In this paper by Astrid De Wit and Frank Brisard, a unified semantics for the English present tense is proposed.
According to their view, the present tense is all about epistemic modality: the present simple is connected to epistemic necessity, and the present progressive is connected to epistemic contingency.
Consider the sentence:
She is living with her parents.
The sentence, then, on our view, means precisely the following:
"She lives with her parents" is true at some epistemically accessible worlds, and false at others.
I'm having trouble grasping this as this seems clearly wrong to me. Can someone elaborate?