 One way to modify SPWS to give truth conditions for sentences is to resort to sets including both possible and impossible worlds (ways things could not have been). Sentences that agree in truth value in very possible world can still be assigned distinct truth-conditions, since those sentences might be true in different impossible worlds. (See  §4.3).  Another way is to use structured meanings, where sentences with the same possible-worlds truth conditions can have different meanings because of the way they are built up. (See  §4.5).  An objection to these approaches can be generalized to any approach that tries to make room for hyperintensionality in a truth-conditional framework.