  The most influential approach to solving the imperfective paradox is due to Dowty (1979). The basic idea is to treat the progressive as a modal operator \((\Box)\) but restrict its domain to inertia worlds. The notion of an inertia world is characterized informally. An inertia world is exactly like the real world up to the time of evaluation; after this it may differ from the real world but is assumed to be as similar to the real world as possible. Given this notion, the following definition introduces truth conditions for sentences in the progressive. 