I think I've changed my view on this (in the past few hours), I've thought it through with hopefully more clarity than before.  

I DON'T think we need to justify the before/after feature, because I think it fits naturally with our syntax (as a few of you have hinted).

We represent list using comma and double-dot, enclosing the list with square or curly braces to mean "one of" or "all of", 
[1667,1668, 1670..1672]
means one of the years 1667, 1668, 1670, 1671, 1672

{1667,1668, 1670..1672}
means all of the years. 

More simply,

means one of the years  1670, 1671, 1672

means all three years.

It seems a natural extension that 

would mean some year preceeding (or equal to) 1672

all years preceeding or equal to 1672.

And that

means some year following (or equal to) 1672

All years including or following 1672

And I would go further to suggest that we replace "open" with double-dot, so 

means the interval beginning January 1 2004 with no end date

I have more to say about intervals but will save it for a later message.