In other words, I'll put some kind of marking on the verbs to indicate whether the action was intentional or not. I'm thinking I ned three, maybe four variations: intentional, accidental, attempted, and maybe one to mark the imperative (giving orders).
the cat eat-INTENTIONAL the mouse = the cat eats the mouse (on purpose)
the cat eat-ACCIDENTAL the mouse = the cat accidentally eats the mouse (how's that happen?)
the cat eat-ATTEMPTED the mouse = the cat tries to eat the mouse
cat eat-IMPERATIVE the mouse = eat the mouse, cat!
The intentional form would be the natural form, I think. And there will be some additional helper words expressing concepts like "should" and "could."