1 The basic difference between spatial and time reasoning
So far, we were considering the time reasoning within a spatiotemporal universe where no formal difference between space and time exists. We can continue this line of reasoning saying that the spatiotemporal universe can be divided into separate sets, e.g., by specifying some set within the universe. However, dealing with the time, we have to admit that there is one division that is inherent to our thinking: in the time dimension, the spatiotemporal universe is divided into two sets, those of Past and Future, with Present as the boundary between both.
As we have seen, this fact does not prevent us from thinking within the undivided spatiotemporal universe. However, any spatial dividing of the universe is to our mind arbitrary in the sense that we have no space division privileged and inherent to our mind. Of course, we are able to think any arbitrary division in time, too. However, one time division of the universe is inherent to our mind, and this fact has, naturally, heavily impact on the natural language.
Therefore, we can consider the time-specific modalities within a time universe that is a one-dimension space divided into two sets (Past and Future) with a boundary between both (Present). The relations between Past, Future, and Present could be naturally explained in the topological terms of interior, boundary, and closure. Present is always the boundary. Past without Present forms the interior of the Past-set that is the complement set of conjunction Present + Future (= closure of the Future-set), and so on.