Thanks everyone for your interesting answers. It seems quite difficult 
to find good meanings for such articles. Some people suggested aspectual 
meanings, and those are fine of course, but just don't work for me.

I especially liked Nikolay Ivankov's idea, even though I'm not sure I 
can use it:

la'o me. Nikolay Ivankov .me cusku di'e
> He a-went home, and he a-saw the crow. = Once he was going home, and he saw
> the craw.
> The meaning is - the crow is definitely someone that he knows, and
> periodically, as he is going home, he sees it. This was one of that
> instances.
> He the-went home, and he the-saw a crow.
> This time it was a particular going home, happening only once in the life.
> And this time seeing the crow was something expected.

This is quite nice, but can you also come up with interpretations for 
the "typical", "all" and "no" articles? Since what you are describing 
there doesn't seem like aspectual meaning, the remaining articles should 
preferably not be aspectual either.

Would anybody have guessed the "for the most part" reading with the 

- Miles