Logical conditional in the context of "Strict conditional"

The material conditional (also known as material implication) is a binary operation commonly used in logic. When the conditional symbol ${\displaystyle \to }$ is interpreted as material implication, a formula ${\displaystyle P\to Q}$ is true unless ${\displaystyle P}$ is true and ${\displaystyle Q}$ is false.

Material implication is used in all the basic systems of classical logic as well as some nonclassical logics. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many programming languages. However, many logics replace material implication with other operators such as the strict conditional and the variably strict conditional. Due to the paradoxes of material implication and related problems, material implication is not generally considered a viable analysis of conditional sentences in natural language.