---
tag: 5JW54NP52K
kind: concept
name: Strict conditional
aliases: [strict-conditionals, strict-implication]
sources:
  - wikipedia: en:663772@r1297606683
    locator: Strict conditional
    note: adopted
    mention: wikipedia://en/663772
    sections: [Summary]
same_as:
  wikidata: Q375520
  wikipedia: Strict conditional
inventory: [YDZNAVM3SM]
---

## Summary

In logic, a **strict conditional** (symbol: $\Box$, or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is [[logically equivalent|06GYGS41JK]] to the [[material conditional|0NMG7W7Q11]] of classical logic, combined with the necessity operator from modal logic. For any two [[propositions|0ZGC7ZESYN]] *p* and *q*, the formula *p* → *q* says that *p* [[materially implies|0NMG7W7Q11]] *q* while $\Box (p \rightarrow q)$ says that *p* strictly implies *q*. 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.