Strict conditional

In logic, a strict conditional (symbol: ${\displaystyle \Box }$, or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necessity operator from modal logic. For any two propositionsp and q, the formulap → q says that pmaterially impliesq while ${\displaystyle \Box (p ightarrow q)}$ says that pstrictly impliesq. Strict conditionals are the result of Clarence Irving Lewis's attempt to find a conditional for logic that can adequately express indicative conditionals in natural language. They have also been used in studying Molinist theology.