P implies Q, how to read in english?

Question

how to read P implies Q in classical logic? example : Distributivity: Ka(X->Y) -> (KaX -> KaY) This is modal logic which uses classical logic rules. KaX : a knows the that X is true. I m curious about how to read implication in english? if then else? **Edit :** in Modal Logic, Ka becomes Box, well it s boxed shape sign, that symbolizes necessiation rule, Rule N, that means, box P , if you have P in a world Delta then all the acessible worlds should also have P. THere is also Diamond P, which means possibility, that there exists one world which has P accessible from the world that Diamond P has.

Answer 1

You're right, implication is an "if then" statement. "P implies Q" can be read "If P is true, then Q is true". In classical logic, this is equivalent to "Q or Not P" -- in particular, "P implies Q" is true if either Q is true or P is false, and "P implies Q" is false exactly when (simultaneously) P is true and Q is false.