Thanks, kmarkley. That's a clean way to look at it. Mapping it back to my classifications your six are:

Personally I prefer the first logic for #6, perhaps because I'm fixated on my lawn mowing example. (Guess what I should have been doing this evening instead of migrating to OmniFocus!) When I complete my mowing I would like the task to show up in 5 days with a 3 day window to complete it. So I'm thinking of the interval as the time in which I don't have to think about mowing. Logically it doesn't matter since with the second logic I can just set an 8 day interval and get the same result. I guess in case #6 with your first logic the interval is a minimum time between actions and a maximum with your second logic.

Missing from your characterization are

"Fixed" seems a strange name to me, which is part of the reason I proposed a graphical representation of the intervals. In my handrolled GTD system I currently use "Repeat every" to mean fixed and "Repeat after" to mean unfixed. That could be accomplished by adding an every/after drop-down menu to the inspector. I think I prefer the graphical version, but I'm very interested in hearing others thoughts. (Interface design is a professional interest of mine.)

- Start-Start
- Due-Due
- Start-Start
- Completion-Start
- Completion-Due
- Completion-Start
*or*Completion-Due

Personally I prefer the first logic for #6, perhaps because I'm fixated on my lawn mowing example. (Guess what I should have been doing this evening instead of migrating to OmniFocus!) When I complete my mowing I would like the task to show up in 5 days with a 3 day window to complete it. So I'm thinking of the interval as the time in which I don't have to think about mowing. Logically it doesn't matter since with the second logic I can just set an 8 day interval and get the same result. I guess in case #6 with your first logic the interval is a minimum time between actions and a maximum with your second logic.

Missing from your characterization are

- Start-Due, and
- Due-Start.

"Fixed" seems a strange name to me, which is part of the reason I proposed a graphical representation of the intervals. In my handrolled GTD system I currently use "Repeat every" to mean fixed and "Repeat after" to mean unfixed. That could be accomplished by adding an every/after drop-down menu to the inspector. I think I prefer the graphical version, but I'm very interested in hearing others thoughts. (Interface design is a professional interest of mine.)