[shun]

Cas,

You wrote:

Past time (-en) is used to start the continuum and Present time (have see) is used to complete it. Time is used in this way to create a span of time, of which a start point and an end point is needed.

My reply: I guess your explanation is solely for the examples such as "I have seen him in the past week", example for the Past Family. :? All the resources have now been turned to the Past Family for the time being. But what about the normal Present Perfect?

In many other examples of Present Perfect, the time doesn't show "a start point and an end point":
Ex: He has seen Mary recently/just/lately.
Ex: We all have met John before/earlier.

Actually, normally, most Present Perfect sentences don't link to any time. They don't imply such a span of time, "of which a start point and an end point is needed".
:wink: Ex: I have lived in Japan. (I live in HK now.)
:wink: Ex: They have been to Paris. (They are back to HK now.)
== Present Perfect structures normally don't reveal a time and they just don't "span".

I am afraid we cannot ignore the normal structures for Present Perfect and, in order to explain the Past Family, say something strange, created solely for the Past Family. I am afraid it is not fair. They are the same Present Perfect tense, I suppose. They deserve the same treatment.
They are of the same tense that, as you analyzed, Past time (-en) is used to start the continuum and Present time (have see) is used to complete it. The analysis works only for the Past Family, but violates most of normal Present Perfect structures. This is why even grammar writers would not do it.

Or we may put them together for contrast: sometimes we span, sometime we don't:
:P Ex: I have seen him in the past week. (we span.)
:P Ex: I have lived in Japan before. (we don't span.)

What is it? A freedom of using tense?