Strict conditional

In <a href="/facts/Logic/8JnpJLtt">logic</a>, a strict conditional (symbol: 
 
 
 
 ◻
 
 
 {\displaystyle \Box }
 
, or ⥽) is a conditional governed by a <a href="/facts/Modal_operator/UHtpPLuH">modal operator</a>, that is, a <a href="/facts/Logical_connective/VkPhUs6M">logical connective</a> of <a href="/facts/Modal_logic/I7uXvYYT">modal logic</a>. It is <a href="/facts/Logical_equivalence/ysCWmsxA">logically equivalent</a> to the <a href="/facts/Material_conditional/hYf4b7AE">material conditional</a> of <a href="/facts/Classical_logic/ls62MAms">classical logic</a>, combined with the <a href="/facts/Logical_truth/N0bUYhUW">necessity</a> operator from <a href="/facts/Modal_logic/I7uXvYYT">modal logic</a>. For any two <a href="/facts/Proposition/0877MFMD">propositions</a> p and q, the <a href="/facts/Well-formed_formula/YpTVlzuj">formula</a> p → q says that p <a href="/facts/Material_conditional/hYf4b7AE">materially implies</a> q while 
 
 
 
 ◻
 (
 p
 →
 q
 )
 
 
 {\displaystyle \Box (p\rightarrow q)}
 
 says that p <a href="/facts/Logical_consequence/AyDXp4dn">strictly implies</a> q. Strict conditionals are the result of <a href="/facts/C._I._Lewis/advJU29e">Clarence Irving Lewis</a>'s attempt to find a conditional for logic that can adequately express <a href="/facts/Indicative_conditional/MUzp5aL0">indicative conditionals</a> in natural language. They have also been used in studying <a href="/facts/Molinism/jEMd2KjR">Molinist</a> theology.

Strict conditional open-in-new

Strict conditional