High Quality Content by WIKIPEDIA articles! In logic, a strict conditional is a material conditional that is acted upon by the necessity operator from modal logic. For any two propositions p and q, the formula p rightarrow q says that p materially implies 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. Such a conditional would, for example, avoid the paradoxes of material implication. The following statement, for example, is not correctly formalized by material implication. If Bill Gates had graduated in Medicine, then Elvis never died. This condition is clearly false: the degree of Bill Gates has nothing to do with whether Elvis is still alive. However, the direct encoding of this formula in classical logic using material implication lead to: Bill Gates graduated in Medicine rightarrow Elvis never died.

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