Either way, you don't really need to convince me; I just wanted to +1 Nathan's "no associativity" idea and run away. And associative or not, IMPLIES is a lot nicer than the NOT-OR construction.
Probably good. I can easily imagine myself seeing a IMPLIES b IMPLIES c and reading (a IMPLIES b) AND (b IMPLIES c) even though I know that's not how Postgres operators work.
Personally, I currently spell IMPLIES as "<=" which would be about as good as you could expect, except that the usual mathematical implication operator visually appears much closer to "=>". Also any NULL input at all results in NULL output even when interpreting the NULL as "unknown" would result in a TRUE result.
