Hey Bobby,
Thanks for the question and welcome to the Forum! I'm not entirely sure I understand what it is that you're asking, but let me take a stab at it and if I miss the mark please don't hesitate to let me know
In conditional reasoning there are a few words, most notably, "unless," "except," "until," and "without," that, based on the implications of their meaning/usage, are inherently negative. That is, each suggests absence or lack: "Unless we do X we'll get Y" means all events where X
isn't done tell us Y (and conversely not getting Y tells us X
was done). The same goes for the other three: "Without X..." means X is missing, and so on; again, negative.
So that inherently negativity, that absence, has to be considered when diagramming statements, and that's where the Unless Equation comes in: whatever "unless" modifies becomes necessary (at the end of the arrow) as-is, and whatever is left becomes sufficient, but—and this is the key!—with the negating force applied. So the non-unless term becomes the opposite of whatever is presented, and
that is your sufficient condition.
A quick example:
Unless it rains we'll go to the park.
Diagrammed out, "unless" modifies "rain" so that becomes necessary, and "go to the park" gets negated to "NOT go to the park" and becomes sufficient:
NOT Park
Rain
And the contrapositive:
NOT Rain
Park
The same would apply to "without rain" and "until it rains" etc. Note too that you could have started with the absence—No (unless, without, until, except) Rain—and seen what that told you: Go to the park. If you'd diagrammed it that way as NOT Rain
Park you'd be fine, as well.
So that's how "unless" (and the others) get treated conditionally.
It occurs to me, however, that you might be asking about diagramming negatives in positive terms to simplify things, like representing "NOT park" as "stay home" or "NOT rain" as "sunny" (or whatever). That's
potentially fine, but only in very specific, binary situations. That is, they need to be situations where only two options are possible, and "NOT A" tells you "B" with certainty. For instance, if you knew that Jill was being picked for either Team A or Team B and you learned Jill was "NOT Team A," you could show that as a positive, "Team B."
But for events where more than two possibilities exist this WON"T work: "NOT park" doesn't mean "stay home," necessarily, since literally anything besides going to the park would work, like "go to a restaurant," or "go to a movie," etc.
So be careful! Understand why those four words have negative implications, how to diagram with them (and take contrapositives), and when you can and can't turn negatives into immediate positives in representing conditions. From there you should be all set!
