Martin (1992: 195-6):
Contingent relations make a distinction between conjunctions incorporating negative polarity (unless and lest) and those which don't. The relevant proportionalities and relevant paradigm are as follows:
UNLESS : IF…NOT ::LEST : SO THAT…WILL + NOT
unless Ben plays you'll lose :if Ben doesn't play you'll lose ::
Ben'll play lest you lose :Ben will play so that you won't lose
But the opposition between "positive" and "negative" values has a different meaning in the context of conditional relations from that in purposives. With conditionals, the opposition is between exclusion and inclusion (or non-exclusive) to be precise). Unless means 'if and only if not'; if on the hand does not preclude the possibility of additional modalised Causes:
EXCLUSIVE[4:60] Unless you go that way ['as long as you don't]you'll be there by six.(It's the only way you can go wrong.)
INCLUSIVE[4:61] If you go that wayyou'll be there by six.(But you could also go the back way.)
In SFL theory, as in formal logic, the logical meaning of positive condition is if P then Q and the logical meaning of negative condition is simply if not P then Q — not "if and only if not":
- If Ben doesn't play, you'll lose.
- If you don't go that way, you'll be there by six.
The opposition of 'exclusive vs non-exclusive' is irrelevant to the logical opposition of positive and negative condition.
See also if and only if.