logiccomputer-scienceboolean-logicimplicationmodal-logic

P implies Q, how to read in english

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.

Solution

  • "P implies Q" is equivalent to "if P, then Q".