There's a similar process for first-order logic. The usual algorithm is to map P
to not P
, and then perform valid translations to move the not
somewhere convenient, e.g.:
Original: (not R(x) => exists(y) (O(y) and P(x, y)))
Negate it: not (not R(x) => exists(y) (O(y) and P(x, y)))
Rearrange: not (R(x) or exists(y) (O(y) and P(x, y)))
not R(x) and not exists(y) (O(y) and P(x, y))
not R(x) and forall(y) not (O(y) and P(x, y))
not R(x) and forall(y) (not O(y) or not P(x, y))
Performing the same on English you'd be negating "If it's not raining here, then there is some activity that is an outdoors activity and can be performed here" to "It is NOT the case that ..." and finally into "It's not raining and every possible activity is either not for outdoors or can't be performed here."
Natural language is a lot more complicated than first-order logic, of course... but if you can parse the sentence into something where the words "not", "and", "or", "exists" etc. can be identified, then you should be able to perform similar translations.