A primary intension is a function from scenarios to extensions.
T5) A sentence token S is a priori (epistemically necessary) iff the primary intension of S is true at all scenarios.
Other treatments of scenarios are possible (see Chalmers 2004), but I will use this understanding here.
If scenarios are understood as centered worlds, this will be a world centered on the speaker and the time of the utterance.
At other worlds and scenarios, however, the values of these intensions may diverge from the original extension, and from each other.
T7) A sentence token S is contingent a priori iff the primary intension of S is true at all scenarios but the secondary intension of S is false at some world.
On this approach, the scenarios that are in the domain of a primary intension do not represent contexts of utterance.
Scenarios are highly specific epistemic possibilities.
On the centered-worlds version of epistemic two-dimensionalism, scenarios are identified with centered worlds.
It is also possible to develop a version of epistemic two-dimensionalism where scenarios are more strongly dissociated from ordinary possible worlds (see Chalmers 2004; forthcoming a), and instead are characterized in more purely epistemic terms (for example, as maximal epistemically consistent sets of sentences in an idealized language).