In logic, formal semantics, and philosophy, a logical relation stronger than material implication. A proposition P logically implies another proposition Q if and only if in all possible worlds in which P is true, Q is also true. For example, if P is "a lit candle is applied to the cotton" and Q is 'the cotton burns", then P materially implies Q; it so happens in the actual world that when a lit candle is aplied to cotton, the cotton burns. However, since there is a possible world in which a lit candle is applied to the cotton, and instead of burning, the cotton freezes, P does not logically imply Q. P does, however, logically imply the proposition R: "a candle is applied to the cotton", since every lit candle in every possible world is a candle.