactly a conditionalized presupposition should be strengthened. For example, Beaver’s model of accommodation, first published in Beaver (1992) treats accommodation as a type of filtering operation. Beaver suggests that due to uncertainty about what the speaker takes the common ground to be, the hearer has to entertain multiple alternative context sets, with some ranking of which is the most plausible. All these alternative contexts are updated simultaneously. Accommodation is then what happens when the update is not defined on what was previously considered to be the most plausible context, in which case the hearer drops that context from contention. What remains is a new set of contexts in which the most plausible one is a context that has been successfully updated.